Hydronic Heating Systems - The Effect of Design on System Sensitivity - Anders Truschel (Book)

THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

HYDRONIC HEATING SYSTEMS The Effect Of Design On System Sensitivity

Anders Trüschel

Department of Building Services Engineering Chalmers University of Technology Göteborg, Sweden 2002

Hydronic Heating Systems The Effect Of Design On System Sensitivity Anders Trüschel ISBN: 91-7291-175-1 © Anders Trüschel 2002 Second edition Doktorsavhandlingar vid Chalmers Tekniska Högskola Ny serie nr 1857 ISSN 0346-718X Document: D62:2002 Department of Building Services Engineering Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone + 46 (0)31-7721000 Printed by Chalmers Reproservice, Göteborg 2002 ii

Hydronic Heating Systems The Effect Of Design On System Sensitivity Anders Trüschel Department of Building Services Engineering Chalmers University of Technology

ABSTRACT This thesis starts from the recognition that a hydronic heating system can be optimised, but can never be totally perfect. Sooner or later, in practice, deviations - caused by one or more components having slightly different characteristics or settings than they are assumed or supposed to have - arise. The aim of this work is to show how system design affects the overall sensitivity to deviations, in terms of the effect on performance and return water temperature. The systems that have been analysed are radiator systems and air heaters controlled by valve groups, both supplied by heat from district heating. In particular, the analysis has been concentrated on differences between high-flow and low-flow systems. Based on fundamental theory in this area, as well as on physical measurements made in test rigs, models have been developed and/or applied in order to investigate system function in the desired manner. The effect of deviations have then been shown and quantified, using results from simulations. The simulations show that thermostatic radiator valves are most effective in low-flow systems. Low-flow systems, too, produce the lowest return temperatures. However, incorrect or changed radiator valve settings can result in substantial increased return temperature and differences in room temperatures in such systems. A direct connection of an air heater (that is without recirculation) presents the least risk of control instability, which means that performance tends to be more stable. In this respect, there is no difference whether the system is balanced for a high flow or a low flow. However, balancing does have a considerable effect on the control performance of valve groups with a recirculation connection and with low-flow systems running a greater risk of instability. Keywords Hydronic Heating, District Heating, Radiator System, Air Heater, Heating Coil, Valve Group, Shunt Group, Water Return Temperature, Room Temperature, Thermal Power Output, Controllability, P-band, Deviations

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This thesis refers to the research project “Heating systems in buildings” by The Swedish District Heating Association and the research grant no. 960493-5 from BFR (Swedish Council for Building Research, now FORMAS).

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PREFACE The work described in this thesis has been carried out at the Department of Buildings Services Systems at Chalmers University of Technology, as part of the Department's aim to improve detailed knowledge of hydronic heating and cooling systems. I would therefore like to tender my special thanks to the Department and its personnel for providing the opportunity of the work, as well as for the resulting valuable and interesting time for me as a PhD candidate. In particular, my thanks are due to my supervisor, Stefan Aronsson, whose help during the work has been invaluable. In addition, I am most grateful for the support and interest of Associate Professor Jan-Olof Dahlenbäck, Professor Per Fahlén and Professor Emeritus Enno Abel. Warm thanks, too, to Tommy Sundström and Josef Jarosz for all their help with the test rigs, as well as to Magnus Thordmark of IMI Indoor Climate AB and Per-Göran Persson of TA Control AB for their assistance with the provision of equipment. I would also like to thank the Monitoring Centre for Energy Research at Chalmers, which made the measurements in the Bankogatan properties, as well, of course, as Familjebostäder and particularly Yngve Andersson for their assistance in connection with these measurements. Another person not to be forgotten is Neil Muir, who translated the material. Finally, I would like to thank all members of the reference group that has monitored the work, and particularly Lennart Berndtsson from HSB who has been responsible for the organisation.

Gothenburg, May 2002 Anders Trüschel

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TABLE OF CONTENTS NOMENCLATURE

xi

1

INTRODUCTION 1.1 Background 1.2 Purpose 1.3 Working method 1.3.1 Systems investigated 1.3.2 Measurement and simulation 1.3.3 The effect of deviations 1.4 Work in this field 1.4.1 Buildings supplied from district heating systems 1.4.2 Low-flow and high-flow balancing 1.4.3 Radiator systems, air heaters and valves 1.4.4 System design and control 1.5 The structure of this thesis

1 1 1 1 2 4 4 5 5 6 7 9 9

2

SYSTEM DESIGN 2.1 Structure 2.1.1 Distribution systems 2.1.2 Valve groups 2.2 Balancing 2.2.1 Valve capacity 2.2.2 Pump and system characteristics 2.2.3 The effect of pipe pressure drop 2.2.4 The effect of lowest balanced differential pressure 2.2.5 The heat-releasing components’ characteristic 2.2.6 Categorisation of systems 2.3 Control valves 2.3.1 Valve characteristic 2.3.2 Valve authority 2.3.3 Two-way and three-way control valves 2.4 The static and dynamic characteristics of the system 2.4.1 Static characteristic 2.4.2 The necessary P-band

11 11 11 13 14 15 16 18 20 22 29 30 30 32 33 35 35 38

3

MEASUREMENTS 3.1 Radiator system 3.1.1 Method of working 3.1.2 Measured results 3.2 Air heater with valve group 3.2.1 Configurations 3.2.2 Setting up and measuring 3.2.3 Some measurement results

43 43 43 44 44 44 45 47

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4

SIMULATION PROGRAMS 4.1 Calculation program in Excel 4.1.1 Structure 4.1.2 Verification 4.2 Flowmaster 4.2.1 Structure 4.2.2 Verification

57 57 57 58 65 66 66

5

SIMULATION – PLANNING 5.1 Radiator system 5.1.1 Configuration 5.1.2 Temperature, flow, pressure 5.1.3 Studied deviations 5.1.4 Planning of simulations 5.2 Air heater with valve group 5.2.1 System configurations 5.2.2 The necessary P-band width 5.2.3 Return temperature 5.2.4 Temperature, flow, pressure 5.2.5 Selection of components 5.2.6 Studied deviations 5.2.7 Planning the simulations

75 75 75 76 82 84 86 86 88 90 93 95 97 98

6

SIMULATION AND RESULTS – RADIATOR SYSTEM 6.1 Performing the work 6.2 The basic cases 6.3 Incorrect valve settings 6.3.1 Fully closed radiator valve 6.3.2 Fully open radiator valve 6.3.3 Deviations from the correct setting of branch valve 6.3.4 Deviations from the correct setting of riser valve 6.3.5 Deviations from the correct setting of main valve 6.3.6 Summary 6.4 Incorrect balancing 6.4.1 Simplest possible balancing 6.4.2 Simplified balancing 6.4.3 Randomised deviations in balancing 6.4.4 Summary 6.4.5 Comparison with a measurement case 6.5 The effect of disturbances 6.5.1 Non-uniform distribution of internal heating 6.5.2 Summary 6.6 The distribution system 6.6.1 Single-pipe system 6.6.2 Two-pipe system 6.6.3 Three-pipe system 6.6.4 Summary 6.7 The effect of the district heating substation radiator heat exchanger

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101 101 101 103 103 111 120 124 128 130 139 140 142 144 156 158 160 161 164 165 165 171 175 177 181

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8

SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP 7.1 Performing the work 7.2 Optimum valve characteristic 7.2.1 The reference case 7.2.2 Different valve size 7.2.3 Varying available differential pressure 7.2.4 Summary 7.3 Actual valve characteristic 7.3.1 Linear and logarithmic valve characteristics 7.3.2 Different valve sizes 7.3.3 Summary 7.4 Deviations in setting of balancing valve 7.4.1 Primary side balancing valve 7.4.2 Secondary side balancing valve 7.4.3 Summary 7.5 The effect of variations in water supply temperature 7.6 The effect of a fouled air heater

187 187 187 187 192 194 195 196 197 199 201 202 202 205 207 208 212

CONCLUSIONS AND DISCUSSION 8.1 Radiator system 8.1.1 High-flow or low-flow balancing 8.2 Air heater with valve group 8.2.1 High-flow or low-flow balancing 8.2.2 Balancing the valve group 8.2.3 Controlled versus constant supply temperature 8.2.4 Selection of the valve group 8.2.5 Choice of valve characteristic

215 215 216 217 218 218 219 220 221

REFERENCES

223

APPENDIX A

TEST RIGS A.1 Test rig for the air heater with valve group A.1.1 Arrangement of the test rig A.1.2 Structure of the ventilation system A.1.3 The control system A.1.4 The measurement system A.1.5 Uncertainty of measurement A.2 The radiator system test rig A.2.1 Arrangement of the test rig A.2.2 The measurement system A.2.3 Uncertainty of measurement

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A-1 A-1 A-1 A-7 A-8 A-9 A-13 A-24 A-24 A-26 A-28

B

CALCULATION RELATIONSHIPS B.1 The radiator system B.1.1 Room heat balance B.1.2 Distribution system B.1.3 Thermostatic radiator valve B.1.4 Media data B.1.5 Limitations B.2 Single-pipe, two-pipe and three-pipe systems B.2.1 Thermal balance in the room B.2.2 Distribution system B.2.3 Limitations B.3 The district heating substation radiator heat exchanger B.3.1 Thermal balance B.3.2 Media data B.3.3 Limitations B.4 Derivation of radiator sensitivity B.4.1 Basic relationships B.4.2 The effect of the flow on the temperature drop B.4.3 The effect of the flow on the thermal output power B.4.4 Limitations B.5 Optimum valve characteristic B.5.1 Necessary static characteristic B.5.2 Valve group characteristic B.5.3 Valve authority B.5.4 Nomogram

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B-1 B-1 B-1 B-2 B-6 B-7 B-8 B-13 B-13 B-13 B-13 B-13 B-14 B-16 B-16 B-17 B-17 B-18 B-19 B-19 B-20 B-20 B-24 B-26 B-27

NOMENCLATURE Capital letters A C D Q& V&

= = =

Area [m²] Thermal capacity flow [W/K] Radiator sensitivity [-]

H Ks Kr K rad L M N NTU

= = = = = = = =

Nu & Q R

= = =

Re Td Tk U & V

= = = = =

Valve opening [%] System gain [%/°C] Controller gain [%/ºC] Radiator constant [W/Kn] Length [m] Thermal capacity [J/K] Number (quantity) [-] Number of Transfer Units (measure of a heat exchanger’s size related to its flow) [-] Nusselts number [-] Thermal power output [W] Relationship between the heat capacity flows for water and air through an air heater [-] Reynolds number [-] Dead time [s] Time constant [s] Coefficient of thermal transfer [W/m²K] Volume flow [m³/s]

Lower-case letters c cp

= =

Velocity [m/s] Specific thermal capacity [J/kgK]

d e kv k vs k & m n p t u

= = = = = = = = = =

Diameter [m] Control error (difference in temperature) [°C] Valve capacity [m³/h] Maximum valve capacity [m³/h] Flow resistance [kPa/(l/h)² ; kPa/(l/h)] or Roughness of pipe [mm] Mass flow [kg/s] Radiator exponent [-] Pressure [Pa] Temperature [°C] Control signal (Valve opening) [%]

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Greek symbols α β λ ϕ

= = = =

∆p ∆t , ∆T η ρ τ ν

= = = = = =

Coefficient of thermal transmittance [W/m²K] Valve authority [-] Coefficient of friction [-] or Thermal conductivity [W/mK] Relationship between the waterflow through a control valve and the waterflow through the corresponding air heater [-] Differential pressure, Pressure drop [Pa] Difference in temperature, Change in temperature [°C] Efficiency [-] Density [kg/m³] Time [s] Kinematic viscosity [m²/s]

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Control port for a control valve Shunt port for a control valve Check valve Constant-flow port for a control valve Heat releasing component Control valve, Controlling Total Reference index Media index for liquid (water) Media index for air Shunt group (i.e. valve group) Radiator Arbitrary index Inlet, Incoming (temperature or media) Outgoing, Outdoor (temperature or media) Internal Valve opening 0 % Valve opening 100 % Critical Necessary Balanced Design Nominal Room Mean value for a certain number of rooms Return (temperature) System Mean value Arithmetic mean value Logarithmic mean value Minimum, Least Maximum

Index A B BV C H R T 0 w a s rad i in out intern fully closed fully open crit nec balanced design nom room room, mean return system m am lm min max

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1 INTRODUCTION

1

INTRODUCTION

1.1

Background

Hydronic heating systems in buildings are designed so that they can maintain a desired indoor temperature, which means that the physical conditions determining the design are more or less given. In addition, if the heating system is supplied (or will be supplied) by district heating, it is also important to ensure that the system provides a low return temperature of the district heating water. When the system is started up, its function and performance will depend on its actual design and on the actual conditions, which often introduce greater or lesser deviations from the parameters that were assumed when designing the system. As used here, “deviations” mean that one or more components have characteristics other than as were originally assumed. Examples of such deviations are oversizing of radiators, poor system balancing, incorrectly operated control valves and so on. These deviations can exist even before the system has been taken into use. In addition, there can be constant changes to the system due to such effects as modifications by the building owners, adjustments or damage caused by users and natural wear and tear, all of which gradually (or otherwise) give rise to deviations. This research project was initiated in order to investigate how an hydronic heating system should and should not be designed in order to ensure its proper function and performance when subjected to a range of deviations.

1.2

Purpose

The purpose of this work has been to show how the function and performance of a hydronic heating system is affected by its design. The intention has been to bring forward basis and information from which, in the extent, working methods can be developed for use during the system design stage in order to ensure subsequent stable operational function. The material should show the advantages and drawbacks of various design and balancing principles, in respect of their ability to reduce the effects of deviations. The work has therefore been intended to contribute to improving the ability to forecast the effects and characteristics of a selected design.

1.3

Working method

The work has been carried out in four stages, of which the first has been to identify and describe typical examples of system types. From this, based on fundamental theory in the field and on measurements of actual systems, appropriate models have then been developed and/or applied that have made it possible to investigate system function in the desired manner. This has been followed by identification and description of typical examples of deviations found in these systems. Finally, the last stage of the work has involved system simulation to identify and quantify the effects of system deviations on various performance parameters.

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1 INTRODUCTION

1.3.1 Systems investigated The purpose of a heating system in a building is to maintain the desired indoor air temperature. How well the system works depends on its ability to handle “disturbances”, i.e. parameter changes. This ability depends primarily on the design of the heating system, and secondarily on how well the control system meets the needs of the heating system. The main emphasis of this thesis is on the design of the heating system, rather than on the control system. There is considerable potential for improving heating systems when the supply of heat to the buildings is temperature-sensitive. This is the case when systems are supplied by district heating, where it is highly desirable to keep both the supply and return temperatures down and to limit the water flow rate. For this reason, it is primarily hydronic heating systems supplied by district heating on which this work has been concentrated. Today's hydronic heating systems supply heat primarily by means of radiators, although to some extent also by means of air heaters. This work has therefore concentrated on systems having radiators (slow thermal response) or air heaters (rapid thermal response), primarily supplied by district heating. Radiator system The interaction between radiators and rooms is a slow process, which means that the dynamic in such a system is not particularly apparent. It is therefore the equilibrium condition in the system that says more about the system's function and performance than does the process between these static levels. It is important to obtain as good an overall picture of the system to be analysed as possible. In the case of a radiator system, a complete, although relatively small, distribution system in a building is therefore analysed. This system is shown in Figure 1 below, and described in detail in Chapter 4. The system starts and finishes at the connections to the heat exchangers in the district heating substation unit, which is therefore not included in the analysis. It has thus been assumed that the supply temperature in the building's heating system can always reach the required levels.

Heat ex.

Figure 1.

The 2-pipe radiator system considered in the analysis.

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1 INTRODUCTION

Air heater with valve group The heat release process from an air heater in a ventilation duct, on the other hand, is considerably faster, which means that the dynamics of the process/equipment are important in determining the function of the equipment when in use. Of course, as for radiator systems, the static properties are also very important. In the case involving analysis of systems incorporating air heaters, both the dynamic and the static characteristics depend largely on the design of the air heater and of its local valve group. In this respect, the difference between it and a radiator system is the considerably faster and more advanced local control of air heaters. In this case, the work is therefore concentrated solely on the air heater and its local valve group. The system boundary conditions are expressed in the form of available pressure drop and of the supply temperature. The flow in heating systems supplied by district heating is always variable, as this provides the most effective cooling of the district heating water. However, it is not always desirable to have a variable flow rate through an air heater, and so valve groups are therefore often used, to maintain a reasonably constant flow rate through the air heater itself. The arrangement of these valve groups can vary, and so three different types have therefore been analysed: • Direct connection; without shunt, which means variable flow through the air heater, controlled by a two-way control valve. • District heating connection; with shunt, which means constant flow through the air heater, controlled by means of a two-way control valve. • The “SABO” connection; with shunt, which means constant flow through the air heater, controlled by means of a three-way control valve. These different types of connections has, in this work, been given the names mentioned in the listing above (instead of different numbers) for instant clarity whenever discussed in the text. Balancing Although the system analyses have compared high-flow and low-flow balancing (and other system arrangements), it is not desirable to make physical changes to the system, such as by using larger or smaller radiators, as this affects the comparison. The analyses for the radiator system have therefore been based on two different basic cases, without deviations: one for each balancing method, with pipe sizes and arrangements, radiators and heat output being the same. The same applies for the system using air heaters. The difference between the two basic cases is that the flow has been assumed to be twice as great in the high-flow case as in the low-flow case. The required condition for these two arrangements to work is that the design supply temperature in the low-flow case should be higher than in the high-flow case.

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1 INTRODUCTION

1.3.2 Measurement and simulation After the selected systems were defined, a number of measurements were made in test rigs in order to investigate the systems' properties and to verify any design relationships that would be required in the next stages, i.e. of simulation of selected cases. When making actual physical measurements, the test conditions may be more or less fixed, depending on the design of the test rig and the measurement system. This means, that in certain cases, it can be time-consuming or even impossible to obtain the required results. This constraint does not exist in the case of simulations, as the conditions can be altered as required. However, the initial physical measurements are important, as they enable the simulation models to be verified. The test rigs that were used consisted of a radiator rig, having two radiators on one branch, and an air heater rig with associated valve group. The design of this valve group is such that it can easily be changed to suit any particular required measurement case. Two simulation programs were used: a commercial program (Flowmaster) for simulation of the air heater and its valve group, and an Excel spreadsheet, designed for simulation of a radiator system. 1.3.3 The effect of deviations As described earlier, this work has been concerned with investigation of what happens in a system when conditions depart from the design conditions. Recapitulating, a deviation means that something in the system is not what it should be. This could be either “software” or “hardware”, i.e. such as an incorrectly selected valve characteristic, an improperly performed balancing operation, a radiator valve that has been turned to a different setting etc. The sensitivity of the system function, depending on its design, can be analysed by regarding different systems in this way. The analyses have been concentrated on investigation of two result parameters: •

Room temperature or supply air temperature, which constitute the criterion of assessment of system function as seen by the occupants of the building. In this investigation, the supply air temperature has been assumed to be the same as the temperature of the air leaving the air heater.

•

The return water temperature, which is the main criterion of system function as seen from the district heating supplier's perspective.

The room temperature and the return temperature are two very important parameters, which provide one way of describing how well the heating system is working. A system deviation affects both the system function and performance, which in turn means that either the room temperature or the supply temperature, or both, is/are affected. The magnitude of the effect depends on the type of deviation and on the design of the system.

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1 INTRODUCTION

1.4

Work in this field

As far as hydronic heating systems are concerned, it is no exaggeration to say that the number of publications concerned with such systems is almost impossible to count. This means that the articles, reports and books mentioned or used in this work represent only a small fraction of everything that has been written. Of necessity, they have been selected on a subjective basis, although with the intention of constituting a firm basis upon which to build. Much has been written, and it could be thought that this is a working area about which little new remains to be said. However, the investigation of various systems in terms of their sensitivity to various deviations, instead of in terms of optimising their performance, does not seem to have been all that common, despite the fact that investigation of the sensitivity of function to system design is the most interesting aspect. Such work is essentially concerned with ensuring the proper function of systems, which should really be an important objective. As previously mentioned, the analysis aspects of the work described here have been concentrated primarily on hydronic heating systems supplied by district heating. In turn, the heating systems have been restricted to radiator systems and air heater systems, which make up a large proportion of existing systems in countries such as Sweden, Denmark, Finland, Germany and Russia. In 1996, district heating supplied about 36 % of the total space heating requirements of buildings in Sweden1, in which radiator systems provided the main form of space heating. There has therefore always been a relatively high level of research into systems of this type in Sweden, which is also reflected in the reference list at the end of this thesis. Conditions in the USA, for example, are different, as district heating and radiator systems are in a minority: instead, it is air-conditioning systems that are most commonly used. It is therefore not surprising that there are relatively few publications from the USA: at least, as far as radiator systems are concerned. A few aspects that have been of interest in this work are briefly described below (1.4.1-1.4.4). Each section describes only one or a few important articles, reports or books. 1.4.1 Buildings supplied by district heating systems Those involved in the district heating sector have conducted various types of research into different heat production units, distribution piping, substation in buildings and other aspects over many years. However, this work has not always considered the onward link from the district heating system to internal heating systems in buildings. In fact, such consideration has often been totally omitted, or only partly recognised as the major heat sink for the district heating system which, despite everything, it actually is. However, this is a heat sink with very varying properties, as shown by Sven Werner in his PhD thesis entitled “The heat load in district heating systems”2 (1984), which is specifically concerned with the load characteristic on district heating systems. Nevertheless, some university-level research into district heating, and involving the hydronic heating systems in buildings in one way or another, has been carried out in 1 2

Statistic from the Swedish District Heating Association. Although this particular thesis is written in English, not all of the material cited in the rest of this chapter or in other chapters of this thesis is necessarily in English. However, for the sake of clarity in this thesis, those titles have been translated into English (placed in clampers) where necessary.

5

1 INTRODUCTION

recent years. Examples of this include Jochen Dahm's thesis “Small district heating systems” (1999), Gunnar Larsson's “Dynamik i fjärrvärmesystem” (Dynamics of district heating systems) (1999) and Lena Olsson's thesis “Lokala fjärrvärmesystem” (Local district heating systems) (2001). It is quite clear today that the supply and return temperatures of district heating systems affect their overall efficiency and thus their economic viability. It is also equally clear that there is a close link between these temperature levels and the design and balancing not only of the consumer service units but also of the downstream domestic hot water, air heating and radiator systems. A paper by Sven Werner and Stefan Petersson in 2000, entitled “Samband mellan produktion och vältrimmade radiatorsystem” (The relationship between production and properly balanced radiator systems) showed, for example, that district heating utilities in Sweden could save SEK 800 million/year if their systems could be operated at maximum efficiency. A substantial proportion of this potential is accounted for by improvements in the efficiency of building heating systems. In this perspective, the importance of analysing building heating systems connected to district heating supplies is patently apparent. 1.4.2 Low-flow and high-flow balancing Low-flow versus high-flow balancing has been a subject of fierce debate for many years. In Sweden it started in the 1960s, when Östen Sandberg balanced a difficult radiator system in a school in Kiruna by drastically reducing the flow rate and increasing the supply temperature. This reduced the pressure drop in the pipes in the system, enabling all the radiators to receive the correct flow. This approach was subsequently given the name of the Kiruna method, or the low-flow method, and is much used today by a number of property companies, such as SABO (a swedish municipal housing organisation). It is described in the book by Torkel Andersson, Per Göransson, Gunnar Wiberg and Bebs Reybekiel, “Kirunametoden – för god energihushållning” (The Kiruna method - for good energy conservation) (1998). Torkel Andersson had previously published a substantial two-part article entitled “Konsten att styra radiatorsystem” (The art of controlling radiator systems) (1993), setting out the benefits of low-flow systems. A long debate occurred at the end of the 1970s and the beginning of the 1980s between Östen Sandberg, who naturally supported the low-flow method, and Sven Mandorff who “defended” the hitherto generally used high-flow method. This debate was conducted on the pages of various HVAC magazines. In it, Sven Mandorff showed the sensitivity of systems to system deviations, e.g. in his article entitled “Kirunametoden – bara fördelar?” (The Kiruna method - nothing but benefits?) (1982). The debate never really reached a firm conclusion in favour of one system or the other, and will probably never do so. In recent years, Stefan Petersson has carried out a performance comparison, based on both measurements and simulation, of high-flow and low-flow systems, describing the results in his licentiate thesis “Analys av konventionella radiatorsystem” (Analysis of conventional radiator systems) (1998) and in the subsequent report published by the Swedish District Heating Association, entitled “Metoder att nå lägre returtemperatur med värmeväxlar-dimensionering och injusteringsmetoder” (Methods of achieving lower return temperatures by heat exchanger design and balancing methods) (2000).

6

1 INTRODUCTION

The high-flow method is still regarded as being the generally accepted method, with the low-flow method often being used as an alternative for balancing existing (often substantially oversized) installations. However, it is not uncommon to encounter a sort of “intermediate-flow” method, so it may be that the various balancing methods are beginning to approach each other. The general view today seems to be that, regardless of the method chosen, it is important that systems are properly balanced. Unfortunately, this has not always been obvious. During the 1970s, it was suggested that balancing of radiator systems was unnecessary if they were complemented with thermostatic radiator valves. However, Sven Mandorff showed, in his articles entitled “Funktionen hos värmesystem med radiatortermostatventiler utan förinställning” (Performance of heating systems with radiator thermostatic valves without presetting) (1979) and “PS om termostatventiler – erfarenheter från ett radhusområde” (A PM on thermostatic radiator valves - experience from a terrace house development) (1977), that such a procedure could result in difficult problems. When considering balancing problems, Robert Petitjean's publication “Total hydronic balancing” (1994) cannot be overlooked. It provides a detailed description of (primarily) high-flow adjustment of hydronic heating systems, together with a number of sensitivity analyses. 1.4.3 Radiator systems, air heaters and valves A lot has been written about radiator systems from a general perspective: an example of this is the BFR report “Värt att veta om vattenburen värme” (Worth knowing about hydronic heating), by Sune Häggbom and Per-Olof Nylund (1989), which provides a general description, mainly of radiator systems. Another example is Lennart Örberg's report “Dimensionering och injustering av vattenburna värme- och kylsystem” (Design and balancing of hydronic heating and cooling systems) (1986). A considerable amount of research into radiator systems was carried out in Sweden during the 1970s and 1980s, concerned primarily with the function and benefit of thermostatic radiator valves, and with discussion of which balancing principle was preferable. The Department of Heating and Ventilation Technology at the Royal Institute of Technology has been the source of much that has been written about heat release from radiators and how they affect the rooms in which they are installed. Examples include “Förenklad bestämning av operativtemperaturen i radiatorvärmda rum” (Simplified determination of the operative temperature in rooms heated by radiators) by Folke Peterson (1975), “Radiatorers yttemperatur” (The surface temperature of radiators) by Tor-Göran Malmström (1975) and “Värmevgivning från radiatorer” (Heat release from radiators) by Stig Hammarsten (1985). All of these publications are in the Royal Institute of Technology series of Technical Notices. Lars Jensen's thesis, “Digital reglering av klimatprocesser” (Digital control of climate processes) (1978), should also be mentioned in this context, as it includes a description of how the room temperature reacts when a radiator is controlled in various ways. As far as thermostatic radiator control valves are concerned, Anders Svensson's status report entitled “Radiatortermostatventilers funktion – lägesrapport” (The function of

7

1 INTRODUCTION

radiator thermostatic control valves) (1978) must be mentioned. In addition, he and Sven Mandorff have written an interesting article entitled “Radiatortermostatventiler på gott och ont” (Radiator thermostats for better or worse) (1977), which emphasised the importance of adjusting the supply temperature to track the ambient temperature in order to ensure correct operation of the thermostatic valves. Further examples of such reports include Lars Jensen's “Analys av termostatventilers statiska egenskaper” (Analysis of the static characteristics of thermostatic radiator control valves) (1986) and the BFR report “Långtidsegenskaper hos radiatortermostatventiler” (Long-term characteristics of thermostatic radiator control valves), by Geron Johansson, Matti Kolehmainen and Lars Waldner (1989). For natural reasons, most of what has been published about radiator systems has been concentrated on two-pipe systems, although there are exceptions. Examples include “Ett-rörs system för värme – Teori, praktik och ekonomi” (Single-pipe systems for heating - theory, practice and economics) by Ulf Järnefors (1978), and the articles “1rörsystemet ger en annan reglerstrategi” (The single-pipe system necessitates a different control strategy) by Hugo Brännström (1987) and “Single-pipe hydronic system design and load-matched pumping” by W.C. Stethem (1994). There are many examples of Swedish work on air heaters. As far as the development and/or study of mathematical models is concerned, Elisabeth Mundt's report “Modeller av luftvärmare för simulering av stationära och dynamiska driftsfall” (Models of air heaters for simulation of stationary and dynamic operating modes) (1988) and Per E. Blomberg's PhD thesis “Experimental validation of dynamic component models – for simulation of air handling units” (1999) should be mentioned. Two other interesting reports are Per Widén's licentiate thesis “Luftvärmare i luftbehandlingsaggregat” (Air heaters in air handling units) (1994) and Hugo Brännström's BFR report “Frysskadesäkra vattenburna luftvärmare” (Frost-resistant hydronic air heaters - field trials and practical application) (1990). The former is concerned with the linear relationships between the temperatures in an air heater through which constant media flows are passing, while the latter is concerned with air heaters without recirculation circuit and how they can be protected from freezing. The choice of control valves is an interesting aspect of this work. A considerable amount of research into this has been carried out in Norway, with Arvid Grindal, Bent Børresen and Einar Magne Hjorthol among those to the fore. Examples of interesting literature include Arvid Grindal's article “Ventilkarakteristikker – er det på tide at vi gjør noe med dem?” (Valve characteristics - is it time to do something about them?) (1988), Bent Børresen's article “Ventildimensjonering og ventilautoritet” (Valve sizing and valve authority) (1994) and Einar Magne Hjorthol's thesis “Optimisation of design values in district heating substations by system simulation” (1990). There are also several examples of applications from the USA dealing with the selection of balancing and control valves, such as “Selecting control and balancing valves in a variable flow system” by Richard A. Hegberg (1997) and “The effect of sizing mismatch on coil valve performance” by Randall J. Amerson (1998), in which the latter provides an analysis of the effects of deviations. An early, very interesting, Swedish article on the same theme is “Att undvika missanpassning av styrventiler” (To avoid mis-sizing of control valves) by Karl-Åke Lundin (1980).

8

1 INTRODUCTION

1.4.4 System design and control How can the correct function of a system be ensured? The answer is that it probably cannot be ensured, although the probability of the occurrence of problems can be reduced by favourable design of the system. But how can this be quantified? One way is to consider the control of the system or, strictly, how the necessary settings of the system regulator must be set in order to avoid instability. The less well designed the system, the greater the risk of control difficulties due to it being more likely for the system to become unstable. In turn, the more difficult it is to control the system, then the greater the risk of sub-standard performance. This approach starts with Ziegler and Nichol's well-known article “Optimum settings for automatic controllers” (1942), with guidelines concerning the setting of control systems. These guidelines have been used in Norway for the classification of the difficulty of control of a system. Although there are several persons who have worked on such aspects, most of the input to this present project has been inspired from Arvid Grindal's and Bent Børresen's many publications, e.g. their excellent joint article “Controllability - back to basics” (1990). As far as research into system control is concerned, Lars Jensen's work must again be mentioned. His PhD thesis, and various of his other publications, have provided the basis for much of the research into this area. Not only has he developed mathematical models for both components and control procedures, but he has also carried out several instrumented investigations of various controlled items. His work has been continued in Vojislav Novakovic's “Digital control of heater coils” thesis (1982), which shows how the settings values for a digital controller can be determined, and how well such a controller operates in comparison with an analogue equivalent. However, the main emphasis of the work described here is not on system control, but on system characteristics. Interest has therefore been concentrated on determination of the system's static and in some extent dynamic characteristics.

1.5

The structure of this thesis

This thesis consists of eight chapters. Chapter 2 is devoted to general theory, describing and defining a number of fundamental concepts concerning the design of a system. This is necessary material for understanding of the following chapters. Chapter 3 describes the measurements; how they were made and a number of independent results, such as thermal stratification in air heaters. Chapter 4 describes the simulation programs used. In addition, it compares the measured results with those of simulation in order to verify the programs. Chapter 5 deals with planning of the simulations. In this chapter the systemconfigurations and deviations that are used in the simulations is being presented, as well as the methods to derive and present the results. Chapter 6, that is rather extensive, is devoted to results from simulation of the effects of deviations in a radiator system. Each section of simulation is followed by a summary and discussion of the particular case concerned. In addition, the chapter is concluded

9

1 INTRODUCTION

with a discussion of other aspects in the field, not dealt with earlier in the thesis, such as the differences between 1-, 2- and 3-pipe systems and the effects of the performance of the district heating heat exchanger connected to the radiator system. Chapter 7 is also devoted to results, but this time from simulation of deviations in a valve group and the associated air heater. Chapter 8 brings together and discuss the results from Chapters 6 and 7. Any more or less general trends are considered, and the consequences of some particular system designs are described. Appendix A describes the test rigs in detail, and considers the effects of uncertainties of measurement. Appendix B describes the theoretical and empirical relationships underpinning the structure of the design program for analysis of deviations in a radiator system. Also the derivation of an expression to describe the sensitivity of radiators to flow deviations is described. The appendix is concluded with a description of the simplified process to derive an optimum valve characteristic.

10

2 SYSTEM DESIGN

2

SYSTEM DESIGN

This chapter describes a number of concepts and definitions that need to be clarified in order to assist understanding of the rest of this presentation. However, it is assumed that a number of fundamental relationships are known by the reader, and so they will not be further discussed here. For a more fundamental review of the concepts relating to the function of a hydronic heating system, see Trüschel (1999), from which some of the material in this chapter has been taken, or (for example) Häggbom and Nylund (1989), who describe both the theory and the practice of hydronic heating systems. The function and performance of the system depend on the interaction between the system design and its control. In this presentation, the focus is entirely on the system design, due to the fact that this must always be considered first. The philosophy is that control of the system must be tailored to the system to be controlled. A control system or control method must not be applied in the hope of compensating for a poorly designed system, and nor can it do so, which is a well-known observation, but nonetheless important to point out (Grindal and Børresen, 1988; Hjorthol, 1990). It is therefore important to understand how the design of a system affects its properties. The better the design, the simpler the necessary control and the better the system will perform. As used here, system design or design of the system refers to the components selected for use in the system, how they are arranged in relation to one another and their capacities (i.e. aspects such as size, torque, power etc.). It is the intention here to characterise system design in terms of the following three main aspects: • Structure (architecture etc.) • Balancing • Control valves The inclusion of balancing as part of the design may perhaps not be regarded as a general mainstream approach. This is because the selection of balancing method represents an indirect measure of the system design, in the form of temperature levels and flow rates. This simplifies the presentation, as balancing is a very important parameter when describing a system.

2.1

Structure

2.1.1 Distribution systems The structure of a system describes primarily how the distribution part of the system has been designed. A common feature of all distribution systems is that the heat (i.e. the hot water) is distributed around the building by means of a supply pipe. After giving up heat in the heat-releasing components, the cooled flow is returned to the heat source via a return pipe. This can be said to apply in general, although distribution systems can be arranged in various ways. The commonest form is that of a 2-pipe system, in which branches are taken off the supply pipe to each heat-releasing component, and from which the flow returns via direct connection to the return pipe, as shown in Figure 2.

11

2 SYSTEM DESIGN

Supply pipe Heat-releasing component Return pipe

Figure 2.

Schematic diagram of a 2-pipe distribution system.

Alternatively, instead of having separate supply and return pipes, they can be combined into a 1-pipe system, with the supply pipe to each component forming the return pipe from the previous component, as shown in Figure 3. Supply pipe Return pipe

Figure 3.

Schematic diagram of a 1-pipe distribution system.

As indicated by the name, the 1-pipe system consists really of only a single pipe, forming a distribution loop that starts and finishes at the heat source, with an appropriate flow being tapped off from the loop to each component. This means that the supply flow to each component consists partly of the cooled return flow from the previous component, so that the supply temperature is progressively reduced as the flow passes each component. In order to compensate for this, the components can either be progressively larger, or the flow tapped off to each component can be increased for components further away from the source in the direction of flow. A further development of the 2-pipe system is what is known as the 3-pipe system or the Tischelmann connection, in which the return pipe is reverse-connected, as shown in Figure 4 below. Supply pipe

Return pipe

Figure 4.

Schematic diagram of a 3-pipe distribution system.

The 3-pipe system works in the same way as the 2-pipe system, except that the return connection is reversed. The purpose of this arrangement is to attempt to reduce the differences in differential pressure across the components, as occurs in a 2-pipe system with direct return. The differential pressure depends on the pressure losses in the supply and return pipes: the further away from the heat source that a component is, the longer are the supply and return connections to and from it, and thus the less is the differential pressure available across the component. It can be seen from Figure 4 that the total distance, in terms of the sum of the supply pipe length and the return pipe length, is the same for each component, which means that the differential pressure available across the components does not vary as much as in the basic 2-pipe system shown in Figure 2. The reason for the interest in attempting to achieve constant differential pressure is that this pressure considerably affects the flow through a component, and thus the amount of 12

2 SYSTEM DESIGN

heat released by it. Balancing, the purpose of which is to balance the flows through each component, so that the flow through the components is set to the desired values, is facilitated if the effect of the differential pressure differences on the distribution system is reduced. 1-pipe systems and (particularly) 3-pipe systems are relatively uncommon, in comparison with the use of 2-pipe systems. As a result, most of the emphasis of this presentation will be on 2-pipe systems, with the other two types being dealt with only in general terms. 2.1.2 Valve groups The concept of structure or architecture of distribution systems, as used here, also includes valve groups, which provide local control of air heaters. The design of such valve groups affects the control principle. The simplest case consists of no valve group at all, which means that the heat provided by the air coil is controlled only by changing the flow through the component. The arrangement is referred to here as direct connection (see Figure 5). Direct connection

Figure 5.

An example of direct connection.

However, in general, control is provided in and by a valve group by mixing the cooled return water flow from the component with hot water from the supply pipe in order to achieve a required inlet temperature, which is defined as being the temperature of the water at the point of entry to a heat-releasing component. The supply temperature is defined as being the temperature of the water entering the distribution system supply pipe after the central temperature control function, which also can be controlled by another valve group, e.g. if an oil-fired boiler is being used as the heat source. The inlet temperature in a heating system will always be lower than the supply temperature, regardless of the type of local control, due to heat losses in the supply pipe. Figure 6 shows two examples of common valve groups, referred to here as the district heating connection (as this arrangement is mostly used in systems connected to district heating supplies), and the SABO1 connection (which is an fairly accepted name for this type of valve group). The right-hand side of the shunt connection, or the bypass connection, is referred to as the secondary side, with the left-hand side being referred to as the primary side. Both valve groups are intended to provide an almost constant flow rate through the air heater (the secondary side), with a variable flow rate in the distribution system (the primary side).

1

SABO is a large country-wide municipal housing association.

13

2 SYSTEM DESIGN

District heating connection Figure 6.

SABO connection

Two valve group arrangements to provide variable flow on the primary side and constant flow on the secondary side.

Figure 7 shows two further valve group arrangements, intended to produce constant flow rates on both the primary and secondary sides. These arrangements are generally known respectively as the Swedish connection and the Norwegian connection. Swedish connection Figure 7.

Norwegian connection

Two valve groups to maintain constant flow rates on both the primary and secondary sides.

Heating systems connected to district heating supplies use valve groups with variable flows on the primary side (Figures 5 and 6) and that is why other types of valve groups will not be further considered in this presentation.

2.2

Balancing

The purpose of balancing is to create a balanced flow in the system. However, the performance of balancing affects not only the distribution of flows through the system, but also the interaction between the heat-releasing components and their individual characteristics. For a fluid to flow, there must be a pressure difference. At the same time, the amount of the flow is restricted by resistance. Flow resistance is due to energy losses in the form of friction, losses caused by changes of direction (e.g. pipe bends etc.) or losses due to sudden velocity changes. The relation between the flow resistance and the differential pressure determines the magnitude of the flow. This is shown by the following simple relationship (which admittedly applies only for full turbulent flow) (Abel et. al, 1997): & = V & V ∆p k

∆p k

(1)

= Flow [m³/s] = Differential pressure [Pa] = Flow resistance [Pa/(m³/s)²]

The purpose of the pump in the circulation system is to create a pressure difference. This pressure difference, which is the driving force behind the flow, is progressively dissipated by pressure drops in the distribution system with increasing distance from the

14

2 SYSTEM DESIGN

pump. This means that the pressure difference across a radiator close to the pump is higher than that across a radiator further away, as shown in Figure 8 below.

Pump

1

2

3

∆p2

∆p3

4

5

Radiator

Pressure

∆ppump

∆p1

∆p4

∆p5

Length

Figure 8.

Available differential pressure in a circulation system with five radiators. It can be seen that the differential pressure across component 1 is considerably higher than that across component 5.

If the flow through each radiator is to be the same, there needs to be a higher flow resistance through radiator 1 and a lower resistance through radiator 5. This is achieved during balancing by means of the balancing valves. Changing the openings of the valves changes their flow resistance. However, it is not the flow resistance of the valves that is specified during balancing, but their capacity. 2.2.1 Valve capacity A measure of the valve capacity is given by its kv value, which is defined as: kv =

& V ∆p ∆p 0 ρ ρ0

= = = = =

& V

(2)

∆p ρ 0 ⋅ ∆p 0 ρ

Volume flow through the valve [m3/h] Pressure drop (differential pressure) across the valve [bar] Reference pressure drop = 1 bar Density of the liquid passing through the valve [kg/m3] Reference density = 1000 kg/m3 (water)

The kv value indicates the magnitude of the flow in [m³/h] passing through the valve for a differential pressure of 1 bar The larger the opening, the higher the valve capacity and the greater the kv value. Closing the valve completely gives a kv value of zero. The liquid in hydronic heating systems is generally water, which can be regarded as an incompressible fluid, so that the 15

2 SYSTEM DESIGN

fluid correction factor (ρ0/ρ) can be expressed as unity. In addition, as the reference pressure drop is 1, the expression for the kv value can be simplified to the following: kv =

& V ∆p

(3)

In many contexts, it is impractical to use the quantities [m3/h] and/or [bar]. There are therefore many different expressions for the kv value, although the differences are due only to the use of different units. (The reference units remain unchanged.) Table 1 shows a number of examples: Differential pressure \ Flow

Table 1.

[m3/h]

[bar]

kv =

[kPa]

kv =

& V ∆p

[l/h] kv =

& 10 ⋅ V

kv =

∆p

& 0,001 ⋅ V ∆p & 0,01 ⋅ V ∆p

[l/s] kv = kv =

& 3,6 ⋅ V ∆p & 36 ⋅ V ∆p

Different expressions for the kv value of a valve, depending on the choice of units.

The maximum kv value of a valve, i.e. its capacity when fully open, is usually referred to as the kvs value. The flow resistance (k) and the valve capacity (kv) symbolise two completely different things, and must therefore not be confused, although this can easily happen as the symbols are so similar. It is, of course, more practical to express the size or setting of a valve by means of a measure of capacity than by means of a measure of its flow resistance (which is a somewhat “empty” expression). 2.2.2 Pump and system characteristics A hydronic heating system consists of a circulation system, in which the water is circulated by a pump. The pump characteristic, which is determined by the design and size of the pump, shows the relationship between the pressure rise in the pump and the flow through it. The heating system has a hydraulic resistance, which expresses itself as pressure drops through/across pipes, valves, heat-releasing components etc. The total pressure drop of the system changes depending on the magnitude of the flow. The relationship between the total flow and the total pressure drop in the system is referred to as the system characteristic. The system operating point will automatically lie at the point where the total flow through the system is such that the total pressure drop in the system equals the pressure rise across the pump.

16

2 SYSTEM DESIGN

Differential pressure System characteristic Operating point

Pump characteristic Flow

Figure 9.

Pump and system characteristics.

The system characteristic depends on the total flow resistance of the system. The greater the flow resistance, the greater the pressure drop in the system for any given flow. This means that whenever anything changes in the system, the position of the operating point will change, giving rise to a new total flow through the system. Balancing, in other words, means that the system characteristic will be changed, due to the fact that the balancing valves are partially closed, as necessary. At the same time, the pressure rise across the pump changes. (Alternatively, one can say that the total pressure drop in the system changes, if preferred.) Differential pressure

New system characteristic Old system characteristic New operating point Old operating point Pump characteristic Flow

Figure 10. Changing the operating point in a system. It can be seen from the figure above that the change in the total flow is due both to the change in the system characteristic and to the shape of the pump characteristic curve. A steep pump characteristic results in only a slight change in the total flow, but a more substantial change in the pressure rise/pressure drop. A flat pump characteristic, on the other hand, produces the opposite results, i.e. a substantial change in the total flow but only a slight change in the pressure rise/pressure drop. This is shown schematically in Figure 11, with steep and flat pump characteristics being symbolised by a vertical and a horisontal straight line respectively.

17

2 SYSTEM DESIGN

Differential pressure

Steep pump characteristic

New operating points, depending on the pump characteristic

Change in the system characteristic Old operating point Flat pump characteristic

Flow

Figure 11. Changes in the operating point, depending on the pump characteristic, in response to a change in the system characteristic. 2.2.3 The effect of pipe pressure drop The interaction, i.e. how individual flow changes affect the flow balance of the entire system, depends on the pressure drops in the pipes of the system and on the magnitude of the pressure drops across the components. The pressure drops in the pipes depend on the size of the pipes and on the flow in them, which is a result of the system balancing. Pipe pressure drop can be described by the following simple relationship, which follows the same principle as that of equation (1): &x ∆p pipe = k pipe ⋅ V where

(4)

∆p pipe = Pipe pressure drop [kPa] k pipe & V x

= The coefficient of flow resistance in the pipe [kPa/(m³/s)x] = Flow [m³/s] = An exponent, which depends on the type of flow [-]

For fully laminar flow, the exponent equals to 1, while for fully turbulent flow it equals to 2 (Abel et. al, 1997). These represent the two limiting cases of flow conditions. The exponent varies, in other words, between 1 and 2, depending on the flow conditions. From the previous equations, we can derive the following relationship, which describes how a change of flow affects the pressure drop. It is valid provided that neither the pipe parameters nor exponent x are changed. Index 1 indicates the value of the quantity before change, and index 2 indicates its value after change. ∆p pipe, 2 ∆p pipe,1

& V =  2 &  V1

  

x

(5)

The magnitude of the interaction depends on by how much the pressure drop across the heat-releasing components (i.e. its associated valves) changes in response to a change of the flow balance in the system. This is illustrated by an example with a group of radiators, as shown in Figure 12. The figure shows the effect of two different pipe

18

2 SYSTEM DESIGN

pressure drops, as could result, for example, from different flows or from different pipe sizes (or from both mechanisms). Control and balance valve 1

2

3

4

Flow:

Radiator branch

5

100 %

50 %

3 kPa

Case 1

1 kPa

2.5 kPa

9 kPa

Case 2

1 kPa

7 kPa

Figure 12. The increase in pressure drop in response to a reduction in flow through the radiator group. A comparison between different pipe pressure drops (2 kPa and 8 kPa). In the first case, the pipe pressure drop in the supply and return pipes is 2 kPa, while the lowest balanced differential pressure (across radiator 5) is 1 kPa. A reduction of 50 % in the flow through the group means that the pipe pressure drop falls to 25 % of its original value, in accordance with equation (5) above (provided that the flow is fully turbulent). The differential pressure across radiator 5 then increases to 2.5 kPa, which will result in an increase of 58 % in the flow if the radiator valve setting is not changed. In the second case, the pipe pressure drop at 8 kPa is four times higher than in case 1, while the lowest balance differential pressure remains at 1 kPa, across radiator 5. A reduction of 50 % in the flow through the group results in a new differential pressure of 7 kPa across radiator 5, resulting in a flow increase of 164 % through it. It can be seen, therefore, that the interaction increases with the pipe pressure drop, which can be affected by balancing and, perhaps primarily, by the size of the pipes. Large pipe sizes also have the advantage that not only is the interaction reduced, but pumping costs are also reduced as there is a lower pressure drop in the system. However, large pipe sizes also involve higher investment costs. In addition, it is not always beneficial to minimise pressure drops in the system, as described in the following section.

19

2 SYSTEM DESIGN

2.2.4 The effect of lowest balanced differential pressure The magnitude of the system flow is not an entirely free choice, as it is linked to the supply temperature and to the sizes of the heat-releasing components. The higher the possible supply temperature, the lower the flow required. This means that other factors, such as the choice of heat source and the size of the components (see the next section) can affect adjustment of the magnitude of the flow. For this reason, the pipe pressure drop cannot be set arbitrarily in connection with balancing. However, there is more room to manoeuvre, from a technical point of view, in deciding on the lowest balanced differential pressure. As the flow through a component depends on both the available differential pressure across it and its flow resistance, a high differential pressure can be compensated for (or offset by) a high flow resistance, and vice versa, without affecting the flow. When balancing the system, a lowest design differential pressure across the component (or, strictly, across its balancing valve) in the system that has the lowest available differential pressure, is determined. This component (that sets the lowest available differential pressure) is usually the one that is furthest from the pump. There is no optimum value for lowest differential pressure: some systems are designed for a lowest differential pressure of 2 kPa, while others use 10 kPa. The greater the differential pressure, the more must the balancing valve be throttled in order to achieve the correct flow. It might seem as a bad idea to choose a high differential pressure, as this will require the balancing valves to be throttled all the more, which means that, in turn, an unnecessarily large pump has to be used in order to overcome the high pressure drops in the system. However, the advantage of a high differential pressure is that a change in a valve setting, due to control, does not have such a great effect on the flow through other parts of the system as it would in a system operating with a low differential pressure. The interaction between the components, in other words, is less with increasing differential pressure. We can clarify this by again showing an example (Figure 13) of the pressure levels in a radiator branch. For the purposes of the example, it has been assumed that the two radiator branches in the comparison are exactly the same: the only difference between the two cases is that the lowest balanced differential pressure (across radiator 5) is 1 kPa in one branch and 10 kPa in the other. The continuous lines in the figure show the full-flow pressure drop in the pipes, which is the same in both cases. When some of the radiator valves close, e.g. as a result of insolation, the flow through the branch is reduced, which also reduces the pressure drops in the pipes. The new pressure drops in the pipes are shown by the dotted lines in the figure. It can be seen that the differential pressure across the radiators increases by the same amounts (in absolute terms) in both cases, but that when expressed in relative terms the difference is considerable, which thus affects the flows through the radiators differently.

20

2 SYSTEM DESIGN

9 kPa

Case 1

1 kPa

18 kPa

Case 2

10 kPa 13 kPa

4 kPa

Figure 13. Increasing the differential pressure in response to a reduction in flow through the group. A comparison between a system balanced for a minimum differential pressure of 1 kPa and one balanced for a minimum differential pressure of 10 kPa. In the first case (with a low balanced minimum differential pressure), the differential pressure across radiator 5 increases from 1 kPa to 4 kPa. This is equivalent to a 100 % increase in flow through radiator 5 if its valve setting remains unchanged, in accordance with equation (1), which applies for fully turbulent flow. In the second case, with a high set minimum differential pressure, the differential pressure across radiator 5 also increases by 3 kPa. However, as it was originally 10 kPa, the relative increase is only 30 %, as against 300 % in the previous case. This means that the flow through the radiator increases by only about 14 %. The higher differential pressure, in other words, helps to reduce the interaction between the heat-releasing components in a system. This means that, if the system is set up to have a high minimum differential pressure, the amount of heat released from a component does not change as much in response to flow changes caused by other components in the system. A general opinion seems to be that this also assists system control, due to the fact that the control valves have a higher valve authority. However, this is not necessarily the case, as is discussed in Section 2.3.2, which considers and explains the concept of valve authority. The drawback of a high differential pressure is that energy is lost in the form of a high pressure drop through the valves, which increases system running costs.

21

2 SYSTEM DESIGN

2.2.5 The heat-releasing components' characteristic As previously mentioned, balancing provides an indirect measure of the design capacity of the system, in the form of temperature levels and flows. It is important, when analysing system function and performance, to be aware of the characteristics of the heat-releasing components, in the form of the relationship between flow and heat release power (or output air temperature). This characteristic depends partly on the size and design of the component and partly on the temperature levels involved. Determining the design/size of a heat-releasing component, such as a radiator, involves ensuring that the component is sufficiently large to be able to provide the necessary heating power. This size also depends on the design temperature levels in the heating system and on the ambient conditions in which the component works, all in accordance with the following well-known equation that describes heat transfer in a heat exchanger: & = U ⋅ A ⋅ ∆t Q m & Q U A ∆t m

= = = =

(6)

Thermal power transferred [W] Coefficient of thermal transmittance [W/m²K] The surface area of the heat-releasing component [m²] The mean temperature difference between the hot and cold flows [°C]

In addition, if there are no heat losses in connection with transfer of the heat, the following equation applies, with index i representing either the hot or the cold medium. & = ρ ⋅V & ⋅ c ⋅ (t − t ) = C ⋅ ∆t Q i i i i ,in i , out i i & Q ρi & V

ci t i ,in

= = = = =

t i ,out

= Exit temperature [°C]

Ci ∆t i

& ⋅ c ) [W/°C] = Thermal capacity flow (= ρ i ⋅ V i i = Temperature drop (= t i ,in − t i ,out ) [°C]

i

(7)

Thermal power transferred [W] Density [kg/m³] Flow [m³/s] Specific thermal capacity [J/kg°C] Input temperature [°C]

Radiators For radiators, the special case applies that the coefficient of thermal transmittance U consists in principle of the coefficient of surface thermal insulance on the outside of the radiator. This coefficient depends on the temperature levels, which in turn enable the following expression to be applied (Abel et. al, 1997): & = K ⋅ ∆t n Q rad rad m & Q rad

(8)

= Thermal power output from the radiator [W] 22

2 SYSTEM DESIGN

K rad n

= Radiator constant, dependent on the size and design of the radiator [W/°Cn] = Radiator exponent, dependent on the size and design of the radiator [-]

The magnitude of the flow through the heat-releasing component has a considerable effect on the amount of heat released. At a low flow rate, the water temperature falls rapidly as the water passes through the radiator and gives up heat. The result is a low return temperature and a relatively low average surface temperature on the radiator, which therefore reduces the amount of heat released. With a high flow rate, on the other hand, the water temperature doesn’t fall so much. This produces a higher return temperature, resulting in a high average surface temperature of the radiator, with high heat release. Figure 14 shows, with a supply temperature of 80 °C and a room temperature of 20 ºC, how the thermal output power varies with the flow for a given radiator. This curve has been produced from the equations shown above. The shape of the curve is characteristic of both radiators and air heaters. 1000 tw ,in = 80 °C

Thermal power output [W]

900 800 700 600 500 400 300 200 100 0 0

10

20

30

40

50

60

70

80

90

100

Flow [l/h]

Figure 14. Flow characteristic of a radiator. As the curve is not straight, a given flow change will have different effects on the thermal power output, depending on at what point on the curve it occurs. At low flow rates, a change in the flow has a considerable effect on the heat output. A flow change at a high flow rate, on the other hand, does not result in any greater change in the thermal output. In this respect, balancing is of interest, as it determines where on the curve the radiator will be operating. However, the actual characteristic depends on the inlet temperature, the room temperature and the design/size of the radiator. This is illustrated in Figure 15, which shows the characteristics of one and the same radiator, but at two different inlet temperatures, of 80 °C and 60 °C.

23

2 SYSTEM DESIGN

1000 tw ,in = 80 °C

Thermal power output [W]

900 800 700

tw ,in = 60 °C

600 500 400 300 200 100 0 0

10

20

30

40

50

60

70

80

90

100

Flow [l/h]

Figure 15. Radiator characteristic of one and the same radiator, but with inlet temperatures of 80 °C and 60 °C. It can be seen that the radiator can provide a design thermal power output of, for example, 700 W with the higher inlet temperature, but that a larger radiator would be required if the lower inlet temperature is used. The slope of the radiator characteristic curve for a given flow shows how sensitive the radiator is to a small change in the flow. This can also be expressed in the form of the following approximate relationship (see Appendix B for derivation), which describes & Q & ) for a relatively small change in the relative change in thermal output power ( dQ & V & ): flow ( dV D Q& V& ≈

2 ⋅ (t w ,in

n ⋅ ∆t w − t room ) − (2 − n ) ⋅ ∆t w

n ∆t w

& dQ & Q = = The radiator's sensitivity to a flow deviation [-] & dV δ & V = Radiator exponent [-] = t w ,in − t w ,out = Temperature drop through the radiator [ºC]

t w ,in

= Inlet (supply) temperature [ºC]

t room

= Room temperature [ºC]

δ

where

D Q& V&

Generally, n varies in value between 1.1 and 1.4 (Petitjean, 1994). For a value of n = 1.33, we obtain the following simplified relationship:

24

(9)

2 SYSTEM DESIGN

D Q& V& ≈

2 ⋅ ∆t w 3 ⋅ (t w ,in − t room ) − ∆t w

(10)

At a zero flow rate (or, strictly, fractionally above zero), the radiator sensitivity obtain a value of 1, as the return temperature would then be the same as the room temperature. This is the maximum value of sensitivity. At the other end of the flow rate, with an infinitely high flow rate, the radiator sensitivity would be 0, which would be the least possible value. Assume that the radiator in Figure 15, for an inlet temperature of 80 ºC, has been balanced for a flow rate of 10 l/h, which would mean that it would be supplying a thermal output of 500 W at a room temperature of 20 ºC. From equation (7), the temperature drop through the radiator would be estimated to about 43 ºC. With this and using equation (10), the radiator sensitivity can be calculated as about 0.63. The same radiator, but now with an inlet temperature of 60 ºC, release a thermal output power of 500 W when the flow is balanced to approximately 30 l/h. The temperature drop is then about 14 ºC, giving a radiator sensitivity of about 0.26. This shows that, in the first case, which is equivalent to a radiator adjusted for a low flow rate, the radiator is almost 2.5 times more sensitive to a flow change than in the second case, which is equivalent to a high flow rate setting. However, it must be pointed out that this applies only to consideration of the radiator in isolation. In actual fact, the flow change through the radiator in the low-flow case would presumably be less than in the high-flow case, which provides a means by which the differences in the radiator sensitivities can be compensated, depending on how the rest of the system is designed (see the previous section). Air heaters The assumption that the coefficient of thermal transmittance of an air heater depends on the temperature levels cannot be made, as the coefficient of surface thermal insulance on the outside of the air heater depends on the forced air flow (Mundt, 1988). The coefficient of the surface thermal insulance on the inside of the air heater tubes also has a significant effect on the coefficient of thermal transmittance. This means that the air heater's UA value is affected by a change in the water flow rate, but hardly at all by a change in temperature. Equation (6) cannot therefore be simplified for an air heater in the same way as for a radiator. However, instead of using equation (6), the efficacy of an air heater can be defined using two efficiencies: one for the air side and one for the water side, as shown in equations (11) and (12) below (Abel et. al, 1997). ηa =

ηw =

t a ,out − t a ,in

(11)

t w ,in − t a ,in t w ,in − t w ,out

(12)

t w ,in − t a ,in

25

2 SYSTEM DESIGN

ηa ηw t a ,out

= Air heater efficiency on the air side [-] = Air heater efficiency on the water side [-] = Output air temperature (after the air heater ) [°C]

t a ,in

= Input air temperature (before the air heater) [°C]

t w ,in

= Water inlet temperature [°C]

t w ,out = Water return temperature [°C] The denominator in both the above expressions shows the maximum theoretical temperature change in the air and water flows. The efficiencies of an air heater are constant as long as the air or water flow rates remain constant (Widén, 1994). The reason is that the UA value does not change unless the flows do so. This applies, of course, provided that there are no changes to the air heater coil. It is therefore easy to determine the output temperatures if the input temperatures and the efficiencies are known. In the case of a direct-connected air heater, through which the flow varies, equation (11) provides a simple measure of the characteristic. In principle, the temperature rise of the air (the numerator) corresponds to the amount of heat picked up from the air heater, which in turn depends on both the efficiency (which is a measure of the design and size of the air heater) and on the incoming temperatures of both the air and water. These temperatures are independent of the flow. However, the flow affects the efficiency, which can be calculated using, for example, the NTU method (Kays and London, 1984). This means that a change in the flow produces a corresponding change in the efficiency, which in turn results in a change in the thermal power released or absorbed. However, in most cases, air heaters are not directly connected, but are connected to a valve group, which returns some of the return flow to the inlet. In many air heaters, the flow through the heater is kept almost constant, which means that the heater characteristic is not as easy to determine as in the case of a direct-connected air heater. The characteristic must link to what is happening in the system as it is controlled: if not, it becomes difficult to link it to system function. The item that is controlled in the system is the control valve, which in turn affects the flow through it. This means that it is necessary for the characteristic of the heat-releasing component to be linked to the flow through the control valve. This is the case with a direct-connected air heater, as described in the last paragraph. However, links become more difficult in the case of an air heater with a valve group that is recirculating some of the return flow. Figure 16 shows a diagram of such an arrangement.

26

2 SYSTEM DESIGN

& V B

tw,out

tw,supply

tw,in

& V R

& V H

Figure 16. A valve group with a return connection. At the mixing point (illustrated) the supply and return temperature are combined to produce the required inlet temperature to the air heater. The following relationships apply at the mixing point (circled in the figure), with the assumption that the specific thermal capacity is assumed to be constant:

where

t w ,sup ply ⋅ C R + t w ,out ⋅ C B = t w ,in ⋅ C H

(13)

CH = CR + CB

(14)

t w ,sup ply = Supply temperature [ºC] t w ,out

= Return temperature [ºC]

t w ,in

= Inlet temperature [ºC]

C & V

& ⋅ ρ ⋅ c [W/ºC] = Thermal capacity flow = V p = Thermal capacity flow through the control valve [W/ºC] = Thermal capacity flow through the bypass [W/ºC] = Thermal capacity flow through the air heater [W/ºC]

R

& V B & VH

Equations (11) and (12), together with (13) and (14), give the following expression: η a ,s = η a ⋅

t a ,out − t a ,in ϕ = ϕ + η w − ϕ ⋅ η w t w ,sup ply − t a ,in

where

η a ,s = Total efficiency on air side for valve group with air heater [-]

and

ϕ=

& V R & VH

27

(15)

2 SYSTEM DESIGN

For the air heater, assuming that no heat is being lost from it, the following equation can be applied (Trüschel, 1999): ηw =

Ca 1 ⋅ ηa = ⋅ ηa Cw R

Ca Cw R

(16)

= Thermal capacity flow of air through the air heater [W/ºC] = C H = Thermal capacity flow of water through the air heater [W/ºC] = Cw Ca

Equation (15), together with (16) give the following expression: η a ,s =

1 1 1 1  + ⋅  − 1 ηa R  ϕ 

=

t a ,out − t a ,in t w ,sup ply − t a ,in

(17)

Equation (17) is analogous with equation (11). The difference is that equation (17) describes the characteristic of an air heater (and its valve group) that is controlled by changing its inlet temperature, while equation (11) describes a flow-controlled air heater. The supply and inlet temperatures in equation (17) are independent of the flow, in exactly the same way as for equation (11). If, in addition, the flows on both the water and the air side are maintained constant, then the efficiencies are independent of the flow. In this case, it is only quantity ϕ on the left-hand side of equation (17) that changes with the flow through the control valve (directly proportional), which has a direct effect on the temperature rise (the numerator on the right-hand side of the equation), and thus on the amount of thermal power released. An expression for the total efficiency on the water side for the valve group with the air heater can also be derived. The relationship between the total efficiency on the air side and on the water side is shown below: η w ,s =

η a ,s Ca C C ⋅ η a ,s = a ⋅ w ⋅ η a , s = CR Cw CR R ⋅ϕ

(18)

where η w ,s = Total efficiency on water side for valve group with air heater [-] Equation (18) together with (17) results in the following expression: η w ,s =

1  1  ϕ ⋅  − 1 + 1  ηw 

=

t w ,sup ply − t w ,return t w ,sup ply − t a ,in

where t w ,retur = Return temperature on the valve group’s primary side [ºC]

28

(19)

2 SYSTEM DESIGN

In the case of a direct-connected air heater ϕ is equal to 1. Expression (17) and (19) then transforms into the ordinary expressions for the effiency of the air heater, that is expression (11) and (12). 2.2.6 Categorisation of systems A heating system that is designed for a maximum average temperature (i.e. the average value of the supply and return pipe temperatures) of 50 °C is said to be a low-temperature system, while systems with higher maximum average temperatures are referred to as high-temperature systems (Fredriksen and Werner, 1993). The system temperatures are usually stated in order to indicate the type of system: e.g. a 75/35 system (supply temperature 75 °C, return temperature 35 °C), or a 60/40 system etc. A common form of balancing is based on the principle of each valve in a group or branch being independently adjusted in respect of its relationship with all the valves in the group or branch. The flow is relatively high, which means that the pressure drops between each valve are significant for the balancing, as the differential pressure available across the valves falls with increasing distance from the pump. Examples of system temperatures in such systems are 80/60, 60/40 and 55/45. They are referred to as high-flow systems, and are thus balanced on the high-flow principle. Low-flow balancing was used for the first time by Östen Sandberg in the 1960s (Andersson et. al, 1998), and involves reducing the flow considerably in comparison with that of a high-flow system. This reduces the pressure drops between the valves on a branch (provided that normal pipe sizes are used), with the result that the differential pressure is almost the same across all the valves. Balancing can then be concentrated on each valve at a time, with the relationship between the valves being essentially ignored. For the same reason, those who recommend this method feel that there is no need for any group or branch valves, as the differential pressure is practically the same across each group or branch. Common system temperatures in low-flow systems are usually somewhere between 70/30 and 80/40 °C. Hydronic heating systems can thus be categorised into low-temperature and high-temperature systems, as well as into low-flow and high-flow systems. The table below shows examples of systems categorised by the respective methods. A high temperature drop can be said to correspond to a low flow, while a high average temperature is indicative of a relatively small heat transfer surface area of the heat-releasing component. Flow

Temperature

Table 2.

High

Low

High

ex. 80/60

ex. 80/40

Low

ex. 60/40

ex. 70/30

Categorisation of different types of systems.

29

2 SYSTEM DESIGN

2.3

Control valves

It must be possible to control a hydronic heating system that supplies a demand for heat. This can be done either centrally, by controlling the heat input to the entire system, or locally by separate control of the thermal power supplied to each individual heat-releasing component. Many systems use both methods in combination, e.g. radiator systems with thermostatic valves. Control is effected by means of two-way or three-way control valves, which alter the flow in the system or sub-system to the required quantity. In order to characterise a system, it is therefore most important to identify which type of control valve is being used. In order to describe control valves' characteristics in this respect, the concepts of valve characteristic and valve authority is being used. 2.3.1 Valve characteristic Different mechanical designs of valves can produce different valve characteristics. Different valve characteristics are suited to different types of systems. The valve characteristic represents the relationship between the amount by which the valve is opened and its capacity (the kv value). The valve opening (H) is a relative measure of by how much the valve head has lifted. A valve opening of 0 % indicates that the valve is fully closed, while 100 % indicates that it is fully open. The valve opening can, of course, also be expressed as a per-unit value (0 to 1), as is also used here. Figure 17 shows a number of examples of various (theoretical) valve characteristics. Capacities in the diagram are expressed as relative values, in the same way as is the valve opening, with 100 % representing the maximum possible value (with the valve fully open). It should be noted that linear and logarithmic characteristics are standardised forms, and that quick-opening characteristics are not normally used in control valves, but are used in shut-off valves (Palmertz, 1993). It should also be pointed out that the logarithmic characteristic shown in the diagram is, in fact, somewhat modified: a real logarithmic characteristic valve does not shut off completely when its valve opening is zero.

Relative kv value [% ]

100 80 Quick Opening 60 Linaer Square-law

40

Logarithmic 20 0 0

20

40

60

80

100

Valve opening [% ]

Figure 17. Four different mechanical valve characteristics - quick-opening, linear, square law and logarithmic (modified).

30

2 SYSTEM DESIGN

The flow through a valve depends on its capacity and on the differential pressure across it, which has previously been described in equation (3), and which can be re-expressed as equation (20) below. & = ∆p ⋅ k V v

(20)

With a constant differential pressure, the relationship between flow and valve capacity is directly proportional, which means that the valve characteristic curve looks the same, regardless of whether the Y-axis (see Figure 17) indicates relative flow or relative kv value. The valve characteristic is often described as the relationship between the valve opening of the valve and the flow through it. In order to distinguish these terms, this is referred to in the rest of this presentation as the true valve characteristic of the valve, while the relationship between the valve opening and the valve capacity is referred to as the mechanical characteristic of the valve. The true valve characteristic can, in other words, be divided up into two parts: one which depends on the mechanical design of the valve (the mechanical valve characteristic), and one which depends on the differential pressure of the valve which, in turn, depends on the design of the system in which the valve is installed. This is exemplified by Figure 18, which shows the constituents of the valve characteristic of a logarithmic valve. Mechanical characteristic Valve capacity

True valve characteristic

2 1

Flow

Valve opening

Effect of differential pressure

3

Flow

1

Valve opening

3 2

Valve capacity

Figure 18. Breakdown of a valve's true characteristic into a purely mechanical characteristic and a characteristic that depends on the differential pressure of the valve. It can be see from equation (20) above that, as said, the flow is directly proportional to the valve capacity if the differential pressure is maintained constant. This is shown in Figure 18 as a straight line in the lower left diagram. The slope coefficient of the line is 31

2 SYSTEM DESIGN

the square root of the differential pressure, which is also indicated by equation (20). However, this straight-line characteristic applies only if the differential pressure across the valve is constant at all settings. If the differential pressure across the valve changes when its capacity is changed, the relationship between the valve capacity and flow through it will no longer be directly proportional, which means that the true valve characteristic will also be altered in relation to the mechanical characteristic. 2.3.2 Valve authority With constant differential pressure across a valve, the mechanical valve characteristic and the true valve characteristic are the same. However, if the differential pressure changes, the true characteristic is altered, which means that it no longer conforms with the mechanical characteristic. In all hydronic heating systems, the differential pressure across control valves changes in one way or another when the heat demand changes. The true valve characteristic then distorts from the mechanical characteristic by varying amounts, depending on the magnitude of the change of differential pressure. A simple measure of this distortion in the characteristic is provided by what is known as the valve authority. The valve authority (indicated by β) is the relationship between the differential pressure across a control valve when fully open and the differential pressure when it is fully closed (Petitjean, 1994), as given by: β=

∆p fully open

(21)

∆p fully closed

The lower the value of the valve authority, the greater the distortion of the valve characteristic. The maximum value of valve authority is 1, which means that the differential pressure across the valve is unchanged, and thus that the true valve characteristic conforms with the mechanical valve characteristic. Exactly how the valve affects the flow is shown by the true valve characteristic, which is a product of both the mechanical characteristic and the valve authority. Figures 19 and 20 show the distortion of the valve characteristics of a linear valve and a logarithmic valve for different amounts of valve authority. Valve authority

60

and

40 20 0

β = 0.1

80 60

give

40

β = 0.5

20

β=1

0 0

20

40

60

80

Valve opening [%]

100

β = 0.25

100 Relative flow [%]

80

True characteristic

β = 0.25

100

100 Relative flow [%]

Relative kv value [%]

Mechanical characteristic

β = 0.1

80 60

β = 0.5

40

β=1

20 0

0

20

40

60

80

100

Relative kv value [%]

Figure 19. Distortion of the valve characteristic of a linear valve.

32

0

20

40

60

80

Valve opening [%]

100

2 SYSTEM DESIGN

Valve authority

60

and

40 20 0

β = 0.1

80 60 40

β = 0.5

give

β=1

20 0

0

20

40

60

80

Valve opening [%]

100

β = 0.25

100 Relative flow [%]

80

True characteristic

β = 0.25

100

100 Relative flow [%]

Relative kv value [%]

Mechanical characteristic

80 60

β = 0.1

40

β = 0.5 β=1

20 0

0

20

40

60

80

100

0

Relative kv value [%]

20

40

60

80

Valve opening [%]

Figure 20. Distortion of the valve characteristic of a logarithmic valve. As said above, the flow in a system is determined by the relationship between the available differential pressure (from the pump) and the total flow resistance of the system. If much of the flow resistance consists of “fixed” resistance such as pipes, radiators, balancing valves etc., then the system flow resistance will increase only marginally when the valves start to close, which means that the flow will hardly alter. It is not until the valve is almost completely closed that its flow resistance can make a substantial contribution to the total flow resistance of the system, and so it is only then that the flow will actually start significantly to be reduced. In other words, the valve has “poor” authority over the system, which is manifested by its valve authority being low. A valve authority of 1, on the other hand, means that the valve has complete control over what happens in the system. The only flow resistance that would exist in such a system would be that of the control valve, which would mean that it would control the flow exactly in accordance with its mechanical characteristic. However, a value of 1 is generally purely theoretical, as all components in a system have a certain flow resistance. Nevertheless, in some contexts, it is possible to achieve a valve authority of 1, but this is in connection with systems or sub-systems in which the flow can be kept constant. The valve authority is therefore affected both by the design/size of the system and by its balancing. The larger the control valve in a given system, the lower the differential pressure across it when it is fully open, and so the lower its authority. However, it must be pointed out that what is important is the shape of the true valve characteristic: it is that which determines how the control valve operates in a system. It is therefore the combination of the mechanical characteristic and the valve authority that is of interest. It can be seen from the diagrams above, for example, that a more or less linear true valve characteristic can be achieved with the help of a linear mechanical characteristic and a high valve authority or a logarithmic mechanical characteristic and a low valve authority. 2.3.3 Two-way and three-way control valves Two-way valves have two ports with the water flowing in through one port and out through the other. They are used in connections with or without bypasses. Their mode of operation is fairly obvious, and so no further explanation is provided here.

33

100

2 SYSTEM DESIGN

Three-way valves consist of three ports, with standard designations as shown in the diagram below. A, ”Control port”

C, ”Constant-flow port”

B, ”Shunt port” Figure 21. Symbols and designations for a three-way control valve. It is only the two “black” ports, i.e. A and B in Figure 21, that are really controlled. As port A closes, port B opens, and vice versa. The “white” port C is not actually affected by the valve operating mechanism. When referring to a three-way valve as being open or closed, it is the A-port being referred to. This means that for a fully closed three-way valve, for example, port A is fully closed while port B is fully open. A three-way valve can be arranged as a mixing valve or as a distribution valve. The difference is shown below in Figure 22. Note the flow directions. Mixing valve & V A

Distribution valve & V A

& V C

& V C & V B

& V B Figure 22. Mixing and distribution valves.

When used as a mixing valve, flows A and B are mixed to form flow C. In the distribution valve mode, flow C is instead divided up to form flows A and B. Regardless of the type of valve, the sum of flows A and B is always equal to flow C. & +V & =V & V A B C

(22)

This fact - that three-way valves have three ports, and thus three different flows - means that their function is not as immediately obvious as that of two-way valves. In order to assist understanding of how a three-valve works, it can be schematically replaced by two two-way control valves. This does not in any way alter the function of the valve, but simply shows that the three-way valve really consists of two different control ports, which can have completely different characteristics.

34

2 SYSTEM DESIGN

A & V C

& V A

& V C

& V A B

& V B & V B

Figure 23. Expressing a three-way valve as two two-way valves. A three-way valve in which ports A and B have similar characteristics is referred to as a symmetrical valve. If the ports are arranged to have different characteristics, the valve is referred to as being asymmetrical. When referring to the valve authority of a three-way valve, it is always that of the A port that is intended. This is not to say that the valve authority of the B port is uninteresting: it is, as said above, the flows through port A and port B together that form the flow through port C, and it is often this flow that supplies the heat, e.g. to an air heater. The mechanical characteristics and the authorities of both ports A and B therefore have a considerable effect on the results of using a three-way valve for control purposes. The balancing valves in valve groups are used to adjust the flow not only when the control valve is fully open, but also when it is completely closed. However, this means that the flow will be correct only when the valve is either fully open or fully closed. In between these two positions, the flow can vary considerably, depending on the mechanical characteristic and authority of the valve. It must be pointed out that control valves and balancing valves are normally indicated by the abbreviation “SV”, although in this presentation we have used “I” for balancing valves and “R” for control valves. This is to provide clearer distinction between the valves. For a more detailed explanation of the characteristics of control valves, see Petitjean (1989), Palmertz (1993) and Trüschel (1999).

2.4

The static and dynamic characteristics of the system

The specific design of a system determines its character. In this presentation, we have used the concepts of static characteristic and necessary P-band in order to describe the character of a system. The static characteristic shows the steady-state characteristics of the system, while the necessary P-band is a measure that also includes the dynamic characteristics of the system. 2.4.1 Static characteristic The overall purpose of a hydronic heating system in a building is to provide and maintain a certain indoor air temperature. This is done by means of control of the control valves in the system. The static characteristic describes the relationship between

35

2 SYSTEM DESIGN

the valve opening of a control valve and the resulting heat release or air temperature (room temperature or supply air temperature) under steady-state conditions, i.e. equilibrium conditions. Different static characteristics are obtained, depending on the design of the system. The static characteristic consists of the mechanical characteristic of the control valve, the authority of the valve and the characteristic of the controlled heat-releasing component, all as shown in Figure 24 which is a schematic diagram of a radiator circuit and thermostatic control valve.

& V

kv

troom 4

3

2 1

H

kv

2

3

Valve authority

Valve characteristic

& V

Radiator characteristic

troom 4

H

1

Static characteristic Figure 24. Make-up of the static characteristic, as illustrated by a radiator circuit. The results are strongly affected by the control valve, as both its characteristic and its size (which in turn affects its authority) affect the static characteristic. This means that, for example, a large logarithmic valve can provide approximately the same static characteristic as a small linear valve, as shown in the following schematic diagrams for an air heater and valve group.

36

2 SYSTEM DESIGN

Logarithmic

Low authority

Valve authority

Linear

Characteristic of the air heater and valve group

H Static characteristic ta,out

ta,out

& V

kv

& V

kv

H

Valve characteristic

ta,out

ta,out

& V

kv

High authority H

& V

kv

H

Figure 25. Comparison schematic of a large logarithmic and a small linear control valve. The static characteristic gives a first indication of where any control problems might arise. If no dynamic aspects are considered, the static characteristic should be linear, as pointed out by Lundin (1980), Avery (1993), Hegberg (1998) and Trüschel (1999), and by others. The steeper the slope of the curve, the greater is the change in thermal power output when the valve opening of the control valve changes. This is referred to as the system gain, and is given by the following equation (Grindal, 1984): Ks =

∆t ∆H

(23)

37

2 SYSTEM DESIGN

where

Ks ∆t

= System gain = Change in outgoing air temperature (for an air heater) or room temperature (for a radiator), for a... = ...change in the valve opening of the control valve.

∆H

The instantaneous gain of the system (for each valve opening) is given by the differential coefficient of the static characteristic. The higher the gain in the system, the more likely it is that control problems will be encountered. However, this is due partly to the dynamic characteristics of the system. 2.4.2 The necessary P-band The static characteristic describes the system under steady-state conditions. However, dynamic changes occur between equilibrium conditions (if the latter are ever achieved at all). In order to acquire an overall picture of the system, the dynamic characteristics also needs to be considered. Before doing that a number of concepts must first be defined. Control When controlling a hydronic heating system, it is always proportional control mode (P) that is used, often together with integrating control mode (PI). The P block in the controller provides a control signal that is a linear function of the error signal (the set value minus the actual value). The equation for this is as shown below (Persson, 1995). u = u0 + KR ⋅e where

u u0 KR e

= = = =

(24)

control signal control signal when the error signal is zero proportionality constant (control system gain) error signal

The relationship between the control signal and the error signal for a thermostatic valve on a radiator in a room is illustrated in Figure 26. H 100 %

0% 18 °C

trum 22 °C

Figure 26. Example of P-control mode (for a thermostatic radiator valve).

38

2 SYSTEM DESIGN

In the example above, it can be seen that the valve starts to close when the temperature in the room exceeds 18 °C. When the temperature has risen to 22 °C, the valve is fully closed. It goes, in other words, from fully open to fully closed for a 4 °C increase in room temperature. This is referred to as the P-band (proportional band) of the controller, and is the inverse of the controller gain, KR (the slope of the line in the figure). The wider the P-band, the lower the gain. If the P-band is wide, control will operate slowly, as changes in the room temperature result in only small changes in the valve position. A narrow P-band, on the other hand, has a higher gain and so increases the speed of control, but with the risk that the control process instead becomes unstable. However, this is considerably affected by the characteristics of the controlled system. The drawback of using only proportional control is that it is not normally possible to achieve the exact set value. This is due to the fact that, in proportional control mode, the control signal is directly proportional to the control error. In other words, to produce a control signal requires a change in the control error, which results unavoidably in the creation of a stationary control error under steady-state conditions. However, these stationary control errors can be eliminated by using an integrating control block, which continuously complements the control signal from the proportional block until there is no longer any control error. With this combination, it is possible to achieve the required set value. A differential (D) block is sometimes also used in the controller, with the effect of increasing the speed of response of the controller. However, differential control is seldom used in the HVAC sector, which is probably due partly to the fact that it is not regarded as necessary and partly because it makes control particularly sensitive to rapid changes, thus increasing the risk of instability (Persson, 1995; Moult, 2000). The Ziegler and Nichols methods and rules of thumb In the 1940s, Ziegler and Nichols developed rules of thumb for setting up controllers, which are still applicable today. They used two different methods of doing so: the step response method and the self-oscillation method. The step response method involves analysing the characteristics of the system in a number of steps. The automatic control system is disengaged, and the output signal from the controller is changed in steps. For each step change, the system dead time (Td), time constant (Tk) and resulting change in the control parameters (∆r) are measured or estimated. The self-oscillation method involves reducing the width of the proportional control band (increasing the gain) until the system becomes unstable and starts to oscillate. The critical proportional band (Pkrit) and the cycle time of self-oscillation (Tcrit) are noted. The following diagrams show how the proportional band, the integrating time and the differentiating time are obtained from the various methods (Ziegler and Nichols, 1942; Persson, 1995; Jacobson et. al, 1997).

39

2 SYSTEM DESIGN

Step response

Self-oscillation

r, u

r ∆u (step)

∆r (response) Time

Time Tcrit

Dead time (Td) Time constant (Tk)

A=

Td Tk

B=

∆r ∆u

Regulator P PI PID

Subtract the effect of any integrating controller by setting the integrating time to its maximum value, and also subtract the differential effect, by setting the differentiating time to zero. Continue by progressively reducing the width of the proportional band until instability just occurs. Note the width of the critical proportional band (Pcrit) and the critical period time (Tcrit). The step response method

The self-oscillation method Fast control P-band = 2 ·Pcrit P-band = 2,2 ·Pcrit I-time = Tcrit / 1,2 P-band = 1,6 ·Pkrit I-time = Tcrit / 2 D-time = Tcrit / 16

P-band = A ·B P-band = A ·B / 0,9 I-time = 3 ·Td P-band = A ·B / 1,2 I-time = 2 ·Td D-time = 0,5 ·Td

Slow control P-band = 4 ·Pcrit P-band = 4,4 ·Pcrit I-time = Tcrit P-band = 3,2 ·Pcrit I-time = Tcrit / 2 D-time = Tcrit / 16

Figure 27. Presentation of the Ziegler-Nichols rules of thumb for setting up controllers using the step response and self-oscillation method. The time constant, which is a measure of the inertia of the system, is defined as the time it takes for the control parameter to change from one equilibrium position to another position in response to a step change in the control signal. It can be derived graphically by drawing a tangent at the point of inflection of the curve of the control parameter, i.e. at the point of maximum slope of the curve. It is then given by the time between the points where the tangent intersects the original equilibrium value and the new equilibrium value, as shown in Figure 27. It should be noted that this applies for higher order systems (Grindal, 1984). The longer the time constant, the simpler is control and the narrower the proportional band can be set.

40

2 SYSTEM DESIGN

The dead time is the time that passes between when the control signal is changed until the control parameter starts to respond. The longer the dead time, the more difficult control becomes (i.e. a greater risk of instability), and the wider the proportional band needs to be set. Control problems The use of Ziegler and Nichols' practical rules of thumb methods enables different types of control circuits, or different systems, to be classified by deriving the necessary settings of the controller. To prevent a system from becoming unstable, the control system must be capable of controlling the worst case conditions, i.e. when the system is most difficult to control. Setting the necessary proportional band of the controller (as needed to avoid instability, regardless of load) thus provides a measure of the system characteristics. If a wide necessary proportional band (or “relative control difficulty” as Grindal refers to it) is needed, it means that the system will be difficult to control, while a narrow necessary proportional band means that the system will be easier to control. This presentation has used the step response method to calculate the width of the necessary proportional band for measurements and simulations. This width is then used to describe how well the system is designed. A poorly designed system necessitates a wide necessary proportional band, thus increasing the risk of poor performance. The width of the necessary proportional band for a given valve opening of the control valve can be calculated from the following equation: Pnec = where

Td ⋅ KS Tk

(25)

Pnec = Necessary proportional band [ºC/-] Td = Dead time [seconds] Tk = Time constant [seconds] K S = System gain (for a given valve opening) =

∆t [ºC/-] ∆H

Rewriting equation (25) from the expression shown in Figure 27 requires that the control parameter is a temperature (this presentation is concentrating on room temperature or outgoing air temperature), and that a certain change in the control signal (∆u) results in a corresponding change in the valve opening of the control valve (∆H). The width of the necessary proportional band varies with the valve opening of the control valve. Control needs to be able to deal with the most difficult case, i.e. when the width of the necessary proportional band is greatest. A well-designed system, in other words is not merely one that can achieve a narrow necessary proportional band, but one that can create the right conditions for a constant-width necessary proportional band, regardless of the valve opening of the control valve. This ensures that the necessary proportional band remains narrow throughout operation, giving good prospects for problem-free control of the system. To illustrate how the necessary proportional band provides a measure of the difficulty of controlling the system, consider an extreme case of a proportional band width of 0 ºC. 41

2 SYSTEM DESIGN

Such a proportional band would result in instability, regardless of system design, as control would operate in an On/Off mode. It would probably not be very successful for a system using air heaters, and would probably result in wide fluctuations of the supply air temperature. On the other hand, the consequences would be unlikely to be so extreme for a radiator system, as has been shown by measurements in Lars Jensen's thesis (1978) “Digital control of climate processes”. This is because of the very high inertia (long time constant) of a radiator system (or, more correctly, of the interaction between the radiator and the room). The proportional band of a thermostatic control valve in a high-flow system is usually about 2 ºC, while some low-flow systems can have proportional band widths as low as 0.5 ºC (depending on the balancing of the radiator valve). It is therefore not likely that the function of a radiator system would be particularly affected by advanced local control (Jensen, 1978), which means that the design of the system has a considerable effect on its overall ability to deal with disturbances. The concept of using the proportional band for classifying the difficulty of controlling a system has been taken primarily from Arvid Grindal's and Bent Børresen's many articles. In particular, Bent Børresen's “Dynamikk i shuntkoplinger” (Dynamics of valve groups) (1985) and Arvid Grindal's “Regleringsteknikk for ingeniøren” (Control methods for engineers) (1988) are therefore recommended for study of static and dynamic characteristics of systems in the HVAC field.

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3 MEASUREMENTS

3

MEASUREMENTS

This chapter briefly describes how the measurements were made, and presents some examples of the results. See Appendix A for further details of the construction of the test rigs, selection of components, control systems and instrumentation systems, as well as information on uncertainty of measurement.

3.1

Radiator system

The purpose of the radiator test rig is to provide measured data for verification of calculation equations dealing with: - heat release (and return water temperature) from a radiator - the interaction between radiators in the same system. 3.1.1 Method of working Two different temperature levels were used for the measurements: 60/40 (equivalent to the high flow rate mode) and 70/30 (equivalent to the low flow rate mode). In addition, the pressure drop in the distribution system was varied, with the aim of investigating how the interaction between the radiators in a system is affected by the pipe pressure drop (or by the distance between the radiators). The method of working in making the measurements accorded with the following pattern: 1. Balancing the system: - The desired supply temperature was set on the electric boiler. - The pump speed was set (three different speeds). - The balancing valve on the return connection was approximately set. - The balancing valve between the radiators was approximately set. - The pre-setting on the respective radiator valves was approximately set. - The differential pressure across the respective radiator connection was measured, If the measured differential pressures were not as desired, the valves were adjusted again. 2. Checking the balancing (after about an hour). The return temperature from each radiator was measured. If the measured return temperatures were not as desired, the valves were adjusted again. 3. Measurement. The pre-setting on one of the radiator valves was changed from fully closed to fully open in a number of steps. After each change, the time was noted, together with the volume that had passed through the respective flow meter. After about an hour, when steady-state conditions had been reached, the following parameters were measured: - Supply temperature to radiator 1 (Ts1) - Supply temperature to radiator 2 (Ts2)

43

3 MEASUREMENTS

-

Return temperature from radiator 1 (Tr1) Return temperature from radiator 2 (Tr2) Return temperature from the branch (Tr) Room temperature (Troom) Zeroed differential pressure (DP0) Pressure drop across radiator 1 (DP1) Pressure drop across radiator 2 (DP2) Volume that had passed through flow meter no. 1, together with the time of reading, which gives the volume flow through radiator 1 (Vw1) - Volume that had passed through flow meter no. 2, together with the time of reading, which gives the volume flow through radiator 2 (Vw2) 3.1.2 Measured results It is difficult to draw any independent conclusions from the measured results alone. They have been used to verify a number of calculation relationships, which means that they must be compared with them. This is done in Chapter 4, and so no measured result are shown here.

3.2

Air heater with valve group

The purpose of the measurements in the air heater test rig was to: - provide background data for verification of the simulation model - provide genuine statistics and dynamic differences between different types of control valves, valve groups and balancing. To be able to fulfil these objectives, we need to obtain both the static and the dynamic characteristics of various configurations of the system, by means of measurements. Static characteristics are those that determine how the valve opening of the control valve affects the outgoing air temperature (or heat release) from the air heater under steady-state conditions. This has been previously defined (in Chapter 2) as the static characteristic of the control circuit. The dynamic characteristics determine the behaviour of change from one steady-state condition to another steady-state condition. One measure of this is how the dead time and time constant of the control circuit are affected by a change in the valve opening of the control valve. 3.2.1 Configurations As previously mentioned (Chapter 1) there are three different types of valve groups that are of interest in this work: direct connection, district heating connection and the “SABO” connection.

44

3 MEASUREMENTS

Direct connection

District heating connection

SABO connection

Figure 28. The three different valve group arrangements that have been investigated. In addition to the different arrangements of valve groups, three different types of control valves have also been used in the measurements: V341-4 (a small logarithmic valve), V341-10 (a large logarithmic valve) and V355-4 (a small linear valve). These designations, and which are used in this presentation, consist of the manufacturer's product code and an index that shows the kvs value of the valve. In addition, two different balancing cases have been used, with the intention that they should correspond to high-flow and low-flow balancing. A supply temperature of about 60 °C has been used for the high-flow balancing case: with the control valve fully open, it results in a rise of air temperature of about 25 °C across the coil, and a return water temperature of about 40 °C. For the low-flow balancing case, the supply temperature is 70-75 °C, the temperature rise across the coil is still about 25 °C and the water return temperature is about 35-40 °C. The above figures were obtained with an incoming air temperature to the air heater of 0-10 °C. Permutating the variations in the valve group, the control valve and balancing, 18 different configurations are obtained, for all of which measurements have been made. The configurations are identified by the following model: valve type (V3XXX-X), flow (H/L), valve group (D/DH/SABO). This means that, for example, a configuration for district heating connection, using the small logarithmic control valve and with a low flow rate, would be indicated by V341-4,L,DH, while a high-flow directly-connected arrangement with a linear control valve would be V355-4,H,D. 3.2.2 Setting up and measuring Setting up The system must be set up before each set of measurements is taken, which is done as follows: 1. The heat source (the boiler) is set to give the required supply temperature. 2. The available differential pressure across the valve group is adjusted approximately by means of balancing valves Ip and Ib (see Figure 29). 3. The valve group and the control valve to be used are adjusted using the shut-off valves. 4. The valve group is adjusted as follows:

45

3 MEASUREMENTS

• The district heating (DH) and the SABO connections: - The control valve is closed and the flow through the circulation circuit adjusted by means of balancing valve I2. - The control valve is fully opened, and balancing valve I1 is set so that no flow passes through the shunt/bypass connection. • Direct connection: - The control valve and the balancing valve I2 are both fully opened, after which the flow is adjusted using balancing valve I1. Ip

I2

Ib

I1 Figure 29. The balancing valves in the test rig. After setting up, the measurements can be made. These are of two different types: step response and self-oscillation measurements. Step response These measurements have mainly been made by recording the step response when the valve opening of the control valve is changed. When making the measurements, the valve opening was changed from fully closed to fully open in ten steps, accompanied by measurements of the ingoing and outgoing air temperatures. By waiting until steady-state conditions have been achieved for each step (i.e. before moving on to the next step), both the static and the dynamic characteristics can be recorded. The controller has naturally been disconnected while making the step response measurements. As the measurements provide the basis for simulation of various systems (different combinations of valve groups, control valves and balancing), it has been of interest to measure, not only the air temperatures and the valve opening of the control valve, but also the water temperatures (at four positions in the valve group), the water flows (on the primary and secondary sides) and the differential pressure available across the valve group. In addition, in order to obtain a measure of the control valve's authority, the differential pressure across the valve has also been continuously measured. Self-oscillation In addition to the step response measurements, certain other measurements have also been made in order to investigate the effect of control on the system (or, rather, how various system configurations affect the choice of control). These measurements have

46

3 MEASUREMENTS

been made with the controller connected. To start with, a wide P-band (30-40 °C) was set, with the I-effect minimised by setting the I-time to as high a value as possible (999 seconds). After the system reached equilibrium, i.e. with the control valve having reached a stable position, the width of the P-band was gradually reduced until the point was reached where instability just occurred. In this context, instability is defined as being the state where the control valve starts to hunt, with no apparent tendency towards convergence. The wider the critical P-band is, the more difficult the system is to control. In all cases, the controller set value has been set to 20 °C, and the incoming air temperature was 4-8 °C. 3.2.3 Some measurement results Although it is mainly the simulations that provide the basis for the results of this work, some conclusions can nevertheless be drawn by studying the measured value results. Static characteristic Figure 30 shows the measured static characteristic for the three different valve groups, using the same control valve (V341-4) and the same type of balancing (high flow).

Relative thermal power output [-]

1.0 V341-4,H,D V341-4,H,SABO

0.8

V341-4,H,DH The X-axis shows the valve opening of the control valve, with the value of 1.0 corresponding to a fully open valve. The Y-axis shows the relative thermal power output or, looking at it another way, the relative temperature rise, with a value of 1.0 representing the maximum thermal power output or the maximum temperature rise (with the control valve fully open).

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Valve opening [-]

Figure 30. Measured static characteristics for the three valve groups using a V341-4 control valve and with high flow rate. It can be seen from the above diagram that there is little difference between the performance of the valve groups, and the same applies for all configurations using the same control valve. This applies, in other words, regardless of the type of balancing (high-flow or low-flow). The reason for this is that the difference in static characteristic between low-flow and high-flow modes is almost non-existent, as shown in Figure 31.

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3 MEASUREMENTS

Relative thermal power output [-]

1.0 V341-4,L,DH 0.8 V341-4,H,DH 0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Valve opening [-]

Figure 31. Static characteristics of two configurations with the same valve group and control valve, but with different flow rates. In addition, the measurements show that the large logarithmic control valve (V341-10) provides approximately the same static characteristic as the (small) linear control valve (V355-4). This can be seen in Figure 32 below.

Relative thermal power output [-]

1.0

0.8

0.6

0.4 V355-4,H,D V341-10,H,D

0.2

V341-4,H,D 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Valve opening [-]

Figure 32. Static characteristics depending on the choice of control valve. In total, therefore, the measurements show that there are essentially only two different types of static characteristics (see Figure 32). The V341-10 and V355-4 control valves provide a strongly curved characteristic, while the V341-4 valve produces a

48

3 MEASUREMENTS

considerably more linear characteristic. In this respect, the effect of high-flow or low-flow mode, and the type of valve group, are largely insignificant. It may seem strange that balancing does not seem to have any effect on the static characteristic. However, the reason for this is that balancing affects both the valve authority and the air heater characteristic in such a way that their effects on the static characteristic more or less cancel each other out (see Chapter 2). However, it must be noted that this applies only for this particular measured case, and must not be interpreted as a general phenomenon. It can be noted that the measurements support the general theory presented in Chapter 2, where it was explained that the static characteristic of a control circuit is determined by the characteristic and authority of the control valve, together with the characteristic of the heater itself. The air heater characteristic Regardless of the type of valve group used, it is important to know the characteristic of the air heater (i.e. its thermal power output as a function of the water flow). With the case of constant flow through the air heater, the characteristic determines the return temperature of the water and thus also affects the air heater inlet temperature (as this is a mixture of the supply temperature and the return temperature). In turn, this affects how the valve opening of the control valve is controlled. With a direct connection arrangement, the air heater characteristic determines the flow required in order to provide the correct thermal output, which therefore affects control of the control valve, as the valve opening of the valve determines the flow through the heater. The type of balancing affects the air heater characteristic, as shown in Figure 33, which is based on measured values.

Thermal power output [kW]

25

20

15

10 60 - 40 °C

5

70 - 40 °C 0 0.0

0.2

0.4

0.6

0.8

1.0

Relative water flow [-]

Figure 33. The effect of balancing on the air heater characteristic, as derived from measured values.

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3 MEASUREMENTS

The X-axis in Figure 33 represents the relative water flow, with the maximum value for each curve being 1.0. The Y-axis shows the absolute values of thermal power output. The quantities in the diagram are the design temperature levels. With a supply temperature of 70 °C, the design flow rate is considerably lower (about 35 % lower) than the design flow rate with a supply temperature of 60 °C. It is interesting to note that both the design return temperature and the design output power rating are the same for both flow rates. The thermal power output, in other words, is not proportional to the mean temperature difference of the air heater (i.e. between the water and air flows). This is because the UA value of the air heater is affected by the water flow rate. The lower the water flow rate, the lower the UA value and the higher the mean temperature difference has to be in order to prevent the thermal power output from being reduced. Compare this with a radiator, of which the thermal power output is directly linked to the mean temperature difference (see Chapter 2). The curves in Figure 33 (the thin lines) are the result of curve matching to the measured values, and clearly show how the characteristics of the air heater are affected by the flow rate. The greater the temperature drop, the straighter the characteristic. Dynamic characteristic (critical P-band) Figure 34 shows an example of how self-oscillation of a system has been determined by progressively reducing the width of the P-band for the V341-4,L,DH configuration. In this example, the critical P-band width is 7 °C, at which point clear signs of instability occur. The vertical lines in the diagram show the points at which the width of the controller P-band has been changed. After each change in the P-band, it can be seen that the measured air temperature at the inlet upstream of the air heater “bounces”, which is due to the fact that the electric heater in the inlet (upstream of the heating coil) is connected for 30 seconds. This is to prevent the system from finding itself on a metastable level, i.e. to prevent the system from appearing to be more stable than it really is, due to the fact that it has not actually been exposed to any disturbances. Table 3 shows the measured critical P-band for a number of different configurations. It also shows the approximate ambient temperature at the time of making the measurements, together with the controller set value (20 °C in all cases). It should be pointed out that, in all cases, the balancing has been almost “perfect” i.e. as good as can be regarded as possible.

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V341-4,L,DH P-band: 30

20 16 14

12

10

25

8

7

6

100

Critical P-band ~ 7 °C

20

Ta,out

90

Ta,in

80

H

70 60

15

50 40

10

30 20

5

10 0 0:00

0:20

0:40

1:00

1:20

1:40

2:00

2:20

2:40

Time [tt:mm]

3:00

3:20

3:40

4:00

4:20

0 4:40

The controller loses contact with the system for about a minute!

Figure 34. An example of trials to set the system into self-oscillation.

Control valve V341-10 V341-10 V341-4 V341-4 V341-4 V341-4 V355-4 V355-4 V355-4 V355-4 V341-4 V341-4 V355-4 V355-4

Table 3.

Balancing (flow rate) H L H L H L H L H L H L H L

Valve group DH DH DH DH SABO SABO DH DH SABO SABO D D D D

Outdoor temperature [°C] 7 7 6 7 6 8 6 7 5 10 3.5 5.5 4.5 3.5

Set value [°C] Critical P-band [°C] 20 6 20 12 20 4 20 7 20 5 20 8 20 6 20 11 20 7 20 14 20 3 20 3 20 6 20 5

Measured critical P-bands for a number of different configurations.

It is important to point out that the critical P-bands in the above table do not necessarily represent the worst cases. If the set value had been changed, or the temperature of the incoming air had been different, the control valve would need to be open to a different amount in order to achieve equilibrium, which would mean that a different sector of the static characteristic would be applicable. It is likely that this would result in a completely different critical P-band: the worst case would produce the highest value of the critical P-band of the system.

51

Valve opening (H) [%]

Temperature [°C]

30

3 MEASUREMENTS

The table shows that the width of the critical P-band of the low-flow district heating and SABO arrangements is approximately twice as wide as for the corresponding high-flow systems. This is presumably due to the fact that the dead time in the low-flow case is approximately twice as long as in the high-flow case, as the flow is only half as great. The table also shows that the lowest critical P-band (for the district heating and SABO connections) occurs when the small logarithmic valve (V341-4) is used, while the other two valves give results that are largely similar to each other. This is in good accordance with the results described above concerning the static characteristic. An interesting observation in the table is that the absolutely narrowest critical P-band occurs in connection with direct connection, and that it is independent of the flow rate. This is because this valve group is fundamentally different from the other two groups. The district heating and SABO connections result in a relatively long time passing from when the valve opening of the control valve is changed until the new inlet temperature reaches the air heater. This is due to the fact that the speed of the temperature wave from the valve group to the air heater is related to the flow velocity in the circulation circuit. The temperature wave is actually somewhat slower than the flow velocity, due to the fact that the water must also raise the temperature of the pipe on its way. The lower the flow rate, the longer the dead time in the system and the wider the critical P-band. However, in the direct connection arrangement, there is no mixing, which means that there is not the same temperature wave effect as in the other systems. Instead, it is simply the flow rate through the air heater that alters, which occurs almost immediately when the valve opening of the control valve is altered. The reason for this is that the flow change front moves at the speed of pressure variations in the system, which in turn move at the speed of sound in water (about 1000 m/s), which is considerably faster than the flow velocity. See Larsson (1999) for a more detailed description of temperature and pressure waves in dynamic systems. The self-oscillation method provides a practical design aid, based on measurements, when deciding the necessary width of the controller P-band (and of any I-time or D-time). However, this method is somewhat more difficult to employ here, where the work is based mainly on simulations. Instead, it is Ziegler-Nichols' step response method (see Chapter 2) which has been used, and which is based to some extent on estimates of dead time and time constant. It can therefore be appropriate here to present a simple comparison of these two methods. Figure 35 shows the results of calculation of the necessary width of the P-band, using Ziegler-Nichols' step response method. The calculations are based on step response measurements for the V341-4,L,DH configuration. The widest necessary P-band is obtained at a 60 % valve opening, which means that it is at this valve opening that it is the most difficult to control the system.

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V341-4,L,DH 20 18 16 Pnec [°C]

14 12 10 8 6 4 2 0 0

10

20

30

40

50

60

70

80

90

100

Valve opening [% ]

Figure 35. Estimation of the necessary P-band (Pnec), using the step response method, for different valve opening of the control valve. According to Figure 34, which is based on the same set of measurements as used for Figure 35, the self-oscillation method identifies a critical P-band width of 7 °C for a set value of 20 °C and an incoming air temperature of about 7 °C. In this case, a P-controller would need to be set to twice the critical P-band width (see Chapter 2), i.e. 14 °C, for effective (rapid) control. Figure 34 shows that oscillation is approximately centred on 45 % valve opening. According to the step response method (Figure 35), this is approximately equivalent to a requisite P-band width of 15 °C. This means that, in this case, the step response method produces almost the same result as the self-oscillation method. The following table presents a number of further comparisons of this type.

Configuration V341-10,H,DH V341-10,L,DH V341-4,H,DH V341-4,L,DH V341-4,H,SABO V341-4,L,SABO V355-4,H,DH V355-4,L,DH V355-4,H,SABO V355-4,L,SABO V341-4,H,D V341-4,L,D V355-4,H,D V355-4,L,D

Table 4.

Self-oscillation method Critical P-band [°C] Necessary P-band [°C] 6 12 4 7 5 8 6 11 7 14 3 3 6 5

12 24 8 14 10 16 12 22 14 28 6 6 12 10

Step response method Necessary P-band [°C] 15 27 8 15 13 19 13 22 17 29 4 4 14 10

Comparison between Ziegler-Nichols' self-oscillation method and the step response method. 53

3 MEASUREMENTS

The comparisons in the table above show that both methods give similar values, which indicates that the step response method can be used to provide a measure (in terms of the necessary P-band width) of how difficult the system is to control. This methodology was described in Chapter 2, and is used in this work to provide a qualitative assessment of the functional reliability of a system. Thermal stratification An advantage of forced circulation of water (or any liquid) through a valve group is that the maximum flow is constantly maintained through the heater (or cooler), regardless of the operational mode. This reduces the risk of substantial thermal stratification and also of freezing. The figure below provides a comparison of the direct connection arrangement and the district heating arrangement in order to give an idea of how the choice of valve group affects temperature distribution (or, more correctly, water flow) in an air heater. V341-4,H,D

35

V341-4,H,DH

30 25 20 15 10 5 0 0

20

40

60

80

100

30 25 20 15 10 5 0

Valve opening [%]

20

40

60

80

0 100

Valve opening [%]

Figure 36. Comparison of thermal stratification between two systems: direct connection (V341-4, H, D) and with a circulating water flow through the air heater (V341-4, H, DH). “Ta-1 (mean)” and “Ta-2 (mean)” in the diagram show the mean values of the measured values from the symmetrically positioned temperature sensors in the ventilation duct, upstream and downstream of the air heater respectively, while “Ta-2,1” – “Ta-2,9” are the measured values from each temperature sensor downstream of the air heater. Differences between these values show the thermal stratification. It can be seen that the valve group providing a circulating flow of water produces definitely less thermal stratification than does the direct connection arrangement. This applies almost throughout the entire working range of the control valve, although the difference in thermal stratification is quite small when the valve is fully open. This is naturally due to the fact that, with the valve fully open, the flow through the direct-connected air heater has reached its maximum value, which is equivalent to the constant flow of the district heating connection. With the control valve fully closed, the measured values from the nine downstream sensors are more or less the same as the mean value of the incoming air temperature, which means that there is insignificant thermal stratification

54

Temperature [°C]

Temperature [°C]

35

Ta-2,3 Ta-2,1 Ta-2,2 Ta-2,6 Ta-2,4 Ta-2,5 Ta-2,9 Ta-2,7 Ta-2,8 Ta-2 (mean) Ta-1 (mean)

3 MEASUREMENTS

upstream of the air heater. Figure 37 shows the profile of the stratification for three control valve positions: fully closed (H = 0), half open (H = 0.5) and fully open (H = 1). The column for each sensor in the diagram shows the difference between the sensor value and the mean value of all the sensors. The positions of the nine sensors in the diagram correspond to their respective positions in the ventilation duct, as seen looking towards the air heater and against the direction of air flow. V341-4,H,D

0 Ta-2,3

Ta-2,2

Ta-2,1

-5

5

5

0 Ta-2,5

Ta-2,4

-5

Ta-2,3

Ta-2,2

Ta-2,1

Ta-2,6

Ta-2,5

Ta-2,4

0

-5 H=1 H = 0.5 H=0

0 Ta-2,9

Ta-2,8

H=1 H = 0.5 H=0

5 Temperature [°C]

5 Temperature [°C]

0

-5

Ta-2,6

V341-4,H,DH

5 Temperature [°C]

5.2

Temperature [°C]

Temperature [°C]

Temperature [°C]

5

Ta-2,7

-5

0 Ta-2,9

Ta-2,8

Ta-2,7

-5

Figure 37. Thermal stratification profile for direct connection (left) and district heating connection (right). It can be seen from the diagram that the air temperature is highest at the top of the duct and lowest at the bottom. This is due to the fact that the inlet connection on the air heater is higher than the return connection. The maximum difference between the highest value (Ta-2.1) and the lowest value (Ta-2.8) in the duct cross-section is about 9 °C for the direct connection arrangement (with the control valve half open), while the district heating connection gives a maximum difference of about 5 °C (with the control valve fully open).

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56

4 SIMULATION PROGRAMS

4

SIMULATION PROGRAMS

Two different simulation programs have been used in this work. This is because they are intended for use with two systems that are completely different in many respects. The commercial Flowmaster program has been used for the air heater and valve group system, while a custom program, based on Excel, has been used for the radiator system.

4.1

Calculation program in Excel

In Trüschel (1999) a static calculation program for a radiator branch is being described. This program, written in Excel, has been developed here to cover an entire system. It has subsequently been modified to some extent in order to agree with the results from the measurements in the radiator rig. 4.1.1 Structure The program is based on known theoretical and empirical relationships, as described in Appendix B. However, it is intended to analyse only steady-state conditions, and cannot therefore deal with dynamic processes. The program considers a radiator system consisting of 20 radiators uniformly distributed on four branches and two risers, as shown in Figure 38 below. The reason for this arrangement is that it enables the interaction between branches and risers to be investigated, without making the simulations difficult because of the need to handle too large a system. 5

4

3

2

1

II

II

I

I

A

B

Heat Ex.

Figure 38. The radiator system processed by the Excel program. The risers are named A and B, as shown in the diagram, while the branches are designated I and II. Radiators are then individually numbered, depending on their position along the branch. Radiator AII3, in other words, is in the middle of the second branch (higher up) on the first riser, as seen from the pump and in the direction of flow. The use of the riser and branch valves is optional, and so they are not a mandatory part of the program. Each radiator, however, is fitted with a control valve, which cannot be omitted. The same applies for the main valve (upstream of the heat exchanger). However, the program does allow the characteristics and sizes of all the valves to be selected as required.

57

4 SIMULATION PROGRAMS

Each radiator valve can be connected to, or disconnected from, a thermostat which, in turn, has either a selectable P-band or a P-band equivalent to the pre-setting of the radiator valve, based on the proportion of the valve head that is available for control after balancing. Each radiator is assumed to supply its room with heat. Room temperatures are calculated using a heat balance for each room, but it is assumed that there is no heat transfer between the rooms. The rooms are similar, with selectable levels of ventilation flow rate and supply air temperature. Additional internal heat supplies can be added for each room. All radiators are of the same size and type, and are defined by the required room temperature with selectable design temperature parameters (supply temperature, return temperature and outdoor temperature). All pipes are defined in terms of length, size and material. In addition, critical Reynold's numbers can be set, determining the change between laminar and turbulent flow, as can the size of a transition zone between the two flow types, as the change cannot occur instantaneously. The pump characteristic can be selected as required, which means that a pressure control over the pump itself could be applied in the form of a suitable pump characteristic. However, it is not possible to simulate pressure control in any other place in the system. Each simulation run is started by calculating an optimal balancing set-up, on the basis of given conditions. The system can then be changed in various ways in order to analyse the effect of the changes. The parameters that can be changed are: - Outdoor temperature - Supply air temperature - Supply main temperature (arbitrarily, or in accordance with a controller characteristic) - Presence or absence of thermostats - Width of P-band (constant or dependent on balancing) - Pump speed - Internal heat contribution - Setting of (any) radiator valves - Setting of (any) branch valves - Setting of (any) riser valves - Setting of the main valve 4.1.2 Verification As the program handles only steady-state conditions, simple equations can be used which, in principle, means that the program is based on two different parts: heat release and hydraulic interaction. Heat release determines how the flow and temperature levels interact for an arbitrary radiator in a room, while the hydraulic interaction between the radiators determines the flows and temperature levels in the entire system. Performance of the program was verified by measured values from the radiator test rig, which consists only of two radiators. However, the simulation analyses performed in

58

4 SIMULATION PROGRAMS

this work have involved considerably more than just two radiators, although the principle is the same. The fundamental relationships that describe the interaction between two radiators are no different than those which describe the interaction between five radiators, or between two branches or two risers: the calculation merely becomes a little more complicated and has to be carried out in more steps. The purpose of the verification in this chapter is therefore to show that the relationships used in calculating the heat release and hydraulic interaction reflect reality sufficiently well. Heat release Chapter 2 showed the following simple and accepted relationships for calculating the heat emitted by a radiator in steady-state conditions: & = K ⋅ ∆t n Q rad rad lm & where Q rad K rad ∆t lm n

(26)

= Heat release (thermal power output) from the radiator [W] = Radiator coefficient [W/ºCn] = Logarithmic mean temperature difference [ºC] = Radiator exponent [-]

If the above expression is to be applicable, Krad must be reasonably constant, regardless of flow, inlet water temperature or room temperature. To check this, the relationship between the thermal power output and the logarithmic mean temperature difference (to the power of the radiator exponent) has been plotted for the two radiators in the test rig, with results as shown below. If the radiator coefficient is constant, the relationship is linear. The figure shows that this seems to be the case. The radiator exponent was set to 1.33 for both radiators. 600 550

Radiator 1

500

y = 4.00x

Radiator 2

450

Qrad [W]

400 350 300 250 y = 2.54x

200 150 100 50 0 0

10

20

30

40

50

60

70

80

n

n

90 100 110 120 130 140

∆ tlm [°C ]

Figure 39. Plotting Krad for each radiator in the test rig. 59

n = 1,33

4 SIMULATION PROGRAMS

The results are based on measured values, with heat release having been calculated on the basis of temperature drop and flow through the radiator (see Chapter 2). The logarithmic mean temperature difference was calculated from the following relationship: ∆t lm =

where t w ,in

t w ,in − t w ,out  t w ,in − t room ln  t w ,out − t room

(27)

   

= Inlet temperature [ºC]

t w ,out = Return temperature [ºC] t room

= Room temperature [ºC]

The straight lines for each radiator, as shown in Figure 39, have been matched to the plotted points using the method of least squares. The mean departure of the thermal power output for radiator 1, between the measured values and the plotted line, amounts to 3.39 W, or 0.6 % of the maximum measured thermal power output. The corresponding mean departure for radiator 2 is 2.11 W, or 0.7 % of the maximum measured thermal power output. The equation for each of the lines is shown in the figure, with the slope coefficient equivalent to the best value of Krad, based on the measured values. For radiator 1, this gives a value of 4.00, while for radiator 2 the value is 2.54. The simple equation (26) therefore shows itself to agree relatively well with the results, and so it has been used for the simulations. It must be pointed out that calculations were also made in order to optimise the radiator exponent, so that the mean departure from the measured values would be as small as possible. In this case, the exponents for the two radiators became relatively high: 1.34 for radiator 1 and 1.42 for radiator 2. However, the reduction in mean departure (as against the case when using an exponent of 1.33) was small, amounting to less than 0.06 W for both radiators. As a result, the accepted exponent of 1.33 was used thereafter. Hydraulic interaction Hydraulic interaction between components in a system occurs when a change of flow through one component affects the pressure levels in the system in such a way as also to change the flow in other parts of the system. This interaction occurs in all flow systems, although its magnitude varies. In order to be able to calculate the magnitude of the effect, it is necessary to know the pressure and flow conditions in the system. This, in turn, requires the flow resistances in the system to be known, both in terms of magnitude and of where they occur. Apart from the need to know the characteristics of the various components, such as valve and pump characteristics, it is also important to decide what type of flow is occurring in the system. In this respect, the simplest assumption is that the flow is fully turbulent in all parts of the system, which means that the pressure drop is proportional to the square of the flow. However, this assumption is not particularly suitable, as it presupposes high flow rates and/or small pipe sizes. 60

4 SIMULATION PROGRAMS

Instead, empirical relationships for calculation of the coefficient of friction (λ) have been used (see Appendix B). Laminar flow is assumed at Re < 4000 (Abel et al., 1997). In order to prevent a jump in calculation of the coefficient of friction when Re = 4000 is passed, the value of the coefficient of friction changes from laminar to turbulent via a transition band, the size of which can be varied, although the calculations have assumed 4000 < Re < 4500. The following two figures show examples of measured and simulated results for flow in two different systems. The first system, having design temperature levels of 70/30 °C, represents a low-flow case with (in principle) no pipe pressure drop (large pipes and very low flows), which results in almost non-existent interaction between the radiators. However, in the second case, which is a high-flow case with design temperature levels of 60/40 °C, the pipe pressure drops have a clear effect on the interaction between the radiators.

70/30 °C 45

Rad 1 (M) Rad 1 (S) Rad 2 (M) Rad 2 (S)

40 35 Flow [l/h]

30 25 20 15 10 5 0 0

2

4

6

8

10

Setting of radiator valve 1

Figure 40. Comparison between measured (M) and simulated (S) values of radiator flow in a low flow rate case.

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4 SIMULATION PROGRAMS

60/40 °C 45

Rad 1 (M) Rad 1 (S) Rad 2 (M) Rad 2 (S)

40 35 Flow [l/h]

30 25 20 15 10 5 0 0

2

4

6

8

10

Setting of radiator valve 1

Figure 41. Comparison between measured (M) and simulated (S) values of radiator flow in a high flow rate case. The interaction shown in the above figures expresses itself in the form of by how much the flow through radiator 2 changes when the setting of radiator valve 1 is changed. In the low-flow case, there is no effect on the flow through radiator 2, which is due to the fact that the pressure drop across this circuit is not affected by the flow change through radiator 1, because the change in the overall pressure drop in the distribution system is essentially negligible. However, in the high-flow case, the flow through radiator 2 changes when the flow through radiator 1 is changed: in other words, the change in pressure drop in the distribution system in this case is not negligible. It can be seen that there is good agreement between measured results and simulated results. The mean departure between simulation and measurement of the flow through radiator 1 is 0.1 l/h for the low-flow case, and 0.8 l/h for the high-flow case. In the case of the flow through radiator 2, the corresponding values are 0.2 l/h in both cases. The total The heat release, together with the hydraulic interaction, defines the total system. In order to provide a picture of how the simulations match the measurements in this respect, the following two figures show examples of how the thermal power output from the two radiators in the test rig is affected by the setting of one radiator valve.

62

4 SIMULATION PROGRAMS

70/30 °C

Thermal power output [W]

700

Rad 1 (M) Rad 1 (S)

600

Rad 2 (M) Rad 2 (S)

500 400 300 200 100 0 0

2

4

6

8

10

Setting of radiator valve 1

Figure 42. Comparison between measured (M) and simulated (S) values of the thermal output power in a low flow rate case.

60/40 °C

Thermal power output [W]

700

Rad 1 (M) Rad 1 (S)

600

Rad 2 (M) Rad 2 (S)

500 400 300 200 100 0 0

2

4

6

8

10

Setting of radiator valve 1

Figure 43. Comparison between measured (M) and simulated (S) values of the thermal output power in a high flow rate case. Figure 40 showed that the flow through radiator 2 was not affected by the flow change through radiator 1 in the low-flow case. The same applies also for the thermal output power, as shown in Figure 42 above. However, it must be pointed out that this is possible only if the pressure drops in the distribution system are almost non-existent, 63

4 SIMULATION PROGRAMS

which is not common. In the above examples, the mean departures between the simulated and measured values for radiator 1 are 9.7 W for the low-flow case, and 5.4 W for the high-flow case. The corresponding values for radiator 2 are 5.8 W and 5.2 W. One result parameter in this work is that of the return temperature. In exactly the same way as for the thermal output power (and the room temperature), this provides a measure of how the system is operating. This section concerning verification is therefore concluded by showing an example of comparison of the simulated and measured values of the return temperature from the radiators. Again, it is the same two systems as previously shown that are considered.

70/30 °C

Return temperature [°C]

60

Rad 1 (M) Rad 1 (S)

55

Rad 2 (M) Rad 2 (S)

50 45 40 35 30 25 20 0

2

4

6

8

10

Setting of radiator valve 1

Figure 44. Comparison between measured (M) and simulated (S) values of the radiators' return temperature in a low flow rate case.

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4 SIMULATION PROGRAMS

60/40 °C

Return temperature [°C]

60 55

Rad 1 (M) Rad 2 (M)

50

Rad 1 (S) Rad 2 (S)

45 40 35 30 25 20 0

2

4

6

8

10

Setting of radiator valve 1

Figure 45. Comparison between measured (M) and simulated (S) values of the radiators' return temperature in a high flow rate case. The above figures show a clear departure between the simulated and measured values for radiator 1 when the radiator valve is fully closed (at setting 0). This is because the trapped water has not had time to cool to room temperature, which to some extent could be due to thermal conduction along the pipes. The simulations, however, have assumed that the stationary water has cooled to the room temperature on equilibrium. If no allowance is made for these “incorrect” values, we obtain a mean departure between the simulated values and the measured values for radiator 1 of 0.6 °C for both the low-flow and the high-flow case. For radiator 2, the mean departure is 0.6 °C for the low-flow case and 0.7 °C for the high-flow case. The calculation program consists of known theoretical and empirical relationships. The verification of the results against the measured data shows relatively small departures between the simulated and the measured results, which indicates that the program can be used for the analyses performed in this work.

4.2

Flowmaster

A program that is to be used to analyse a system with valve groups and air heaters must be able to handle relatively rapid thermal and hydraulic processes. A high level of detail is required in order to be able to simulate the dynamic processes in such systems. There are several programs that could be suitable: the final choice was Flowmaster, but this must not be taken as meaning that there are no other programs that could do the work just as well, or possibly even better. However, Flowmaster had been in use for some time by others in the Department, which meant that it would be quicker to become familiar with it, and it also met the above requirements.

65

4 SIMULATION PROGRAMS

4.2.1 Structure As its name indicated, Flowmaster is primarily a program for simulation of flow systems. Temperature and heat transfer are really of secondary interest, although the program does contain a calculation model for simulation of heat transfer, which can easily be activated. The level of detail in Flowmaster is high, and the characteristics of components in the program can easily be changed, either in accordance with examples included in the program or as specifically required. The program has a graphical interface, with the system for investigation being built up by connecting appropriate components, which are represented by typical figures. The components in the program are not represented by physical items, but by “black boxes”. Their characteristics are determined by curves, surfaces and equations. The advantage of this is that it makes it relatively simple to establish the necessary relationships between the large quantities of data that have been produced in this work. See the Flowmaster manual for more details of the program. 4.2.2 Verification As the characteristics of the components in Flowmaster can be determined from the actual measured results, it has been possible to create a fairly accurate model that reflects the actual physical systems on which measurements were made. Verification therefore involves: - determination of the characteristics of individual components, using the measured data, and possibly comparing these characteristics with theoretical, empirical or accepted relationships. - checking that the overall system's measured characteristics and simulated characteristics match, both statically and dynamically. Components It has been possible to make actual measurements of the hydraulic parameters and conditions of most components, as there are instrumentation connection points at many positions in the test rigs. An exception to this is the balancing valves, for which commercial product data has been used. This chapter shows measured values for the most important components: these values have been used in the simulations. Figure 46 shows examples of measured characteristics for the control valves. Each point along the curves represents the equilibrium values, calculated as the mean value of 18 sequential samplings, over a period of 1.5 minutes.

66

4 SIMULATION PROGRAMS

kv value [m³/h]

10 9

V341-10

8

V355-4

7

V341-4

6 5 4 3 2 1 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Valve opening [-]

Figure 46. Measured valve characteristics (port A) of the control valves. The fact that the valve characteristics do not reach the specified kvs values can be due to the fact that, for practical reasons, the pressure measurement points are not positioned right up against the ends of the valves in the test rig, but a small distance away. This can mean that a slight element of pipe pressure drop is included in measurement of the kv value of the valve, which means that the measured kvs values are slightly lower than the actual values for the valves. Admittedly, if so, the calculated kvs value for the V355-4 valve should differ the most from the specified value, as this valve is positioned furthest from the pressure measurement points, but this does not appear to be the case. Another possible factor for the differences is simply that of manufacturing tolerances. From a thermal perspective, it is naturally the air heater that is of the most interest, and it is also the only component of which the thermal characteristics have been determined by measurements. Although there are theoretical relationships, such as the NTU method, that can be used when calculating the performance of air heaters, problems arise when attempting to determine the UA value of heaters. This value depends on the size, shape and media flows in the heater. Figure 47 shows how the UA value in the air heater used in this work changes with the water flow. The figure is based on measured values from both the low-flow and high-flow configurations. The value has been calculated for a counterflow-connected air heater, which is a modification of the real conditions. In actual fact, the flows in the air heater are partly counterflow and partly cross-flow. Allowance for this is usually made by multiplying the UA value by a correction factor (F), which accounts for the UAF designation shown on the Y-axis.

67

4 SIMULATION PROGRAMS

900 800

UAF [W/°C]

700 600 500 400 300 200 100 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Flow [m³/h]

Figure 47. The UAF value of the air heater as a function of water flow. The measured values in the above diagram form a curve, the slope of which becomes steeper as the water flow through the air heater is reduced. Chapter 3, describing the measured results, showed the effects of this. However, when using the Flowmaster program, it is more suitable to indicate how the efficiency of the air heater changes with the water flow, as shown in Figure 48 below. 1.0 0.9

Efficiency on the water side

0.8

Efficiency on the air side

Efficiency [-]

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Flow [m³/h]

Figure 48. Efficiencies of the air heater as a function of water flow. It should be pointed out that, in Flowmaster, the efficiency of the air heater is defined as being the higher of the water or air side efficiencies. If the program is to simulate a larger or smaller (or dirty) air heater, it is the UA value of the air heater that is changed

68

4 SIMULATION PROGRAMS

accordingly, which means that it is the curve in Figure 47 that needs to be modified. New efficiencies can then be derived, starting from the new relationship between the flow and the UA value, in accordance with the NTU method. As far as the pump (Grundfos UPS 25-60 180) is concerned, its measured characteristics for two different speeds are shown in Figure 49. 60

Pressure [kPa]

50 40 30 2 20 1 10 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

3

Flow [m /h]

Figure 49. The circulation pump characteristics. The main pump has not been included in these simulations: instead, a pressure rise across the valve group has been assumed. This differential pressure has been continuously measured as part of all the test measurements, and has then been used as input data for verification of the simulations. The same applies for the electric boiler output temperature (i.e. the supply temperature in the system) and the incoming air temperature to the air heater. The total system The following diagrams show comparisons between measurements and simulations for three different configurations (V341-10,H,DH, V341-4,L,SABO and V355-4,H,D) in respect of outgoing air temperature (supply air temperature), return water temperature and water flows.

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4 SIMULATION PROGRAMS

V341-10,H,DH

Supply air temperature [°C]

35 30 25 20 15 10

Measured

5

Simulated

0 1200

2400

3600

4800

6000

7200

8400

9600

Time [s]

V341-4,L,SABO

Supply air temperature [°C]

35 30 25 20 15 10

Measured

5

Simulated

0 1800

3000

4200

5400

6600

7800

9000

10200

Time [s]

V355-4,H,D

Supply air temperature [°C]

35 30 25 20 15 10

Measured

5

Simulated

0 600

1800

3000

4200

5400

6600

7800

Time [s]

Figure 50. Comparisons between measured values and simulated values of supply air temperature.

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4 SIMULATION PROGRAMS

V341-10,H,DH

Return temperature [°C]

40 35 30 25 20 15 10

Measured

5

Simulated

0 1200

2400

3600

4800

6000

7200

8400

9600

Time [s]

V341-4,L,SABO

Return temperature [°C]

40 35 30 25 20 15 10

Measured

5

Simulated

0 1800

3000

4200

5400

6600

7800

9000

10200

Time [s]

V355-4,H,D

Return temperature [°C]

40 35 30 25 20 15 10

Measured

5

Simulated

0 600

1800

3000

4200

5400

6600

7800

Time [s]

Figure 51. Comparisons between measured values and simulated values of return temperature.

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4 SIMULATION PROGRAMS

V341-10,H,DH 1.4 Secondary flow

1.2 Flow [m³/h]

1.0 0.8

Primary flow

0.6 0.4

Measured

0.2

Simulated

0.0 1200

2400

3600

4800

6000

7200

8400

9600

Time [s]

V341-4,L,SABO 1.4 1.2

Measured

Flow [m³/h]

1.0

Simulated

0.8

Secondary flow

0.6 0.4

Primary flow

0.2 0.0 1800

3000

4200

5400

6600

7800

9000

10200

Time [s]

V355-4,H,D 1.4 1.2 Flow [m³/h]

1.0 0.8 0.6 0.4

Measured

0.2

Simulated

0.0 600

1800

3000

4200

5400

6600

7800

Time [s]

Figure 52. Comparisons between measured values and simulated values of flow.

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4 SIMULATION PROGRAMS

Table 5 shows the mean departures between measured values and simulated values for the listed cases, as shown in Figures 50 - 52.

V341-10,H,DH V341-4,L,SABO V355-4,H,D Table 5.

Supply air temperature [ºC] 0.22 0.51 1.03

Return temperature [ºC] 0.42 0.60 1.35

Flow [m³/h] Primary / Secondary 0.03 / 0.02 0.08 / 0.01 0.03

Mean departure between measured values and simulated values.

The mean departure between measured values and simulated values can be calculated from the following equation: sm = where s m N xM,i xS,i

1 ⋅ N

= = = =

N

∑ (x i =1

− x S, i )

2

M ,i

(28)

Mean departure The number of measured value and simulation data samples Measured data for sample no. i Simulation data for sample no. i

The table shows that the measured departure is relatively small for all configurations. The best agreement is that of the V341-4,H,DH configuration, while the worst is that of V355-4,H,D. The mean departure has been calculated for all time steps (every fifth second). It should be pointed out that the mean departure in respect of the return temperature for V355-4,H,D is based on measured and simulated values for the time of 1700 seconds and onward. The reason for this can be clearly seen on the left of Figure 51, where the measured return temperature has not reached equilibrium but is slowly cooling as the water is stationary, while the simulations are based on an equilibrium state, which means that the conditions for comparison of measured and simulated values are not equivalent until simulation and measurement have started from the same starting point, which occurs at the time of 1700 seconds. Nevertheless, the mean departure of the return temperature is considerably higher for V355-4,H,D than it is for the other configurations. Most of this departure (70 %) occurs when the control valve changes from 0 % open to 10 % open (up to time 2800 seconds in the diagrams). When the water starts to flow through the air heater, its temperature rises considerably more quickly, as indicated by the measurements, than as indicated by the simulations. Again, the explanation lies in the fact that the water in the pipe (the supply pipe) has not cooled sufficiently, with the result that the dead time in the simulations is considerably longer than in the measurements. It should also be pointed out that the flow meters produce considerable noise at water flow rates close to zero. This has not been included in the diagrams in Figure 52. In addition to the cases described above, several other configurations have also been investigated in order to assess the accuracy of the simulations. However, these cases 73

4 SIMULATION PROGRAMS

will not be described here, but they do give similar results to those described above. In general, it is the district heating connection that shows the closest agreement between measurements and simulations, while the direct connection has the poorest agreement, as shown in the table above. Nevertheless, the differences are relatively small, and so the simulation model is regarded as being fully acceptable.

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5 SIMULATION - PLANNING

5

SIMULATION - PLANNING

Before the simulations can be run, they must be planned. This chapter, which can be seen as a general introduction to the next two chapters (which describe the results of the respective simulations for the radiator system and for the air heater with valve groups), describes how the simulations have been prepared and how they have been run.

5.1

Radiator system

5.1.1 Configuration The starting point for the design of systems that are suitable for comparison with each other is a single common system. This original system was designed for (approximate) temperature levels of 66/42 ºC at a design outdoor temperature of -15 ºC. The desired indoor temperature was 20 ºC. When the system was balanced, it resulted in a high flow rate. After starting up, it was found that the room temperature was too high, due to an additional input of heat from an internal source and/or insolation. For simplicity, it was assumed that this additional heat input was constant at 170 W throughout the year, having the effect of increasing the indoor temperature by about 2.5 ºC. This problem could be tackled in two ways: either by reducing the supply temperature or by reducing the water flow rate. Applying both of them result in two different types of systems, and it is those that provide the basis for the comparisons in this chapter. In the one case, the design supply temperature is reduced to 60 ºC, which results in a return temperature of about 40 ºC. The flow rate is not changed, and so this alternative is a high-flow system. The desired indoor temperature of 20 ºC is achieved. In the second case, the flow rate is reduced, which mean that the system becomes a low-flow system. At the same time, the supply temperature is increased: with the flow rate being reduced to half of the original value, the design supply temperature must be increased to 73.3 ºC. This results in a return temperature of 33.3 °C, with the desired room temperature of 20 ºC being achieved. As both the systems are derived from one and the same original system, the physical arrangement is identical. Radiators, valves and pipes is the same, thus making it possible to perform a true comparison. However, changes can be made to the systems in their simulated forms in order to study differences such as those between a system with thermostats and a system without thermostats. The number of different system configurations simulated is shown in the following table.

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5 SIMULATION - PLANNING

Without thermostat

With thermostat

Without riser and branch valves With riser and branch valves Without riser and branch valves With riser and branch valves

Normal pump Pressurecontrolled pump Normal pump Pressurecontrolled pump Normal pump Pressurecontrolled pump Normal pump Pressurecontrolled pump

High flow (60/40) High Low ∆pmin ∆pmin X X

Low flow (73/33) High Low ∆pmin ∆pmin X X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Table 6. A number of different systems can be simulated. Each X in the diagram shows a possible system configuration. Ringed values represent the reference systems. The table shows 32 Xs, symbolising different system configurations. ∆pmin refers to the lowest balanced differential pressure in the system, which occurs across the radiators that are furthest away from the pump. The difference between a normal pump and a pressure-controlled pump is that the former has a “natural” pump characteristic, as for a pump without speed control, while the latter indicates that the speed of the pump is controlled and varied. It must be added that, in these simulations, pressure control could be applied only across the actual pump itself, although the pump characteristic in those cases could be arbitrarily assumed. The two systems described - high-flow and low-flow - constituted the reference systems for the simulations. The reference systems are assumed to be fitted with riser and branch valves, but not with thermostats. The pump is not controlled, and the lowest balanced differential pressure is high. The reference systems are shown in Table 6 by circled Xs. 5.1.2 Temperature, flow, pressure Temperature levels The high-flow balanced system has, as said above, a design supply temperature of 60 ºC and a resulting return temperature of 40 ºC, while balancing the system for low flow results in a supply temperature of 73.3 °C and a return temperature of 33.3 ºC. The two sets of design temperature levels are therefore indicated by 60/40 and 73/33 respectively, as shown (beneath the headings of the high-flow and low-flow columns) in Table 6.

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The size and UA value of each room could be selected arbitrarily in the simulation program. In the same way, the ventilation air flow rate and the incoming supply air temperature could also be arbitrarily selected as required. In the simulations, the radiator system provides all the heat required in the room, apart from the 170 W that are assumed to be supplied from internal heat sources. The distribution pipes are not assumed to be providing any heat contribution, and nor is any preheating of the ventilation air assumed. This means that, in the simulations, the supply air temperature is assumed to be the same as the outdoor air temperature, thus corresponding to mechanical ventilation without heating the supply air. The simulations assume a ventilation air flow rate of 0.5 air changes per hour. In the design case, transmission heat losses amounts to 877 W, while ventilation heat losses amounts to 293 W. The additional internal heat input is, as said above, 170 W. This means that each radiator has to provide 1000 W in the design case, which in turn requires a water flow rate of 43.6 l/h in the high-flow case, and 21.8 l/h in the low-flow case. The necessary supply temperature control curve characteristic for the respective systems could be produced from these data. The curve shows how the supply temperature is controlled as a function of the outdoor temperature, as shown in Figure 53. The return temperature for each case is also shown in the diagram. The supply temperature is indicated by “Supply”, the return temperature with “Return”, the high-flow system with “High” and the low-flow system with “Low”.

Water temperature [°C]

80 70 Supply, Low

60 50 40

Supply, High Return, Low

30

Return, High

20 -15

-10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 53. Control characteristics for the high-flow and low-flow cases, with allowance for internal heat input. The control curve characteristics shown in Figure 53, which allow for the internal heat contribution of the building (and/or insolation), thus provide the required indoor temperature of 20 ºC up to an outdoor temperature of 15 ºC, at which temperature the heating season is assumed to end. Unless otherwise mentioned, the control curve characteristics as shown in Figure 53 are used for the simulated systems, as is the assumption of a basic internal heat input of 170 W.

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Pressure levels Setting the pressure levels is slightly difficult. If the physical arrangement of the high-flow and low-flow systems are to be exactly the same for a comparison, the lowest balanced differential pressure in the low-flow system would be very high. This is because the pump would not be suited to the low pressures and flow rates in the system. It is therefore necessary to make an exception for this point, so that the pumps for the two systems are assumed to be matched to their systems in such a way as to provide a minimum balanced differential pressure of 10 kPa in system with high ∆pmin, and 2 kPa in system with low ∆pmin. When choosing the pipe sizes and pipe lengths, it is the objective that, as far as possible, the pressure drop per metre of pipe should be about 100 Pa/m, which is a common guide value for system designs, and should not exceed 250 Pa/m for the high-flow case. The pipe dimensions and pipe lengths for the high-flow system are chosen to give pipe pressure drops of 1 kPa between each radiator (i.e. the sum of the pressure drops in the supply and return connections), 3 kPa between each branches and 5 kPa between each risers. This means that the pipe sizes in the system varies between 10 mm and 22 mm. The pipes in the low-flow case are the same as those in the high-flow case, which means that the specific pressure drop per metre of pipe in the low-flow system varies between about 30 Pa/m and 70 Pa/m. The maximum pressure drop between the radiators are about 0.5 kPa. The flow through the heat exchanger are assumed to be fully turbulent, with a pressure drop of 10 kPa in the high-flow case and 2.5 kPa in the low-flow case. Radiator valves The maximum kv value of the radiator valves can be calculated knowing the necessary flow and minimum differential pressure. The highest kv value is obtained in the case of a high-flow system with a low balanced differential pressure across the radiator furthest from the pump (radiator BII5), and amounts to 0.31 m³/h. Some of the smallest radiator valves on the market have a kvs value of about 0.7 m³/h, which are therefore quite sufficient for the purposes of the simulations. The radiator valve used in the simulations therefore has the following characteristic, which is based on the characteristics of an existing valve available on the market.

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0.8

In this case, the valve opening provides a relative measure of the pre-setting value, such that a valve opening of 0.1 corresponds to a pre-setting value of 1, etc. The maximum valve opening, 1, corresponds to a pre-setting value of 10, and means that the valve is fully open.

0.7

kv value [m³/h]

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Valve opening [-]

Figure 54. The radiator valve used in the simulations. It can be seen that the characteristic is almost a square function. Other commercially available radiator valves can have completely different characteristics and so, at the end of the simulations, a complementary sensitivity analysis is performed for the case of a valve with a quick-opening characteristic, which is completely different to the square law characteristic. Thermostat Central control of a radiator system follows a characteristic curve, which varies the system supply temperature in response to changes in the outdoor temperature. Most modern systems also include local control at each radiator, in the form of a thermostatic control valve. The simulations permits these radiator thermostatic valves to be included or excluded, as required. The width of the P-bands of the thermostats could also be varied: either fixed, regardless of the setting of the radiator valve, or also varied to allow for the setting of the valve (i.e. how much of the valve head travel is available for control), and referred to here as the adjusted P-band. When using an adjusted P-band, the thermostat's P-band is modified by the pre-setting of the valve. In the simulations, this is linked directly proportional to the valve setting, so that unity valve opening corresponds to the maximum P-band width (i.e. the entire travel of the valve head is available for control), while zero valve opening represents a P-band width of 0 ºC (i.e. no valve travel is available for control). A setting of 0.5 represents half the maximum P-band width, as half of the valve travel/length is available for control. The simulations uses a maximum P-band width of 2 ºC, which is then modified to match the valve setting. Branch and riser valves The sizes of the branch and riser valves are chosen to accommodate the maximum kv value assumed. This means that, for the branch valve in branch I, it must be able to create a pressure drop equal to that between the branches, i.e. 3 kPa (see above,

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“Pressure levels”). This gives a kv value of 1.26 m³/h. The riser valve in riser A must be able to create a pressure drop equal to that between the two risers, i.e. 5 kPa, equivalent to a kv value of 1.95 m³/h. The branch and riser valve used in the simulations has been selected in order to be able to provide these kv values. Its characteristic is as shown below, and is based on the characteristic of an existing valve available on the market. 3.0

kv value [m³/h]

2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 55. Characteristic of the branch and riser valve used in the simulations. It can be seen that this characteristic, too, is almost a square law function, as was the case for the radiator valve. The pump Which of the two pump characteristics that is used depends on the particular balancing mode that is being simulated and on the type of curve selected. Figure 56 shows the falling characteristic used for both the high-flow case (continuous lines) and low-flow case (dotted lines). The two case characteristics are then further separated into a characteristic for a high balanced differential pressure, with the lower curve showing the characteristic for a low balanced differential pressure.

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80 Pressure rise [kPa]

70

High-flow system

60 50 40 30

Low-flow system

20 10 0 0

250

500

750

1000

1250

1500

Flow [l/h]

Figure 56. Pump characteristics used in the simulations. It must be added that, when using a pressure-controlled pump in the simulations, a level, horizontal characteristic is assumed, representing the case when the pump pressure rise is maintained constant, regardless of the system flow rate. This characteristic is shown in Figure 57 below. 80 Pressure rise [kPa]

70 60

High-flow system

50 40 30

Low-flow system

20 10 0 0

250

500

750

1000

1250

1500

Flow [l/h]

Figure 57. Pump characteristics as used in the simulations for pressure-controlled pumps. As described above, for the non speed-controlled pumps, the upper characteristic in each set is that for the system with a high balanced differential pressure, while the lower characteristic is that for the pump in the low balanced differential pressure system. The main valve The size of the main valve depends on the size of the pump. If the pump creates a higher pressure than is required, the additional pressure has to be dropped across the main valve. In the simulations, the pump is not assumed to be perfectly matched to the system: the pump characteristic and the main valve characteristic are selected in such a

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way as to require the main valve to be 75 % open, regardless of whether simulation relates to a high-flow or low-flow system, or to systems with high or low balanced differential pressures. The valve characteristic used in the simulations is taken from that of an existing valve available on the market, and is shown in Figure 58. 6.0

kv value [m³/h]

5.0 4.0 3.0 2.0 1.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 58. Valve characteristic of the main valve used in the simulations. It must, however, be pointed out that, when simulating a pressure-controlled pump, it is assumed that this is perfectly matched to the system, so that the main valve is fully open. 5.1.3 Studied deviations Table 6 showed a number of systems without deviations, which means that they are all perfectly balanced (i.e. with all radiators having the same flow through them) and with exact supply temperatures. In such cases, the room temperatures and return temperatures are the same for all rooms/radiators. In the rest of this presentation, these “perfect” systems will be referred to as basic cases. Each system could then be exposed to a number of different deviations, in order to investigate its sensitivity. The following is a description of the deviations that are applied in this work: • Incorrect valve setting (for one valve) - Radiator valve This deviation is a relatively common one of the user, or of some other person, changing the balanced setting of a radiator valve in order to change the heat output from the radiator concerned. This has the effect of changing the flow balance in the system, which can adversely affect other users. This deviation is simulated by fully opening or closing a radiator valve, in order to study the effect in terms of heat release from other radiators in the system.

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- Branch valve It is not only the setting of radiator valves that can be changed, but also branch valves. Simulation here involves opening or closing a branch valve by ± 0.25 of the valve opening from correct setting, in order to investigate the effect on the radiators connected to that particular branch, and also to investigate heat release from the radiators connected to the other branches. - Riser valve The settings of the riser valves can also be altered. Simulation of the effects of changes to their settings is investigated in the same way as for branch valves. - Main valve A change in the setting of the main valve need not necessarily mean that the flow balance of the system would be affected. However, it would affect the magnitude of the flow, and the result of this can be simulated by opening or closing the valve, e.g. by ± 0.25 of its valve opening. • Imperfect balancing (for all radiator valves) - Simplest possible balancing In practice, perfect balancing can hardly ever be achieved. Systems are sometimes balanced in as simple a manner as possible, i.e. with all valves at the same setting. - Simplified balancing One way of simplifying balancing is to assume a constant differential pressure across all radiators connected to any given branch, and then to balance them according to the assumed differential pressure. With this procedure, the kv values of the radiator valves will all be the same if the flows through the radiators are supposed to be the same. The branch, riser and main valve (if there is one) are then set so that the total flow through the branches is correct. The result of this simplified method of balancing is that the first radiators on each branch have slightly too high a flow, while the last radiators have too low a flow. - Random differences in balancing As said above, it is not always so simple to perform a good balancing operation, which means that balancing is sometimes less successful. This is arranged in the simulations by allowing the valve settings to vary randomly by a maximum of ± 0.05 in valve opening, in relation to the perfect basic case. In other words, if the valve goes from fully open to fully closed over only one turn, this random deviation represents a maximum of one-twentieth of a turn away from the perfect setting. • Disturbances - Internal heat The system can be disturbed by an increase or decrease in the supply of internal heat from the room. This can be modelled separately for each room.

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- Response “Response” means that something in the system has been changed in order to deal with the problems that have occurred. Such problems could be, for example, that one or more users thinks that it is too cold or too hot in the room, and so the resulting response in many properties is to increase or decrease either the pump pressure or the supply water temperature. - Pump pressure Changing the pump pressure is probably not the first response likely to be applied, although it can be justified if the flow in the system, or in certain parts of it, is clearly too low. In order to investigate the effect of changing the pump pressure, the speed of the pump in the simulated system can be arbitrarily changed. - Supply temperature Problems often occur, and complaints are often received, in connection with too low indoor temperatures. In such cases, the natural response is to raise the control curve characteristic, i.e. to change the relationship between the supply temperature and the outdoor temperature. The simulations mirror this by allowing the supply temperature to be set in accordance with a theoretical “optimum” control curve characteristic, or at some arbitrary level. 5.1.4 Planning of simulations A couple of the ways in which the results of the simulations are presented include duration diagrams and data calculated from the outdoor temperature duration over the year. This provides a means of indicating the effect of outdoor temperature on room temperature and return temperature in a natural manner. Duration diagrams also have the advantage of providing a graphical means of displaying any differences in the amount of thermal energy used over the year. To produce a duration diagram requires a number of simulations at different outdoor temperatures, which therefore vary between –15 °C and +28 ºC, in 1 ºC increments. Each diagram therefore requires 44 simulations. The diagrams are based on conditions for Gothenburg, with the outdoor temperature being provided in the form of a mean curve of temperatures for the period from 1983 – 1992. The mean outdoor temperature over the year is 8.0 ºC, while the mean outdoor temperature during the heating season (defined in this case as being that period of the year during which the outdoor temperature does not exceed 15 ºC) is 5.6 ºC. Regardless of whether or not the duration diagrams are shown in each case, they have provided the basis for calculation of a weighted mean value of return water temperature over the year. It should be pointed out that such weighting tends to produce a value that is apparently too low. In actual fact, a deviation that changes the weighted value of return temperature by only a few tenths of a degree can cause differences of two or three degrees in the design conditions. It would also be possible to produce a weighted value of the room temperatures in the simulated systems, but this would provide only a partial picture of how the consumption of thermal energy over the year is affected by a departure from design operating conditions. For such an analysis, it is therefore more suitable to consider this change directly, based on the actual simulated heat release from each radiator in the systems.

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It is not possible to show all the results in full detail: they must, of course, be sorted. Nor is it practical to attempt to simulate all possible combinations of deviations in the different systems, partly due to the sheer resulting volume of work, and partly because the results would be lost among the sheer quantity. The simulations have therefore been run in accordance with the following limited selection, (which also shows the section numbers in the following text that provide more detailed information). Nevertheless, the amount of results (in the form of diagrams) are rather extensive and the reason that they are all shown is that they give a graphical insight, in respect of comparison, to each set of simulations that would be lost in a table. 6.2

The basic cases (no deviations)

6.3 Incorrect valve setting 6.3.1 Fully closed radiator valve Reference system Reference system without branch or riser valves Reference system with low balanced differential pressure Reference system with thermostats (adjusted P-band) Reference system with thermostats and pressure-controlled pump 6.3.2 Fully open radiator valve Reference system Reference system without branch or riser valves Reference system with low balanced differential pressure Reference system with thermostats (adjusted P-band) Reference system with thermostats and pressure-controlled pump 6.3.3 Deviations from the correct setting of branch valve Reference system Reference system with low balanced differential pressure 6.3.4 Deviations from the correct setting of riser valve Reference system Reference system with low balanced differential pressure 6.3.5 Deviations from the correct setting of main valve Reference system Reference system with low balanced differential pressure Reference system with thermostats (adjusted P-band) 6.3.6 Summary 6.4 Incorrect balancing 6.4.1 Simplest possible balancing Reference system with fully open branch, riser and main valves Reference system with low balanced differential pressure Reference system with thermostats (adjusted P-band) 6.4.2 Simplified balancing Reference system Reference system with low balanced differential pressure Reference system with thermostats (adjusted P-band) 6.4.3 Randomised deviations in balancing (maximum ± 0.05 in valve opening) Reference system Reference system without branch and riser valves Reference system with low balanced differential pressure

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6.4.4

Reference system with thermostats (adjusted P-band) Reference system with thermostats (adjusted P-band) and pressure-controlled pump Reference system, response applied (pump pressure increased) Reference system, response applied (supply temperature increased) Reference system with thermostats, response applied (supply temperature increased) Reference system after long time (maximum + 0.25 in valve opening) Summary

6.5 Disturbances 6.5.1 Non-uniform distribution of internal heating Reference system Reference system with thermostats (constant P-band) Reference system with thermostats (adjusted P-band) Reference system with thermostats (adjusted P-band) and pressure-controlled pump 6.5.2 Summary 6.6 The distribution system 6.6.1 Single-pipe system 6.6.2 Two-pipe system 6.6.3 Three-pipe system 6.6.4 Summary 6.7 The district heating substation radiator heat exchanger The above cases form a rough framework that enables the structure of the simulation to be appreciated more clearly. In addition, further sub-cases may be simulated (parts of systems or for a particular parameter) in order to clarify the results. Each section is concluded with a sub-section that summarises and discusses the results of the particular simulations. It should be added that Chapter 6 is concluded with a simple comparison of three different types of distribution systems (single-pipe, two-pipe and three-pipe) in respect of their abilities to deal with deviations in the setting of valves. In addition, there is a brief discussion, based on simple calculations, of how the return temperature on the district heating side is affected by deviations in the radiator system. See the guide above.

5.2

Air heater with valve group

5.2.1 System configurations The system configurations analysed in this work have been earlier described in Chapter 3, “Measurements”, and so only a quite brief description of the various arrangements will be given here. There are three parameters that define the characteristic of the valve group:

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- Arrangement - Balancing - The type of control valve The interface with the rest of the system (which is not considered in the simulations) consists of the available differential pressure across the valve group and the supply temperature in each operating case. Arrangements The valve groups analysed here are normally used in systems supplied with hot water from district heating. A relatively low return water temperature is desirable, and so the primary flow is controlled in all these valve groups in order to achieve this. The three connection arrangements, shown below in Figure 59, are direct connection, district heating connection and the SABO connection.

Direct connection

District heating connection

SABO connection

Figure 59. The three valve group arrangements considered in the simulations. The flow through the air heater in the direct connection arrangement is regulated by a two-way valve, with balancing being provided by a balancing valve in series with the two-way valve. The thought behind the district heating connection is that the water flow through the air heater should be constant, with the primary flow being controlled by a two-way control valve. The secondary flow is balanced by a valve in the circulation circuit, while the primary flow is balanced by another valve in series with the control valve. Finally, a check valve is fitted in the bypass connection between the supply and return sides in order to prevent flow in the wrong direction, which might otherwise occur if the system is incorrectly balanced or if the circulation pump is not working The SABO connection works in the same way as the district heating connection, but with one important difference: that the thermal output power is controlled by a three-way control valve, controlling the mixing of the primary flow and the flow through the bypass in order to provide the necessary inlet temperature to the air heater. Balancing Each valve group can be balanced for either high flow or low flow, corresponding to the design temperature levels.

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The control valve The number of types of control valves (in terms of their control characteristics) used in the simulations has been limited to three: logarithmic, linear and optimum. In this context, an optimum control valve is a “virtual” control valve that makes control of the air heater as simple as possible, i.e. so that the width of the necessary P-band is constant and as narrow as possible, under all operating conditions. The optimum characteristic depends on the system configuration, including selection of the type of valve group, balancing and the size of the valve (i.e. the kvs value of the valve). It also depends on how the available differential pressure varies during operation, the distance to sensors, pipe lengths etc. Chapter 7 starts with a short description of how the optimum characteristic is arrived at, while Appendix B describes a somewhat simplified way of doing so. Designations The designations used for each system in the simulations are analogous with those used in Chapter 3, “Measurements”. In the simulations, the control valves are referred to as either “Log”, “Lin” or “Opt”, while the valve groups are referred to as “D”, “DH” or “SABO”. High-flow balancing is referred to as “High-flow”(or just “H”), while low-flow balancing is referred to as “Low-flow” (or just “L”). This means that, for example, a valve group using the district heating connection arrangement, balanced for a high flow rate and having a logarithmic characteristic valve with a kvs value of 4.0 m³/h, would be identified as Log-4,H,DH. A direct connection arrangement, with a low flow, and having a control valve with an optimum characteristic and a kvs value of 10 m³/h, would therefore be designated as Opt-10,L,D. The reference cases In exactly the same way as for the radiator systems in Chapter 6, the simulations in Chapter 7 start from a number of reference cases without deviations. These reference cases are all fitted with a control valve having an optimum valve characteristic. With three valve groups, each having two different types of balancing (high flow or low flow), there are therefore six reference cases. 5.2.2 The necessary P-band width When simulating valve groups controlling air heaters, there is little point in investigating how the outgoing (supply) air temperature from the air heater is affected by deviations. This is because the whole purpose of control of these systems is to maintain a desired air temperature, even under less favourable conditions. It is therefore more interesting to investigate how the design of a valve group affects the ability to do so, and this is quantified in the simulations in the form of the systems' necessary P-band widths, as described in Chapter 2. In order to be able to determine the width of the necessary P-band, we need to know the static and dynamic characteristics of the system, and it is in this respect that the simulations are involved. The same method of determining the static and dynamic characteristics of the various system configurations (with or without deviations) is used as was used in the

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measurements, i.e. investigation of the response to step changes. These step changes are applied in ten steps, from a fully closed to a fully open control valve. When the system characteristics have been determined in this way, the width of the necessary P-band for each step can be calculated. This provides information on the performance of the system, so that the need for a wide necessary P-band indicates that the system is difficult to control, while a narrow necessary P-band indicates simpler control. The better designed the system, the narrower the necessary P-band, and thus the less the risk of control problems occurring. The equation for determining the necessary P-band width has been given in Chapter 2, but is repeated here as a reminder to assist understanding of the description of the simulations. Pnec =

Td ⋅ KS Tk

(29)

where Pnec = Necessary P-band width [ºC] Td = Dead time [seconds] Tk = Time constant [seconds] K S = System gain (at a particular valve opening) =

∆t [ºC] ∆H

The necessary P-band width for each stage is determined as shown in the diagram below, which shows how ∆t, ∆H, Td and Tk are obtained. 26.0

0.45 Valve opening

25.5 0.40

25.0 24.5 24.0

∆ ta,out

∆H

0.35

23.5 23.0

Valve opening [-]

Outgoing air temperature [°C]

Outgoing air temperature

0.30

22.5 22.0 -100

Td Tk -50

0

50

100

150

200

250

0.25 300

Time [s]

Figure 60. An example of a step response. The example shown in Figure 60 shows how, at time 0, the valve opening of the control valve is changed from 0.3 to 0.4, which has the effect of raising the outgoing air temperature from about 22.55 ºC to 25.30 ºC. Based on the point of intersection of the tangent with the temperature line for 22.55 ºC, the dead time is estimated as 15 seconds, 89

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while its point of intersection with the 25.30 ºC line gives a time constant of 40 seconds. Entering these values in Equation 29 indicates that the width of the necessary P-band is 10.5 ºC for a valve opening of 0.4. 5.2.3 Return temperature Knowledge of the dynamic response of a valve group is particularly important in order to be able to analyse its function with an air heater. However, as far as the return temperature is concerned, the conditions are different: the return temperature value depends on the design of the system from a static perspective. The dynamic response delays and complicates analysis in this respect. For this reason, it is only the static characteristics of the valve group (and of the air heater) that are considered when determining the system return temperature for various operational cases. The method of working is split into two parts: - Determination of the static characteristics of the system - Selection of a control curve (i.e. the relationship between the water supply temperature and the outdoor temperature). The static characteristics of the system could be described by how the total efficiencies of the valve group (with the air heater) on the air and water sides change as the valve opening of the control valve changes. Expressions for the total efficiencies were given in Chapter 2, and are repeated here. η a ,s =

η w ,s =

where

1 1 1 1  + ⋅  − 1 ηa R  ϕ  1  1  ϕ ⋅  − 1 + 1  ηw 

=

=

t a ,out − t a ,in t w ,sup ply − t a ,in

t w ,sup ply − t w ,return t w ,sup ply − t a ,in

η a ,s

= The total efficiency of the valve group on the air side [-]

η w ,s

= The total efficiency of the valve group on the water side [-]

ηa ηw ϕ R CR CH Ca

= = = = = = =

(30)

(31)

The efficiency of the air heater on the air side [-] The efficiency of the air heater on the water side [-] CR/CH [-] C w C a [-] Thermal capacity water flow through the control valve [W/ºC] Thermal capacity water flow through the air heater [W/ºC] Thermal capacity air flow through the air heater [W/ºC]

Cw = C H = Thermal capacity water flow through the air heater [W/ºC] t w ,sup ply = Supply water temperature [ºC]

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t w ,return

= Return water temperature on the primary side of the

t a ,out

valve group [ºC] = Outgoing (supply) air temperature (after the air heater) [°C]

t a ,in

= Incoming air temperature (before the air heater) [°C]

Changing the valve opening of the control valve affects the flow through the valve, which in turn affects ϕ. If, in addition, the valve opening affects the flow through the air heater, then R, ηa and ηw will also be affected. This means that ηa,s and ηw,s will also be affected by the valve opening of the control valve. Just how this occurs depends on the design of the system, and can be determined from static analysis of the step change response simulations described above in connection with determination of the necessary P-band widths. An assumed control curve characteristic can be applied, when the static characteristic of the system has been determined from the step change response simulations and Equations 30 and 31, in order to obtain the return temperatures as functions of various outdoor temperatures. The method of working is illustrated graphically and schematically in the diagram below.

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ηa,s

tw,supply

η a ,s =

t a ,out − t a ,in

Necessary ηa,s as a function of the outdoor temperature (in order to to be able to achieve the desired air temp.)

t w ,sup ply − t a ,in

tout

tout

Control curve ηa,s

H Necessary H as a function of the outdoor temperature (in order to to be able to achieve the desired air temp.)

ηa,s = f (H)

tout

H Static attributes of the valve group and air heater

ηw,s

ηw,s

ηw,s = f (H)

Resulting ηw,s as a function of the outdoor temperature

tout

H tw,return

tw,return = f (tout)

η w ,s =

t w ,sup ply − t w ,return t w ,sup ply − t a ,in

tout

Figure 61. Simulation and calculation procedure in order to arrive at the return water temperature, depending on the static characteristics of the system and the assumed control curve characteristic. It can be seen from the diagrams above that, if the static characteristics are known, the return temperature can be calculated regardless of what control curve characteristic is used. This means that the “only” simulations that need to be performed are those for the step responses, as they provide the necessary information on both the static and dynamic characteristics, from which the necessary P-band width, and return water temperature as

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a function of the outdoor temperature, can be determined, regardless of the choice of control valve characteristics. However, it should be pointed out that, although the calculated necessary P-band widths and return temperatures admittedly apply for the same type of system, this is so for different temperature levels. It is only the static attributes in respect of flows and pressure levels that are the same, and which are used when calculating the return temperature. A higher supply temperature means that there will be a higher air temperature when performing step change response analyses, which will therefore also increase the width of the necessary P-band (see Section 7.5). However, this is not too important, as long as the effect is consistent for all the systems considered, as it is not the absolute values that are of interest, but the comparison between the performance of different systems and different deviations. 5.2.4 Temperature, flow, pressure Temperature levels for step change analyses When performing the step change response analysis simulations, the incoming air temperature is held constant at 0 °C. With the control valve fully open, the outgoing air temperature should be 30 °C, and so the flow rate and supply temperatures are adjusted in the simulations in order to produce this condition without any deviations. The size of the air heater is constant, regardless of the type of system. In the high-flow system, the design supply temperature is approximately 60 °C, and the return temperature approximately 40 °C. The low-flow system uses the same air heater as the high-flow system, which means that, in order to achieve the same result in terms of temperature increase of the air flow, the supply temperature has to be about 80 °C, giving a resulting return temperature of just below 40 °C. These temperatures are somewhat imprecise, which is due to the fact that it is the flow rate and the capacity of the air heater that determine the necessary supply temperatures. This means that it is necessary to some extent to adjust the supply temperature, depending on the particular operating case, in order to achieve the required design temperature rise on the air side of the air heater. Temperature levels when determining the return temperature In the simulations, it is the outdoor temperature that is varied when calculating how the return temperature is affected by the system configuration and deviations. The design outdoor temperature is -20 °C, and the required air temperature from the air heater is assumed to be +20 °C, held constant regardless of the outdoor temperature. The same system configurations are used as for the step change response simulations, although the air temperatures are different. This is because determination of the air temperature is based on the static characteristics of each system having first been determined by means of the step change response simulations. When determining the return temperatures, it is assumed that the air treatment system is not fitted with any means of heat recovery, which means that the air stream must be heated through 40 K at the design case. This requires a higher supply temperature than is used in the step change response simulations. The figure below shows the control curve characteristics that have been assumed for the high-flow and low-flow systems.

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Supply temperature [°C]

90 80 Low-flow system

70 60 50

High-flow system 40 30 20 -20

-15

-10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 62. Assumed control characteristics for the two systems. The characteristics are such that, in principle, the control valve must be fully open at the design outdoor temperature of -20 °C, and fully closed for an outdoor temperature of +20 °C, provided that the systems are not afflicted with any deviations. As the air heater in the simulations is based on the measured properties of a real heater, it has not been desirable to simulate a smaller heater, as this would therefore not be based on true measured data. In addition, no properties of any form of heat recovery equipment have been measured, and so no heat recovery equipment is used in the simulations, which leaves the air heater to provide the entire temperature rise of the incoming air. This explains the need for a relatively high water supply temperature, particularly in the low-flow systems. It should perhaps be added that the water supply temperature is defined as being the incoming water temperature on the primary side, while the inlet temperature consists of the water temperature at the inlet of the air heater itself, on the secondary side of the valve group, after control by the valve group. The return temperature is the same on both the primary and secondary sides. Flow levels The magnitude of the flow depends on the type of balancing used. In the high-flow system, the necessary primary flow (and secondary flow) is about 1.2 m³/h with the control valve fully open. The necessary flow in the low-flow system is only half as much, i.e. about 0.6 m³/h with a fully open control valve. It is these flow rates that determine the necessary supply temperatures for the design cases. Pressure levels The available differential pressure across each valve group is assumed to be 30 kPa in the high-flow system under design conditions. For the low-flow system, the differential pressure is assumed to be only one quarter of this, i.e. 7.5 kPa, which is due to the fact

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that the rate of flow is only half, with fully turbulent flow being assumed. This is not necessarily correct, but is probably very close. However, the main thing is that the driving force for the flow should be in such a relationship to the flow that there is a certain amount of capacity available for operation of the valves in the valve group. Too high a differential pressure at a low flow rate would mean that the balancing valve on the primary side of the valve group would have to be almost completely closed, which would make it particularly sensitive to deviations. The differential pressure is assumed to be constant, regardless of the valve opening of the control valve. However, this is not particularly likely to occur in reality, and so some simulations have been run with varying differential pressures. However, the difference is really related only to the authority of the control valve, as described further on in Chapter 7. 5.2.5 Selection of components Most of the components represented in the simulations have a characteristic that has been measured from physical components in the test rig. The only exception to this consists of the control valves, which have a more theoretical characteristic when used in the simulations, and the balancing valves, the characteristics of which are based on manufacturers' product data. Control valves The control valves used in the simulations have either logarithmic, linear or optimum characteristics. The optimum characteristic varies from case to case, but the other two are constant, as shown in the diagram below. The logarithmic characteristic is somewhat modified, in order to enable the valve to close fully.

Relative kv value (kv/kvs ) [-]

1.0 0.9 0.8 0.7 0.6 0.5

Linear

0.4 0.3

Logarithmic

0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 63. Linear and logarithmic valve characteristics. The reason for using theoretical valve characteristics is to make the presentation a little more general.

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In the reference cases, the control valve is assumed to have a kvs value of 4.0 m³/h, which is therefore its maximum capacity. However, some simulations have been run using other sizes of control valves. Balancing valves The characteristic of the balancing valves used in the simulations is the same as for the balancing valves used when making the measurements, and is shown in the following diagram. 16 14 kv value [m³/h]

12 10 8 6 4 2 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 64. Balancing valves' characteristic. The pump The measured pump characteristic was shown in Chapter 4 (Figure 49). The same pump curves have been used in the simulations, with pump characteristic No. 1 being used for the low-flow systems, and characteristic No. 2 being used for the high-flow systems. The air heater The air heater properties have been measured, and are described in Chapters 3 and 4. The Flowmaster program requires the air heater characteristics to be specified in the form of the air heater efficiency (i.e. the maximum efficiencies on the air and water sides). This characteristic is shown in the following diagram.

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Efficiency [-]

1.0 0.9

Air side

0.8

Water side

0.7

Maximum

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

Flow [m³/h]

Figure 65. The air heater efficiencies. 5.2.6 Studied deviations The deviations simulated in Chapter 7 are described below. • Actual valve characteristics No control valve has an optimum characteristic suited exactly to the system which it is to control. It can therefore be interesting to display the difference in the effect on the system between a “real” characteristic and an optimum characteristic. In this case, the “real” characteristic consists either of an out-and-out linear characteristic, or of a somewhat modified theoretical logarithmic characteristic, as shown in Figure 63. • Deviations in settings of the balancing valves Balancing affects both the static and the dynamic characteristics of the system. The systems considered in these simulations have two balancing valves (only one in the direct connection arrangement) that can be incorrectly set. The effect of so doing is therefore investigated for each of the two valves: - Balancing valve on the primary side (I1) Adjustment of I1 is intended to provide the correct maximum flow through the air heater when the control valve is fully open. However, in the case of the district heating connection, the most important aspect is to ensure that no flow passes through the bypass connection when the control valve is fully open. In order to investigate the effect in this respect of incorrect setting of the valve, simulations is being run with the valve opening of the valve departing by ± 0.1 from its correct setting. For the particular type of valve concerned, this is equivalent to a mis-setting of less than half a turn of the valve knob. - Balancing valve on the secondary side (I2) The setting of I2 is intended to ensure that the flow in the recirculation connection (in those valve groups that have such a connection) is correct. In exactly the same

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way as for I1, the effect of incorrectly setting I2 by a ± 0.1 deviation in its valve opening from the correct setting has been investigated. • Variation in available differential pressure The differential pressure across a valve group changes as the operating conditions change, which itself constitutes a deviation from the reference case, which assume constant differential pressure. In the simulations, it is assumed that the magnitude of this variation depends on the primary flow rate. At maximum flow, the differential pressure is the same as in the reference case, but the pressure rises as the flow rate is reduced, in accordance with the following equation: & 2 ∆p T = ∆p 0 − k ⋅ V w ,1 where ∆p T ∆p 0 k & V w ,1

= = = =

(32)

Available differential pressure [kPa] Pump pressure [kPa] Coefficient of flow resistance (assumed to be constant) [kPa/(m³/h)2] Primary flow [m³/h]

The pump pressure is assumed to be twice as high as the available differential pressure in the reference case. • Variation in water supply temperature The system supply temperature affects the results, both in terms of the necessary P-band width and of the return temperature. For this reason, the simulations have also investigated the effect of constant supply temperature as against a controlled supply temperature, which has been done by performing a number of step change response simulations at different outdoor temperatures and supply temperatures. • The effect of a dirty air heater As the air heater is heating outdoor air, its capacity will eventually be reduced by the accumulation of dirt on it. This has been simulated by assuming a 10 % reduction in its UA value, thus changing its efficiency. 5.2.7 Planning the simulations The results of the radiator simulations are presented in some extend in the form of duration diagrams and the same approach is desirable when it comes to simulation of air heaters with valve groups. Although the advantage of the duration diagram, used in the simulation of radiator system, is that it consists of weighted measured values for the 10-year period from 1983 to 1992, it also involves a certain drawback as the lowest outdoor temperature in that diagram is only -15 ºC. However, the air heater is designed for an outdoor temperature of -20 ºC. In order to be able to calculate return temperatures for this design outdoor temperature, a duration diagram for 1985, which was a cold year with a lowest outdoor temperature of -21 °C, has been used in these simulations. Over the whole year, the mean value of the outdoor temperature was 6.1 ºC: ignoring the effect of outdoor temperatures above +20 ºC reduces this mean value to 5.7 ºC. The results of the simulations are presented in accordance with the following pattern: 98

5 SIMULATION - PLANNING

7.2 Optimum valve characteristic 7.2.1 Reference case 7.2.2 Different valve size 7.2.3 Varying available differential pressure 7.2.4 Summary 7.3 Actual valve characteristic 7.3.1 Linear and logarithmic valve characteristics 7.3.2 Different valve size 7.3.3 Summary 7.4 Deviations in setting of balancing valve 7.4.1 Primary side balancing valve 7.4.2 Secondary side balancing valve 7.4.3 Summary 7.5

The effect of variations in water supply temperature

7.6

The effect of a dirty air heater

The above headings form a rough framework of the structure of the simulations. Additional simulations are also described in some of the sections in order to illustrate the performance of subsystems or the effects of changes of a particular parameter.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

6

SIMULATION AND RESULTS – RADIATOR SYSTEM

6.1

Performing the work

The planning of the simulations is described in the previous chapter. The simulation results described in this chapter have been used to compare the performances of various system configurations with each other. There are really two types of comparisons that are of interest: those between systems of the same type, with and without deviations, and comparisons of dissimilar systems, but with similar deviations. Each section in this chapter is followed by a summary of the particular cases concerned. The architecture of the simulated system has been shown in diagrams in earlier chapters, but is shown here again in order to facilitate the presentation in this chapter. 5

4

3

2

1

II

II

Radiator valve I

I

Branch valve Pump Heat Ex.

A

B

Riser valve Main valve

Figure 66. The architecture of the simulated radiator system. A and B indicate the two risers, while I and II indicate the positions of the branches on the risers. Numerals 1-5 indicate the positions of the radiators on the branches.

6.2

The basic cases

Regardless of how the system is made up; the pressure levels that are used, whether thermostatic radiator valves are fitted or what the pump characteristic is, the temperature levels will remain the same if there are no incorrect settings and no deviations and the system is not affected by any disturbances. These systems constitute the basic cases in the simulations. In Chapter 5 the control curve characteristics was shown for the respective reference systems and also how the return temperatures were affected. Figure 67 below shows the same thing, but in the form of a duration diagram. As before, the supply temperature is indicated by “Supply”. the return temperature by “Return”, the high-flow system by “High” and the low-flow system by “Low”. In addition, the outdoor temperature is indicated by “Out” and the mean value of indoor temperature (in all 20 rooms) by “Room (mean)”.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

80 70 60

Supply, Low

Temperature [°C]

50 40

Supply, High

30

Return, Low

Return, High Room (mean)

20 10

Out

0 -10 -20 0

1460

2920

4380

5840

7300

8760

Time [h]

Figure 67. Duration diagram for the reference systems (no deviations). It is with these “ideal” curves that many of the comparisons in this chapter have been made. The weighted mean value of the return temperature throughout the year (or, strictly, during the period while heat was required) amounted to 28.6 °C for the high-flow system and 26.3 ºC for the low-flow system. The reference systems were, of course, designed for the design rating case, when the water temperatures are at their highest. As the water temperatures fall, in response to rising outdoor temperatures, the physical properties of the water change, with the result that flows and thermal properties of the system are also changed. In this respect, it is the branches furthest out in the systems that are most affected, as they are furthest from the pump and the heat source, and so suffer the greatest risk of effects to the flow. The overall result of this is that, in the basic cases, the indoor temperature will not be exactly 20 °C as the outdoor temperature rises. Figure 61 shows how heat release from each branch of the systems changes with the outdoor temperature, due to changes in the density, specific thermal capacity and kinematic viscosity of water as a function of temperature. The change is related to the heat releases of the systems if the properties of the water had been assumed to be constant, and to the values applicable in the design case.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

High-flow system

0.8 0.6 0.4 0.2

AI

0.0

AII BI

-0.2

BII

-0.4

Low-flow system

1.0 Change in heat release [% ]

Change in heat release [% ]

1.0

-0.6 -0.8

0.8 0.6 0.4 0.2

AI

0.0

BI

-0.2

AII

-0.4 -0.6

BII

-0.8 -1.0

-1.0 -15

-10

-5

0

5

10

-15

15

-10

-5

0

5

10

Outdoor temperature [°C]

Outdoor temperature [°C]

Figure 68. The effects on the respective branches of changes in the flow and thermal properties of the water in the systems, as a function of outdoor temperature (which in turn affects the water temperatures). It can be seen that the low-flow system is the more affected by changes in the physical properties of the water, with this effect being particularly noticeable for the furthermost branches.

6.3

Incorrect valve settings

One way of investigating the importance of the valve settings for system function and performance is to see what happens if a valve in the system is not correctly set. It could, for example, have been tampered with by users, have been incorrectly set from the start or have failed. 6.3.1 Fully closed radiator valve In the simulations, one valve in the systems assumes not to be correctly set. This is valve AI1, which is closest to the pump. It is ringed in Figure 69.

Figure 69. System schematic, showing radiator valve AI1.

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What usually happens is that the radiator valves close, or are closed, somewhat more than their adjusted setting, as this is a facility which is often permitted to the user. In addition it can, of course, occur automatically if the radiator has a thermostatic valve. Closure of a radiator valve has the effect of moving the operating point on the pump curve upwards (see Chapter 2), which reduces the total flow in the system and increases the pump pressure. This increases the differential pressure across all the risers, and therefore also across all the branches, and so finally across all the radiators. This increased differential pressure increases the flow through the other radiators, i.e. through all except that of which the valve has closed. The higher flow rate through the radiators increases their rate of heat release and also increases the water return temperature. The magnitude of the effect on the room temperature and on the return temperature depends on the design of the system. The following text therefore discusses the effects of a completely closed radiator valve on different system arrangements. The reference system The following duration diagrams show how the room temperature and return temperature in the reference systems are affected by a completely closed radiator valve (AI1). The diagrams do not show the supply temperatures, as these are the same for the basic cases. 45 40 35 Return, High Return, Low

Temperature [°C]

30 25

Room (mean), High Room (mean), Low

20 15 10

Out

5 0 -5 -10 -15 0

730 1460 2190 2920 3650 4380 5110 5840 6570 7300 8030 8760 Time [h]

Figure 70. The effect of a completely closed radiator valve (AI1) on the reference systems. In comparison with the basic case, the mean annual value of return temperature increases by 0.2 ºC in both systems. Energy consumption during the year falls by 4.4 % in the high-flow system, and by 4.1 % in the low-flow system. If there was no interaction between the radiators in the systems, the reduction ought to have been

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

simply 5 %, to reflect the fact that one radiator out of 20 was fully closed. This means, therefore, that the heat release from the remaining 19 radiators increases by about 0.7 % in the high-flow system, and by about 0.9 % in the low-flow system. Figure 71 shows the effect on the distribution between the branches. The diagram shows the change in heat release from each branch. It must be pointed out that the change in heat release from branch AI is based on the four radiators connected to the branch, with unaltered valve settings. This means that the heat release from the radiator with the closed valve has not been included when calculating the change in total heat release from the branch. This applies also in all following presentations of the effect of a closed radiator valve. High-flow system

4 3 2

AI

1

AII BII BI

0 -15

-10

-5

0

5

Low-flow system

5 Change in heat release [% ]

Change in heat release [% ]

5

4 3 2

AI AII

1

BII

BI

0 10

15

Outdoor temperature [°C]

-15

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 71. Changes in the heat release from the respective radiator branches in both system types, in response to closure of valve AI1. Note that the change in heat release from branch AI does not include the loss of heat output from radiator AI1, to which the closed valve is fitted. It can be seen that the overall heat release increases, particularly from the other radiators connected to the branch to which the closed valve is connected. The next greatest increase in heat release is obtained from the other branch on the same riser, while the branches connected to riser B are least affected. Reference system with radiator valve BII5 closed It can be interesting to see what the effect is of the position of the closed valve in the system. It turns out that, if the valve at the far end of the system (BII5) is fully closed, the effect is marginally greater than that of closing valve AI1. Figure 72 shows the change in heat release from each branch.

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High-flow system

4 3 2

BII

1

BI AII AI

0 -15

-10

-5

0

5

Low-flow system

5 Change in heat release [% ]

Change in heat release [% ]

5

4 3 BII

2

BI

1

AII AI 0

10

15

Outdoor temperature [°C]

-15

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 72. Changes in the heat release from the respective radiator branches in both system types, in response to closure of valve BII5. It must be pointed out that the position of the branch in the system does not have any effect: in other words, it does not matter which of the radiator valves at the far ends of the branches are closed in this respect. The effect on the branch concerned, and on the other branches, remains the same. This is due to the fact that the system uses branch and riser valves, which ensure that the differential pressure is the same across all the branches after the respective branch valve. To some extent, it is namely the magnitude of the differential pressure across the valves that determines their effect on the system. This will be explain further on. Reference system without branch or riser valves The purpose of branch and riser valves is primarily to facilitate balancing, although they can also have an adverse effect in determining the response of the system to incorrect settings. The effect on return temperature and energy consumption is only slightly less if the system does not have branch and riser valves, although the spread between branches is very much less. This is shown in the following diagram.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM High-flow system

4 AI

3

AII BI BII

2

Low-flow system

5 Change in heat release [% ]

Change in heat release [% ]

5

1 0

4 AII 3

AI

2

BI BII

1 0

-15

-10

-5

0

5

10

15

-15

-10

Outdoor temperature [°C]

-5

0

5

10

Outdoor temperature [°C]

Figure 73. Changes in the heat release from the respective radiator branches in both system types, in response to closure of valve AI1. The system has no branch or riser valves. It can be seen from the diagram that there is approximately the same increase in heat release from all the branches. However, the differences between the branches is greater in the cases where the systems have branch and riser valves (see Figure 71). This is due to the fact that, generally, the differential pressure across the radiator valves is less in the systems having these valves. Reference system with low balanced differential pressure Chapter 2 showed that a low balanced differential pressure increased the interaction between the radiators, and the same applies for the interaction between the branches in the system. However, the simulations do not show any greater differences between a low balanced differential pressure and a high balanced differential pressure. Relative to the basic case, the increase in weighted return temperature is 0.2 °C in the high-flow system and 0.3 °C in the low-flow system. The increase in energy output from the other radiators is somewhat greater than in the reference case: 0.7 % in the high-flow system and 1.1 % in the low-flow system. Analysis of the heat release from the branches shows the differences between low balanced and high balanced differential pressures somewhat more clearly. Figure 74 shows that the interaction between the branches is greater in the low balanced differential pressure case (cf. Figure 71).

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High-flow system

4 3 AI 2 1

AII BII BI

0 -15

-10

-5

0

5

Low-flow system

5 Change in heat release [% ]

Change in heat release [% ]

5

4 AI 3 2

AII

1 BII BI 0

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 74. Changes in the heat release from the respective radiator branches in both system types, in response to closure of valve AI1. The balanced differential pressure is low. Reference system with a pressure-controlled pump The pump characteristic is a further parameter that affects the sensitivity of the system to incorrect settings. The simulations used a pump without pressure control. If a pressure-controlled pump (as defined in the simulations) is used, there will be no change in the pressure rise across the pump if the flow in the system is changed. This is otherwise one of the causes (i.e. with a non pressure-controlled pump) that is responsible for the differential pressure across the radiators changing in response to an incorrect setting of any of the valves in the system. The results of the simulation show that, in both systems, the return temperature rises by 0.1 °C, which is, in turn, 0.1 ºC lower than would have been the case if a pump without pressure control had been used. The increase in the amount of thermal energy supplied by the other radiators in the system over the year amounts to 0.5 % for both systems. The effect on heat release from the respective branches is shown in the diagram below.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

High-flow system

4 3 2 AI 1

AII BI BII

0 -15

-10

-5

0

5

Low-flow system

5 Change in heat release [% ]

Change in heat release [% ]

5

4 3 2 AI 1

AII BI BII

0 10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 75. Changes in the heat release from the respective radiator branches in both system types, in response to closure of valve AI1. The systems pumps are pressure-controlled. The difference between the high-flow and low-flow systems in this respect is quite small. A comparison with Figure 71 shows that the interaction between the branches is less if the pump is pressure-controlled. Reference systems with other pipe pressure drops Chapter 2 described, in principle, how the pipe pressure drop affects the interaction between the radiators in a system. In order to exemplify this, simulations have been run of the different systems with “swapped-over” pipe pressure drops: i.e. the high-flow system was simulated using the pressure drops previously employed for the low-flow system, and the low-flow system was simulated with the pressure drops as for the high-flow system. The results showed that, in the high-flow system, the return temperature was the same as if the system had its “normal” pipe pressure drops, while in the low-flow system, on the other hand, the return temperature did drop slightly, although by less than 0.1 °C. This means that the amount of energy released by the high-flow system remained unaltered, while that released by the low-flow system decreased by 0.2 percentage points. Figure 76 shows how the heat released by the respective branches changed, relative to the basic case.

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High-flow system

4 3 2 AI

1

Low-flow system

5 Change in heat release [% ]

Change in heat release [% ]

5

AII

4 3 AI 2 AII 1 BII BI

BII BI 0

0 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 76. Changes in the heat release from the respective radiator branches in both system types, in response to closure of valve AI1. Pipe pressure drops have been “exchanged”. Comparison with Figure 71 shows that a lower pipe pressure drop reduces the interaction between the radiators on the branch affected (AI). This applies, too, for the other branch (AII) on the same riser, although there is only a very slight difference between Figure 71 and Figure 76 in this respect. As far as the change in heat release from the radiators connected to riser B is concerned, the figures show that the interaction is less with the higher pipe pressure drop. This is due to the fact that a high pipe pressure drop also gives rise to a higher differential pressure across certain parts which, in turn, reduces the effect of a flow change in the system (see Chapter 2). The effect on system sensitivity of the relationship between the pipe pressure drop and the differential pressure is described in more detail further on in the summary (Section 6.3.6). Reference systems with thermostatic radiator valves The effect of a closed valve can be reduced through the use of thermostatic valves on the radiators. This is indicated by the fact that the return temperature increases by only 0.1 ºC in this case, whether for the high-flow or the low-flow system. The amount of energy released by the other radiators during the year increases by only 0.4 % in the high-flow system and by only 0.3 % in the low-flow system, both as referred to the basic case. There is also less interaction between the radiators connected to the branch concerned, and also between the branches, as shown by Figure 77.

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High-flow system

4 3

AI

2

BII BI

Low-flow system

5 Change in heat release [% ]

Change in heat release [% ]

5

AII

1 0

4 3

BII AII

2

AI BI

1 0

-15

-10

-5

0

5

10

15

Outdoor temperature [°C]

-15

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 77. Changes in the heat release from the respective radiator branches in both system types, in response to closure of valve AI1. The system is fitted with thermostatic radiator valves. The reason for the effect being least in the low-flow system in this case is that the P-band of the thermostats on this system is narrower, which is in turn due to the fact that the valves are more closed than in the high-flow system. In other words, less of the valve head is available for control. Another contributing reason is that the radiators in the low-flow system are more sensitive to flow changes as described by Equation (9) in Chapter 2. 6.3.2 Fully open radiator valve The previous section described the effects of a fully closed radiator valve, which is quite a normal case. However, although it is not desirable for users to be able to open the valves more than the setting to which they have been adjusted during balancing, this can happen. Apart from the fact that some handy persons will be able to manipulate the valves (i.e. the radiator flow balancing valves), there is nothing to say that the valve has been correctly set from the start. If a radiator valve is opened, the overall system characteristic will be changed in such a way as to move the operating point downwards on the pump curve (see Chapter 2). This will have the effect of reducing the pump pressure and increasing the total flow, thus also increasing the pipe pressure drop in the system. The differential pressure across all the risers falls, reducing the differential pressure across all the branches and, finally, across all the radiators. In order to make this a little clearer following Diagram is shown.

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Differential pressure

Pump characteristic

Old system characteristic New system characteristic

Old differential pressure over radiator valve

Old pipe pressure drop

New differential pressure over radiator valve

Pipe characteristic

New pipe pressure drop

Flow

Figure 78. Change in the differential pressure across valves when the system characteristic is changed due to the effect of opening one or more of the valves. The lower differential pressure results in the flow through the radiators falling, with the exception of that radiator of which the valve has been opened. This reduced flow through the radiators reduces the amount of heat released by them, and also reduces the return temperature. However, the increased flow through the radiator with the opened valve results in a significant increase in the amount of heat released by it and in the return temperature, with the magnitude of these effects on the room temperature and the system return temperature depending on the room and system design. The following analysis therefore considers the effects of a fully open radiator valve on various types of systems. Reference systems with radiator valve AI1 fully open The duration diagram below shows how the room temperatures and return temperatures in the reference systems are affected by a fully open radiator valve (AI1).

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM 45 40 35

Return, High

Temperature [°C]

30

Return, Low

25

Room (mean), High

20

Room (mean), Low

15 10

Out

5 0 -5 -10 -15 0

730 1460 2190 2920 3650 4380 5110 5840 6570 7300 8030 8760 Time [h]

Figure 79. The effect of a fully open radiator valve (AI1) in the reference systems. The diagram shows that the return temperature in the low-flow system is quite noticeably affected by the fully open radiator valve. The mean annual value of the return temperature in the high-flow system is 28.9 ºC, while in the low-flow system it is 28.2 ºC. This means that, compared with the basic case, the respective increases are 0.3 ºC and 1.9 ºC. The fully open radiator valve increases the total flow in the high-flow system by 3 %, and by no less than 10 % in the low-flow system. Nevertheless, in both cases, the amount of thermal energy released over the year declines: by 2.2 % in the high-flow system and by 6.1 % in the low-flow system. The differences between the two systems are due primarily to two factors. Most of the effect is due to the fact that the radiators in the low-flow system are considerably more sensitive to changes in the flow, which means that there are significant changes in the amount of heat released and in the return temperature when the flow changes in this system. In addition, there is the fact that the differential pressure across the open valve does not fall as much in the low-flow system as it does in the high-flow system, which in turn means that the flow through the valve and radiator increases more in the low-flow system. This is due to some extent to the low pipe pressure drop in the low-flow system. It can be seen from Figure 78 that a low pipe pressure drop results in less reduction of the differential pressure across an opened valve, which means that the flow through the valve increases more. The simulations showed that the effect of an open valve in either a high-flow or a low-flow system is such that it “steals” such a substantial amount of the flow through the branch that the heat release from the branch concerned is the lowest of that from all the branches in the system. This can be seen in Figure 73, which shows the change in the heat release from each branch in the systems. Note that this change is based on the

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

heat release from all radiators on the branches, i.e. including the radiator of which the valve is fully open. High-flow system BI BII -2

AII

-4

Low-flow system

0 Change in heat release [% ]

Change in heat release [% ]

0

AI

-6 -8 -10

-2 BI BII

-4 -6 -8

AII AI

-10 -15

-10

-5

0

5

10

15

-15

-10

Outdoor temperature [°C]

-5

0

5

10

15

Outdoor temperature [°C]

Figure 80. Changes in the heat release from the respective radiator branches in both system types, when AI1 is fully opened. It can be seen from the diagram that it is the heat release from branch AI, carrying the fully open radiator valve AI1, that is most affected.. The next most affected branch is AII, which is connected to the same riser as AI. Riser B is least affected, with more or less insignificant differences between the branches on this riser. It can also be seen from the diagram that the differences between all four braches are considerably less in the high-flow system than in the low-flow system. Reference systems with radiator valve BII5 fully open In exactly the same way as for the case for the closed radiator valve, it can be interesting to study the effect of where the fully open valve is in the system. If, instead of valve AI1, it is valve BII5 that is fully opened, the weighted mean annual value of return temperature becomes 28.8 ºC in the high-flow system and 27.3 ºC in the low-flow system, being increases of 0.2 ºC and 1.0 ºC respectively in comparison with the basic case. Energy emissions during the year falls by 0.7 % and 2.3 % respectively. The difference between this case, and the effects of opening valve AI1, are quite considerable, and particularly in the low-flow system. In other words, the system is less sensitive to a fully open valve if the differential pressure across the valve is low. The interaction between the branches in this case is shown in Figure 81, which should be compared with Figure 80 above.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

High-flow system

AI AII

-4

Low-flow system

0 Change in heat release [% ]

-2

BII BI

-6 -8 -10

-2 -4 BII -6

AI

-8

AII BI

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 81. Changes in the heat release from the respective radiator branches in both system types, when BII5 is fully opened. Reference systems without branch or riser valves The branch and riser valves tend to reduce the effect of incorrect settings of this type, as is shown by the following duration diagram, which represents the case where the simulated systems are not fitted with branch or riser valves (cf. Figure 79). 45 40 35

Return, High

30 Temperature [°C]

Change in heat release [% ]

0

Return, Low

25

Room (mean), High

20

Room (mean), Low

15 10

Out

5 0 -5 -10 -15 0

730 1460 2190 2920 3650 4380 5110 5840 6570 7300 8030 8760 Time [h]

Figure 82. The effect of a fully open radiator valve (AI1) in the reference systems, without branch or riser valves.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The return temperature during the year amounted to 29.2 ºC in the high-flow system and 29.0 °C in the low-flow system, these values being 0.3 ºC and 0.8 °C respectively higher than the return temperatures if the systems had been fitted with branch and riser valves. Energy emissions decreased by 2.9 % in the high-flow system and by 7 .0 % in the low-flow system, in comparison with the basic case, and so being 0.7 and 0.9 percentage points respectively lower than the case for systems having branch and riser valves. It can therefore be seen that the use of branch and riser valves reduces the rise in return temperature, and particularly in the low-flow system. There is also less effect on energy release if branch and riser valves are used. However, heat release from the branch concerned is stabilised for the system without such valves, although the effect on the other branches increases, as shown in Figure 83 below. High-flow system

AI

-2

BI

BII

-4

Low-flow system

0 Change in heat release [% ]

Change in heat release [% ]

0

AII

-6 -8 -10

-2

AI

-4 -6 BI

BII

-8

AII

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

15

Outdoor temperature [°C]

Figure 83. Changes in the heat release from the respective radiator branches in both system types, when AI1 is fully opened. The systems have no branch or riser valves. The reason for there being very little effect on heat release from the branch having the radiator with the fully opened valve is due to the fact that the differential pressure across the opened valve is high, and so there is a high flow through it, which compensates for the reduction in flow through the other radiators connected to the branch. At the same time, this also means that the return temperature from the branch increases. Further, the increased total flow results in an increase in the pipe pressure drop, which therefore acts to reduce the differential pressure across the other branches in the system, and thus explains the increased interaction with the other branches, in comparison with the case where branch and riser valves were used. Reference systems with low balanced differential pressure A high differential pressure across the opened valve seems to result in substantial changes in flow. The following duration diagram is therefore shown for comparison, showing how the room temperature and return temperature are affected by fully opening

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

radiator valve AI1 in a system having a low balanced differential pressure (2 kPa across the furthermost radiator). 45 40 35

Return, High

Temperature [°C]

30

Return, Low

25

Room (mean), High

20

Room (mean), Low

15 10

Out

5 0 -5 -10 -15 0

730 1460 2190 2920 3650 4380 5110 5840 6570 7300 8030 8760 Time [h]

Figure 84. The effect of a fully open radiator valve (AI1) in the reference systems, with low balanced differential pressure. The mean annual value of the return temperature is 28.8 ºC in the high-flow case and 27.1 ºC in the low-flow case, equivalent to increases of 0.2 ºC and 0.8 ºC respectively in comparison with the basic case. It is quite clear that, particularly in the low-flow system, the return temperature is affected less in this case than it would be in a system with a high differential pressure (cf. Figure 79). In addition, there is also less reduction in energy emission in comparison with the basic case: 1.6 % in the high-flow system and 4.7 % in the low-flow system. Figure 85 shows the reduction in heat release from each branch of the system.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

High-flow system BI BII AII

-2

AI

-4

Low-flow system

0 Change in heat release [% ]

Change in heat release [% ]

0

-6 -8 -10

BI BII

-2 -4

AII

-6 -8

AI

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 85. Changes in the heat release from the respective radiator branches in both system types, when AI1 is fully opened. The systems are balanced with low differential pressures. Reference systems with pressure-controlled pumps The use of a pressure-controlled pump increases the return temperature in the high-flow system by 0.4 ºC, and in the low-flow system by 2.1 ºC, when AI1 is opened, which temperatures are 0.1 ºC and 0.2 ºC respectively higher than if the systems did not have pressure-controlled pumps. Compared with the basic case, the reductions in energy emission are 2.0 % in the high-flow system and 4.7 % in the low-flow system, which are smaller changes than in the case when the systems do not have pressure-controlled pumps. This indicates that the interaction within the system is reduced through the use of a pressure-controlled pump, as can be seen by the interaction between the branches illustrated in Figure 86.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

High-flow system BI BII

-2

AII

-4

Low-flow system

0 Change in heat release [% ]

Change in heat release [% ]

0

AI

-6 -8 -10

BI -2

BII

-4 -6

AII

-8

AI

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 86. Reduction in the heat release from the respective radiator branches in both system types, when AI1 is fully opened. System pumps are pressurecontrolled. It could be seen from Figure 75 that, if a radiator valve is closed, the interaction between the radiators and the branches is reduced if the system has a pressure-controlled pump, resulting in a lesser increase in the return temperature. If, instead, the valve is fully opened, there is the same effect in terms of reducing the interaction between the radiators and the branches, but the return temperature of the system increases. This is due to the fact that the differential pressure across the opened valve does not decreases as much if the pump pressure rise is maintained constant. Reference systems with “exchanged” pipe pressure drops What is the effect of the pipe pressure drop on system sensitivity in the case of a fully open valve? To investigate this, simulations were run of reference systems having “exchanged” pipe pressure drops, in exactly the same way as for the case with a closed valve. In other words, the high-flow system was simulated as having the pipe pressure drops of the low-flow system, while the low-flow system was simulated with the pipe pressure drops of the high-flow system. The results show that the return temperature increases only slightly in the high-flow system (by less than 0.1 °C), in comparison with the case where it has its normal pipe pressure drop. The reverse applies for the low-flow system, with the return temperature being as high as in the case with its normal low pipe pressure drop. Even so, the difference amounts to only 0.3 °C. The emission of thermal energy from the high-flow system is reduced by 1.8 %, while that from the low-flow system is reduced by 7.9 %, both as related to the basic case. These values are respectively 0.4 percentage points less, and 1.8 percentage points more, than in the cases with normal pressure drops. The changes in heat release from the respective system branches are shown in Figure 87.

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High-flow system

Low-flow system

0 BI BII

-2

AI

Change in heat release [% ]

Change in heat release [% ]

0

AII

-4 -6 -8

BI

-2

BII

-4 -6 AII

-8

AI -10

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

15

Outdoor temperature [°C]

Figure 87. Reduction in the heat release from the respective radiator branches in both system types, when AI1 is fully opened. The pressure drops in the two systems have been “exchanged”. The diagram shows that a lower pipe pressure drop clearly reduces the interaction in the system, while a higher pipe pressure drop increases the interaction. Reference systems with thermostatic radiator valves The condition here, for analysis of the effect of a fully open radiator valve, is that the valve is just fully open, regardless of other conditions. As the heat release from all the other radiators drops as a result of the open valve, any thermostats fitted to them have no effect on their performance: they cannot open the valves by more than the setting to which the valves have been balanced. 6.3.3 Deviations from the correct setting of branch valve The branch valves facilitate balancing the system radiator valves, as the radiator valves connected to each branch can be individually adjusted. The branches can then be balanced with each other by means of the branch valves. This means that, provided that they are correctly balanced with respect to each other, the radiator valves do not need to be re-adjusted if the flow to their branch should be changed during operation: instead, the branch valve can be used to increase or decrease the flow in the branch as necessary. However, changing the setting of any of the branch valves naturally has an effect on the rest of the system. This section is devoted to showing the effects of the branch valves on the system if this setting should be changed or be incorrect. The cases considered are those for incorrect settings of ± 0.25 of the valve opening of the valve from the basic case condition. These are indicated as “reduced setting” (- 0.25) and “increased setting” (+ 0.25). The particular valve concerned, and the effects of which have been considered in the simulations, is valve AI, the position of which is shown in the following diagram.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

AII

BII

BI

AI

Figure 88. The position of branch valve AI. Reference systems with reduced settings of the branch valve Closing a branch valve reduces the flow through the branch and through the system which, together with a possible resulting increase in the pump pressure (depending on whether and/or how the pump is controlled), results in an increase in the differential pressure across the other branches. The flow through the radiators on the branch concerned is reduced, while that through the other radiators on the system is increased. If the valve opening of branch valve AI is reduced by 0.25 relative to the correct setting, the weighted annual mean value of the system return temperature falls by 0.1 ºC in the high-flow system, and by 0.2 ºC in the low-flow system, both as relative to the basic case. The diagrams below show how the thermal output power changes in the branches. Over the year, the total output of thermal energy falls by 0.8 % in the high-flow system, and by 1.3 % in the low flow system. High-flow system

5 AII BI

0

BII

-5

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

AI

-10

5 AII

BI

0

BII

-5 AI -10

-15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 89. Change in thermal output powers from the branches in response to partial closure of branch valve AI. If, instead, it is branch valve BII of which the valve opening is reduced by 0.25, the return temperature remains virtually unchanged as related to the basic case, and this applies for both the high-flow and the low-flow systems. The change in the amount of

121

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

thermal energy released over the year also remains essentially negligible for both systems (less than 0.1 %). This is also indicated by the fact that the interaction between the branches is almost non-existent, as shown in the diagrams below. High-flow system BI AII

5

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

AI BII

0

-5

-10

BI AII

5

AI BII

0

-5

-10 -15

-10

-5

0

5

10

15

-15

-10

Outdoor temperature [°C]

-5

0

5

10

15

Outdoor temperature [°C]

Figure 90. Change in thermal output powers from the branches in response to partial closure of branch valve BII. Reference systems with increased setting of the branch valve If, instead of being closed, the valve opening of branch valve AI is increased by 0.25, the return temperature in the system increases. However, this increase is only marginal, amounting to less than 0.1 ºC for both the high-flow and the low-flow systems. The corresponding increase in energy emission is also small, being less than 0.1 % for the high-flow system and just over 0.1 % for the low-flow system. The interaction with the other branches is also more or less insignificant, as shown by the following diagrams. High-flow system

5 AI BI BII

0

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

AII

-5

-10

5 AI BI BII

0

AII

-5

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 91. Change in thermal output powers from the branches in response to increased setting of branch valve AI.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

This may seem somewhat strange; that opening a branch valve actually has less effect on the system than if a radiator valve is opened (cf., for example, Figure 80). The reason for this is that the balanced kv value of the branch valve is so high that it has hardly any effect on the system characteristic. Radiator valves, on the other hand, have a relatively low kv value after balancing, which means that they present a higher flow resistance to the system. The greater the effect that a valve has on the total flow resistance of the system (i.e. on the system characteristic), the greater will be the change in the total flow if the setting of the valve is altered, and so the greater the effect on the system. Even if an excessively large branch valve had been chosen, full opening of it would still not significantly affect the system. This has been checked by a simulation in which the kvs values of the branch valves have been set at 10 m³/h. Under these conditions, a fully opened AI branch valve would result in an increase of 0.1 ºC in the return temperatures in both systems, as compared with the basic case. Reference systems with reduced settings of the branch valve and low differential pressure If the balanced differential pressure in the system is low, the effect of closing branch valve AI becomes somewhat greater, with the return temperature of the high-flow system increasing by 0.1 ºC, and that of the low-flow system increasing by 0.2 ºC, both as compared with the basic case. Thermal energy emissions fall by 1.2 % and 2.2 % respectively. The interaction between the valves is shown in the diagrams below. High-flow system

5 AII BI

0

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

BII

-5

5

AII BI BII

0

-5

AI

AI

-10

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 92. Change in thermal output powers from the branches in response to increased setting of branch valve AI. The systems have been balanced with low differential pressures. This shows once again how the differential pressure affects the sensitivity of the system to changes in valve settings (cf. Figure 89). The lower the differential pressure, the greater the effect of a reduced valve opening on the system.

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15

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Reference systems with increased settings of the branch valve and low differential pressure If, instead of closing, the valve opening of branch valve AI increases, in a system having a low balanced differential pressure, the effect on the system is greater than it would be if the system had a high balanced differential pressure. However, this has no significant effect on the return temperatures, as they are hardly changed, and nor on the emission of thermal energy. However, the interaction between the branches increases, as shown in the following diagrams. High-flow system

5 AI 0

BI BII

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

AII

-5

-10

5 AI 0

BI BII AII

-5

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 93. Change in thermal output powers from the branches in response to increased setting of branch valve AI. The systems have been balanced with low differential pressures. It can be seen from the two diagrams that the heat release from the branch concerned (AI) changes more in a system with a low balanced differential pressure than it does in a system with a high balanced differential pressure (cf. Figure 91). The same also applies for the other branches in the system, which means that this case is not analogous with the corresponding comparison for the effect of radiator valves, where it was found that the interaction between the branches if the radiator valve if opened is less for a system with a low balanced differential pressure. 6.3.4 Deviations from the correct setting of riser valve In the same way as the setting of a branch valve can depart from the correct value, riser valves can also be set incorrectly. The terms “reduced setting” for a 0.25 reduction in valve opening, and “increased setting” for an increase of 0.25 in valve opening, are also used here. The simulations have been based on a change in the setting of riser valve A, the position of which is shown in the following diagram.

124

15

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

A

B

Figure 94. The position of riser valve A. Reference systems with reduced settings of the riser valve Partly closing a riser valve reduces the flow in the riser and in the system which, together with a possible rise in the pump pressure, results in an increase in the differential pressure across the other risers. The effect is to reduce the flow through the radiators connected to the riser of which the valve has been partly closed, and to increase the flow through the other radiators on the system. Reducing the valve opening of riser valve by 0.25, as compared with the perfect basic case, reduces the annual weighted value of system return temperature by 0.3 °C in the high-flow case, and by 0.5 ºC in the low-flow case, as compared with the basic case. The two diagrams below show the changes in the thermal emissions from the branches in the respective systems. In total, thermal emission over the year is reduced by 1.8 % in the high flow system and by 2.5 % in the low flow system. High-flow system

5 BII BI

0

AI

-5

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

AII -10

5 BII BI

0

-5

AI AII

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 95. Change in thermal output powers from the branches in response to partial closure of riser valve A. Figure 95 show that there is a significant reduction in heat release from the radiators connected to riser A, and a slight increase in heat release from those connected to riser B.

125

15

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

If, instead, it is riser valve B that is closed, the return temperatures in both cases are reduced by only 0.1 °C, with the amount of thermal energy output during the year falling by 0.4 % in the high-flow system and by 0.5 % in the low-flow system. Reference systems with increased settings of the riser valve Increasing the opening of riser valve A by 0.25 from the correct setting increases the return temperatures in both systems by only 0.1 °C. Thermal energy emission increases by 0.3 % in the high-flow system and by 0.5 % in the low-flow system. The changes in thermal output power from the respective branches in the systems are shown in the diagrams below. High-flow system

5 AI

AII

BI

BII

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

0

-5

-10

5 AI

AII

BI

BII

0

-5

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 96. Change in thermal output powers from the branches in response to partial opening of riser valve A. Slightly opening the riser valve has considerably less effect on the system than a corresponding slight closing. On the other hand, the difference in effects on the highand low-low systems is more or less insignificant. Reference systems with reduced settings of the riser valve and low differential pressure If the systems are balanced to have low differential pressures, the effect of closing riser valve A is greater than it would be if it was in systems set to have a high balanced differential pressure. The return temperature in the high-flow system is reduced by 0.3 °C, while that in the low-flow system is reduced by 0.5 °C, both as compared with the basic case. The emission of thermal energy is also reduced: by 2.2 % in the high-flow case and by 3.8 % in the low-flow case. The difference between the outputs from the respective branches is shown in the diagrams below.

126

15

6 SIMULATION AND RESULTS – RADIATOR SYSTEM High-flow system

5 BII

BI

0

-5

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

AI AII

-10

5

BII BI

0

-5 AI

AII

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

15

Outdoor temperature [°C]

Figure 97. Change in thermal output powers from the branches in response to partial closure of riser valve A. The systems are balanced for low differential pressures. Reference systems with low balanced differential pressures and increased settings of the riser valves Increasing the valve opening of riser valve A has the same effect on the return temperature in a system having a low balanced differential pressure as it does in a system having a high balanced differential pressure: in both cases, the increase in the return temperature is 0.1 °C. Thermal emission increases by 0.3 % in the high flow-case, and by 0.4 % in the low-flow case, both as compared with the basic case. The difference between the branches is shown in the following diagrams. High-flow system

5 AII

AI

0 BII

Low-flow system

10 Change in heat release [% ]

Change in heat release [% ]

10

BI

-5

-10

5 AII AI 0

BI BII

-5

-10 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 98. Change in thermal output powers from the branches in response to partial opening of riser valve A. The systems are balanced for low differential pressures.

127

15

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

This case, and the previous one above, show that the effect is greater with a low differential pressure, and that there is also some difference between the two systems. It can be seen that the low-flow system is definitely the more sensitive to a change in the setting of a riser valve. 6.3.5 Deviations from the correct setting of main valve The main valve is used to set the total flow in the system as a whole. Any change in its setting will produce a corresponding increase or decrease in the flow through the entire system: the difference between the branches will be minimal. The following cases therefore show diagrams of the change in thermal output from any branch only when there are differences between the branches. Reference systems with reduced settings of the main valve Reducing the valve opening of the main valve by 0.25 has the effect of reducing the weighted annual mean value of system return temperature by 0.4 °C in the high-flow case, and by 0.5 °C in the low-flow case, both as compared with the basic case. Over the year, thermal energy emission from the high-flow system is reduced by 1.5 %, and from the low-flow system by 1.9 %. Reference systems with increased settings of the main valve If, instead, the valve opening of the main valve is increased by 0.25, relative to the correct setting, the return temperature in both systems increases by only 0.1 °C. Thermal energy emission from the high-flow system increases by 0.4 %, and that from the low-flow system by 0.5 %. In other words, increasing the valve opening of the main valve has considerably less effect on the system than does closing it. Reference systems with reduced setting of the main valve and low balanced differential pressure In the case of systems with a low balanced differential pressure, the return temperature from the high-flow system increases by 0.5 ºC, while that from the low-flow system increases by 0.7 ºC. Thermal energy emissions increase by 1.7 % and 2.8 % respectively. Reference systems with increased setting of the main valve and low balanced differential pressure Increasing the valve opening of the main valve has the same effect on the return temperature in a system having a low balanced differential pressure as it does in a system having a high balanced differential pressure. In both cases, the increase in the return temperature is 0.1 °C. The thermal emission increases by 0.4 % in the high-flow case, and by 0.5 % in the low-flow case, both as compared with the basic alternative.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Reference systems with reduced setting of the main valve and without branch or riser valves If the systems have no branch or riser valves at all, closing the main valve has a greater effect. The mean annual return temperature of the high-flow system is reduced by 0.9 ºC, while that of the low-flow system is reduced by 1.0 ºC. Thermal energy emissions are reduced by 3.1 % and 4.1 % respectively. Reference systems with increased setting of the main valve and without branch or riser valves For systems with neither branch nor riser valves, increasing the setting of the main valve increases the return temperature in both systems by 0.2 ºC. The increase in thermal energy output is 0.7 % in the high-flow system, and 0.9 % in the low-flow system, both as compared with the basic case. The lack of branch or riser valves in the systems, in other words, means that any change in the setting of the main valve has a greater effect. This is due to the fact that, in this case, the main valve has a greater effect on the total system flow resistance. Reference systems with increased setting of the main valve and thermostatic radiator valves If the system is fitted with thermostatic radiator valves, increasing the valve opening of the main valve will be compensated by closing of the thermostatic valves. This means that, in both the high-flow and low-flow systems, the return temperature increases by less than 0.1 °C, while the emission of thermal energy increases by only 0.2 %. However, there is some difference between the branches, as shown in the diagrams below. High-flow system

0.8 0.6 0.4

BII AII BI

0.2

Low-flow system

1.0 Change in heat release [% ]

Change in heat release [% ]

1.0

AI 0.0

0.8 0.6 BII

0.4

AII 0.2

BI AI

0.0 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 99. Change in thermal output powers from the branches in response to partial opening of the main valve. The systems are fitted with thermostatic radiator valves.

129

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Branches AI and BI are least affected, and are also less affected in the low-flow system than in the high-flow system. This is due to the fact that the P-band of the thermostats is narrower in the low-flow system than in the high-flow system, due to the more closed radiator valves in the former system. Branches AII and BII are affected more in the low-flow system than they are in the high-flow system, although this is due to the fact that the basic cases, with which the systems are compared, give a room temperature that is somewhat lower than 20 °C for these two branches. This is due in turn to the fact that the properties of the water in the system change with temperature. See also Section 6.2 concerning the basic cases. 6.3.6 Summary The following table is a summary of the simulations carried out to investigate how the return temperature and the heat emission are affected by changes in the valve settings away from the correct settings for various system configurations. System

Deviation

Reference system Reference system Reference system - no branch or riser valves - low balanced diff. pressure - pressure-controlled pump - different pipe pressure drops - with thermostats Reference system Reference system - no branch or riser valves - low balanced diff. pressure - pressure-controlled pump - different pipe pressure drops - with thermostats Reference system Reference system Reference system - low balanced diff. pressure - low balanced diff. pressure Reference system Reference system Reference system - low balanced diff. pressure - low balanced diff. pressure Reference system Reference system - no branch or riser valves - no branch or riser valves - low balanced diff. pressure - low balanced diff. pressure - with thermostatic valves

AI1 closed BII5 closed AI1 closed AI1 closed AI1 closed AI1 closed AI1 closed AI1 open BII5 open AI1 open AI1 open AI1 open AI1 open AI1 open AI closed setting BII closed setting AI open setting AI closed setting AI open setting A closed setting B closed setting A open setting A closed setting A open setting M closed setting M open setting M closed setting M open setting M closed setting M open setting M open setting

Table 7.

High-flow system ∆tw,return [ºC] ∆Qsystem [%] 0 0 + 0.2 - 4.4 (+ 0.7) + 0.2 - 4.4 (+ 0.7) + 0.2 - 4.5 (+ 0.6) + 0.2 - 4.4 (+ 0.7) + 0.1 - 4.5 (+ 0.5) + 0.2 - 4.4 (+ 0.7) + 0.1 - 4.7 (+ 0.4) + 0.3 - 2.2 + 0.2 - 0.7 + 0.5 - 2.9 + 0.2 - 1.6 + 0.4 - 2.0 + 0.3 - 1.8 + 0.3 - 2.2 - 0.1 - 0.8 0 - 0.1 0 + 0.1 + 0.1 + 1.2 0 0 - 0.3 - 1.8 - 0.1 - 0.4 + 0.1 + 0.3 - 0.3 - 2.2 + 0.1 + 0.3 - 0.4 - 1.5 + 0.1 + 0.4 - 0.9 - 3.1 + 0.2 + 0.7 - 0.5 - 1.7 + 0.1 + 0.4 + 0.1 + 0.2

Low-flow system ∆tw,return [ºC] ∆Qsystem [%] 0 0 + 0.2 - 4.1 (+ 0.9) + 0.3 - 4.1 (+ 1.0) + 0.2 - 4.3 (+ 0.8) + 0.3 - 3.9 (+ 1.1) + 0.1 - 4.5 (+ 0.5) + 0.2 - 4.4 (+ 0.7) + 0.1 - 4.7 (+ 0.3) + 1.9 - 6.1 + 1.0 - 2.3 + 2.6 - 7.0 + 0.8 - 4.7 + 2.1 - 4.7 + 1.6 - 7.9 + 1.9 - 6.1 - 0.2 - 1.3 0 - 0.1 0 + 0.1 + 0.2 + 2.2 0 0 - 0.5 - 2.5 - 0.1 - 0.5 + 0.1 + 0.5 - 0.5 - 3.8 + 0.1 + 0.4 - 0.5 - 1.9 + 0.1 + 0.5 - 1.0 - 4.1 + 0.2 + 0.9 - 0.7 - 2.8 + 0.1 + 0.5 + 0.1 + 0.2

Results from simulations of valve settings departing from the correct settings.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The table shows the results for each simulated case, in the form of the change in the weighted mean value of return temperature (∆tw,return) and of the change in the amount of thermal energy supplied over the year (∆Qsystem). The values not in, or outside, brackets are based on all radiators, while those values in brackets are based on all radiators except the one affected by the particular change in the valve setting. However, these second figures have been calculated only for the cases involving closed radiator valves. The abbreviation “M” refers to the main valve. In general, the table shows that it is not until a radiator valve is opened that significant differences with the basic case, and between the high-flow and low-flow systems, occur. It also shows that a reduction in the valve opening of a branch, riser or main valve results in considerably more marked effects than does a corresponding increase in the valve opening of the valve. However, the difference between the high-flow and the low-flow systems is not particularly noticeable in these cases. In the following, these conclusions and some othert results are being discussed a little closer. Adjusting a radiator valve

50

22

45

21

Heat release [kW]

Return temperature [°C]

The simulations show that, regardless of whether a radiator valve is opened or closed, the result is to increase the return temperature and to reduce the total amount of heat emission from the radiators. This is further illustrated in the diagrams below, which apply for the reference systems at the design outdoor temperature of -15 °C. It can be seen how the return temperature and the heat emission vary with the valve opening of a radiator valve in the system. The circled positions in the diagrams indicate the points of perfect balancing of the valve in each system.

High-flow, total 40

35

Low-flow, total

High-flow, total

20

Low-flow, total 19 Outdoor temperature = - 15 °C

Outdoor temperature = - 15 °C

18

30 0.0

0.2

0.4

0.6

0.8

0.0

1.0

0.2

0.4

0.6

0.8

Valve opening of radiatorvalve AI1 [-]

Valve opening of radiatorvalve AI1 [-]

Figure 100.The effect of the valve opening of radiator valve AI1 on the system's (total) return temperature and on system’s total heat release. The effect of a closed radiator valve is relatively slight, provided that allowance is made for the fact that it effectively closes one of the radiators in the system. If there was no interaction, the thermal output power in the above diagram would be 19 kW with the radiator valve completely closed. On the other hand, the result of fully opening a radiator valve is much more noticeable, particularly in the low-flow system. Despite the fact that the flow through the particular valve increases considerably, thus raising the

131

1.0

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

system return temperature, the total heat emission from the system as a whole nevertheless declines as a result of the overall reduction of flow through the other radiators. The differences between the high-flow effects and the low-flow effects are due to several factors. Obviously, the difference in the valve settings can be assumed to be one reason. As, in general, the valves in the low-flow system arrangement are more closed than are the corresponding valves in the high-flow system arrangement, opening the valves in the low-flow system has a greater effect on the system characteristic. However, this is not decisive. Although specially modified valves are used in the low-flow system, opening a valve nevertheless results in a greater rise in the return temperature than does a corresponding valve opening in the high-flow system, (Trüschel, 1999). Instead, the true reason for this depends on primarily two factors: • The radiator characteristic in the low-flow system gives rise to high return temperatures when the flow through the radiator increases, while a reduction in the flow results in a substantial reduction in the thermal emission power (see Chapter 2). • The low pressure drops in the low-flow distribution system result in relatively high differential pressures across the open valve. This point is explained further below. Differential pressure, pipe pressure drops and pump characteristic It is clear that the differential pressure across the valve of which the setting has been changed has a considerable effect on the sensitivity of the system to such changes. In a given system, the interaction between the radiators declines with rising balanced differential pressure, but only provided that the change consists of a radiator valve closing. If, instead, the valve is opened, conditions are reversed, with the interaction increasing. This is clarified by the diagram below, which shows the results of simulations of the high-flow system with high and low balanced differential pressures. It can be seen how the change in differential pressure (i.e. as related to the reference case) across the radiator valves on a branch is affected by the balanced differential pressure (∆pmin), and by whether the valve concerned is fully open or fully closed. The relative change of differential pressure provides a measure of by how much the flow through the valve changes if the valve setting remains unchanged.

132

Relative change in differential pressure [% ]

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

100

Rad 1 closed, 2 kPa Rad 1 closed, 10 kPa Rad 1 fully open, 2 kPa Rad 1 fully open, 10 kPa

80 60 40 20 0 -20 -40 -60 -80 -100 Branch + valve

Rad 1

Rad 2

Rad 3

Rad 4

Rad 5

Figure 101.The effect of the magnitude of the balanced differential pressure on the change of differential pressure across the radiator valves connected to a branch if one valve is opened or closed. It can be seen from the diagram that, with a low balanced differential pressure, there is a relatively substantial change in the differential pressure if the valve closes, while the change in the differential pressure would be less in a system having a high balanced differential pressure. In other words, the interaction between the radiators increases on a system having a low balanced differential pressure if one of the valves on the branch closes. If, instead, the valve is opened, then the effects will be the opposite, which can be seen in the diagram by a low balanced differential pressure resulting in a smaller change in the differential pressure in the branch (and thus having less interaction effect), than would be the case with a high balanced differential pressure. The simulations also showed that opening a radiator valve on a system having a high pipe pressure drop resulted in a lesser rise in the return temperature than did opening a valve on a system having a low pipe pressure drop. What is this due to? Put simply, the return temperature depends on the magnitude of the differential pressure across the open radiator valves. The greater the pressure drop in the system, the smaller the differential pressure drop across the opened valve, and thus the lower the return temperature. As explained, the flow through an opened valve depends on the magnitude of the differential pressure after the change in the valve setting. This differential pressure can be expressed as: ∆p 2 = ∆p1 + ∆(∆p pump ) − ∆ (∆p pipe ) where: ∆p 2 ∆p1

(33)

= Differential pressure across the valve after changing the valve setting = Differential pressure across the valve before changing the valve setting

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

∆ (∆p pump ) = Change in pump pressure (= ∆p pump, 2 − ∆p pump,1 )

∆ (∆p pipe ) = Change in pressure drop up to the valve (= ∆p pipe, 2 − ∆p pipe,1 ) If a radiator valve is opened, the total flow through the system increases while the pump pressure rise normally decreases, as a result of the pump characteristic curve. This means that, in order to minimise the risk of high flow through the opened valve, thus resulting in a significant increase in the return temperature, the balanced differential pressure in the system should be set low. At the same time, the pressure drops in the system should be high, with a steep pump characteristic, thus resulting in a low differential pressure across any opened valve. Together with the radiator sensitivity, this is why the return temperature does not rise as much in the high-flow system as it does in the low-flow system. It also explains why the return temperature rises more in a system with a lower pipe pressure drop and with a pressure-controlled pump. The above reasoning is naturally somewhat artificial, and a more realistic way of limiting the effect of an open valve would presumably be to choose a small valve from the start, so that the balanced kv value does not differ too greatly from the valve's kvs value. For this reason, it is again preferable to have a low balanced differential pressure, as in this case the valve does not need to be closed so much as would be the case with a high differential pressure. Another way of achieving a low differential pressure across the radiator valve is to fit a second valve, less easily accessible, across which some of the available differential pressure can be dropped. This is why the use of branch and riser valves seems to reduce the impact of an open radiator valve. Regardless of whether the radiator valve is opened or closed, the change in differential pressure across it also affects the flow through the other valves connected to the same branch. This means that, to some extent, the change in flow in the rest of the branch is dependent on the relative change of the differential pressure across the valve of which the setting has been changed. If this valve is the first one on the branch, the change in flow through the other radiators on the branch will be almost proportional (depending on the flow) to the root of the relative change in differential pressure across the opened valve. The relative change in differential pressure can be expressed as: ∆p 2 ∆(∆p pump ) − ∆ (∆p pipe ) = +1 ∆p1 ∆p1

(34)

The change in the flow through the rest of the system can be estimated, starting from the closest system junction after/from which the system is unchanged. At this point, the change in the flow is more or less proportional to the root of the relative change of differential pressure. The expression for the change in differential pressure at this point is the same as the above expression, except that the differential pressures naturally relate to those at this point instead of that across a valve. It is not possible to provide a general, exact expression for the change of flow through the system valves when a change occurs from conditions without deviations. However, the above equations indicate that the change in flow (or the change in differential pressure across a valve) depends on the pump characteristic, the pipe pressure drop and the balanced system differential pressure.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The above means that, in order to minimise the interaction between the radiators on a system, the ideal is to have a high balanced differential pressure, a low pressure drop in the distribution system and a flat pump curve. This explains why the pressure-controlled pump in the simulations reduces the interaction of the system. Proportion of radiator valves with changed settings The simulations showed that opening a valve had a considerable effect on the system. However, what would be the result of opening several valves? The diagram below shows how the design return temperature is affected by the proportion of radiator valves in the system that are fully opened. The pale lines in the diagram also show how the weighted mean annual return temperatures from the respective systems change in proportion to the numbers of fully open radiator valves. 55 Low-flow system

Return temperature [°C]

50 45

High-flow system 40 35 30 Outdoor temperature = - 15 °C

25 0

10

20

30

40

50

60

70

80

90

100

Proportion of fully open radiator valves [% ]

Figure 102.The effect of the proportion of fully open radiator valves on the return temperature. It can be seen from the diagram that the return temperature in the low-flow system rises rapidly when one or more valves is opened, reaching a maximum (which depends on how the flow varies throughout the system) for a certain number of open valves. In the system considered here, with 20 radiators, it is sufficient for two radiator valves (i.e. 10 %) to be fully open for the return temperature in the low-flow system already to exceed that in the high-flow system. Regardless of whether high-flow or low-flow balancing is chosen, it is important that it should be carried out correctly. If only a few valves, or even just one valve, are/is incorrectly set, there will be a noticeable effect on system performance. However, it is better that the valves should be slightly too closed than that they should be slightly too open, as the former has less effect on the rest of the system.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The size of the system The effect of a valve setting changed away from its ideal setting decreases as the system size increases. This is illustrated in the simulations by the fact that the effect declines with increasing distance from the valve concerned. This can be seen more clearly in the following diagrams, which show how the return temperatures in various parts of the system are affected by a change in the setting of one radiator valve. The diagrams are based on the effects in a reference system at design conditions. High-flow system

Low-flow system

55

55 Radiator

50

Return temperature [°C]

Return temperature [°C]

Radiator Branch

45

Riser 40

Total

35 30

0.2

0.4

0.6

0.8

Branch 45

Riser

40 Total 35 30 Outdoor temperature = - 15 °C

Outdoor temperature = - 15 °C

25

25 0

50

0

1

0.2

0.4

0.6

0.8

1

Valve opening of radiatorvalve AI1 [-]

Valve opening of radiatorvalve AI1 [-]

Figure 103.The effect of the valve opening of radiator valve AI1 on return temperatures in different parts of high-flow and low-flow systems. In principle, the above diagrams show the differences in the effect on return temperatures between different sizes of systems. The return temperature from the directly affected radiator can be regarded as representing the effect on a system consisting of only one radiator, with the branch return temperature representing the effect on a system of five radiators, the riser return temperature representing the effect on a system of ten radiators and the overall system consisting, as known, of 20 radiators. The position of the altered valve in the system As previously mentioned, the sensitivity to a change in a radiator setting depends largely on the magnitude of the differential pressure and on whether the valve is opened or closed. The simulations show that opening the “end” radiator valve (i.e. at the furthest point of the system), has less effect than if the “first” radiator valve is opened. If, on the other hand, the respective valves are closed, then the effects are reversed (although the difference is very slight in this respect). This can be illustrated by a diagram showing how the differential pressure in the branch to which the changed valve is connected changes relative to the basic case. The diagram is for a reference system, set up with a high flow.

136

Relative change in differential pressure [% ]

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

150 125 100 75

Rad 5 closed Rad 1 closed Rad 5 fully open Rad 1 fully open

50 25 0 -25 -50 -75 -100 Branch + valve

Rad 1

Rad 2

Rad 3

Rad 4

Rad 5

Figure 104.The effect of the position of the altered valve on the differential pressure in a branch, depending on whether the valve is opened or closed. It can be seen from the diagram that the change in differential pressure across the unaltered valves is somewhat less when radiator valve 1 is closed than if radiatorvalve 5 is closed. When looking at the diagram, it is important to bear in mind that the differential pressure across the closed valve does not affect the situation, as no flow is actually passing through it. It can also be seen from the diagram that the interaction between the radiators is greater when radiator valve 1 is opened than when radiator valve 5 is opened. A detail that can be seen from the diagram is that the change in the differential pressure across the branch (including the branch valve) is greatest when radiator valve 1 is opened. This means that the total flow through the system increases the most in this case, resulting in the highest pressure drop in the distribution system and thus the greatest effect on the other branches connected to the system. Branch, riser and main valves The branch, riser and main valves all reduce the differential pressure across the radiator valves which, as pointed out above, has an adverse effect on the sensitivity if any valve is closed, or a positive effect if any of the radiator valves are opened. The effect of a change in the setting of a branch valve or riser valve is linked to its effect on the rest of the system or, put another way, to the magnitude of the pressure drop that the valve is intended to create in relation to the total pressure drop of the system. The simulations show that the effect of the branch and riser valves increases as the balanced differential pressure of the system decreases. The difference between this situation and the case of a radiator valve with a changed setting is that the differential pressure across the branch or riser valve is not related to the balanced differential pressure in the system, but to the pressure drop between the

137

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

branches (or risers), which does not change with the value of the balanced differential pressure. A low balanced differential pressure means that the system's radiator valves do not need to be closed as much as would be the case with a high balanced differential pressure. As the balancing of the branch valves is not affected by the balanced differential pressure in the system as a whole, the influence of the branch valves on the total flow resistance of the system increases as the balanced differential pressure is reduced. Any change in the setting of the branch valve therefore gives rise to a greater change in the system characteristic, leading in turn to a larger change in the total flow. As the settings of the other branches have not been changed, an increased flow will reduce the differential pressure and thus reduce the flow through the branches. In other words, the interaction with other branches, caused by a change in the setting of a branch valve, increases with reducing balanced differential pressure. However, interaction decreases as a result of reducing the pipe pressure drop, as the branch valve then loses some of its effect on the system characteristic. The effect of a change in the setting of a branch valve could be investigated in exactly the same way as for a change in the setting of a radiator valve. The diagram below shows how the return temperatures from the system and from the branch are affected by a change in the setting of branch valve AI. The diagram is based on design conditions.

Return temperature [°C]

55 50 45

High-flow, total

High-flow, branch

40 Low-flow, total 35

Low-flow, branch

30 Outdoor temperature = - 15 °C

25 0

0.2

0.4

0.6

0.8

1

Valve opening of branch valve AI [-]

Figure 105.The effect of the valve opening of branch valve AI on branch and system return temperatures for high-flow and low-flow reference systems. In comparison with the effect of fully closing a radiator valve, the effect of fully closing a branch valve is naturally greater. However, on the other hand, the effect of fully opening a branch valve has less effect on system return temperature than does fully opening a radiator valve (see Figure 100). This is due to the fact that the increased flow through the branch is shared equally among the radiators, thus avoiding a corresponding surge in the flow, with resulting high return temperature, as caused by fully opening a radiator valve. In other words, systems are more sensitive to an open radiator valve than to an open branch or riser valve.

138

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The following diagram shows how the thermal output power is affected by the setting of the branch valve. As with Figure 105, this is based on design conditions.

Heat release [kW]

22

21

Low-flow, total

20

High-flow, total 19 Outdoor temperature = - 15 °C

18 0

0.2

0.4

0.6

0.8

1

Valve opening of branch valve AI [-]

Figure 106.The effect of valve opening of branch valve AI on heat release powers from the reference systems. Once again, comparison with a closed radiator valve shows that the effect of closing a branch valve has the greater effect on the system, as it closes off five radiators instead of just one. In the same way, fully opening a radiator valve has a considerably greater effect on the total heat release from the system than does fully opening a branch valve. Figures 105 and 106 show an almost insignificant difference between the performances of the high-flow and low-flow systems, not only in terms of change of return temperature but also in terms of change in heat emission. This is because the radiator sensitivity, which is greater in the low-flow system (see Equation (9) in Chapter 2), is compensated for by the fact that the flow-related interaction between the branches is lesser in the low-flow system due to a considerably lower pipe pressure drop (see Equation (34)).

6.4

Incorrect balancing

The basic case assumed that the system was perfectly balanced, i.e. that each radiator received exactly the correct flow needed in order to be able to provide the exact heating power required. This, of course, is a Utopian situation, and is unlikely to be achievable in practice. Nor can it even be said to be desirable, as it would presumably require considerable time and resources to achieve, probably for little benefit. Perfect balancing is not necessarily automatically considerably better than simple balancing. This section describes the effects of various deviations from perfect balancing. The difference between it and the previous section, concerned with the effects of deviations in the settings of individual valves, is that, in this section, the settings of virtually all the valves depart from the ideal basic case settings. As before, the emphasis of the analyses 139

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

is on how sensitive the various system arrangements are to deviations of various valve settings from the ideal. The deviations from the ideal that have been analysed are simplest possible balancing, simplified balancing and randomised deviations from ideal balancing. 6.4.1 Simplest possible balancing The simplest possible balancing case is that represented by the assumption that the differential pressure across all the radiator valves is constant. All the valves would then be adjusted to one and the same kv value, equivalent to the required flow rate at the assumed differential pressure. It is further assumed, for this case, that none of the branch, riser or main valves would be adjusted, but simply set to their fully open positions. Reference system For the reference system, the valve opening of the radiator valves in the high-flow system would be 0.44 which, for the simplest possible balancing arrangement, would provide the required radiator flow for a differential pressure of 10 kPa with the particular valve concerned. For the low-flow system, the corresponding valve opening would be 0.31. The results of this would give an increase in the weighted annual mean return temperature of 0.4 °C in the high-flow system and 0.5 °C in the low-flow system, both as compared with the basic case. The respective increases in the amount of thermal energy supplied over the year would be 1.0 % and 1.9 %. The spread in room temperature is shown in the following diagrams. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22

Max

21

Mean

20 19

Min

18 17 16

23 22

Max

21

Mean

20

Min

19 18 17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 107.Maximum, minimum and mean temperatures in the rooms for the simplest possible balancing setting. The systems are balanced for a high differential pressure.

140

15

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The spread in the room temperature is not particularly large in either of the systems, although that of the high-flow system is somewhat larger than that of the low-flow system. However, compared with the performance of the basic case, the increase in mean room temperature is greater in the low-flow system. Reference systems with low balanced differential pressure If the differential pressure across all the radiator valves is assumed to be 2 kPa, the required valve opening of the radiator valves are 0.66 in the high-flow case and 0.47 in the low-flow case. The corresponding increases in the return temperatures are 0.5 ºC in the high-flow system and 0.8 ºC in the low-flow system. The amount of thermal energy supplied over the year is reduced by 0.5 % in the high-flow system, while it increases by 1.7 % in the low-flow system, both as compared with the basic case. The spread in room temperatures is shown in the following diagrams. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22

Max

21 Mean

20 19 18 17

Min

16

23

Max

22 21

Mean

20 19 18

Min

17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 108.Maximum, minimum and mean temperatures in the rooms for the simplest possible balancing setting. The systems are balanced for a low differential pressure. The spreads of the room temperatures are considerably greater in this case than in the case with a high balanced differential pressure and so are the changes in return temperatures. However, the amount of thermal energy supplied is less, due to the fact that the mean value of the room temperature does not change as much in this case. Reference systems with thermostatic radiator valves The effect of simple balancing is reduced if the system is fitted with thermostatic radiator valves, as shown in the following diagrams, which are for systems that have been balanced for a high differential pressure. The increase in the return temperature is 0.2 °C for the high-flow system and 0.1 °C for the low-flow system. Corresponding increases in energy emissions are 0.6 % and 0.4 % respectively, compared with the basic case.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM Low-flow system

25

25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system

23 22 21

Max Mean Min

20 19 18 17

23 22 21 19 18 17

16

16

15

15 -15

-10

-5

0

5

10

Max Mean Min

20

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

15

Outdoor temperature [°C]

Figure 109.Maximum, minimum and mean temperatures in the rooms for the simplest possible balancing setting. The systems are balanced for a high differential pressure and are fitted with thermostatic radiator valves. 6.4.2 Simplified balancing Instead of merely adjusting the radiator valves to give a required flow for an assumed constant differential pressure, as was described above, the method can be complemented by correction of the total flow using the main, branch and/or riser valves. Reference systems The diagrams below show the spread in room temperature for both systems when the total flow has been corrected using the main, branch and riser valves. The valve opening of the radiator valves is 0.44 in the high-flow system and 0.31 in the low-flow system (see the previous section). Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max Mean Min

20 19 18 17 16

23 22 21

Max Mean Min

20 19 18 17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 110.Maximum, minimum and mean temperatures in the rooms for the simplified balancing setting.

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It can be seen from the diagrams that using these valves to balance the total flow results in the required mean annual room temperature. There is also less spread in the room temperature compared with what would be the case if the total system flow had not been corrected. The maximum spread occurs at design conditions, and amounts to about 1 °C in both systems. The increase in return temperature is insignificant (less than 0.1 ºC), as is the change in emission of thermal energy over the year. This applies for both systems. Reference systems with low balanced differential pressures The spread in the room temperatures becomes greater with low balanced differential pressures, as shown in the following diagrams. For both systems, the increase in the return temperature is 0.1 °C, while the emission of thermal energy falls by 1.8 % for the high-flow system and by 1.0 % for the low-flow system. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max

20

Mean

19 18

Min

17

23 22 20 18

15

15 -5

0

5

10

15

Min

17 16

-10

Mean

19

16 -15

Max

21

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 111.Maximum, minimum and mean temperatures in the rooms for the simplified balancing setting. The systems are balanced for a low differential pressure. The spread is significantly greater in the case with a low balanced differential pressure, which is due to the fact that, in relative terms, the magnitudes of the differential pressures across the radiator valves differ more from each other. This means that the effect of the pipe pressure drop will be greater for a low differential pressure, with the result that the kv value that has been set for each radiator valve will be further from the ideal setting. Reference systems with thermostatic radiator valves Fitting the system with thermostatic radiator valves reduces the effect of the simplified balancing process, as shown in the diagrams below. In comparison with the basic case, the return temperature actually falls in this case. However, the reduction is slight, being less than 0.1 °C for both systems. The amount of thermal energy released also declines, by 0.2 % for the high-flow system and by 0.3 % for the low-flow system.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max Mean Min

20 19 18 17 16

23 22 21

Max Mean Min

20 19 18 17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 112.Maximum, minimum and mean temperatures in the rooms for the simplified balancing setting. Both systems are fitted with thermostatic radiator valves. A comparison with Figure 109 shows that, if the systems are fitted with thermostatic radiator valves, the simplest possible balancing process actually results in somewhat less spread than does the simplified process. This is due to the fact that, when the thermostatic valves attempt to reduce the flow in parts of the system, there is less leeway for increases in the flow in other parts of the system, due to the fact that the main, branch and riser valves have been balanced. 6.4.3 Randomised deviations in balancing The purpose of considering the case of random deviations in balancing is that this presumably reflects real conditions. “Ideal” balancing is more or less impossible to achieve, which means that, in the best case, results are probably only somewhere in the vicinity. No matter how good a balance is aimed at, there will unavoidably be deviations in the settings of the valves. In addition, these deviations are likely to increase with time if nothing is done to correct them. This section therefore analyses the effect of random deviation in the settings of all radiator valves in the system. This has been done in the simulations by randomly changing the settings of all 20 radiator valves in the system by a maximum of ± 0.05 of the valve opening. The same deviations have been used in both the high-flow and low-flow cases. It must be added that the sum of the changes for the 20 valves has been + 0.2 in the valve opening, or + 0.01 as a mean value per valve (see Figure 54 in Chapter 5 to see what this means for the kv value). The tables below show how the valve opening was changed for each individual valve.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Radiator AII5 AII4 AII3 AII2 AII1

∆H [-] + 0.01 0.00 + 0.04 − 0.03 − 0.01

Radiator BII5 BII4 BII3 BII2 BII1

∆H [-] + 0.01 + 0.02 0.00 − 0.03 + 0.04

Radiator AI5 AI4 AI3 AI2 AI1

∆H [-] − 0.02 + 0.03 + 0.04 + 0.02 + 0.05

Radiator BI5 BI4 BI3 BI2 BI1

∆H [-] − 0.02 + 0.01 − 0.03 + 0.05 + 0.02

Table 8.

Changes in the radiator valve settings to represent random deviations from the ideal settings.

The table shows quite small deviations from the ideal settings, intended to represent the difficulties of exactly achieving a particular kv value for a radiator valve before the system is in operation, due to such factors as the method of adjustment, manufacturing tolerances for the valves and approximate calculations of the required kv values. Reference systems As far as changes in the return temperature or emission of thermal energy over the year are concerned, the effect of the random changes in the settings of the reference system are not large. The weighted return temperature increases by 0.1 ºC in the high-flow system, and by 0.3 ºC in the low-flow system, both compared with the basic case. Thermal energy emissions decrease by 0.1 % in the high-flow case, and increase by 0.2 % in the low-flow case. However, the “new” set-up does display some spread in the room temperatures in the systems, as shown in the diagrams below.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Low-flow system

25

25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system

23 22 21

Max Mean Min

20 19 18 17

23 22 20

17

15

15 -5

0

5

10

15

Min

18 16

-10

Mean

19

16 -15

Max

21

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 113.Maximum, minimum and mean temperatures in the rooms for random deviations of valve settings in balancing. The overall effect of the deviations of the settings is a general slight increase in the valve opening. It can be seen that the spread in room temperature is quite large, particularly in the low-flow system. What this says is that only quite small changes in the valve opening of the valves are needed in order to have a considerable effect on the flow balance in the system, but yet without significantly affecting the total heat release from the system. The deviation in the valve settings result in a slight decrease of total flow resistance in the system, which has the effect of slightly increasing the total flow. If we reverse the size of the valve opening of the valves in Table 8, so that the total change in valve opening is -0.2, the flow resistance increases and the total flow falls. This changes the return temperature only very slightly in comparison with the basic case, by less than 0.1 °C in both systems. Over the year, emission of thermal energy decreases by 0.4 % in the high-flow system and by 1.6 % in the low-flow system. The diagrams below show the spread in room temperatures.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21 20

Max Mean

19

Min

18 17 16

23 22

Max

21 20

Mean

19 18

Min

17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 114.Maximum, minimum and mean temperatures in the rooms for random deviations of valve settings in balancing. The overall effect of the deviations of the settings is a general decrease in the valve opening. The simulations show that a general increase in the valve opening of the radiator valves affects the return temperature, but has little effect on the total heat emission. The opposite applies for a general reduction in the valve opening of the valves, i.e. it affects the heat release but has little effect on the return temperature. This applies especially in the case of the low-flow system. Reference systems without branch or riser valves The effect of the random deviations from ideal settings becomes greater if the systems are not fitted with branch or riser valves, with the return temperature increasing by 0.1 ºC in the high-flow system and by 0.4 ºC in the low-flow system. The amount of thermal energy emitted is reduced by less than 0.1 % in the high-flow system, but increases by 0.3 % in the low-flow system. The spread in the room temperatures is shown in the diagrams below.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max

20

Mean Min

19 18 17 16

23 Max

22 21

Mean

20 19 18

Min

17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

15

Outdoor temperature [°C]

Figure 115.Maximum, minimum and mean temperatures in the rooms for random deviations of valve settings in balancing. The systems are not fitted with branch or riser valves. The overall effect of the deviations of the settings is a general increase in the valve opening. Reference systems with low balanced differential pressure The effect of random deviations of the valve settings from the ideal is less in the case of systems set up to have a low balanced differential pressure, with the return temperature increasing by less than 0.1 °C in both systems. The thermal energy emission decreases by 0.2 % in the high-flow system and by 0.4 % in the low-flow system. The spread in room temperatures is shown in the following diagrams. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max Mean Min

20 19 18 17 16

23 22

Max

21

Mean

20 19

Min

18 17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 116.Maximum, minimum and mean temperatures in the rooms for random deviations of valve settings in balancing. The systems are balanced to have a low differential pressure. The overall effect of the deviations of the settings is a general increase in the valve opening.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Reference systems with other valve characteristics The simulations assume that the radiator valve characteristics are essentially that of a square law. However, as the deviation from the ideal balanced setting relate to the valve opening of these valves, the shape of the characteristic has a considerable effect on the results. This has been demonstrated by a simulation of the use of radiator valves having a quick-opening characteristic, as shown in the diagram below. 0.7

kv valve [m³/h]

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 117.Quick-opening characteristic. The effect of this is that, for random deviations in the settings of such valves, the return temperature would increase by 0.2 °C in the high-flow system, but by no less than 2.2 °C in the low-flow system, both as compared with the basic case. Thermal energy emission over the year would decline by 1.5 % in the high-flow system, and by no less than 11.0 % in the low-flow system. These values are considerably greater than those for corresponding cases using the valves with a square law characteristic. A slight increase in the valve opening of a quick-opening valve tends substantially to increase the flow, resulting in a large increase in the return temperature. On the other hand, a slight decrease in the valve opening effects a substantial reduction in the flow, which has the effect of drastically reducing the amount of heat emission. This effect is particularly severe in the low flow case, as the radiators in this system are very sensitive to changes in the flow. If the system is fitted with thermostatic valves having a quick-opening characteristic, local control of the radiator would probably tends to be in On/Off mode. The effect of this is noticed to some extent in the simulations, by being unable to achieve equilibrium with this configuration. Reference systems with thermostatic radiator valves Even if the systems are fitted with thermostatic valves, they are not sufficient to offset the deviation from the ideal settings. The return temperature falls by less than 0.1 °C in

149

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

the high-flow system, and by 0.2 °C in the low-flow system. Thermal energy emissions also fall, by 0.2 % in the high-flow system and by 0.9 % in the low-flow system. The spread in room temperatures is reduced, due to the fact that the thermostatic valves respond to the room temperature in those rooms where the temperature exceeds 20 ºC. The effect of this is shown in the following diagrams. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max Mean Min

20 19 18 17

23 22 21 19 17 16

15

15 -10

-5

0

5

10

15

Min

18

16 -15

Max Mean

20

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 118.Maximum, minimum and mean temperatures in the rooms for random deviation of valve settings in balancing. The systems are fitted with thermostatic radiator valves. The overall effect of the deviation of the settings is a general slight increase in the valve opening. Reference systems with thermostatic radiator valves and pressure-controlled pumps The effect of random deviations in the settings of the valves becomes even greater if the system pressure level is controlled by a pressure-controlled pump. The return temperature in the high-flow system falls by 0.1 °C, while that of the low flow system falls by 0.2 °C, with emissions of thermal energy declining by 0.3 % and 1.1 % respectively. The spread in room temperatures is shown in the following diagrams.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max Mean Min

20 19 18 17 16

23 22 21

Max Mean

20 19

Min

18 17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 119.Maximum, minimum and mean temperatures in the rooms for random deviation of valve settings in balancing. The systems are fitted with thermostatic radiator valves, and the pump is pressure-controlled. The overall effect of the deviation of the settings is a general slight increase in the valve opening. Reference systems with response applied (pump pressure increased) The simulations of random deviations in the valve settings show that certain rooms in the systems have low temperatures, and particularly in the low-flow system case. This can be compensated for by increasing the flow in the system by raising the pump pressure. This has therefore been done in the simulations by increasing the pump pressure to such a level that the temperature of the coldest room reaches 20 °C. This involved increasing the total flow by 20 % in the high-flow system, and by over 30 % in the low-flow system. The increase in total flow naturally results in a rise in the return temperature, and also of the amount of heat emitted by the systems. This is shown in the following duration diagram, in which the return temperature in the high-flow system increases by 1.0 °C, while that in the low-flow system increases by 2.3 °C. Over the year, thermal energy emission from the high-flow system increases by 2.9 %, while that from the low-flow system increases by 8.1 %.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

45 40 35

Return, High

Temperature [°C]

30

Return, Low

25

Room (mean), Low

20

Room (mean), High

15 10 Out

5 0 -5 -10 -15 0

1460

2920

4380

5840

7300

8760

Time [h]

Figure 120.The effect of increasing total system flow in order to raise the temperature in the coldest room in the system, with random deviations in valve settings. The spread in room temperatures after this response is shown in the following diagrams. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22

Max Mean Min

21 20 19 18 17

22 20 18 17 16 15

-5

0

5

10

15

Min

19

15 -10

Mean

21

16 -15

Max

23

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 121.Maximum, minimum and mean temperatures in the rooms for random deviation of valve settings in balancing. The lowest room temperature on the systems has been dealt with by raising the pump pressures.

152

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Reference systems, response applied (supply temperature increased) Instead of increasing the pump pressure to raise the temperature of the coldest room in the system, the supply temperature could be increased. In the design cases, the necessary increase in supply temperature is 2.5 °C for the high-flow system and over 8.0 °C for the low-flow system. This has less effect on the return temperatures in the system than does an increase in the flow, but has a greater effect on the heat emission and spread of room temperatures. The weighted annual return temperature in the high-flow system increases by 0.7 °C, while that in the low-flow system increases by 1.8 °C, both as compared with the basic case, while the thermal energy emissions increase by 4.1 % and 11.6 % respectively. The spread in room temperatures is shown in the diagrams below. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22

Max Mean Min

21 20 19 18 17 16

Max

23

Mean

22 21 20

Min

19 18 17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 122.Maximum, minimum and mean temperatures in the rooms for random deviation of valve settings in balancing. The lowest room temperature on the systems has been dealt with by raising the supply temperatures in the systems. Reference systems with thermostatic radiator valves, response applied (supply temperature increased) As described in the preceding case, the temperature in the coldest room can be brought up to 20 ºC by increasing the supply temperature. If, in addition, the systems are fitted with thermostatic radiator valves, the room temperatures in the rooms that exceed 20 °C will be reduced. The overall result of this is to give a very slight decrease (less than 0.1 C) in the return temperature in the high-flow system, as compared with the basic case. The return temperature in the low-flow system is reduced by 0.8 °C, while thermal energy emissions increase by 1.9 % in the high-flow system and by 1.7 % in the low-flow system. The spread in room temperatures is substantially reduced, with the maximum difference between the lowest and highest room temperatures amounting to 0.15 °C in both systems.

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Reference systems after a long time (maximum + 0.25 of valve opening) It is not possible to run a simulation that exactly describes the deviations in valve settings (and their effects) that occur in a system after a long period of operation. This is naturally because these deviations can vary widely from one system to another, while they sometimes are perhaps not even noticed at all. Previously, it is only relatively small random deviations in the valve opening of the radiator valves that have been considered, and they have also been arranged both to increase and to decrease the valve opening of the valves. The intention behind this approach was that these deviations in the settings could be linked to the actual balancing of the system. The simulation described below is instead intended to give an idea of the effects of major random deviations in the settings of the valves, as a result of changes or interference by users, wear and tear, maintenance corrections etc. It is not particularly likely that the valve opening of the valves will be reduced: instead, if anything, they are more likely to be increased relative to the original settings. This simulation has assumed a maximum change in the valve opening of any individual valve of + 0.25, with an aggregated change for all the valves of + 2.0, which is equivalent to an average change in valve opening of + 0.1 of each valve. The table below show the deviation from the ideal valve opening of each individual valve. Radiator AII5 AII4 AII3 AII2 AII1

∆H [-] + 0.02 + 0.01 + 0.07 + 0.17 + 0.18

Radiator BII5 BII4 BII3 BII2 BII1

∆H [-] + 0.05 + 0.08 + 0.12 + 0.01 + 0.09

Radiator AI5 AI4 AI3 AI2 AI1

∆H [-] + 0.09 + 0.20 + 0.14 + 0.04 + 0.18

Radiator BI5 BI4 BI3 BI2 BI1

∆H [-] + 0.06 + 0.03 + 0.24 + 0.19 + 0.03

Table 9.

Changes in the radiator valve settings to represent large random deviations from the ideal settings.

With the above random deviations of the valve settings from the ideal settings, the weighted return temperature during the year increases by 0.3 °C in the high-flow system, and by 1.6 °C in the low-flow system, with the amount of thermal energy emitted falling by 0.4 % in the high-flow system and increasing by 2.2 % in the low-flow system, both as compared with the basic case.

154

6 SIMULATION AND RESULTS – RADIATOR SYSTEM 45 40 35

Return, High

Temperature [°C]

30

Return, Low

25 Room (mean), Low

20

Room (mean), High

15 10 Out

5 0 -5 -10 -15 0

1460

2920

4380

5840

7300

8760

Time [h]

Figure 123.The effect of major deviations of the valve settings from the ideal settings. It can be seen from Figure 123 that the return temperature in both the high-flow and the low-flow case is higher than in the basic case. But the change in the mean temperatures of the rooms is almost non-existent in the high-flow case and just somewhat larger in the low-flow case. The spread of the room temperatures is shown in the following diagrams. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22

Max

21 20

Mean

19

Min

18 17

23 22 21 19 18 17 16

15

15 -10

-5

0

5

10

15

Mean

20

16 -15

Max

Min

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 124.Maximum, minimum and mean temperatures in the rooms for substantial random deviations of the valve opening of the radiator valves. The results of this simulation show that, depending on the system, deviations in the valve opening of the radiator valves from their ideal settings can result in a relatively substantial spread in the room temperatures and that this also effects the system return

155

15

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

temperatures. However, the heat emission, and therefore also the mean temperature in the building, need not necessarily be significantly affected by these deviations. This is an interesting observation, which can be compared with measured data from a real system, as further discussed in the following summary. 6.4.4 Summary The following table shows a summary of the simulations of the effects on the return temperatures and heat emissions of departures in system settings from the ideal settings, for various system configurations. System

Deviation

Reference system Reference system - low balanced diff.press. - with thermostats Reference system - low balanced diff.press. - with thermostats Reference system

Simplest balancing Simplest balancing Simplest balancing Simplified balancing Simplified balancing Simplified balancing Random Random (reversed signs) Random Random

Reference system - no branch or riser valves - low balanced diff.press. - with quick-opening characteristic - with thermostats - with thermostats and pressure-controlled pump Reference system Reference system - with thermostats - after long time

High-flow system ∆tw,return [ºC] ∆Qsystem [%] 0 0 + 0.4 + 1.0 + 0.5 - 0.5 + 0.2 + 0.6 0 0 + 0.1 - 1.8 0 - 0.2 + 0.1 - 0.1

Low-flow system ∆tw,return [ºC] ∆Qsystem [%] 0 0 + 0.5 + 1.9 + 0.8 + 1.7 + 0.1 + 0.4 0 0 + 0.1 - 1.0 0 - 0.3 + 0.3 + 0.2

0

- 0.4

0

- 1.6

+ 0.1 0

0 - 0.2

+ 0.4 0

+ 0.3 - 0.4

Random

+ 0.2

- 1.5

+ 2.2

- 11.0

Random

0

- 0.2

- 0.2

- 0.9

Random

- 0.1

- 0.3

- 0.2

- 1.1

+ 1.0

+ 2.9

+ 2.3

+ 8.1

+ 0.7

+ 4.1

+ 1.8

+ 11.6

0

+ 1.9

- 0.8

+ 1.7

+ 0.3

- 0.4

+ 1.6

+ 2.2

Random + action (increased pump press.) Random + action (higher supply temp.) Random + action (higher supply temp.) Random (major deviations)

Table 10. Results from simulations of non-ideal settings. The table shows the results for each simulated case, in the form of the change in the weighted mean value of return temperature (∆tw,return) and of the change in the amount of thermal energy supplied over the year (∆Qsystem). Note that the table does not include the spread in room temperatures. In general, the table shows that there is relatively little effect from deviations of settings from their ideal values. This applies in particular to the simplified balancing case, where there is essentially no difference in principle between it and the basic case. However, it must again be emphasised that Table 10 does not include the spread in room temperatures, which can give the impression that certain system configurations and/or deviations of settings from the ideal have hardly any effect. The simulations therefore show that there is no apparent link between the spread and the mean values of room temperatures. 156

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The table also shows that a low differential pressure has an adverse effect in conjunction with simple or simplified balancing. However, low differential pressure has reduced the effects of incorrect settings of the valve openings, which is due to the fact that it reduces the effect of valves that are open more than necessary. The simulations indicate that good results can be achieved merely by employing simplified balancing of the systems. However, this presupposes a sufficiently high system differential pressure, as otherwise there would be an excessive spread of room temperatures, as shown in the diagram below.

Maximum difference in room temperatures [°C]

8 7

High-flow system

6

Low-flow system

5 4 3 2 1 0 0

2

4

6

8

10

Applied differential pressure [kPa]

Figure 125.Maximum spread in room temperatures as a function of applied differential pressures: simplified balancing. In addition, increasing the number of radiators connected to the system branches produces a corresponding increase in the difference in room temperatures, as shown by Petitjean (1994) and also by Trüschel (1999). Another important prerequisite for this type of balancing is that the system should be fitted with branch valves and riser valves, so that the flows in the various parts of the system can be correctly set. Many of the simulations described in this report have been concentrated on investigating the effects of changing the setting of a single valve in the system. This is partly because such changes can, in some cases, give rise to substantial system changes, and partly because they help to explain the effects of changes in the settings of several valves in the system. For example, a general increase in the valve opening of the radiator valves in a system has a greater effect than a corresponding general decrease in the valve opening of the valves, which can be traced back to the fact that an opened valve has a greater effect on the system than has the closed valve. It should be pointed out that minor deviations of radiator valve settings from the ideal values, resulting from the balancing procedure, do not have a significant effect on either

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

the return temperature or overall system heat release. However, they do affect the spread in room temperatures. It is not until substantial deviations in valve settings from the ideal values occur that corresponding substantial changes occur in the return temperature. Such changes will also occur if some arbitrary rough-and-ready adjustment is carried out in order to raise the lowest room temperature in the system to an acceptable level, instead of properly performing a new balance of the system. The risk of such a response is that it will result in a substantial increase in the average temperatures of the rooms in the system, unavoidably resulting in high return temperatures and high usage of thermal energy. The problem of high return temperatures is therefore not due to closure of valves in the system, as such closures hardly affect the return temperature. Instead, they tend mainly to be due to system valves being opened more than they should be. The simulations showed that it is only when some drastic, substantial change was made, or when there was a general change in the settings of the valves, that system return temperature increased substantially. This can be compared with the results of real measurements on a district heating substation performed as part of the work, as described below. 6.4.5 Comparison with a measurement case The measurements were started in the spring of 2000 on a district heating substation in a property on Bankogatan in Gothenburg, supplying space heating and domestic hot water to 144 apartments in six buildings. The substation provided two space heating supplies: one to buildings 3, 5 and 7, and the other to buildings 9, 11 and 13. The radiator systems in the buildings were balanced early in the autumn of 2000, which was followed by new measurements made during the winter and spring of 2000-2001. The measurements were made by The Montoring Centre for Energy Research at Chalmers University of Technology, and included determination of the following parameters: -

Supply temperature, district heating Supply temperature, radiator systems in buildings 3, 5 and 7 Supply temperature, radiator systems in buildings 9, 11 and 13 Return temperature, district heating Return temperature, radiator systems in buildings 3, 5 and 7 Return temperature, radiator systems in buildings 9, 11 and 13 Flow rate, district heating Flow rate, radiator systems in buildings 3, 5 and 7 Flow rate, radiator systems in buildings 9, 11 and 13 Thermal output power, district heating Thermal output power, radiator systems in buildings 3 – 13

The following diagram shows how the temperatures from the substation were related to the outdoor temperature, prior to balancing.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Temperature levels - Bankogatan (prior to balancing) 110 District heating - Supply

Temperature [°C]

100

District heating - Return

90

Building - Supply

80

Building - Return

70 60 50 40 30 20 -15

-10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 126.Measured temperatures in the district heating substation prior to balancing. The outcome of the balancing was that the radiator valves were replaced and that the flow in the radiator systems were reduced (from approximately 30 m³/h to 18 m³/h at design conditions). This had the effect of reducing the return temperature, while leaving the supply temperature of the radiator system more or less unchanged. Figure 127 shows the temperature levels after balancing. Temperature levels - Bankogatan (after balancing) 110

District heating - Supply

Temperature [°C]

100

District heating - Return

90

Building - Supply

80

Building - Return

70 60 50 40 30 20 -15

-10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 127.Measured temperatures in the district heating substation after balancing.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Figure 128 shows the thermal output powers from the radiator system before and after balancing. Thermal power output (radiator system) - Bankogatan 700 Thermal power output [kW]

After balancing 600

Prior to balancing

500 400 300 200 100 0 -15

-10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 128.Measured thermal power output from the radiator system before and after balancing. It can be seen that the thermal power output from the radiator systems hardly changed at all as a result of the balancing. This indicates that the mean temperatures in the building were not significantly reduced, despite the fact that the flow rate was reduced without changing the supply temperature. For this to have been the case, there must have been a substantial imbalance in flow distribution in the system prior to balancing. One of the simulation cases is similar to this scenario. In this case (referred to as “Reference systems after a long period of operation”), the valve opening of all the radiator valves were randomly increased. This resulted in an increase in the return temperature, while at the same time not having much effect on heat release. The same thing seems to apply for the actual measured case, where balancing seems to have reduced the spread in room temperatures by balancing the system flows, substantially reducing the return temperature but not affecting the total heat release. Alternatively, reversing the chronological order, it can be said that substantial changes in the settings of the valves result in a wide spread of room temperatures, thus substantially increasing the return temperature without significantly affecting heat release.

6.5

The effect of disturbances

The simulations described so far in this chapter have not considered the effects of system disturbances, despite the fact that, in real life, disturbances of one sort or another are likely to occur all the time. This has been because the simulations have been intended as far as possible to show the effects of non-ideal settings. The following simulations, however, are based on ideal settings, but with the input of system

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

disturbances in the form of changed heat inputs in the rooms supplied by the systems, with the aim of showing the resulting effects on the various systems and their abilities to deal with them. 6.5.1 Non-uniform distribution of internal heating This disturbance represents the effect of uneven “loading” of the system. It has therefore been assumed that the heat inputs in the rooms supplied by the radiators connected to riser A have doubled to 340 W (which could be due to such a cause as greater insolation or some additional source of internal heat), while the heat load in the rooms supplied by the radiators connected to riser B is unchanged at 170 W. Reference systems In the first case, it has been assumed that the reference systems are unevenly loaded, which has had the effect of increasing the weighted mean return temperature by 0.7 ºC in the high-flow system, and by 1.1 ºC in the low-flow system, both as compared with the basic case. The reductions in thermal emission from the radiator systems are 10.6 % and 9.0 % respectively. The diagrams below show the differences in room temperatures between maximum and minimum values, with the maximum values corresponding to the room temperatures connected to riser A, and with the minimum temperatures corresponding to those connected to riser B. Low-flow system 25

24

24

23

Room temperature [°C]

Room temperature [°C]

High-flow system 25

Max

22

Mean

21

Min

20 19 18 17 16

Max

23 22

Mean

21 20

Min

19 18 17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 129.Maximum, minimum and mean temperatures in the rooms with uneven distribution of internal heat loads. The difference between the two risers is somewhat less in the high-flow system, which is due to the fact that there is a greater reduction in heat emission from the radiators in this system when the room temperature rises.

161

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Reference systems with thermostatic radiator valves (constant P-band) If the balancing valve is separated from the thermostatic valve, the systems will have the same P-band width, regardless of the results of balancing. If the width of this constant P-band is assumed to be 2 ºC in both systems, then the return temperature in the high-flow system will be reduced by 0.3 °C, while that in the low-flow system will be reduced by 0.6 °C, both as compared with the basic case. Thermal energy emissions will be reduced by 17.7 % in the high-flow case, and by 19.1 % in the low-flow case, which shows that the low-flow system is definitely more efficient, even though the width of the system P-bands is the same. This is due to the fact that the sensitivity of the radiators to a change in flow through them is greatest in the low-flow system (see Equation (9) in Chapter 2). The following diagrams show the spread in room temperatures. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 Max

21

Mean

20

Min

19 18 17

23 22 21 20

17

15

15 -5

0

5

10

15

-15

Outdoor temperature [°C]

Min

18 16

-10

Mean

19

16 -15

Max

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 130.Maximum, minimum and mean temperatures in the rooms with uneven distribution of internal heat loads. The systems are fitted with thermostatic radiator valves, having constant P-band widths. Reference systems with thermostatic radiator valves (adjusted P-band) If the same valve is used both for system balancing and for control, the use of thermostatic valves will result in the narrower P-band width for the low-flow system, as it is in this system that the valves are most closed. In this case, with a P-band width that depends on the valve setting, the return temperature is further reduced as the internal, unevenly distributed, heat load increases. In the high-flow system, the return temperature falls by 0.4 °C, while in the low-flow system it falls by 0.8 °C, both as compared with the basic case. The corresponding reductions in thermal energy emissions are 20.6 % in the high-flow case and 21.8 % in the low-flow case, which shows that the adjusted P-band widths of the thermostats further improve the efficiencies of the systems. In the low-flow case, the width of the P-band is about 0.6 °C, while in the high-flow case it is about 0.9 °C. The spread in room temperatures is shown in the following diagrams.

162

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Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max

20

Mean

Min

19 18 17 16

23 22 21

Max

20

Mean

Min

19 18 17 16

15

15 -15

-10

-5

0

5

10

15

-15

Outdoor temperature [°C]

-10

-5

0

5

10

15

Outdoor temperature [°C]

Figure 131.Maximum, minimum and mean temperatures in the rooms with uneven distribution of internal heat loads. The systems are fitted with thermostatic radiator valves, having adjusted P-band widths. Reference systems with thermostatic radiator valves (adjusted P-band widths) and pressure-controlled pumps Fitting the systems with pressure-controlled pumps will further reduce the spread in room temperatures, such that the return temperature in the high-flow system is reduced by 0.8 °C, and that in the low-flow system is reduced by 0.9 °C. Thermal energy emissions are reduced by 21.0 % in the high-flow case, and by 22.1 % in the low-flow case. Spread in room temperatures is shown in the following diagrams. Low-flow system 25

24

24 Room temperature [°C]

Room temperature [°C]

High-flow system 25 23 22 21

Max

20

Mean

Min

19 18 17

23 22 21

17

15

15 -5

0

5

10

15

-15

Outdoor temperature [°C]

Min

18 16

-10

Mean

19

16 -15

Max

20

-10

-5

0

5

10

Outdoor temperature [°C]

Figure 132.Maximum, minimum and mean temperatures in the rooms with uneven distribution of internal heat loads. The systems are fitted with thermostatic radiator valves, having adjusted P-band widths, and with pressure-controlled pumps.

163

15

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

6.5.2 Summary The following table shows a summary of the simulations of how uneven distribution of the internal heat load affects return temperatures and heat emissions of various system configurations. System Reference system Reference system - with thermostats (constant P-band) - with thermostats (adjusted P-band) - with thermostats (adjusted P-band) and pressure-controlled pump

Disturbance Uneven distribution of internal heat Uneven distribution of internal heat Uneven distribution of internal heat Uneven distribution of internal heat

High-flow system ∆tw,return [ºC] ∆Qsystem [%] 0 0

Low-flow system ∆tw,return [ºC] ∆Qsystem [%] 0 0

+ 0.7

- 10.6

+ 1.1

- 9.0

- 0.3

- 17.7

- 0.6

- 19.1

- 0.4

- 20.6

- 0.8

- 21.8

- 0.8

- 21.0

- 0.9

- 22.0

Table 11. Results of simulations of uneven internal heat load. The table shows the results for each simulated case, in the form of the change in the weighted mean value of return temperature (∆tw,return) and of the change in the amount of thermal energy supplied over the year (∆Qsystem). Note that the table does not include the spread in room temperatures. The table shows major differences in the responses to this particular disturbance of the systems with and without thermostatic radiator valves. The most effective system is the low-flow system. Although the widths of the thermostats' P-bands are the same in both systems, the low-flow system makes best use of the additional thermal energy inputs in the rooms, which is due to the sensitivity of the radiator valves on this type of system. System efficiency is further improved by an adjusted P-band width, considerably narrower than that of the constant width. The spread in room temperatures is least, while the values of room temperature, return temperature and thermal energy emissions are lowest, if the systems are also fitted with pressure-controlled pumps. This is due to the fact that the differential pressure across the thermostatic valves rises less when the valves start to close. It is not possible to draw any conclusions from the results of the simulations as to how well thermostatic radiator valves operate. This is due to a limitation of the program, which assumes that all thermostatic valves operate in an ideal manner. In reality, their performance would be affected by factors such as hysteresis, thermal conductance, sensitivity to differential pressure, mechanical and dynamic responses and other factors. However, this was not investigated in this work, which means that the thermostatic valves in the simulations could have only favourable effects on the ability of the system to reduce the effects of deviations and disturbances. This assumes, of course, that all the thermostatic valves in the system are working. If one of the valves is not working properly, the flow through it could increase substantially if other valves close.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

6.6

The distribution system

The simulations described so far have been concerned only with two-pipe systems. Although this is by far the most common type of system, there are also single-pipe and three-pipe systems. This section presents a brief, simplified description of certain differences between these three arrangements, postulating a very small system, with only five radiators, in order to do so. The simulation program for this small system is constructed in exactly the same way as that for the two-pipe system with 20 radiators that has hitherto been used. However, in addition to the size of the system, there is also a relatively important difference, in that all flow in the small system is assumed to be fully turbulent. This is because the program is intended only to investigate the differences between single-pipe, two-pipe and three-pipe systems, and not between high-flow and low-flow systems, for which the difference in flow can have some effect. It is also for this reason that only the high-flow system has been considered in these simulations. The simulations have assumed that each radiator is to provide 1000 W at the design outdoor temperature of -15 °C, supplying heat to one room, to maintain an indoor temperature of 20 °C. The internal heat load in each room is 170 W. Transmission losses at the design outdoor temperature are 877 W, while ventilation heat losses amount to 293 W. The radiator valves are of the same type as used for the earlier simulations (see Figure 55 in Chapter 5). The pump has the same characteristic as before, but as the speed can be freely selected, it has been set to provide a pump pressure that corresponds to the system pressure drop with correctly balanced flow. 6.6.1 Single-pipe system The arrangement of the single-pipe system is shown in Figure 133.

Figure 133.Schematic arrangement of the single-pipe system. The diagram above shows the system with a dotted return connection. This does not actually exist in the simulation program: instead, the return connection from the final radiator is connected immediately to the suction input of the pump. The differential pressure across each radiator in the simulations is assumed to be 5 kPa, with a pipe pressure drop of 1 kPa between each radiator, giving a necessary pump pressure of 30 kPa. The figure below shows the pressure drops in the system.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

∆p [kPa]

Rad 1 Rad 2 Pump

Rad 3 Rad 4 Rad 5 L [m]

Figure 134.Pressure drops in the single-pipe system. In single-pipe systems, the inlet temperature to each radiator falls progressively along the system. This means that designing and balancing a single-pipe system can start from two different limit cases: either increasing the radiator flow, or increasing the radiator size, for each radiator that is passed. In the first case, the flow through the radiators is progressively increased, so that the first radiator has the lowest flow, while the furthest radiator has the highest flow. In the second case, each radiator receives the same proportion of the flow through the loop (the total flow), but the sizes of the radiators increase with increasing distance from the pump. These two methods can, of course, be combined, so that both the flow through the radiators, and the sizes of them, increase along the system. However, the commonest case is for the flow to be assumed to be the same through all radiators, being indicated in the form of the proportion of the total loop flow passing through the radiators (Järnefors, 1978). It is this method that has been used in these simulations. Figure 135 shows how the total radiator size (the sum of all the radiators connected to the loop) changes with the proportion of the loop flow that passes through the radiator and with the number of radiators connected to the loop. The total radiator size has been standardised in the diagram, which means that radiator size 1 corresponds to the size of a radiator in the two-pipe or three-pipe systems (in which all radiators are of the same size). Radiator size 2, therefore, corresponds to two radiators in the other systems, and so on. For comparison, the diagram also shows the total radiator size for the two-pipe and the three-pipe systems.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

12 Total standardised radiator size

11 10 Proportion of the loop flow through each radiator

9 8 7 6

30%

5 4

40%

3 2

60%

1

Two- and three- pipe system

0 0

1

2

3

4

5

6

7

8

9

10

Number of radiators

Figure 135.Total standardised radiator size in the single-pipe system, as a function of the proportion of the loop flow through each radiator and of the number of radiators connected to the loop. It can be seen from the diagram that, in terms of total radiator size, there is not a very great difference between the single-pipe system and the two-pipe and three-pipe systems. However, radiator flows less than 30 % of the loop flow should be avoided, as they result in unnecessarily large radiators. If, on the other hand, the flow through the radiators is a high proportion of the total loop flow, closure of a radiator valve will mean that the total flow through the loop will fall considerably, thus having a significant effect on the performance of the other radiators. The extreme case is if the radiator flow equals 100 % of the loop flow, which would mean that the radiators were connected in series without any bypasses. Closing any radiator valve would therefore have the effect of stopping the flow through the entire loop. The effect of this is shown in the diagram below, which represents closure of a radiator valve (the first radiator on the loop) for varying proportions of radiator flow. The loop supplies five radiators.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

50 Return temperature (from the loop)

45

Temperature [°C]

40 35 30 25

Room temperature (mean value for room 2 - 5)

20 15 10 5 0 0

10

20

30

40

50

60

70

80

90

100

Proportion of the loop flow through each radiator [% ]

Figure 136.The effect of a closed radiator valve (no. 1) on loop return temperature and room temperatures in the other rooms, as a function of different proportions of loop flow passing through the radiators. It can be seen from the diagram that, when the radiators are taking more than 60 % of the loop flow, the room temperatures in the other rooms start to fall below 20 °C if one radiator on the loop is turned off. This drop in temperature becomes drastic if the proportion of flow passing through the radiators exceeds 80 %. How stable is a single-pipe system? To answer this question, the same type of simulation has been performed as previously described, i.e. investigating the effect of a change in the valve opening of a radiator valve. A difference, however, is that in this case this has been done only for the design outdoor temperature. The diagram below, which is based on a flow through the radiators of 40 % of the total loop flow, shows the effect on total heat release from the loop, as well as from the other radiators, of closing the first radiator valve. The small circle in the diagram show the correct setting of the valve.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Single-pipe system Change of heat release [% ]

20

10 Radiator 2 - 5 0

-10

Total Outdoor temperature = - 15 °C

-20 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 1 [-]

Figure 137.Change in heat released, from all radiators and from radiators 2-5, as a function of the valve opening of radiator valve 1. The effect on the return temperature from the loop is shown in the diagram below. Single-pipe system Return temperature [°C]

50

45

40

Outdoor temperature = - 15 °C

35 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 1 [-]

Figure 138.The effect on loop return temperature as a function of different valve opening of radiator valve 1. The above diagrams do not give a direct indication of the effect of a fully open valve on the system, as the radiator valves that have been used are already almost fully open when correctly set. However, for comparison, it can be said that if the valve had had a kvs value of, for example, 3.0 m³/h (instead of 0.7 m³/h), the change in the amount of heat released by radiators 2-5 would have amounted to + 1.8 %, with the return temperature being 41.1 ºC, for a fully open valve. If the valve characteristic had been the same, the correct setting of this valve would then have been a valve opening of about 0.35.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

If, instead, it is the final radiator valve (no. 5) of which the settings are changed, the following diagrams of the effects on heat release and return temperature are obtained. Single-pipe system Change of heat release [% ]

20

10 Radiator 1 - 4

0

-10

Total Outdoor temperature = - 15 °C

-20 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 5 [-]

Figure 139.Change in heat released, from all radiators and from radiators 1-4, as a function of the valve opening of radiator valve 5. Single-pipe system Return temperature [°C]

50

45

40

Outdoor temperature = - 15 °C

35 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 5 [-]

Figure 140.The effect on loop return temperature as a function of different valve opening of radiator valve 5. The effect on the other radiators is greater if it is radiator valve 1 that is closed, as compared with radiator valve 5. The reverse applies for the return temperature, where closing radiator valve 5 results in a greater increase in the return temperature. The diagrams show in general that a closing of the valve has a considerably greater effect on the system than does an opening of the valve. A major difference between the behaviour of a single-pipe system and a two-pipe system is just that the return temperature in a single-pipe system increases if any thermostatic radiator valves start to

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

close, while the reverse is the case for a two-pipe system, as previously pointed out by Brännström (1987) and others. The supply temperature control curve characteristic (i.e. as a function of the outdoor temperature) can be optimised in both two-pipe and three-pipe systems, so that the desired room temperature can be maintained regardless of the outdoor temperature, and without having to alter the flow through the radiators. This, of course, presupposes correct balancing of the system and no disturbances, which means that this response is likely to be the ideal, rather than as actually achieved in practice. However, it cannot be achieved, even in theory, in a single-pipe system. The diagram below shows how the temperatures in the rooms containing the five radiators connected to the single pipe loop vary with outdoor temperature. The supply temperature has been optimised to give an indoor temperature of 20 ºC in the room containing the first radiator, regardless of the outdoor temperature.

Room temperature [°C]

22

21

20 Room 5 Room 4 Room 3 Room 2

19

Room 1 18 -15

-10

-5

0

5

10

15

Outdoor temperature [°C]

Figure 141.Room temperature deviations as a function of outdoor temperature on a single-pipe system. 6.6.2 Two-pipe system Figure 142 shows the arrangement of the two-pipe system considered in these simulations.

Figure 142.Schematic diagram of the two-pipe system.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The differential pressure across the radiator furthest from the pump (no. 5) has been assumed to be 5 kPa, with a pipe pressure drop of 1 kPa between each radiator, in exactly the same way as for the single-pipe system case. This gives a total system pressure drop of 15 kPa, as illustrated in the diagram below. ∆p [kPa]

Pump

Rad 1

Rad 2

Rad 3

Rad 4

Rad 5

L [m] Figure 143.Pressure distribution in the two-pipe system. As opposed to the single-pipe system, balancing of the radiator valves in the two-pipe system results in their being set to different valve opening, as the differential pressure across the valves changes with distance from the pump. On the other hand, the same size of radiators can be used, as the radiators are not affected by the return temperature from the preceding radiator. The following diagram shows how the valve opening of the first radiator affects total heat release from the system and heat release from the other radiators. Two-pipe system Change of heat release [% ]

20

10 Radiator 2 - 5 0

-10

Total Outdoor temperature = - 15 °C

-20 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 1 [-]

Figure 144.Change in heat released, from all radiators and from radiators 2-5, as a function of the valve opening of radiator valve 1.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The effect of the valve opening on system return temperature is shown in the diagram below. Two-pipe system Return temperature [°C]

50

45

40

Outdoor temperature = - 15 °C

35 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 1 [-]

Figure 145.The effect on loop return temperature as a function of different valve opening of radiator valve 1. Both heat emission and the return temperature are affected more in a two-pipe system than in a single-pipe system. As previously noted, the effect on the return temperature of a fully open valve is relatively great in a two-pipe system. However, the differential pressure across the valve concerned in the above diagrams is 13 kPa at design flow rate in a two-pipe system, while in a single-pipe system the corresponding differential pressure across the valves is only 5 kPa. It can therefore be of interest to investigate the effect of changing the valve opening of the last radiator valve (no. 5) in a two-pipe system, across which the differential pressure is only 5 kPa. The following diagrams show the effect on heat emission and return temperature when the valve opening of radiator valve 5 is changed.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Two-pipe system Change of heat release [% ]

20

10 Radiator 1 - 4 0

-10

Total Outdoor temperature = - 15 °C

-20 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 5 [-]

Figure 146.Change in heat released, from all radiators and from radiators 1-4, as a function of the valve opening of radiator valve 5. Two-pipe system Return temperature [°C]

50

45

40

Outdoor temperature = - 15 °C

35 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 5 [-]

Figure 147.The effect on loop return temperature as a function of different valve opening of radiator valve 5. The return temperature increases slightly more when valve 5 is closed than it does when valve 1 is closed. However, the greater difference in effect between changes in the settings of the two valves occurs when they open. The increase in return temperature when valve 5 opens is nowhere near as great as the increase caused by opening valve 1. This effect was also noted in the earlier simulations of the larger two-pipe system with 20 radiators. However, the two-pipe system still results in a higher return temperature in response to an open valve than does the single pipe system.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

6.6.3 Three-pipe system The schematic arrangement of a three-pipe system is shown in Figure 148 below.

Figure 148. Schematic diagram of a three-pipe system. In the same way as for the single-pipe system case, the differential pressure across all radiators is assumed to be 5 kPa, with a pipe pressure drop of 1 kPa between each radiator. The return connection shown in the diagram above is assumed to present a pipe pressure drop of 5 kPa at the nominal design flow rate. This gives a total pressure drop in the system of 15 kPa, distributed as shown in the diagram below. ∆p [kPa]

Rad 1 Pump

Rad 2

Rad 3

Rad 4

Rad 5

L [m] Figure 149.Pressure drops in the three-pipe system. The following diagram shows how the valve opening of the first radiator affects total heat release from the system and heat release from the other radiators.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Three-pipe system Change of heat release [% ]

20

10 Radiator 2 - 5 0

-10

Total Outdoor temperature = - 15 °C

-20 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 1 [-]

Figure 150.Change in heat released, from all radiators and from radiators 2-5, as a function of the valve opening of radiator valve 1. The effect of the valve opening on system return temperature is shown in the diagram below. Three-pipe system Return temperature [°C]

50

45

40

Outdoor temperature = - 15 °C

35 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 1 [-]

Figure 151.The effect on loop return temperature as a function of different valve opening of radiator valve 1. Heat release and (particularly) the return temperature in a three-pipe system are affected less by the changes than they are in a two-pipe system. The effect on the return temperature is comparable with the corresponding effect in a single-pipe system. It should be noted that it does not matter which valve setting is changed in the three-pipe system: the result is the same. This is due to the fact that there is the same differential pressure drop across all the radiator valves, and so the effect on the total flow is the same, regardless of which valve is opened or closed. However, this is somewhat of a simplification, as it presupposes completely stepless design of the pipe system sizes.

176

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

An aside in this context is that if the same pipe sizes and pipe lengths had been used between the radiators, then it would be the radiator in the centre (no. 3 in the diagram) that would be the design-determining radiator in the three-pipe system. This is due to the fact that it would be this radiator across which the differential pressure would be lowest. In a single-pipe system, the differential pressures across the radiators do not affect each other when the system is balanced, while in a two-pipe system it is the radiator furthest away from the pump (no. 5) that determines the design. 6.6.4 Summary The following diagram can be drawn to illustrate the results of the simulations of single-pipe, two-pipe and three-pipe systems, showing the effect of a change in the valve opening of the first radiator valve in the system on the mean room temperatures in the other rooms.

Room temperature, mean [°C]

22

21 1-pipe 20 3-pipe 19 2-pipe Outdoor temperature = - 15 °C

18 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 1 [-]

Figure 152.The effect of valve opening of the first radiator valve in the system on room temperatures in the other rooms. It can be seen from the diagram that the effect of a change in the opening of the first valve on a single-pipe system is different from that of a valve in a two-pipe or three-pipe system, of which latter behave in a similar manner. Regardless of the type of system, the total flow is reduced when a valve is closed, and increased when a valve opens. In the two-pipe and three-pipe systems, a reduction in the total flow results in a greater differential pressure across the radiator valves. This increases the flow through the valves of which the settings have not been changed, the effect of which can be seen in the diagram by an increase in room temperature as the valve opening of the first valve decreases. In the same way, an increase in the total flow means that the differential pressure across the other valves is reduced, thus having the effect of lowering the room temperatures as the opening of the valve increases. Things are different, however, in a single-pipe system. Here, a reduction in the total flow results in a lower differential pressure across the other valves, thus reducing the flow through them. However, this cannot be seen in the above diagram, as the effect on

177

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

the room temperature seems to be exactly the opposite when the valve opening of the first radiator valve is reduced. However, this is due to a different phenomenon. When a valve is closed, the supply temperature to the next radiator on the loop increases, thus increasing the heat release from that radiator. The combined result is that the reduction in the radiator flow and the increase in the supply temperature counteract each other, which explains why the room temperature first falls and then increases as the valve opening of the first radiator valve is reduced. At first, when the valve starts to close, it is the effect of the flow reduction that dominates, but as the flow approaches zero through the first radiator, it is the increase in supply temperature that dominates. If, instead, it is the last radiator valve that is closed, this effect does not arise, and so there is no corresponding increase in the room temperatures of the other rooms. This is shown in the following diagram, which also includes the effect of closures of valves in two-pipe and three-pipe systems.

Room temperature, mean [°C]

22

21 1-pipe 20 3-pipe 19

2-pipe Outdoor temperature = - 15 °C

18 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 5 [-]

Figure 153.The effect of valve opening of the last radiator valve in the system on room temperatures in the other rooms. The above reasoning also explains to some extent the change in room temperature when the valve opening of a radiator valve is changed. In two-pipe and three-pipe systems, the return temperature depends on the distribution of the total system flow between the radiators. A fully closed valve increases the flow through the other radiators, thus increasing the return temperature. Although, on the other hand, a fully open valve results in a reduced flow through the other radiators, it also substantially increases the flow through its radiator, which has the effect of increasing the system return temperature. However, in a single-pipe system, flow through the other radiators is reduced when a valve is closed. Although this ought to result in a lower return temperature, this is offset by the increased supply temperature which, instead, results in an increase in the return temperature. When, instead, the radiator valve is opened, the flow through all radiators increases, which naturally increases the return temperature.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

The diagram below shows the effect on the return temperature of changing the valve opening of the first radiator valve in single-pipe, two-pipe and three-pipe systems.

Return temperature [°C]

50 2-pipe 45

3-pipe 40

1-pipe

Outdoor temperature = - 15 °C

35 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 1 [-]

Figure 154.The effect of valve opening of the first radiator valve in the system on the return temperature. It can be seen from the diagram that closing a radiator valve has the greatest effect on the return temperature in a three-pipe system, which is due to the fact that the differential pressure across the radiators is relatively low in this type of system (see Section 6.3.6 concerning the effect of differential pressure). The differential pressure across radiator valve 1 is considerably higher in a two-pipe system, which means that the effect on the return temperature of closing this valve is not as great in such a system. For the same reason, fully opening this valve has a much greater effect on the return temperature in a two-pipe system than in a three-pipe system. If, instead, it is the setting of the last radiator valve that is changed, the change in the return temperature of a two-pipe system due to a fully open valve is not as great (see Section 6.3.6 concerning the effect of the position of the valve in the system). In this case, there is little difference between the effect in a two-pipe system and that in a three-pipe system, as can be seen from the following diagram.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

Return temperature [°C]

50

45 2-pipe 3-pipe

40

1-pipe

Outdoor temperature = - 15 °C

35 0

0.2

0.4

0.6

0.8

1

Valve opening of radiator valve 5 [-]

Figure 155.The effect of valve opening of the last radiator valve in the system on the return temperature. The following conclusions can be drawn, and views put forward, on the basis of the simple analysis of the differences in the responses of the different systems: • Most of the difference between two-pipe and three-pipe systems is due to the fact that the differential pressure across the radiators varies considerably more in the two-pipe systems. It should therefore be simpler to balance a three-pipe system; this can be compared with simplified balancing of a two-pipe system, but with the difference that simplified balancing of two-pipe systems will virtually always result in deviations from the ideal design settings. • The difference in sensitivity between the two-pipe and the three-pipe systems is due only indirectly to the structures of the systems, to the extent that it is the differential pressure that determines how great the effect of an open or closed valve will be. In the two-pipe system, the difference depends on which valve or valves have had their settings changed, while this is of lesser importance in a three-pipe system. In other respects, the systems behave similarly. • The behaviour of the single-pipe system is quite different from that of the two-pipe and three-pipe systems, whether in respect of pressure, flow or temperature considerations. Despite this - or perhaps just because of it - the performance of single-pipe systems seems to be quite stable. However, this is not necessarily the case, as the static consideration approach that has been used in this work tends to work in favour of the single-pipe system. This is due to the fact that the effects of a flow increase, with resulting decreasing in the supply temperature to the downstream radiators, tend to counteract each other, with the result that there is little overall effect on the system, as seen from a static perspective. In actual fact, the flow changes quickly, while the temperature changes only slowly, which means that the effect of a flow disturbance can be relatively considerable before steady-state conditions are again re-established. 180

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

• A problem area with single-pipe systems is that of choosing an appropriate size of radiators, with it being necessary to decide on the supply temperature of each radiator connected to the loop. If the wrong radiator size is chosen, operational problems can arise even if corrective countermeasures are attempted. Changing the flow through an incorrectly sized radiator affects the supply temperature to the downstream radiators, causing knock-on problems in the entire system. Another problem is that of control of the supply temperature. Regardless of how this is arranged, there will be deviations in the design heat release performance of the radiators, as has been shown in the simulations. Further, one-pipe systems have a serious drawback when connected to district heating systems, in that when the heat demand falls and any thermostatic radiator valves (if fitted) close, the return temperature rises, which is undesirable. It must be added that the above analysis is fairly simple and very theoretical (no physical measurements having been made to confirm the results of the simulations in this respect), which means that the results should be regarded with some caution. In addition, only certain aspects concerning the system's sensitivity to deviations have been considered: for example, differences in capital or running costs, service considerations, maintenance etc. have not been considered. This applies, of course, to all the analyses performed in this work.

6.7

The effect of the district heating substation radiator heat exchanger

Any deviation clearly affects the return temperature in the building's heating system. At the same time, it also affects the return temperature on the district heating side. The link between the district heating system and the building's heating system is provided by the heat exchangers in the district heating substation. The change in the district heating return temperature resulting from deviations in the building's heating system can be due to three different factors: • A change in the return temperature of the heating system. A change in the return temperature of the building's heating system changes the temperature difference between the district heating water and the building's space heating water. This causes a change in the amount of thermal power transferred, and thus a change in the return temperature of the district heating water. • A change in the building's space heating system flow. A change in the flow on the secondary side of the heat exchanger (i.e. the building space heating system side) affects the coefficient of thermal transmittance. This changes the amount of thermal power transferred, thus changing the return temperature on the district heating side. • The above two changes affect not only the return temperature of the district heating water, but also the supply temperature of the water in the building's space heating system. In order to maintain the required supply temperature, it is necessary to control the thermal power transfer, which is done by varying the flow through the 181

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

primary side of the heat exchanger. Again, this has the effect of changing the district heating water return temperature. It is the combined effect of these three changes that determines the return temperature of the district heating water. A simple design model of a flat plate heat exchanger has been used to demonstrate this. It is described in Appendix B, and is based on the equations, recommendations and parameters described in “Värmeväxlare” (Heat exchangers) (1994) and “Fjärrvärmecentralen” (District heating substation units) (1996) from Fjärrvärmeföreningen (Swedish District Heating Association) and by Hjorthol (1990). Two model heat exchangers have been designed: one for a high-flow system and one for a low-flow system. The design temperatures of the high-flow system heat exchanger are 100/43 ºC on the primary side, and 60/40 ºC on the secondary side. This gives a terminal temperature difference of 3 ºC, i.e. the return temperature of the district heating water is 3 °C higher than the return temperature of the space heating water. The heat exchanger for the low-flow system is designed for the same terminal temperature difference, with primary side design temperatures of 100/36.3 ºC and secondary side temperatures of 73.3/33.3 ºC. The thermal power transmission capacity at the design outdoor temperature is 20 kW, which means that the high-flow system heat exchanger has been designed for an NTU value of 4.0, while the low-flow system heat exchanger has been designed for an NTU value of 5.9. The NTU value is a measure of the heat exchanger's heat transfer capacity, and is defined as: NTU = where NTU U A C min

= = = =

U⋅A C min

(35)

Number of Transfer Units [-] Coefficient of thermal transmittance of the heat exchanger [W/m²K] Heat transfer area of the heat exchanger [m²] Minimum thermal capacity flow of the heat exchanger [W/K]

The NTU value is not constant, but changes continuously during operation. In order to investigate the effect of deviations in the radiator systems on the district heating return water temperature, we can analyse the effect of the radiator systems' return temperatures and flows at varying proportions of fully open radiator valves. This was done for the radiator systems described in Section 6.3.6. The values from these simulations can now be applied to the heat exchanger, which gives the following diagrams for the design case at an outdoor temperature of -15 ºC.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

High-flow system District heating return temperature [°C]

55

50

45

40 Outdoor temperature = - 15 °C

Return temperature

35

Return temperature and flow Return temperature, flow and control

30 0

10

20

30

40

50

60

Proportion of fully open radiator valves [% ]

Figure 156.The effect of the proportion of fully open radiator valves on the district heating return temperature (high-flow system). Low-flow system District heating return temperature [°C]

55

50

45

40 Outdoor temperature = - 15 °C

Return temperature

35

Return temperature and flow Return temperature, flow and control

30 0

10

20

30

40

50

60

Proportion of fully open radiator valves [% ]

Figure 157.The effect of the proportion of fully open radiator valves on the district heating return temperature (low-flow system). The various curves in the diagrams show the effect of considering a change in the radiator system return temperature alone, a change in both the return temperature and the flow and, finally, the effect of a change in the return temperature and the flow, in 183

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

combination with control of the radiator system supply temperature. From a real-life perspective, it is really only the final case, considering all three parameters, that is of interest. However, comparison with the other two cases shows the magnitude of the effects of the respective parameters on the return temperature. For example, the district heating water return temperature is reduced only very little by a change in the radiator system flow in the high-flow system. This reduction is greater in the low-flow system, and for this there is hardly any need to control the district heating water flow at all in order to maintain the necessary supply temperature. In this respect, the increase in radiator system return temperature and the increase in radiator system flow rate tend to counteract each other, so that there is hardly any change in the supply temperature, despite the fact that there is a drastic change in the return temperature. As previously pointed out, only two radiator valves (10 % of the number) need to be fully opened for the return temperature in the low-flow system to exceed the return temperature in the high-flow system. The same applies if it is the district heating return temperature that is considered, as can be seen from Figures 156 and 157 above. The following diagram, which shows the effect of the radiator system's return temperature and flow (both high-flow and low-flow systems), provides a more general picture of how deviations in the radiator systems affect the return temperature of the district heating water. It illustrates conditions for the design cases, with the supply temperature being held constant by controlling the district heating water flow. The ringed positions indicate the ideal positions.

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6 SIMULATION AND RESULTS – RADIATOR SYSTEM

47 High-flow system

46

NTU : 4.0 District heating : 100/43 °C

District heating return temperature [°C]

45

Radiator system : 60/40 °C

44 43 42 41 Change in the radiator systems' flow + 20 % + 10 % 0% - 10 % - 20 %

40 39 38 37 36 35

Low-flow system

34

NTU : 5.9 District heating : 100/36.3 °C

33

Radiator system : 73.3/33.3 °C

32 -5

-4

-3

-2

-1

0

1

2

3

4

5

Change in the radiator system return temperature [°C]

Figure 158.The effect of changes of return temperature and flow in the radiator systems on the district heating return water temperature. The radiator system supply temperature is maintained constant. The above diagram shows that, in the low-flow system, the curves are somewhat closer to each other then they are in the high-flow system, which indicates that the return temperature of the district heating water is somewhat less sensitive to deviations in the flow of the low-flow system. At the same time, the slope of the low-flow system curves is somewhat steeper. This indicates that the heat exchanger - or, rather, the return temperature of the district heating water - is somewhat more sensitive to changes in the radiator system return water temperature when connected to a low-flow system. An increase of 1 ºC in the radiator system return temperature increases the district heating return temperature by 0.6 - 0.7 ºC if it occurs in a high-flow system, while the corresponding increase if connected to a low-flow system is about 0.8 ºC, regardless of the flow rate.

185

6 SIMULATION AND RESULTS – RADIATOR SYSTEM

186

7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

7

SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

7.1

Performing the work

The purpose of the simulations described in this chapter is to show how the particular choice of system configuration affects both the static and the dynamic characteristics, and how they affect the sensitivity of the system to deviations. The planning of the simulations in this chapter is described in Chapter 5.

7.2

Optimum valve characteristic

The optimum valve characteristic is one that is so tailored to each system that the width of the necessary P-band is constant, regardless of the valve opening of the valve, and thus also at a minimum. These are ideal values that show the potentials of the systems when set up to have the least possible difficulty of control, and operating without any deviations. The process of arriving at the optimum valve characteristic, as described in this chapter, has been carried out by iteration, which is quite time-consuming. The dead time and the time constant can be arrived at by assuming a particular valve characteristic, and then analysing the results of a step change response simulation with this characteristic. They are then used to calculate a suitable static characteristic which, when applied in conjunction with the particular valve authority (which depends on the size of the control valve, and not on its characteristic), provides a new valve characteristic, which is then used for the next iteration, and so on. The end result of this process is to arrive at an optimum valve characteristic, giving a more or less constant P-band width when simulating step change responses. For further reading, see Grindal (1994 and 1995), whose work provided the inspiration for this presentation. In Appendix B a slightly simplified method of arriving at the optimum characteristic is described, just to give an idea of the process. 7.2.1 The reference case The following table shows the necessary P-band widths arrived at for the six reference cases, i.e. in which there are no deviations, and the control valve is of optimum type. In the case of the SABO connection, which uses a three-way valve, the characteristic of the shunt port is assumed to be partly linear and partly logarithmic, while the characteristic of the control port has been optimised. This explains the reason for two values for the respective balancing settings of this arrangement.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

Valve group Direct District heating SABO (Linear) SABO (Log)

Balancing High flow Low flow 7.3 7.1 8.7 14.1 10.6 15.9 16.5 23.2

Table 12. Necessary P-band widths with an optimum valve characteristic for each valve group and balancing condition. The narrowest necessary P-band width is that of the directly connected valve group, with the high-flow and low-flow systems giving approximately the same value. For the other connection arrangements, there is a clear difference between the values for the high-flow and the low-flow systems, due primarily to the fact that the dead time is considerably greater in the low-flow systems. The SABO connection requires the widest P-band width: in fact, it can be seen from the table that the use of a SABO connection with a logarithmic shunt port should be avoided, in order to reduce the risk of control problems, as this arrangement requires a relatively wide P-band width. For this reason, unless otherwise stated, any further references to, or calculations of, the SABO connection will refer only to its arrangement with a linear shunt port. The optimum characteristic, as used for arriving at the values in Table 12, is shown in the following diagrams. It should again be pointed out that these characteristics have been derived in order to produce as narrow a constant P-band width as possible, regardless of the valve opening. This means that some of the valve characteristics may have a somewhat unusual shape. This applies particularly for the SABO arrangement, with a logarithmic shunt port, and so this is once again considered here. The reason for the somewhat unusual shape of this characteristic is that the logarithmic shunt port effects the flow in the circulation circuit for any valve opening other than fully open and fully closed. In turn, this affects the dead time, which has to be compensated for by the optimum valve characteristic of the control port. For comparison, the diagrams also show the previously described linear and logarithmic characteristics (pale lines).

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

Relative kv value (kv/kvs ) [-]

Direct connection 1.0 0.9 0.8 0.7 0.6

Low-flow system High-flow system

0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 159.Optimum valve characteristic for the direct connection

Relative kv value (kv/kvs ) [-]

District heating connection 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Low-flow system High-flow system

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 160.Optimum valve characteristic for the district heating connection.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

Relative kv value (kv/kvs ) [-]

SABO connection (Linear shunt port) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Low-flow system High-flow system

0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 161.Optimum valve characteristic for the SABO connection, with a linear shunt port.

Relative kv value (kv/kvs ) [-]

SABO connection (Logarithmic shunt port) 1.0 0.9 0.8 0.7

Low-flow system High-flow system

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 162.Optimum valve characteristic for the SABO connection, with a logarithmic shunt port. In the above diagrams, the optimum valve characteristics have been matched to the valve authorities, the characteristic of the heat-releasing component, the dead time and the time constant for each step in the valve opening of the valve. It can be seen that there is little difference in the optimum valve characteristic for each valve group between high-flow and low-flow systems (possibly with the exception of the direct connection arrangement). The following diagrams (one for each type of balancing) show how the return temperature is affected in the six reference cases. As previously shown (in Chapter 5), the supply temperature is controlled as a function of the outdoor temperature, in order to maintain the temperature of the air leaving the air heater constant at 20 ºC. The overall 190

7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

efficiency of the valve groups in the design case, which is the same as the efficiency of the air heater, is 0.48 on the air side and 0.35 on the water side for high-flow systems, with corresponding values of 0.36 and 0.55 for low-flow systems. High-flow system 40 38

Temperature [°C]

36 34 32 30

DH SABO (Lin)

28

D

26 24 22 20 -20

-15

-10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 163.Return temperatures for the high-flow system reference cases. Low-flow system 40 38

Temperature [°C]

36 34 32 30

DH

28

SABO (Lin) D

26 24 22 20 -20

-15

-10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 164.Return temperatures for the low-flow system reference cases. It can be seen from the diagrams that there is little difference in the return temperatures from the different types of valve groups, and also that there is little difference between the performances of the high-flow and low-flow systems in this respect. The lowest 191

7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

return temperature is provided by the directly connected arrangement, which can also be seen from the following table, which shows the weighted return temperatures for the reference cases over the year.

Valve group Direct District heating SABO (Linear)

Balancing High flow Low flow 24.1 23.0 25.1 23.8 25.1 23.6

Table 13. Weighted annual return temperature for the reference cases (that is optimum valve characteristic and no deviations). It can be seen from the table that the return temperatures for the high-flow and low-flow systems are more or less the same for the district heating and the SABO connections, while the return temperature for the direct connection is slightly lower. This is due to the controlling of the flow in the direct connection. A more flat control curve characteristic (this means that the supply temperature does not change so much with outdoor temperature) would result in a bigger difference, which is shown in Section 7.5. The difference in the return temperatures from the high-flow and low-flow systems is only little more than 1 ºC, which is surprisingly small. This is due to the size of the air heater and the flow values for the respective balancing set-ups. Higher flows would presumably have resulted in a greater difference in the return temperatures. However, as such higher flows were not measured in the actual physical measurements, it is doubtful whether they should be used in the simulations. But it must be pointed out that the difference in the return temperatures between the high-flow and low-flow systems is not particularly relevant at this stage, since focus remains on the effect of deviations on return temperature. 7.2.2 Different valve size In the reference cases described above, the sizes of the control valves are defined by their maximum capacities (kvs values) of 4.0 m³/h. It is thefore natural to wonder how a different valve size would affect the optimum valve characteristic, the necessary P-band width and the resulting return temperature. In order to quantify this, simulations of the district heating valve group in the high-flow arrangement have been run with one larger and one smaller valve size, that is with kvs values of 2.5 and 10.0 m³/h respectively. Each system has been correctly balanced, and the optimum valve characteristic developed. The table below shows the results, in terms of the necessary P-band width and the weighted annual return temperature as functions of the valve size. In addition, the table also shows how the valve authorities are affected by the valve sizes.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

Valve group Opt-2.5,H,DH Opt-4,H,DH Opt-10,H,DH

Necessary P-band width [ºC] 8.7 8.7 8.7

Return temperature [ºC] 25.1 25.1 25.1

Valve authority [-] 0.72 0.30 0.05

Table 14. The effect of control valve size on the necessary P-band width, return temperature and valve authority. The table shows that the size of the control valve has no effect on either the necessary P-band width or the weighted annual return temperature. This means that the valve authority on its own does not really affect the control performance of the system: instead, it is the combination of valve characteristic, valve authority and the characteristics of the heat-releasing component, together with the dynamic properties of the system, that determine the results. It must also be emphasised that the valve characteristics differ in the three cases represented in the table. The three optimum characteristics are shown in the following diagram, which also shows the linear and logarithmic characteristics (pale lines) for comparison.

Relative kv value (kv/kvs ) [-]

District heating connection (High-flow) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Valve authority 0.72 0.30 0.05

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 165.The effect of control valve size (expressed as valve authority) on the optimum valve characteristic. The fact that the characteristics are different is due to the valve authorities being different in the three cases. A low valve authority results in considerable “distortion” of the characteristic, which therefore requires a considerably distorted mechanical valve characteristic in order to compensate for it. See also Chapter 2. It can be appropriate here to point out that corresponding simulations have also been run for the district heating connection with a low balanced flow. The results are the same as those described above for the high-flow system, that is with no difference in the necessary P-band width or return temperature in response to changes in the size of the control valve.

193

7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

7.2.3 Varying available differential pressure The simulations described so far have assumed a constant available differential pressure across the valve groups. In reality, this pressure varies with the flow in the system. When the control valve is almost closed, system flow is low, with the result that the pressure drop in the rest of the distribution system is low, thus increasing the available differential pressure across the valve group. The main pump characteristic also affect the available differential pressure. For this reason, a simulation has been run with a varying available differential pressure. Assuming that the flow is fully turbulent, the differential pressure varies with the square of the flow, as previously shown by Equation (32) in Chapter 5. The differential pressure is assumed to be twice as high at zero flow as at design flow. In the case of the high-flow system, this means that the available differential pressure is 60 kPa when the control valve is fully closed, and 30 kPa when it is fully open. If the same size of control valve is used as in the reference case (kvs value of 4.0 m³/h), there will be no difference in the balancing. In comparison with the reference case, the only difference that occurs is that the valve authority in the district heating connection case drops from 0.30 to half as much, that is to 0.15. This is naturally due to the fact that the differential pressure across the fully closed control valve is twice as high, as the available differential pressure is also twice as high. In the previous section it was shown that, as long as the valve characteristic was optimised, the effect of the valve authority on the necessary P-band width and the weighted return temperature was insignificant. There is therefore no difference in the necessary P-band width or weighted return temperature even if the available differential pressure varies with the primary flow through the valve group. In this case, the optimum valve characteristic required is as shown in the following diagram, which also shows the optimum characteristics for the three different valve sizes in the previous section (from Figure 165).

Relative kv value (kv/kvs ) [-]

District heating connection (High-flow) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Valve authority 0.72 (Small valve) 0.30 (Original valve) 0.15 (Varying diff. Press.) 0.05 (Large valve)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 166.The effect of valve authority on the optimum valve characteristic.

194

7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

The diagram shows the progressive additional distortion of the optimum valve characteristic required as the valve authority is reduced, regardless of what the change in the valve authority depends on. In the rest of this chapter, unless otherwise stated, the available differential pressure across the valve groups will be assumed to be constant. 7.2.4 Summary The simulations show that the various system arrangements have different characteristics in terms of their potential responses to control, even before the particular type of control valve has been selected. The concept of an optimum valve characteristic helps to demonstrate this. Regardless of balancing, the direct connection is the simplest type of system arrangement to control: in the other systems, balancing affects the subsequent ease or difficulty of control. A low flow rate increases the system dead times as far as circulation is concerned, and thus makes control more difficult. The difference in the requisite P-band width between the district heating connection and the SABO connection is also related to the dead time. The diagram below shows how the primary and secondary flows in a SABO connection can be affected by the choice of control valve. SABO connection (High-flow) 1.0 0.9 Relative flow [-]

0.8 0.7 0.6 0.5 0.4 0.3

Log - Lin

0.2

Log - Log

0.1 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure 167.Relative primary and secondary flows in a SABO connection, depending on the type of control valve. The diagram shows that the flow on the secondary side falls as the control valve is opened, and rises to the balanced value when the valve is fully opened. As the dead time increases with decreasing secondary flow, the result is to increase the difficulty of control (that is the necessary P-band width) as the secondary flow is reduced. To compensate for this, the control port must have a more linear characteristic, but at the same time this means that the gain (that is the temperature rise of the air across the air

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

heater) increases for a small valve opening, which also complicates control of the system. This means that the optimum characteristic of the control port will unavoidably result in a secondary flow that is not constant. The effect of this is that the dead time in the SABO connection will always be somewhat longer than in the district heating connection, so that the SABO connection is also somewhat more difficult to control. For the same reason, a logarithmic recirculation port is unsuitable, as this will increase the system dead time and so also the difficulty of control. Although the simulations also show that the size of the valve, or the variation in the differential pressure of the system, affect the valve authority, this does not necessarily automatically mean that the difficulty of control will be affected. A low valve authority can be compensated for by a suitable choice of valve characteristic. Taking this further, this can mean that the control valve characteristic can be chosen in such a way as to compensate for the variation in the system differential pressure. However, this naturally presupposes that the variation of the differential pressure in the system is known, and this is probably uncommon. The return temperature does not seem to be significantly affected by the choice of valve group, and nor by the valve authority at all. Admittedly, the direct connection arrangement results in a somewhat lower weighted annual return temperature, but the difference is not particularly great. This is because control of the supply temperature means that it is not necessary to reduce the flow rate very much as the outdoor temperature rises, and so the effect on the return temperature is not as great in the direct connection arrangement as it would have been if the supply temperature had been constant. See Section 7.5. The effect of balancing on the return temperature is also modest. In the low-flow case, the weighted annual temperature is reduced by only slightly more than 1 °C as the result of balancing. However, this is not a general phenomenon, but is due to the size of the air heater and the balanced flows. A low flow gives a low UA value, which needs to be compensated for by a high mean temperature, so that the supply temperature is also high, giving a correspondingly relatively high return temperature in the low-flow system. Higher flows would presumably have resulted in a greater difference in the return temperature, but such flows were not measured during the actual physical measurements, and so it is doubtful whether they can be used in the simulations.

7.3

Actual valve characteristic

In practice, optimum valve characteristics are highly unlikely to be encountered: the range of control valves available, whether in terms of technical performance or of price, renders it highly improbable. In addition, it is far from clear which characteristic is most suitable for each item to be controlled. This section therefore considers the effect of “actual” valve characteristics on the systems. Two different standardised characteristics (linear and logarithmic) are used in the simulations in order to show the effect that the deviation in respect of the valve characteristic always represents. It must also be pointed out that the logarithmic characteristic is not strictly in accordance with the logarithmic standard, but somewhat modified in order to allow the valve to close completely.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

7.3.1 Linear and logarithmic valve characteristics The diagrams below show the effect of linear and logarithmic valve characteristics on the necessary P-bands of the six combinations of valve groups and balancing as used in the reference cases. The control valve sizes are represented by a kvs value of 4.0 m³/h. For comparison, the diagrams also show the necessary P-bands for the reference cases of the respective combinations, as achieved using the optimum valve characteristic arrived at as described in the previous section. Direct connection, Low-flow

40

Necessary P-band width [°C]

Necessary P-band width [°C]

Direct connection, High-flow Lin Log Opt

35 30 25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

40 Lin Log Opt

35 30 25 20 15 10 5 0

1.0

0.0

0.2

Valve opening [-]

0.4

0.6

0.8

1.0

Valve opening [-]

Figure 168.Necessary P-band width for direct connection with linear, logarithmic and optimum valve characteristics. DH connection, Low-flow

40

Necessary P-band width [°C]

Necessary P-band width [°C]

DH connection, High-flow Lin Log

35 30

Opt

25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

40 Lin Log

35 30

Opt

25 20 15 10 5 0 0.0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 169.Necessary P-band width for the district heating connection with linear, logarithmic and optimum valve characteristics.

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SABO connection, Low-flow Necessary P-band width [°C]

Necessary P-band width [°C]

SABO connection, High-flow 40 Lin Log Opt

35 30 25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

40 Lin Log Opt

35 30 25 20 15 10 5 0 0.0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 170.Necessary P-band width for the SABO connection with linear, logarithmic and optimum valve characteristics. It can be seen from the diagrams that, in all cases, the logarithmic characteristic is closer to the optimum characteristic (and results in a narrower P-band width in general) than is the linear characteristic. In the high-flow cases, the logarithmic characteristic results in an almost insignificant increase in the maximum value of the necessary P-band width. However, in the low-flow case, when used with the district heating and SABO connections, the logarithmic characteristic results in an increase of about 30 % in the necessary P-band width. For the direct connection case, the increase in the necessary P-band width is approximately the same in both the high-flow and low-flow cases. Admittedly, the linear characteristic results in a particularly narrow P-band width when the valve opening of the control valve exceeds about 50 %, but the width increases substantially when the control valve is nearly closed. The overall result of this is to produce difficult control conditions in this part of the working range of the control valve. The weighted annual return temperatures for each of the six combinations of valve groups and balancing, with the respective types of control valves, are shown in the table below. Control valve (kvs: 4.0 m³/h) Optimum Logarithmic Linear System H, D 24.1 24.1 24.1 L, D 23.0 23.0 23.1 H, DH 25.1 25.1 25.1 L, DH 23.8 23.8 23.8 H, SABO 25.1 25.1 25.0 L, SABO 23.6 23.7 23.7 Table 15. Weighted return temperatures, as determined by the reference cases and types of control valves.

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The difference between the real conditions of logarithmic or linear control characteristics, and the optimum characteristic (the left-hand column), does not exceed 0.1 ºC in any of the reference cases, which means that the choice of type of control valve is, in fact, of little interest as far as the return temperature is concerned. 7.3.2 Different valve sizes Changing the size of the control valve alters its authority, and thus the effect of the necessary P-band width. This is exemplified in the following diagrams by the effect in the case of the district heating connection. It can be seen how the necessary P-band width varies with the size of the linear or logarithmic control valves. kvs: 10.0 m³/h (β ≈ 0.05) DH connection, Low-flow Necessary P-band width [°C]

Necessary P-band width [°C]

DH connection, High-flow 40 Lin Log Opt

35 30 25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

40 Lin Log Opt

35 30 25 20 15 10 5 0 0.0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 171.The effect of a large control valve (kvs = 10.0 m³/h) with a low authority (β ≈ 0.05) on the necessary P-band width when using the district heating connection.

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kvs: 4.0 m³/h (β ≈ 0.30) DH connection, Low-flow Necessary P-band width [°C]

Necessary P-band width [°C]

DH connection, High-flow 40 Lin

35

Log Opt

30 25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

40 Lin

35

Log Opt

30 25 20 15 10 5 0

1.0

0.0

0.2

Valve opening [-]

0.4

0.6

0.8

1.0

Valve opening [-]

Figure 172.The effect of the original control valve (kvs = 4.0 m³/h) with the original authority (β ≈ 0.30) on the necessary P-band width when using the district heating connection. kvs: 2.5 m³/h (β ≈ 0.72) DH connection, Low-flow

40

Necessary P-band width [°C]

Necessary P-band width [°C]

DH connection, High-flow Lin Log Opt

35 30 25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

40 Lin Log Opt

35 30 25 20 15 10 5 0 0.0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 173.The effect of a small control valve (kvs = 2.5 m³/h) with a high authority (β ≈ 0.72) on the necessary P-band width when using the district heating connection. The above diagrams show how the necessary P-band “rotates” around the optimum line as the valve characteristic changes. In each case, the system has been correctly balanced, without deviations. It can also be seen that the linear characteristic is directly unsuitable for use with a low valve authority, although becoming increasingly suitable as the valve authority increases (that is as the valve size decreases). The effect on the

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necessary P-band width of a linear characteristic valve, with a capacity of 2.5 m³/h and a valve authority of 0.72, is approximately the same as that of the logarithmic valve. The difference is that the logarithmic characteristic is most difficult to control when the valve is almost fully open, while the linear characteristic is most difficult to control when the valve is almost fully closed. Comparison of the change in the necessary P-band width in response to the valve opening shows that it is similar in both high-flow and low-flow systems, although the low-flow systems require the greatest widths of necessary P-band in all cases. The same factors apply for the other valve groups. Unless otherwise stated, it is the results of the simulations using the logarithmic valve characteristics that will be described in the rest of this presentation, as this clearly provides results that are closest to those of the optimum case as far as the necessary P-band width is concerned. Table 16 shows the weighted return temperatures for all system configurations with linear and logarithmic valve characteristics, as well as for different valve sizes. The system designations describe the valve size, type of system balancing and type of valve group.

System 2.5, H, D 4, H, D 10, H, D 2.5, L, D 4, L, D 10, L, D 2.5, H, DH 4, H, DH 10, H, DH 2.5, L, DH 4, L, DH 10, L, DH 2.5, H, SABO 4, H, SABO 10, H, SABO 2.5, L, SABO 4, L, SABO 10, L, SABO

Optimum 24.1 24.1 24.1 23.0 23.0 23.0 25.1 25.1 25.1 23.8 23.8 23.8 25.1 25.1 25.1 23.6 23.6 23.6

Control valve Logarithmic 24.1 24.1 24.1 23.0 23.0 23.0 25.1 25.1 25.1 23.8 23.8 23.8 25.0 25.1 25.1 23.7 23.7 23.8

Linear 24.1 24.1 24.1 23.0 23.0 23.0 25.1 25.1 25.1 23.8 23.8 23.8 25.1 25.0 25.1 23.8 23.7 23.8

Table 16. Weighted return temperatures for various system configurations. It can be seen from the table that neither the size nor characteristic of the control valve have any significant effect on the return temperature. 7.3.3 Summary An “actual” valve characteristic involves a negative deviation in the systems, as compared with the optimum characteristic. The necessary P-band width increases. The

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

simulations show that a linear control valve is more difficult to control when it is almost closed, while (in most cases) a logarithmic valve is closer to the optimum valve characteristic. It is not until the valve has a high authority that a linear valve characteristic can be considered. A high efficiency of the air heater (on the water side) also tends to favour a linear characteristic. Børresen (1994) has developed rules of thumb for this, which say that a linear characteristic should be selected only if the product of the air heater efficiency (on the water side) and the valve authority equals or is greater than 0.3. The results of this work agree well with this rule of thumb, regardless of the type of valve group. Figure 173 (above) represents an example of this, with the product of efficiency and valve authority having a value of 0.25 for the high-flow system in the left-hand diagram, and 0.40 for the low-flow system in the right-hand diagram. It can be clearly seen from the diagram that the logarithmic valve requires a somewhat narrower maximum necessary P-band in the high-flow system, while the linear valve is preferable (just) in the low-flow system. The simulations also show that the choice of control valve, whether in terms of size or characteristic, has little effect on the return temperature. Instead, it is the balancing of the system that determines the effect on the return temperature, as described below.

7.4

Deviations in setting of balancing valve

Up to now, all the systems simulated have been correctly balanced. In practice, perfect setting of the balancing valves is highly unlikely, which means that real systems depart from the ideal to a greater or lesser extent. The effect of such departures from ideal balancing depends on whether it is the balancing valve on the primary or on the secondary side that is the main reason for the non-compliance, and so the two valves will be considered individually. In the case of the direct connection, it will be considered as if the balancing valve is on the primary side. The simulations assume that the settings of the valve opening of the balancing valves depart from the correct values by ± 0.1. 7.4.1 Primary side balancing valve Table 17 shows the correct and incorrect settings of the primary side balancing valves in the respective systems, as used in the simulations.

System Log-4,H,D Log-4,L,D Log-4,H,DH Log-4,L,DH Log-4,H,SABO Log-4,L,SABO

Valve opening [-] More closed (- 0.1) Correct More open (+ 0.1) 0.27 0.37 0.47 0.27 0.37 0.47 0.29 0.39 0.49 0.31 0.41 0.51 0.22 0.32 0.42 0.25 0.35 0.45

Table 17. Correct and “out of balance” settings of the balancing valves on the primary sides in the six systems considered.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

The fact that, in some cases, the settings are quite similar in both the high-flow and low-flow cases is due to the fact that the available differential pressures differ for the various balancing cases. The following diagrams show how the width of the necessary P-band is affected by the changes in the settings of the primary side balancing valve. This valve are indicated by I1 in the diagrams, with the deviation in the valve opening being indicated by either - 0.1 or + 0.1. Direct connection, Low-flow

40

Necessary P-band width [°C]

Necessary P-band width [°C]

Direct connection, High-flow I1: + 0.1 Correct balancing

35 30

I1: - 0.1

25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

40 I1: + 0.1

35

Correct balancing

30

I1: - 0.1

25 20 15 10 5 0

1.0

0.0

0.2

Valve opening [-]

0.4

0.6

0.8

1.0

Valve opening [-]

Figure 174.The effect on the necessary P-band width of changes in the setting of the primary side balancing valve for direct connection. DH connection, Low-flow Necessary P-band width [°C]

Necessary P-band width [°C]

DH connection, High-flow 40 I1: + 0.1 Correct balancing

35 30

I1: - 0.1

25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

40 I1: + 0.1

35

Correct balancing

30

I1: - 0.1

25 20 15 10 5 0 0.0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 175.The effect on the necessary P-band width of changes in the setting of the primary side balancing valve for the district heating connection.

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SABO connection, Low-flow

40

Necessary P-band width [°C]

Necessary P-band width [°C]

SABO connection, High-flow I1: + 0.1

35

Correct balancing

30

I1: - 0.1

25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

40 I1: + 0.1

35

Correct balancing

30

I1: - 0.1

25 20 15 10 5 0 0.0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 176.The effect on the necessary P-band width of changes in the setting of the primary side balancing valve for the SABO connection. It can be seen that, in all cases, there is an increase in the necessary P-band width as the valve opening of the balancing valve on the primary side increases. Correspondingly, a reduced valve opening narrows the necessary P-band width, which might be thought to be favourable, until it is realised that the drawback of the reduced valve opening is that it is not possible to achieve the design conditions, as either the flow is too low when the control valve is fully open (for the direct connection and the SABO connection), or because the design inlet temperature cannot be achieved (for the district heating connection). Table 18 shows how the design exit air temperature from the air heater (indicated by ta,out,design), and the weighted return temperature (indicated by tw,return), are affected by the changes in the valve opening of the balancing valve on the primary sides. In those cases when the outlet air temperature does not reach 20 °C under design conditions, with the balancing valve closed too much, the values in brackets show what the weighted return temperature would be if, in these cases, the control curve characteristic (the water supply temperature) was increased in order to correct the low air temperature.

System Log-4,H,D Log-4,L,D Log-4,H,DH Log-4,L,DH Log-4,H,SABO Log-4,L,SABO

I1 = - 0.1 ta,out,design tw,return 16.9 23.9 (23.7) 16.1 22.4 (22.4) 16.9 25.0 (25.2) 16.9 23.6 (23.8) 17.9 25.0 (25.1) 19.3 23.6 (23.6)

Correct ta,out,design tw,return 20.0 24.1 20.0 23.0 20.0 25.1 20.0 23.8 20.0 25.1 20.0 23.7

I1 = + 0.1 ta,out,design tw,return 20.0 24.1 20.0 23.0 20.0 25.1 20.0 23.9 20.0 25.1 20.0 23.8

Table 18. Design output air temperature (ta,out,design) and weighted annual return temperature (tw,return), as varying with changes in the settings of the balancing valve on the primary side. It can be seen from the table that, in most cases, there is little change in the return temperature. The exceptions consist of those cases where the balancing valve is closed

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too much, resulting in too low an output air temperature and thus also in low return water temperatures. The effects of this are to produce a system that is incapable of providing the necessary performance, as it cannot supply the necessary heating power when called upon to do so. It can therefore be noted that the setting of the primary side balancing valve does not have much effect on the return temperature, apart from when overall function of the system is affected. 7.4.2 Secondary side balancing valve Table 19 shows the correct and incorrect settings of the secondary side balancing valves in the respective systems, as used in the simulations.

System Log-4,H,D Log-4,L,D Log-4,H,DH Log-4,L,DH Log-4,H,SABO Log-4,L,SABO

Valve opening [-] More closed (- 0.1) Correct More open (+ 0.1) 0.30 0.40 0.50 0.08 0.18 0.28 0.48 0.58 0.68 0.10 0.20 0.30

Table 19. Correct and “out of balance” settings of the balancing valves on the secondary sides in the six systems considered. The following diagrams show how the width of the necessary P-band is affected by the changes in the settings of the secondary side balancing valve. This valve are indicated by I2 in the diagrams, with the deviation in the valve opening being indicated by either - 0.1 or + 0.1. DH connection, Low-flow

40

Necessary P-band width [°C]

Necessary P-band width [°C]

DH connection, High-flow I2: - 0.1 Correct balancing

35 30

I2: + 0.1

25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

40 I2: - 0.1

35

Correct balancing

30

I2: + 0.1

25 20 15 10 5 0 0.0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 177.The effect on the necessary P-band width of changes in the setting of the secondary side balancing valve for the district heating connection.

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SABO connection, Low-flow

40

Necessary P-band width [°C]

Necessary P-band width [°C]

SABO connection, High-flow I2: - 0.1

35

Correct balancing

30

I2: + 0.1

25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

40

I2: - 0.1

35

Correct balancing

30

I2: + 0.1

25 20 15 10 5 0 0.0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 178.The effect on the necessary P-band width of changes in the setting of the secondary side balancing valve for the SABO connection. The diagrams - and particularly Figure 177 for the district heating connection - show that the necessary P-band width gets wider (in order to avoid instability) when the balancing valve on the secondary side is closed more than necessary. At the same time, the reduction in the valve opening of the valve means that the design thermal output power cannot be achieved, as the flow through the air heater is insufficient. If, on the other hand, the balancing valve is open more than necessary, the width of the required P-band is reduced, which is an advantage. However, the drawback of this is that the circulation flow is higher than desired, which can result in higher return temperatures. This effect can be seen in Table 20, which also shows the air output temperatures for the various cases at the design outdoor temperature. The values shown in brackets correspond to the weighted annual return temperatures that would result if the water supply temperature was increased in order to compensate for the insufficient flow rate.

System Log-4,H,D Log-4,L,D Log-4,H,DH Log-4,L,DH Log-4,H,SABO Log-4,L,SABO

I2 = - 0.1 tw,return ta,out,design 18.8 25.0 (25.0) 11.9 20.4 (22.2) 19.6 25.1 (25.1) 13.9 21.7 (22.6)

Correct ta,out,design tw,return 20.0 25.1 20.0 23.8 20.0 25.1 20.0 23.7

I2 = + 0.1 ta,out,design tw,return 20.0 25.0 20.0 24.3 20.0 25.1 20.0 24.1

Table 20. Design output air temperature (ta,out,design) and weighted annual return temperature (tw,return), as varying with changes in the settings of the balancing valve on the secondary side. It can be seen from the table that it is only the low-flow systems in which there is a significant change in the weighted annual return temperature: this is because it is in these systems that there are the greatest changes in flow in response to the incorrect balancing settings. It can also be seen that the output air temperature changes significantly in these systems if the balancing valve is closed more than necessary, as

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compared with the effect in the high-flow systems. In other words, there must be quite substantial deviations in the high-flow systems before the effects are noticed on the outgoing air and water return temperatures, while the low-flow system is much more sensitive in this way. It must be pointed out that the increased valve opening of the balancing valve in the district heating connection results in an inability to reach the design inlet water temperature: despite this, the table above shows the outgoing air temperature as being reached. This is because the increased water flow compensates for the reduced inlet temperature. However, this will not necessarily always be the case, why it is necessary to adjust the balancing valve on the primary side to ensure that there is no reduction in the inlet water temperature. This then creates the situation in which there is a risk of both primary and secondary side balancing valves being open more than necessary, leading both to a high return temperature and unnecessarily difficulty in control. 7.4.3 Summary The simulations show that any deviation in the setting of the balancing valves can have three different possible adverse effects, which can be ranked in descending order, from the most serious to the least serious: - The system is unable to supply the desired thermal power under design conditions. This situation is caused by the balancing valve on the primary or secondary side being closed far too much. The result is a system incapable of fulfilling its intended purpose. - Control is more difficult than necessary. This is because the balancing valve on the primary side is open more than necessary, or because the balancing valve on the secondary side is closed more than necessary. This results in a system that is unnecessarily difficult to control, with a potential risk of instability. - The return temperature is higher than necessary, due to the balancing valve on the secondary side being open more than necessary. The simulations indicate that high-flow systems are considerably less sensitive to this than are low-flow systems. As it is most important to avoid the first of these cases – that is producing a system that does not do what it is supposed to do – there is a risk that both the primary and secondary balancing valves might be set more open than necessary, simply in order to be on the safe side. This creates a system with unnecessarily high return temperatures, difficult to control and thus not as fast in its responses as it could have been if balancing had been correct. In addition, it should be pointed out that any unnecessarily high flow, whether on the primary or on the secondary side, results in a certain degree of overcapacity. Although this can be a benefit if, for some reason, further capacity is required, it can also be a drawback as the control valve cannot utilise its entire operating range.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

7.5

The effect of variations in water supply temperature

The control curve characteristics that describe how the water supply temperature changes in response to a changing outdoor temperature can naturally be set more or less arbitrarily: the main thing is to ensure that it is always possible to provide the necessary heating power during operation. However, control of the system supply temperature is also an important element in overall control of the system. Constant supply temperature, for example, is regarded as complicating local control of the heat-releasing components, as has been pointed out by Petitjean (1994) and others. In order to provide an example of this, the performance of a system (Log-4,L,DH) has been simulated with both a regulated water supply temperature, in accordance with the control curve characteristic previously described, and with a constant supply temperature of 90 °C. Thus the studied system is a low-flow district heating connection system, with a logarithmic control valve having a kvs value of 4.0 m³/h. The position of the control valve must be varied as needed to ensure that, for each value of outdoor temperature, the required air output temperature can be maintained. Simulation has therefore involved a number of step responses for various outdoor temperatures, with corresponding water supply temperatures. Figure 179 shows the static characteristic, that is how the steady-state output air temperature is affected by the valve opening for the control valve, as indicated by the results of these step response simulations. This is shown for a number of outdoor temperatures, from -20 °C to +20 °C, at 5 °C intervals, both for controlled and for constant water supply temperature. 30 25 20 15 10 5 0 -5 -10 -15 -20

Constant supply water temperature Supply air temperature [°C]

Supply air temperature [°C]

Controlled supply water temperature

Rising outdoor temperature 0

0.2

0.4

0.6

0.8

1

30 25 20 15 10 5 0 -5 -10 -15 -20

Rising outdoor temperature 0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 179.Static caracteristic for a number of outdoor temperatures for systems with controlled and constant supply water temperatures respectively. It can be seen from the diagram that, in both cases, the slope of the static characteristic decreases with increasing outdoor temperature, although it decreases considerably more rapidly in the case of the system having a controlled water supply temperature than in the case of the system having a constant water supply temperature. The slope, or gain, affects the width of the necessary P-band, which means that the less steeping slope in the case of the system having a controlled water supply temperature results in control being simpler at higher outdoor temperatures.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

The rings in the diagram show the equilibrium positions of the control valve for each outdoor temperature, as needed in order to achieve an output air temperature of +20 °C. Joining these points produces a curve as shown in Figure 180. 1.0 0.9

Controlled

Valve opening [-]

0.8 0.7 0.6 Constant

0.5 0.4 0.3 0.2 0.1 0.0

-20 -15 -10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 180.Necessary valve opening of the control valve in order to provide an output air temperature of +20 °C. It should be pointed out that the shape of the curve does not really reflect the difficulty of control, but merely shows the equilibrium positions of the valve as a function of outdoor temperature. For example, if the water supply temperature was matched exactly to the requirements as set by the outdoor temperature, the equilibrium position of the valve would always be fully open, regardless of the outdoor temperature. However, this does not say anything about control between the equilibrium positions, but such information is given by the width of the necessary P-band, as shown for the two cases in the diagram below. Controlled supply water temperature

Constant supply water temperature 40

Rising outdoor temperature

35 30

Necessary P-band [°C]

Necessary P-band [°C]

40

25 20 15 10 5 0

Rising outdoor temperature

35 30 25 20 15 10 5 0

0

0.2

0.4

0.6

0.8

1

0

Valve opening [-]

0.2

0.4

0.6

0.8

Valve opening [-]

Figure 181.The necessary P-band width, according to the outdoor temperature, for controlled and constant water supply temperatures.

209

1

7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

The change in the necessary P-band width, as shown in the diagram, is in fact more or less proportional to the change in the static characteristic, which indicates that dead time and time constant are more or less independent of the outdoor temperature and of the water supply temperature. An increase in the outdoor temperature results in a change in the temperature rise of the air passing over the air heater, giving a corresponding change in the width of the necessary P-band. In the case of the system having a controlled water temperature, this means that the width of the P-band is substantially reduced as the outdoor temperature rises, while the corresponding reduction in the case of the system having a constant water supply temperature is considerably less. This can be clearly seen in the diagram, and shows that control in general becomes simpler as the outdoor temperature rises, even in the constant water supply temperature case. However, the equilibrium positions (the rings in the diagram) show that, for each steady-state condition, the difficulty of control does not actually decrease in proportion to the rising outdoor temperature in any of the cases. The following diagram shows how the width of the necessary P-band, at equilibrium, varies with the outdoor temperature. It must be added that the values in the diagram constitute a measure of the least possible difficulty of control of the system. In actual fact, the path from one steady-state condition to another can require a wider necessary P-band than is needed at the steady-state conditions. 40

Log-4,L,DH

Necessary P-band (at equilibrium) [°C]

35 30 Constant

25 20 15 10 5

Controlled

0 -20 -15 -10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 182.The necessary P-band width for the steady-state position of the control valve, as a function of outdoor temperature, for the cases of a controlled and constant supply temperature. The diagram applies for a Log-4,L,DH system. The fact that the necessary P-band width for the equilibrium position initially increases with rising outdoor temperature, and then decreases, is a result of the choice of control valve. If, instead, a linear control valve were to be used in the system, the curves for both cases would be completely different, as shown in the following diagram.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

40 Necessary P-band (at equilibrium) [°C]

35

Lin-4,L,DH Constant

30 25 20 15 Controlled

10 5 0 -20 -15 -10

-5

0

5

10

15

20

Outdoor temperature [°C]

Figure 183.The necessary P-band width for the steady-state position of the control valve, as a function of outdoor temperature, for the cases of a controlled and constant supply temperature. The diagram applies for a Lin-4,L,DH system. Both Figure 182 and Figure 183 show that, regardless of the outdoor temperature, a controlled water supply temperature results in a narrower necessary P-band width than does the case of a constant water supply temperature. The greatest difference occurs in the case of a linear control valve, for which a controlled water temperature is almost a necessity if the system is to be able to operate in practice. The risk of instability declines with a controlled water temperature, which favours the use of a narrower P-band and thus increases the speed of control. The effect of the water supply temperature on the return temperature depends on whether the flow on the secondary side through the air heater changes as a result of any change in the position of the control valve. This is the case for the direct connection, where the return temperature changes if the shape of the control curve characteristic is changed. However, for the district heating connection, the shape of the control curve characteristic has no effect on the return temperature as long as the system is correctly balanced. The return temperature from the SABO connection can change in response to a change in the control curve characteristic, but only if the choice of control valve ports is such that the flow on the secondary side is changed when the valve opening changes, as will be the case with, for example, a symmetrical logarithmic three-way valve with a high authority (see Trüschel, 1999). Table 21 shows how the weighted annual return temperature changes if the system uses a constant water supply temperature instead of a controlled temperature, in accordance with the previously described control curve characteristics.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

System Log-4,H,D Log-4,L,D Log-4,H,DH Log-4,L,DH Log-4,H,SABO Log-4,L,SABO

Supply temperature Controlled Constant 24.1 22.6 23.0 21.1 25.1 25.1 23.8 23.7 25.1 25.2 23.7 23.6

Table 21. Weighted annual return temperatures, for controlled and constant water supply temperatures. It can be seen from the table that, for the direct connection case, the return temperature decreases if the supply temperature is constant, relative to what happens if the supply temperature is controlled. The decrease in return temperature is somewhat greater in the low flow case (1.9 ºC) than in the high-flow case (1.5 ºC). The change in return temperature is insignificant for the other systems.

7.6

The effect of a fouled air heater

After having been in use for some time, the surfaces of the air heater will be fouled. To model this case (in a simplified way), the UA value of the air heater in the simulations has been reduced by 10 %. This has the effect of abstracting less heat from the water, with the result that the design heating capacity cannot be achieved. In principle, the relative reduction in the thermal power output gives rise to a corresponding reduction in the necessary P-band width, due to proportional reduction of the system gain. This reduction is of the order of 4–7 %, with the lower value being applicable for low-flow systems. Table 22 shows how a 10 % reduction of the air heater's UA value affects the output air temperature (in the design case) and the weighted mean annual return temperature. The values in brackets indicate what the weighted return temperature would be if the reduced UA value was compensated for by increasing the supply temperature in order to achieve the design outlet air temperature.

System Log-4,H,D Log-4,L,D Log-4,H,DH Log-4,L,DH Log-4,H,SABO Log-4,L,SABO

Reduced UA (-10 %) tw,return ta,out,design 17.3 26.8 (26.8) 18.5 26.0 (26.0) 17.3 27.0 (27.2) 18.1 25.9 (26.0) 17.3 27.1 (27.3) 18.5 26.0 (26.0)

Correct UA ta,out,design tw,return 20.0 24.2 20.0 23.0 20.0 25.1 20.0 23.8 20.0 25.1 20.0 23.7

Table 22. Design output air temperature and weighted annual return temperature, resulting from a 10 % reduction in the air heater's UA value. The increase in the return temperature is noticeable in all systems, although by far the greatest in the direct-connected systems, the return temperatures of which become approximately the same as those in the other systems. In the direct-connection systems,

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

the flow through the air heater has to be increased in order to compensate for the reduced UA value, during the year. However, in the other valve group arrangements, this reduction is compensated for by increasing the inlet water temperature, which does not have as great an effect on the return temperature. The table also shows that the increase in the return temperature is somewhat greater in the low-flow systems than in the high-flow systems, which means that the reduced UA value is compensated for to a greater degree by an increased average temperature in these systems. This explains why the effect of a reduction in the UA value has less effect on the outlet air temperature in low-flow systems. The simulation results of a fouled air heater indicate the effects of incorrect capacity determination. If an air heater is too small, its UA value is too low, which is what has been described here. The result is that the return temperature increases. Similarly, too large an air heater should result in lower return temperatures, but this particular case has not been simulated in this work.

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7 SIMULATION AND RESULTS – AIR HEATER WITH VALVE GROUP

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8 CONCLUSIONS AND DISCUSSION

8

CONCLUSIONS AND DISCUSSION

This final chapter presents the most important conclusions of the work, together with a number of discussion aspects, treating the radiator systems and the air heaters separately.

8.1

Radiator system

The most important conclusions concerning radiator systems can be summarised in the following points: • Both the simulations and measured results from an actual physical case show that substantial deviations in the valve openings result in significantly increased return water temperatures and a wide spread in room temperatures, but without significantly affecting the total amount of heat supplied to the building. • If a building heating system is connected to a district heating supply, it is important to maintain as low a return temperature as possible, which means that radiator valves or balancing valves must not be open more than necessary, as this tends to result in a substantial increase in the return temperature. In this respect, low-flow systems are considerably more sensitive than are high-flow systems. As far as the systems considered in this work are concerned, this can be exemplified by the fact that the return temperatures in both systems become approximately the same if only 10 % of the radiator valves are fully open. For this reason, it is also important not to fit valves considerably larger than necessary, as the effect of a fully open valve increases with its size. • In general, system design affects the interaction between the radiators and the risk of high return temperatures in such a way that when one increases, the other decreases. An example of this is that a flat pump characteristic curve or pressure control of the pump, low pipe pressure drops and high balanced differential pressures all act to reduce the interaction between the radiators, while at the same time increasing the risk of high return temperatures if any of the valves is/are opened more than it/they should be. On the other hand, a steep pump characteristic, high pipe pressure drops and low balanced differential pressures increase the interaction between the radiators, but at the same time reduce the effect of radiator valves that are open more than they should be. • Thermostatic radiator valves are most effective in low-flow systems, partly due to the radiators' sensitivity to flow changes, and partly because the P-band of the thermostat is often narrower as a result of balancing of such systems. • Branch, riser and main valves all reduce the interaction between radiators if one or more of the radiator valves is open more than it should be. On the other hand, they have an adverse effect on the interaction if one or more of the radiator valves is closed. • A simple analysis of a district heating heat exchanger (supplying the radiator system) shows that an increase in the return temperature of the radiator system results in a 215

8 CONCLUSIONS AND DISCUSSION

somewhat lesser increase in the return temperature of the district heating water. If, at the same time, the flow in the radiator system increases, the effect on the district heating return water temperature also increases. In the cases considered, it was the low-flow system that resulted in the greatest increase in the district heating water return temperature. 8.1.1 High-flow or low-flow balancing It is important to point out that the systems that have been compared in this work were balanced with either a high flow rate or a low flow rate. However, this does not automatically mean that the process was necessarily done according to a high-flow or a low-flow balancing method, as these concepts can be associated with completely different levels of flows and pressures in the system. In addition, they can also include other adjustment of the systems, such as the use of different valves or pumps. The results of the simulations show that, regardless of the balanced flow, it is important that the systems are actually balanced, and that balancing is carried out properly. Provided that the systems are properly balanced, it is the performance of the low-flow system that is the better. This is based partly on the fact that the return temperature in such a system is lowest, and partly on the fact that thermostatic radiator valves are most effective in such systems, which means that best use can be made of any internal heat. In addition, there are also other effects such as lower pump energy, although this has not been considered in this work. It is not until the systems are called upon to deal with deviations that the benefits of a high balanced flow become apparent. In principle, all the simulations indicate that the effect of such deviations is greatest in low-flow systems. Admittedly, there is often least effect upon the actual flow in such systems, but at the same time the radiators in low-flow systems are most sensitive to any changes in the flow. A still lower balanced flow results in even less interaction between the radiators but, at the same time, greater sensitivity to flow changes. In low-flow systems, this sensitivity can also result in steps being taken that actually exacerbate the problem. An example of this could be increasing the pump pressure or raising the supply temperature to deal with unnecessarily low room temperatures. It is therefore particularly important that the settings of the individual valves should be carefully checked in such systems, instead of simply making some quick change that affects the entire system. This should also, of course, apply for high-flow systems. The sensitivity of low-flow systems to flow changes can be seen as either an advantage or as a drawback, depending on the results and performance required. The advantage is that heat release from the radiators falls off more rapidly than it does in a high-flow system, as any internal heat in the room increases. This presupposes, of course, the use of thermostatic radiator valves. The drawback is that any undesired change in flow conditions has more effect on the heat release. This resolves to the question that, if the sensitivity of the system is regarded as positive or negative, should it be as insensitive as possible to deviations, or should the radiators react quickly to changes? At the same time, this latter alternative can mean that deviations can be quickly detected. The following are a number of reflections on the effects and performances of different system designs in this respect.

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8 CONCLUSIONS AND DISCUSSION

- In a system with thermostatic radiator valves, it is naturally important that the interaction between the radiators on the system should be as little as possible when the valves close. In order to ensure the least effect on the flow through other radiators when a valve closes, the system should therefore be designed (and balanced) for a high differential pressure, low pipe pressure drops and a pump characteristic with as little slope as possible. A low balanced flow means that the radiators are sensitive to flow changes, which can be unsuitable in this system. However, at the same time, it means that the radiators can make best use of any internal heat. A relatively high flow and “normal” supply temperature mean instead that the sensitivity of the radiators is reduced in terms of response to changes in system flows. The drawback of this is that it also means that the radiators do not react as quickly when internal heat is available. - If there is a risk that occupants of the building might fiddle with the valves, the differential pressure should not be too high, as a low differential pressure reduces the risk of high flow rates in the system if one or more of the valves is fully opened. To achieve a relatively stable system, in which a deviation preferably does not result in too great an effect, the system should be balanced to have a high flow and a low supply water temperature. However, in order to deal with a problem quickly, it may be beneficial to balance the system for a low flow. This has the effect that an increase in the flow results in a significant rise in the return temperature, which will be spotted relatively quickly by temperature measurements or simply by feeling the pipes. - If the most important consideration is to achieve a low return temperature, the system should be balanced for a low flow. The differential pressure should not be unnecessarily high, and the pump characteristic should be relatively steep, all in order to reduce the effects of any open valves in the system. The fact that high-flow and low-flow systems have different advantages and drawbacks means that they can be chosen to suit different requirements. In general, the simulations show that low-flow systems result in the lowest return temperature, which is naturally attractive to district heating utilities. At the same time, such systems are more sensitive to deviations, which can have the effect of increasing the return temperature, but tend particularly to result in a greater spread in room temperatures in the building. High-flow systems, on the other hand, generally result in a lesser spread in room temperatures, which is more likely to be of interest to building owners or operators.

8.2

Air heater with valve group

The most important conclusions concerning air heaters supplied by valve groups are as follows: • The theoretically best possible control potential of a system depends on its design, capacities and balancing, which means that it is already determined before the control valve is selected. When the valve is chosen, we arrive at the true control potential of the system, which will always be poorer than the best theoretically possible. The effect of the control valve on controllability is considerable, particularly as far as the choice of valve characteristic is concerned. This means that, in the worst case, the

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8 CONCLUSIONS AND DISCUSSION

wrong choice of control valve can cancel out the control potential of a properly designed and balanced valve group. • As long as the valve authority is modest, a control valve or control port having a logarithmic valve characteristic is almost always preferable to one with a linear characteristic. However, a high valve authority is favoured more by a straighter valve characteristic. A three-way control valve with a linear bypass port (the B port) is preferable, as a logarithmic bypass port makes control unnecessarily difficult. • The measurements and the simulations show that the direct connection arrangement results in by far the lowest value of necessary P-band width, and should therefore be the easiest to control. In addition, the controllability of this type of arrangement is not significantly affected by the choice of balancing. However, the choice of balancing has a considerable effect on controllability for the two other valve groups, which have recirculation connections. In this respect, the greatest difficulty of control occurs in low-flow systems, which is due to such systems' longer dead time. • The simulations show that, for a given air heater, the return temperature is affected mainly by changes in the secondary flow or by a change in the coefficient of heat transmittance (for the air heater) caused by, for example, fouling. 8.2.1 High-flow or low-flow balancing The difference in return temperatures between the high-flow and low-flow systems that have been considered is not great, amounting to only slightly more than 1 °C in total over the year. This is because a low flow results in a low UA value of the air heater, which necessitates a high mean temperature difference in the air heater. As a result, an air heater is much more sensitive to the magnitude of the flow than is a radiator, which is relatively insensitive in this respect, which means that it is not obvious that a low balanced flow through an air heater would result in a low return temperature. In addition, the simulations show that any deviations in respect of balancing of the secondary side has a considerably greater effect on the return temperature in a system having a low balanced flow than it does in a system having a high balanced flow. The design and control of a valve group is more forgiving of deviations in the setting of the balancing valve from design conditions than is a radiator valve. This means that the return temperature is not affected as much by such system deviations in air heater systems as it is in radiator systems. 8.2.2 Balancing the valve group The simulations show that there is a risk of the system failing to perform properly if either the primary or secondary side balancing valves are closed too much. The effect of a balancing valve on the primary side being opened too much is that it becomes more difficult to control the air heater, as the width of the necessary P-band increases. This effect is greatest in low-flow systems. However, an incorrectly balanced valve on the primary side has no effect on the return temperatures in any of the systems, as long as system performance can be maintained.

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8 CONCLUSIONS AND DISCUSSION

On the secondary side, a balancing valve that is open more than it need to be results in an increase in the return temperature, and particularly in low-flow systems that are considerably more sensitive in this respect than are high-flow systems. The advantage of a high secondary flow rate is that control is simplified, as the dead time is reduced. The direct connection arrangement is quite insensitive to the effect of incorrectly set balancing valves on the return temperature. In the worst case, with an excessively closed balancing valve, it may not be possible to achieve the design air temperature, in exactly the same way as for the other valve groups. Raising the supply water temperature in order to deal with the problem reduces the return temperature in a direct connection arrangement, while doing so does not affect the return temperature in valves groups having recirculation connections. Chapter 7 ranked the effect of any deviations due to incorrect balancing in descending order of seriousness. This ranking is repeated below: - The system is unable to supply the desired thermal power under design conditions. This situation is caused by the balancing valve on the primary or secondary side being closed far too much. The result is a system incapable of fulfilling its intended purpose. - Control is more difficult than necessary. This is because the balancing valve on the primary side is open more than necessary, or because the balancing valve on the secondary side is closed more than necessary. This results in a system that is difficult to control, which in the worst case can lead to instability. - The return temperature is higher than necessary, due to the balancing valve on the secondary side being open more than necessary. The simulations indicate that high-flow systems are considerably less sensitive to this than are low-flow systems. As it is most important to avoid the first of these cases - i.e. producing a system that does not do what it is supposed to do - there is a risk that both the primary and secondary balancing valves might be set more open than necessary, simply in order to be on the safe side. This creates a system with unnecessarily high return temperatures, difficult to control and thus not as fast in its responses as it could have been if balancing had been correct. 8.2.3 Controlled versus constant supply temperature The maximum necessary P-band width occurs at the design outdoor temperature, and is unaffected by whether the supply temperature varies as a function of the outdoor temperature or is constant. As the outdoor temperature rises, so the necessary width of the P-band decreases. This decrease is considerably greater if the supply temperature is regulated than if the supply temperature is constant. This means that a controlled supply water temperature facilitates local control of a valve group during operation. However, in order to avoid the system becoming unstable under any conditions, the setting of the regulator P-band must be such as to be able to accommodate the worst case, which is that of design outdoor temperature (that is the lowest outdoor temperature). One way of improving the speed of response of control, and to improve

219

8 CONCLUSIONS AND DISCUSSION

its performance, is therefore to arrange for the width of the regulator P-band to be varied in response to changes in the outdoor temperature. With one exception, the effect on the return temperature is the same, regardless of the shape of the supply temperature control curve characteristic. This exception is that the return temperature from a directly connected heater supplied at a constant temperature is lower (over the year) than in the case when supply temperature is regulated. 8.2.4 Selection of the valve group It must again be pointed out that the main reason for the direct connection arrangement having the narrowest P-band is due to the difference in dead time between this type of connection and the other arrangements. The measurements show that the dead time of the direct connection arrangement in this work can be estimated as about five seconds, regardless of balancing, while that for the other types of valve groups is about three times as much for a high-flow balanced system, and no less than six times as much for a low-flow balanced system. On the other hand, the time constant of a valve group having a recirculation connection is considerably greater (compared with the direct connection), which is illustrated by the fact that the difference in the necessary P-band width between the direct connection arrangement and the district heating connection arrangement is just over a factor of one for a high-flow system, and about two for a low-flow system. This means that, to a considerable degree, the high time constant in the district heating connection compensates the difference in dead time. A conclusion in this respect is therefore that the direct connection arrangement has a considerable advantage in the form of its short dead time. At the same time, systems with recirculation connections also have a valuable benefit in the form of their long time constants. The dead time in valve groups having recirculation connections can be affected in various ways: by reducing the length of the recirculation inlet connection or by increasing the flow rates. However, as far as the first possibility is concerned, these valve groups are often mounted on the air heater or close to it, which means that the dead time is relatively short. The time constant, too, can also be affected to a considerable degree in valves having recirculation connections, by such means as increasing the length of the recirculation return connection (see Børresen, 1985). However, this is not possible for a direct connection arrangement, the time constant of which is difficult to influence. The potential for accurate control is therefore greater for a valve group having a recirculation connection than it is for the direct connection arrangement. However, such valve groups must be correctly designed. In this respect, the direct connection arrangement is less sensitive, as there is still going to be a relatively high probability of a direct connection arrangement providing better control in practice than does a valve group having a recirculation connection. But then again, there are a number of significant drawbacks with the direct connection arrangement, such as a risk of freezing, uneven temperature distribution in the outgoing air flow and a risk of control problems at very low flow rates.

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8 CONCLUSIONS AND DISCUSSION

8.2.5 Choice of valve characteristic Selection of the best valve characteristic for a control valve is not simple, and is also naturally affected by the types available. However, it does simplify things to know approximately what characteristic the valve ought to have, so that as good a valve as possible can be selected. There has been considerable discussion on which characteristic is most suitable, and much has been written on the subject. In this respect, see particularly Grindal (1988 and 1995). The presentation in this work does not claim to provide any further theoretical information over and above what has already been written: instead, it describes the effect on an optimum valve characteristic of various different system configurations. The simulations show considerable similarities in optimum valve characteristics from one system configuration to another. There is little difference in the optimum valve characteristic, for example, between high-flow and low-flow systems, or between different valve group arrangements. However, this applies only as long as the valve authority remains relatively unchanged. As shown in Appendix B, the optimum valve characteristic depends on the static characteristic, the total efficiency of the valve group and the valve authority. The most important of these factors is presumably the valve authority, as there can be relatively substantial variations in it between different systems. It is therefore very important to make the correct choice of control valve in terms of both characteristic and size. The larger the valve, or the greater the variation in available differential pressure, the more the valve characteristic needs to depart from a straight line.

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222

REFERENCES

REFERENCES Abel E., Jagemar L. och Widén P. 1997, ”Energiteknik”, Institutionen för Installationsteknik, CTH, Göteborg Amerson R.J. 1998, ”The effect of sizing mismatch on coil valve performance”, ASHRAE Transactions, vol.104, part 1 Andersson S., Sandberg O. 1989, ”Värmeavgivning från rör vid låga flödeshastigheter”, BFR Rapport R47:1989. Andersson T. 1993, ”Konsten att styra radiatorsystem”, VVS-Forum, nr.10 Andersson T., Göransson P., Wiberg G. och Reybekiel B. 1998, ”Kirunametoden – för god energihushållning”, SABO Avery G. 1993, “Designing and commissioning variable flow hydronic systems”, ASHRAE Journal, July Bengtsson L. och Magnusson P. 1998, ”Projektering och byggande av radiatorsystem”, Institutionen för Installationsteknik, CTH, Göteborg. Blomberg P.E. 1999, ”Experimental validation of dynamic component models – for simulation of air handling units”, Institutionen för Installationsteknik, KTH, Stockholm Brännström H. 1987, ”1-rörssystemet ger en annan reglerstrategi”, VVS & Energi, nr.2 Brännström H. 1990, ”Frysskadesäkra vattenburna luftvärmare – Fältprov och praktisk tillämpning”, Statens råd för byggnadsforskning Børresen B. 1985, ”Dynamikk i shuntkoplinger”, SINTEF Rapport STF15 Børresen B. 1994, ”Ventildimensjonering og ventilautoritet”, Norsk VVS, nr.13 Dahm J. 1999, ”Small district heating systems”, Institutionen för Installationsteknik, CTH, Göteborg Fahlén P. 1992, “Värmemätning i vätskesystem”, BFR-rapport R13:1992 Fredriksen S. och Werner S. 1993, ”Fjärrvärme – Teori, teknik och funktion”, Studentlitteratur Grindal A. 1984, ”Hva alle VVS-ingeniører som et minimum bør vite om regulerbarhet”, Norsk VVS, nr.11 Grindal A. 1988, ”Regleringsteknikk for ingeniøren”, Skarland Press A/S Grindal A. 1994, ”Hvilke erfaringer har de siste 15 årene gitt oss?”, Norsk VVS, nr.13

223

REFERENCES

Grindal A. 1995, ”Ventilkarakteristikker – er det på tide at vi gjør noe med dem?”, Norsk VVS, nr.16 Grindal A. och Børresen B. 1988, ”Regulering av varmebatterier i en datatid”, Norsk VVS, nr.4 Grindal A. och Børresen B. 1990, ”Controllability - back to basics”, ASHRAE Transactions Hammarsten S. 1985, ”Värmeavgivning från radiatorer”, Tekniska meddelanden, Institutionen för Uppvärmnings- och ventilationsteknik, KTH, Stockholm Hegberg R.A. 1997, ”Selecting control and balancing valves in a variable flow system”, ASHRAE Journal, June Hegberg R.A.1998, “Application of control valves and balancing valves in a variableflow hydronic system”, ASHRAE Transactions Hjorthol E.M. 1990, ”Optimization of design values in district heating substations by system simulation”, Institutt for Varme-, ventilasjons- og sanitærteknikk, NTH, Trondheim Häggbom S. och Nylund P-O. 1989, ”Värt att veta om vattenburen värme”, BFR Rapport, R42:1989 Jacobson S., Osbeck M. 1997, “Styr- och reglerteknik”, Institutionen för Elektroteknik, Ingenjörs- och sjöbefälsskolan, Göteborg Jensen L. 1978, ”Digital reglering av klimatprocesser”, Department of automatic control, LTH, Lund Jensen L. 1986, ”Analys av termostatventilers statiska egenskaper”, Institutionen för Byggnads- och konstruktionslära, LTH, Lund Johansson G., Kolehmainen M. och Waldner L. 1989, ”Långtidsegenskaper hos radiatortermostatventiler”, BFR Rapport, R110:1989 Järnefors U. 1978, ”Ett-rörs system för värme – Teori, praktik och ekonomi”, Meddelande M78:12, Statens institut för byggnadsforskning Kays W.M. och London A.L., 1984, ”Compact Heat Exchangers” (third edition), McGraw-Hill Book Company, USA Larsson G. 1999, ”Dynamik i fjärrvärmesystem”, Institutionen för Termo- och fluiddynamik, CTH, Göteborg Lundin K-Å. 1980, ”Att undvika missanpassning av styrventiler”, VVS, nr.5-6 Malmström T-G. 1975, ”Radiatorers yttemperatur”, Tekniska meddelanden nr.73, Institutionen för Uppvärmnings- och ventilationsteknik, KTH, Stockholm

224

REFERENCES

Mandorff S. 1977, ”PS om termostatventiler – erfarenheter från ett radhusområde”, VVS, nr.11 Mandorff S. 1979, ”Funktionen hos värmesystem med radiatortermostatventiler utan förinställning”, VVS, nr.3 Mandorff S. 1982, ”Kirunametoden – bara fördelar?”, VVS, nr.4 Moult R. 2000, “Fundamentals of DDC”, ASHRAE Journal, Nov. Mundt E. 1988, ”Modeller av luftvärmare för simulering av stationära och dynamiska driftsfall”, Meddelande nr.8, Institutionen för Installationsteknik, KTH, Stockholm Olsson L. 2001, ”Lokala fjärrvärmesystem”, Institutionen för Termo- och fluiddynamik, CTH, Göteborg Palmertz H. 1993, ”Ventilhandbok – Teori och praktik”, TA AB & Liber Utbildning AB, Karlebo-serien Persson P-G. 1995, ”Reglerhandbok”, TA AB & Liber Utbildning AB, Karlebo-serien Peterson F. 1975, ”Förenklad bestämning av operativtemperaturen i radiatorvärmda rum”, Tekniska meddelanden nr.70, Institutionen för Uppvärmnings- och ventilationsteknik, KTH, Stockholm Petersson S. 1998, “Analys av konventionella radiatorsystem”, Institutionen för Energiteknik, CTH, Göteborg Petersson S. 2000, “Metoder att nå lägre returtemperatur med värmeväxlardimensionering och injusteringsmetoder”, Fjärrvärmeföreningen, FoU 2000:42 Petitjean R. 1994, ”Total hydronic balancing”, TA Hydronics AB Stethem W.C. 1994, ”Single-pipe hydronic system design and load-matched pumping”, ASHRAE Transactions Svensson A. 1978, ”Radiator-termostatventilers funktion – lägesrapport”, Meddelande M78:4, Statens institut för byggnadsforskning Svensson A. och Mandorff S. 1977, ”Radiatortermostatventiler på gott och ont”, VVS, nr.4 Svensson A. och Johansson P. 1999, ”Metoder för mätning av luftflöden i ventilationsinstallationer”, BFR-rapport T22:1998 Trüschel A. 1999, ”Värmesystem med luftvärmare och radiatorer – En analys av funktion och prestanda”, Institutionen för Installationsteknik, CTH, Göteborg

225

REFERENCES

Werner S. 1984, ”The heat load in district heating systems”, Institutionen för Energiteknik, CTH, Göteborg Werner S. och Petersson S. 2000, ”Samband mellan produktion och vältrimmade radiatorsystem”, Presentation at Swedish District Heating Associations’ theme day: ”Avkylning – från produktion till kundanläggning” Widén P. 1994, ”Luftvärmare i luftbehandlingsaggregat”, Institutionen för Installationsteknik, CTH, Göteborg Ziegler J.G. och Nichols N.B. 1942, ”Optimum settings for automatic controllers”, A.S.M.E. Transactions, Nov Örberg L. 1986, ”Dimensionering och injustering av vattenburna värme- och kylsystem”, Insam AB, Rapport 8606 Product Catalogues Danfoss, 1999 Grundfos, 1995 TA Hydronics, 1998 TA Control, 2000 Wirsbo Radiatorrör, brochure, 1998 Simulation program Flowmaster 2, version 6.1, Flowmaster International Ltd.

226

APPENDIX A – TEST RIGS

A

TEST RIGS

Two test rigs have been used for making the measurements: one for the air heater (and its associated valve group), and the other for radiators.

A.1 Test rig for the air heater with valve group A.1.1 Arrangement of the test rig The test rig was based on an existing facility, that had been designed for work by Per Widén investigating the relationship between air and water temperatures. This resulted in his licentiate thesis ”Luftvärmare i luftbehandlingsaggregat” (Air heaters in air handling units) in 1994. As much as possible of the original rig was used, although the valve group was replaced and the out-of-date measurement system was replaced. Figure A1 shows an isometric sketch of the original facility with the ringed valve group being that which was replaced in the “new” rig.

Figure A1. The original test rig, showing the valve group that was replaced when converting to the new test rig. This diagram is taken from Widén (1994).

A-1

APPENDIX A – TEST RIGS

Combined valve group The reason for modifying the test rig was first and foremost because the old valve group had been arranged in the “Swedish” connection style, one of the effects of which is to maintain the water flows constant on both the primary and secondary sides. This is patently incompatible with a system designed to have variable primary flow. In addition, it was desirable easily to be able to change the valve group and also the control valve. The purpose of the new arrangement was therefore to give the valve group the necessary flexibility to be operated in a number of ways, as shown in the following diagram. Temperature sensor, Pt100

Pressure measurement point

Balancing valve

Inductive flow sensor Check valve

Circulation pump

Air heater Shut-off valve

Three-way control valve

Figure A2. The new combined valve group after conversion. By appropriate arrangement of the shut-off valves, it is possible to set the test rig up for measurements of three different valve group arrangements, as shown in the schematic diagrams below, in which filled shut-off valves are closed and unfilled shut-off valves are open. The diagram also shows the designations that have been used in this work to identify the three different arrangements.

A-2

APPENDIX A – TEST RIGS

Direct connection

District heating connection

SABO connection

Figure A3. The combined valve group can be set up to provide three different connections, depending on which shut-off valves are open and which are closed. Control valves The three parallel-connected three-way control valves in Figure A2 provide a simple means of setting up the rig to represent different control arrangements. In order to be able to use the three-way valves also as two-way valves, the shunt connection has been given a shut-off valve, which can be used to isolate the shunt port of the three-way control valves. Table 1 shows data for the three control valves. Valve name V341 V341 V355

Manufacturer TA Control TA Control TA Control

kvs value [m³/h] 10 4 4

Control port (charact.) Log. Log. Lin.

Shunt port (charact.) Lin. Lin. Lin.

Actuator Forta Forta EM52L-4

Position in the rig Furthest in Centre Furthest out

Table A1. Data for the three control valves used in the rig. The figures below show the three control valve characteristics as used for the control port. These curves are taken from the TA Controls product catalogue.

A-3

APPENDIX A – TEST RIGS

V355 - 4

5.0

5.0

4.0

4.0

kv [m³/h]

kv [m³/h]

V341 - 4

3.0 2.0 1.0

3.0 2.0 1.0

0.0

0.0 0

0.2

0.4

0.6

0.8

1

Valve opening (H) [-]

0

0.2

0.4

0.6

0.8

Valve opening (H) [-]

V341 - 10 10

The identification above each diagram is made up of the valve type (V341 or V355) followed by the valve’s kvs value. This principle of identification has been used throughout this work.

kv [m³/h]

8 6 4 2 0 0

0.2

0.4

0.6

0.8

1

Valve opening (H) [-] Figure A4. The three valves' characteristics as given by the manufacturer. The reason for this choice of control valves is that it makes it possible to compare different valve characteristics (linear / logarithmic) for the same valve authorities, as well as different valve authorities (kvs: 4 / kvs: 10) for the same valve characteristics. Balancing valves There are four balancing valves (TA Hydronics' STAD, size DN32) in the valve group, although only two are used for adjusting the primary and secondary flows. The other two valves are installed in the connections to the valve group, and are used for setting the required differential pressure across the valve group. The schematic diagram below shows the positions of the balancing valves, their functions and the identifications used in this work.

A-4

1

APPENDIX A – TEST RIGS

Ip

I2

Ib

I1 I2 is used to set the required circulation flow (with the control valve fully closed) I1 is used to set the design flow rate (with the control valve fully open) Ip is used to set the total flow in the system (from the boiler) Ib is used to set the flow that bypasses the valve group. Figure A5. The positions and functions of the balancing valves in the valve group. The reason for the bypass connection, controlled by Ib, is to ensure that the available differential pressure across the valve group does not vary excessively, without having to employ some form of differential pressure control, which might interfere with the function of the other control valves. This also models the real-life situation of a system with several valve groups. The system flow between the boiler and the bypass connection must be considerably higher than the design flow rate through the valve group itself. In other words, even when the control valve is fully open, there must be a fairly substantial flow through the bypass connection. When the control valve closes, this flow does not change very much, with the result that there is a relatively constant differential pressure across the bypass connection, and so also across the valve group. This means that, by varying the settings of Ip and Ib, the magnitude of the differential pressure and, to some extent, also the amount by which it varies, can be adjusted. Shut-off valves As it is necessary for the combined valve group to be rearrangeable into different configurations, both in terms of the valve group arrangement and of the control valve, the group contains no less than eleven shut-off valves. Most of these (seven) are new (TA 500), while some of them are from the original test rig (AJ3545T). Pipes The pipes are 32 mm diameter (nominal) galvanised steel tubes, insulated with glass fibre split pipe sleeves, with aluminium foil on the outside. Air heater The air heater has not been changed, but is part of the original unit. It is a two-row unit (500 x 600 mm), type designation VAH 0506.20, and supplied by the then Stratos Ventilation. A-5

APPENDIX A – TEST RIGS

Circulation pump The original circulation pump in the valve group was found to be leaking quite considerably, particularly at low water temperatures. As a result, the original (dry) pump was replaced by a new wet pump. This new pump (Grundfos UPS 25-60 180) is a triple-speed unit, having the following pump characteristics (as shown in the Grundfos product catalogue).

Figure A6. Pump characteristics for the valve group's Grundfos UPS 25-60 180 circulation pump. The main pump The main pump supplying the boiler was also changed, in order to make it possible to create relatively high available differential pressures across the valve group. In the same way as for the circulation pump in the valve group, the new boiler pump (Grundfos UPS 40-180) is also a three-speed unit, having characteristics as shown below.

A-6

APPENDIX A – TEST RIGS

Figure A7. Pump characteristics for the main Grundfos UPS 40-180 pump (connected to the boiler). Miscellaneous The heat source equipment is as for the original test rig, and consists of a Parca EL-150 electric boiler with a rating of 70 kW, switchable to 19 power levels, connected to a CTC Parca Cetevac 500 litre hot water storage tank, which maintains the supply temperature at a constant level. See Widén (1994) for a more detailed description of the system. A.1.2 Structure of the ventilation system The purpose of the ventilation system is to supply the air heater in the heating system with cold outdoor air. The original ventilation system is used, with only one change: the frequency converter that had been used to control the fan speed was replaced by a more modern converter when the original one failed. Figure A8 shows the general arrangement of the system.

A-7

APPENDIX A – TEST RIGS

Explanations Uteluftsintag Luftbehandlingsdel Omblandningsbox Hastighets .... Testsektion Trappa... Testbatteri Avluft Fläktdel Delar av... Ackumulator Elpanna Expansionskärl

= = = = = = = = = =

Outdoor air intake Air treatment unit Mixer box Flow smoother Test section Staircase up to mezzanine Test air heater Exhaust air Fan section Parts of the heating system (below the mezzanine) = Hot water storage tank = Electric boiler = Expansion vessel

Figure A8. Arrangement of the existing ventilation system. Picture taken from Widén (1994). Before the incoming air reaches the air heater at the heart of the test rig, it passes through an air treatment section that consists of a cooling coil and an electric heater. However, the cooling coil has never actually been connected to any refrigerating machinery, and so for this reason it has not been possible to make use of it in the measurements. In order to ensure that the air in the ventilation duct has a uniform temperature and is flowing with a uniform velocity, it is mixed in a mixing box, after which it passes a perforated plate to even out the flow velocity. An orifice plate (for measurement of the air flow rate) and a grid of temperature sensors are installed upstream of the air heater. A similar grid of temperature sensors is installed downstream of the air heater, and upstream of the fan portion. These items of instrumentation are described in more detail below (A.1.4). The final part of the ventilation system, before the air is discharged to the exhaust duct, consists of the fan unit, made up of a fan and silencers. A.1.3 The control system The system can be controlled in three different ways: manual control, computer control or automatic control.

A-8

APPENDIX A – TEST RIGS

Manual control Manual control means that the valve opening of the control valves can be controlled directly by means of a potentiometer, from which the desired valve opening (from 0.0 to 99.9 %) can be set directly. This method is used primarily when balancing the system. Computer control Most of the measurements were concerned with ascertaining how the valve opening of the control valve affected the flow and temperature levels in the various types of systems (i.e. in respect of the type of valve group, the type of control valve and the flow mode). This work was performed under computer control, with the control valve being opened in 10 % steps from originally closed to 100 % valve opening. After each step, the system was allowed to settle to steady-state conditions, involving a wait of about 10-20 minutes, before the next step could be taken. By using the computer to construct a program under which the valve opening of the valve was determined by the time, it was possible essentially to automate these measurements, which naturally facilitated the work. Automatic control It was also desirable to be able to produce measurements that simulated real conditions, i.e. those in which a regulator automatically adjusts the control valve in response to the temperature of the air leaving the air heater. The air temperature was measured by an EGL temperature sensor (from TA Control), from which the output signal was connected directly to the automatic system controller, and not to the measurement system. This controller was in the form of a TA Control Xenta 302 PI controller, in which the temperature set value, the width of the P-band and the length of the I-time could all be adjusted. By varying the width of the P-band (and/or the I-time) the system can be induced to oscillate, which provides an indication of the sensitivity of the system. Setting up the three control modes was done in a straightforward manner by connecting the control valve actuator to the required control output on a central unit. These three outputs on the unit are in turn connected to either the potentiometer, the computer (via the data-logger) or the conventional controller. The design of the necessary connection system, together with programming of the computer and data-logger for the measurement and control system, was carried out by Tommy Sundström and Josef Jarosz, both employed by the Department of Building Services Systems. A.1.4 The measurement system The purpose of the measurement system is to collect the necessary measured data from a number of measurement points throughout the system. The diagram below represents a simplified schematic of the valve group, showing the measurement points and their names/numbers, together with a table identifying the measurement points and providing further information.

A-9

APPENDIX A – TEST RIGS

6

4 A

B

24

23

22

27

26

25

2

1

28

15

14

13

18

17

16

21

20

19

D

C

8

7

5

E

F

3

K

11

G

H

I

J

12 A

0 B

G

I

10

9

E

H

0

K

Temperature sensor for the control system (TAC EGL)

F

No. in the diagram 1-2

Name

Description

Sensor

Ta-1,8 - 1,9

Air temperature upstream of the air heater

3 4 5 6 7 8 9 10 11 12 13 - 21

Tw-2,1 Tw-1,2 Tw-1,1 Tw-2,2 Vw-1 Vw-2 DP-1 DP-2 H-ventil H-signal Ta-2,1 - 2,9

22 - 28

Ta-1,1 - 1,7

Water temperature, secondary side, supply Water temperature, primary side, return Water temperature, primary side, supply Water temperature, secondary side, return Water flow rate, primary side Water flow rate, secondary side Differential pressure Differential pressure Degree of opening, actual value Degree of opening, set value Air temperature downstream of the air heater Air temperature upstream of the air heater

Temperature sensor, Cu-Konstantan, type T Pt-100 (3 mm) Pt-100 (3 mm) Pt-100 (3 mm) Pt-100 (3 mm) Scylar II QN 2,5 Scylar II QN 2,5 Validyne DP15, membrane 38 (square) Validyne DP103, membrane 38 (round) Internal voltage in the actuator Output voltage from the control system Temperature sensor, Cu-Konstantan, type T Temperature sensor, Cu-Konstantan, type T

Figure A9. Measurement points in the system. Differential pressure All test points identified by letters in the above diagram are pressure measurement points. However, only eight of them (A, B, E, F, G, H, I, K) were used. They were connected by reinforced rubber hoses to a pressure manifold (circled in the diagram above) containing two differential pressure sensors, with each input being controlled by a small shut-off valve A-10

APPENDIX A – TEST RIGS

(TA 400). The pressure sensors, which are Validyne DP15 (no. 9) and Validyne DP103 (no. 10) could in turn be isolated from each other by means of a further four shut-off valves, so that they could be used to measure different differential pressures in the system at the same time. Two inputs on the pressure manifold were connected together in order to be able to zero the differential pressure: these two inputs are shown in the diagram by “0”. Water temperature The temperature of the water was measured at four points in the valve group. As seen in the direction of flow, the supply temperature was measured upstream of the control valve (5), the inlet temperature was measured immediately before the air heater (3), the return temperature on the secondary side was measured immediately after the air heater (6), and the return temperature on the primary side was measured after the shunt connection (4). The temperature sensors were Pt100 sensors, in direct contact with the water flow. The reason for not using sensor pockets was because they would delay the response to temperature changes in the water. It should also be added that the Pt 100 sensors were connected to the data-logger using the four-wire method, which means that power supply and measurement were separated into two loops, which improves accuracy. Air temperature Two grids, each consisting of nine temperature sensors, were mounted in the air duct upstream and downstream of the air heater. The temperature sensors themselves were of type T, i.e. copper and konstantan. Each sensor was separately connected to the data-logger. Reference temperature was measured internally in the data-logger. However, it was found that this was not particularly appropriate, as described below in section A.1.5, Uncertainty of Measurement. Another temperature sensor (TA Controls EGL) was also fitted in the air duct downstream of the air heater and connected to the control system, as described above in section A.1.3. This sensor provided a signal to the automatic control system, and not to the measurement system. Water flow Two inductive flow meters (Scylar II QN 2.5) were installed in the valve group: one (7) to measure the flow on the primary side, and one (8) to measure the flow on the secondary side. These flow meters were originally intended for digital recording of the flow, by counting pulses, with each pulse corresponding to a certain quantity of water passing through the unit. However, this was not a desirable procedure in this project, as pulse counting involves a relatively high uncertainty of measurement at low flow rates or when the flow changes rapidly, i.e. over a short period of time. The meters were therefore fitted with analogue outputs, so that the flow could be measured instantaneously in the form of a 4-20 mA current signal. Air flow All measurements were made at a constant air flow rate. This was measured by the existing orifice plate, installed upstream of the air heater, in the form of a 2 mm thick plate, A-11

APPENDIX A – TEST RIGS

Mass flow [kg/s]

with a rectangular opening in the centre. Four pressure measurement points were fitted on each side of the orifice plate, connected together and then connected to a U-tube manometer. From this, the measured value was obtained simply visually, by reading the manometer. The air flow rate could be controlled by varying the fan speed, under control of its inverter, although a constant fan speed was used for all the measurements. This involved supplying the motor at a frequency of 40 Hz, which created a differential pressure of 39 ± 1 kPa across the orifice plate. This equated to a mass flow of 1.01 ± 0.01 kg/s, as shown in the diagram below, which is a reworking of a calibration curve produced for the plate (Widén, 19994). This reworking consisted of modifying the curve for an air temperature of 5 °C, instead of the approximately 17 °C for the original curve. This was because the incoming air temperature during this work varied between 0 °C and 10 °C. 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Density = 1,2565 kg/m³ (5 °C)

0

5

10 15 20 25 30 35 40 45 50 Pressure drop [kPa]

Figure A10.Reworked calibration curve for the air flow measurement orifice plate. It is of course very risky to use a 10-year-old calibration curve, and one which, in addition, has been reworked to match it to other temperatures. Some tracer gas measurements were therefore made in order to measure the air flow rate somewhat more accurately. This involved supplying nitrous oxide (N2O) to the air stream immediately after the air heater. At the same time, the concentration of the gas was measured about 7 m further downstream in the duct. (It should be pointed out that mixing of the nitrous oxide with the air stream should be satisfactory, as the distance between the two points includes both a bend and the fan.) The nitrous oxide measurement showed that, if anything, the mass flow rate of the air was somewhat higher (about 1.07 kg/s) than as indicated by the calibration curve of the orifice plate (about 1.01 kg/s). The valve opening of the control valve It was most important during the measurements to obtain a continuous measure of the valve opening of the control valve. This was done by measuring an internal voltage in the current actuator (11), which provided a measure of the position of the valve head and thus of the valve opening of the valve. A-12

APPENDIX A – TEST RIGS

Figure 8 also shows an input signal to the valve (12), which is not strictly correct. This signal comes from the control system, and is supplied to the valve actuator in order to control opening of the valve. However, the signal is also recorded by the instrumentation system, and so it is included in the figure. Data-logger and measurement computer An HP 34970A data-logger, connected to a computer in which all the measured data was stored, was used for collecting all the measurement signals. The logger contains three separate boards, providing a total of 28 inputs and 2 outputs. This meant that all the inputs were in use during the measurements. A.1.5 Uncertainty of measurement Differential pressure - Validyne Different measuring ranges can be used, depending on what membranes the Validyne differential pressure gauges are fitted with. Both have been fitted with a no. 38 membrane, providing a measurement range of 0-55 kPa. According to the manufacturer, the maximum uncertainty of measurement is guaranteed not to exceed ± 0.25 % of maximum value. The signals from the differential pressure sensors are converted by two signal converters to a standard 0-10 V output signal. However, this voltage has to be manually adjusted initially. When setting up the signal converter, the first step is to zero the output voltage signal, which is why the hydraulic short circuit has been provided on the pressure manifold between the two connection points marked “0”. If possible, the next step is to apply the maximum differential pressure (55 kPa in this case), so that the output signal can be adjusted to 10 V. A lower maximum differential pressure would reduce the accuracy. Setting the signal converters was performed using a U-tube manometer connected to the pressure manifold. After further checks of the setting, the following characteristic diagram could be produced.

A-13

APPENDIX A – TEST RIGS

50 45

Manometer [kPa]

40 35 30 25 20 15

DP103

y = 0.9358x - 0.1651 sx = +/- 0.23

DP15

y = 0.8574x - 0.0810 sx = +/- 0.51

10 5 0 0

10

20

30

40

50

60

Differential pressure sensor [kPa]

Figure A11.Calibration of the differential pressure sensors and their signal converters. The diagram above shows how the voltage signal (converted to an equivalent differential pressure) from each differential pressure sensor accords with the corresponding value on the U-tube manometer. The dotted line in the figure represents full agreement, from which it can be seen that the settings of the signal converters were not quite correct. The poorest agreement is that of the DP15 differential pressure sensor. The equations shown in the figure represent the departures between the differential pressure sensors and the U-tube manometer. These equations have been applied to the measured values in the analyses in order to eliminate the differences. Statistically, the random uncertainties of measurement, or the estimated uncertainties of measurement (Type A), as defined by BIPM (Fahlén, 1992), can be calculated as the spread of the measured values compared with the equations for correction of the values. The standard error of the spread can be calculated from the following equation: N

∑ (x

sx = where s x N xi x

i =1

i

− x)

2

(A1)

N2 − N = = = =

Standard error of the measurement Number of measured values Individual measured value Expected value of the measurement series (mean value)

A-14

APPENDIX A – TEST RIGS

In this case, x is the “true” value, as measured using the manometer. The standard errors of the spreads of DP15 and DP103 can be calculated as 0.51 kPa and 0.23 kPa respectively. There is always some risk of misreading the value shown by a manometer. In this case, the error has been estimated as not exceeding one scale division on the tube. This gives an expected uncertainty of measurement (Type B) of ± 0.13 kPa for both DP103 and DP15. The total uncertainty of measurement is given by: 2

Ux = k ⋅ sx + w x where U x k sx wx

= = = =

2

(A2)

Total uncertainty of measurement Coverage factor (normally equal to 2) Estimated uncertainty of measurement Expected uncertainty of measurement

After correction by the equations shown in Figure A11, this gives a total uncertainty of measurement for DP15 of ± 1.05 kPa, and a corresponding uncertainty of measurement for DP103 of ± 0.54 kPa. Pt100 temperature sensors According to their manufacturer (Pentronic), the Pt100 temperature sensors have a maximum as-delivered uncertainty of measurement of ± 0.05 °C. This uncertainty of measurement was regarded as satisfactory for the purposes of this work, and so the sensors were not further calibrated in order possibly to improve the known uncertainty of measurement. However, they were jointly calibrated in order to compare them with each other. This simply involved running the system without the electric boiler and main pump. Both the shunt and the bypass connection were closed at the valve group, so that the water flow circulated past all the temperature sensors, as shown in the simplified diagram below. The diagram shows only the relevant sensors in this context: in addition, all the shut-off valves and valve group and bypass connections have been removed.

A-15

APPENDIX A – TEST RIGS

6

4 8

7

5

3

Figure A12.Simplified diagram of the valve group when performing common calibration of the temperature sensors. In order to reduce the effect of heat transfer from the warmer surroundings in the test hall (where the test rig was installed) to the colder outdoor air in the ventilation duct, this joint calibration was performed on a hot summer day, when the difference between the temperature of the air in the ventilation duct and the temperature of the air in the test hall was relatively little. Measurement continued for some hours, and showed a mean departure of 0.03 ºC between all four Pt100 sensors and the mean value of them. The maximum instantaneous difference between two sensors amounted to 0.10 °C. The mean departure as stated here has been previously defined, in Chapter 4. It is used to describe the differences between two values, whether between measured and simulation values, the measured value from a sensor against the mean value of all connected sensors or simply between two individual sensors. The fact that it is the mean departure that is used, instead of calculating the estimated uncertainties of measurement using equation (A1), is due to the fact that such calculation is quite difficult, as the outdoor temperature varied during the progress of the measurements. It becomes impossible to distinguish between temporary departures and those that are due to an actual temperature change, with the result that it is not possible to arrive at a stable mean value of the measured values from a sensor over a given period of time, which complicates estimation of the estimated uncertainties of measurement. The thought behind the use of mean departures is to provide quantitative measures of the agreement between the temperature sensors in the system, which in turn provides an indication of the uncertainty of measurement of the sensors. This applies particularly to the thermoelements which, in this way, can be related to the Pt 100 sensors, the uncertainty of which is documented by the manufacturer. Temperature sensors -thermoelements According to their manufacturer, Pentronic, the uncertainty of measurement of the thermoelements is not more than ± 0.10 °C. However, as their uncertainty of measurement depends to some extent on the way in which they are connected to the data-logger (with an A-16

APPENDIX A – TEST RIGS

internal reference temperature producing poorer accuracy), and particularly due to the fact that they have not been replaced since the test rig was originally built, it was essential to check them. However, it would have been undesirable to dismantle the rig in order to reach them: instead, they too have been checked against each other by means of a common calibration. At equilibrium, both the air and the water temperatures in the system should be the same, as described above in connection with common calibration of the Pt 100 sensors. Figure A13 shows the results of this common calibration, which lasted for 24 hours with measurements every minute. The diagram shows the mean value of the Pt 100 sensors in the valve group (Tw), the mean value of the thermoelements in the ventilation duct upstream of the air heater (Ta-1) and the mean value of the thermoelements in the ventilation duct downstream of the air heater (Ta-2). However, it must be pointed out that only two of the nine thermoelements upstream of the air heater showed themselves to be reliable, and so the measured value from those elements that were not working have been omitted from the analyses. But the drawback of this is that any thermal stratification of the air upstream of the air heater would not be picked up by the sensors, and so it was not certain that the two working sensors would necessarily provide a representative measure of the incoming air temperature. However, the common calibration does show that the mean value of the measured air temperature from the two working sensors upstream of the air heater agrees well with the mean value from the sensors after the air heater. As no heat is supplied to the incoming air flow, it is reasonable to assume that the sensors upstream of the air heater do in fact provide a representative measure of the mean value of the incoming air temperature. In addition, it was found in connection with the joint calibration that the spread of measurement between the sensors downstream of the air heater was relatively narrow. A mean departure (against the mean value of all the sensors measurements) of only 0.26 °C and a maximum instantaneous departure of 0.80 ºC (for sensors Ta-2,9 against the mean value) indicates that there is little thermal stratification in the ventilation duct. However, when heat is supplied, some thermal stratification does occur downstream of the air heater, as described in Chapter 3 in connection with the measurements.

A-17

APPENDIX A – TEST RIGS

16.0

Temperature [°C]

15.5

Ta-1 (mean) Ta-2 (mean)

15.0

Tw (mean)

14.5 14.0 13.5 13.0 0

2

4

6

8

10

12

14

16

18

20

22

24

Time [h]

Figure A13.Mean values from the water and air temperature sensors as obtained by the common calibration. Measurement showed that the mean value of temperature as indicated by the thermoelements in the first grid (upstream of the air heater) differs from the mean value of the measured water temperatures (as measured by the Pt 100 sensors) by + 0.03 °C (systematically). The corresponding value of the second grid array, downstream of the air heater, was + 0.006 °C. The mean departure between the mean temperature of the first grid array and the mean value of the Pt 100 sensors has been calculated as amounting to 0.002 °C, while the corresponding figure for the second grid array is 0.001 °C. This shows that the mean value of the measured values from the thermoelements provides a representative measure of the true air temperature. The total uncertainty of measurement of these sensors was estimated as being ± 0.10 °C, which is based on the calculated values (of the uncertainty of measurement of the Pt 100 sensors and the measured mean departures stated above) and on what is stated by the manufacturer. Air flow measurement - orifice plate/tracer gas Both the existing orifice plate and tracer gas measurements were used when determining the air flow in the ventilation duct. An adjusted calibration curve for the orifice plate indicated a mass flow of about 1.01 kg/s of air, while the tracer gas measurements indicated a mass flow of 1.07 kg/s. This difference can depend on three factors: measurement error(s) when determining the air flow using the orifice plate, inward leakage of surrounding air at the air heater or measurement error(s) when making the tracer gas measurements. It is difficult to estimate measurement error when using the orifice plate. Errors or uncertainties can of course arise in connection with reading the U-tube manometer, but this uncertainty is estimated as not exceeding ± 1 Pa. On the other hand, the reliability of using an old, readjusted calibration curve has to be regarded as being a major problem in this context. A-18

APPENDIX A – TEST RIGS

It is possible that there is a slight inward leakage of air from the surroundings. However, it should be more or less insignificant, as all joints in the ventilation duct, and particularly where the duct joins the air heater, had been sealed with silicone sealant and tape. The measurement error associated with the tracer gas measurement is estimated as about ± 7 % (Svensson and Johansson, 1999). In the rest of this work, it is the tracer gas measurements that will be used as a basis for estimating the air flow. In other words, this means that the air flow is assumed to be 1.07 kg/s, with an uncertainty of ± 7 %. However, it must be pointed out that the air flow as such is not an important parameter in the measurements: instead, the important factor is that the air flow should be relatively constant. It is reasonable to assume that, in fact, the air flow has been constant, as the supply frequency to the fan motor has been held constant at 40 Hz, and no changes have been made to the ventilation system while making the measurements. This has also been shown by the fact that the U-tube manometer, connected across the orifice plate, has steadily shown a value of 39 Pa ± 1 Pa. The Scylar II QN 2.5 water flow meter The calibration of the flow meters from Scylar are accredit by the German DAR (Deutscher Akkreditierungs Rat) laboratory. The measurement deviation of the meters, and the uncertainty of measurement during calibration, were determined for three different flows, as shown in the following table. Meter no. 7 (Vw1, on the primary side) Flow [l/h] Measurement Uncertainty of error [%] measurement [%] 2487.28 0.2 0.6 252.56 0.1 0.6 26.69 -1.1 0.6 Meter no. 8 (Vw2, on the secondary side) Flow [l/h] Measurement Uncertainty of error[%] measurement [%] 2484.85 -0.3 0.6 255.99 0.5 0.6 26.68 2.2 0.6 Table A2. Measurement errors of the flow meters. During the measurements, the flow through Vw1 (meter no. 7) on the primary side changes drastically, which provides an opportunity to calculate the standard errors for the various flows, as shown in Figure A14.

A-19

APPENDIX A – TEST RIGS

5.0 4.5 Standard error [% ]

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

3

Flow [m /h]

Figure A14.Calculated standard error for flow meter Vw1 (meter no. 7) on the primary side. The figure shows that the standard error is low, as long as the flow exceeds 0.2 m³/h. Lower flows result in a substantial increase the standard error. It must be added that the flow through Vw2 (meter no. 8) on the secondary side was never recorded for values less than 0.5 m³/h, which was due to the fact that, during a certain period (while making the measurements on the directly connected air heater) the meter did not work. A check of the standard error of Vw2 showed that it had the same values as those for Vw1 for flow rates exceeding 0.5 m³/h (see the above figure). With the help of Table A2, and using the calculated standard errors for the meters, it is possible to estimate the total uncertainty of measurement to give a result as shown in Figure A15, which shows the total uncertainty of measurement for meter Vw1 (for all flows) and for Vw2 (for flows exceeding 0.5 m³/h).

A-20

Uncertainty of measurement [% ]

APPENDIX A – TEST RIGS

10 8 6 4 2 0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

3

Flow [m /h]

Figure A15.Estimated total uncertainty of measurement (coverage factor 2) for Vw1. HP 34970A data-logger The data-logger's uncertainty of temperature measurement is stated as being ± 1.0 °C for type T thermoelements, and as ± 0.06 °C for Pt100 sensors (as quoted in the HP34970A manual). The total uncertainty of measurement of the Pt100 sensors and data-logger together can be calculated as ± 0.08 °C (the square root of the sum of 0.052 and 0.062), with a coverage factor of 2. The mean value of the thermoelements was jointly calibrated with the mean value of the Pt100 sensors. There was little difference between these mean values, as was also the case in respect of any difference between the readings from the Pt100 sensors. As the data-logger was connected during the joint calibration, any measurement errors in it were included in the value for the total uncertainty of measurement. This means that the previously stated uncertainty of measurement, of ± 0.10 °C, should be added with the datalogger’s uncertainty of measurement for the Pt100 sensors. This gives an total uncertainty of measurement of ± 0.12 ºC (the square root of the sum of 0.102 and 0.062), for the thermoelements. Calculation of thermal output power The water side of the air heater provides a suitable means of calculating the thermal output power from the air heater, using the following equation. & = ρ ⋅V & ⋅ c ⋅ (t Q w w w wi w ,in − t w ,out ) & where Q w ρw & V w

(A3)

= Thermal output power on the water side [W] = Density [kg/m³] = Flow [m³/s] A-21

APPENDIX A – TEST RIGS

cw t w ,in

= Specific thermal capacity [J/kg°C] = Input water temperature [°C]

t w ,out = Return water temperature [°C] After converting to logarithms and differentiating, we obtain: & & ∆Q ∆ρ w ∆V ∆c ∆(∆t w ) w w = + + w + & & ρw cw ∆t w V Q w w

(A4)

This enables the total uncertainty of measurement to be calculated from (Fahlén, 1992): U Q& w  Uρ =  w & Q w  ρw where U

2

2

  U V& w   U c w  +  +   V &   c   w   w

2

  U ∆t w  +   ∆t   w

   

2

(A5)

= Total uncertainty of measurement, with a coverage factor of 2.

The values of density and specific thermal capacity have been assumed to be constant, at 988 kg/m³ and 4177 J/kgK respectively, although this represents a fairly substantial departure for the density, amounting at most to about 1 %, while the departure of the specific thermal capacity is only 0.3 % for this procedure. The total uncertainty of measurement of the temperature difference amounts to ± 0.11 °C (multiplying the uncertainty of measurement of the Pt100 sensors by √2). The uncertainty of measurement of the water flow depends on its magnitude. However, in most cases, the flow on the secondary side is either about 1.1 m³/h (for the high flow mode) or about 0.55 m³/h (for the low flow mode). These two flow values have respective uncertainties of measurement of ± 0.63 % and ± 0.61 %, as shown in figure A15. The following characteristic can be plotted for these constant flows, showing the total uncertainty of measurement of the calculated thermal output power, as measured on the secondary side.

A-22

Uncertainty of measurement [% ]

APPENDIX A – TEST RIGS

10 8 High-flow

6

Low-flow

4 2 0 0

5

10

15

20

25

Calculated thermal output power [kW]

Figure A16.Total uncertainty of measurement of calculated thermal output power, as measured on the secondary side.

Uncertainty of measurement [% ]

The uncertainty of measurement of the thermal output power, as measured on the primary side, is shown in the following diagram, which is valid for both the high-flow and low-flow modes. 14 12 10 8 6 4 2 0 0

5

10

15

20

25

Calculated thermal output power [kW]

Figure A17.Total uncertainty of measurement of calculated thermal output power, as measured on the primary side. The fact that the uncertainty of measurement is somewhat higher when the water flow is measured on the secondary side is due to the smaller temperature difference. This means that the effect of the uncertainty of measurement of temperature is greater in this case.

A-23

APPENDIX A – TEST RIGS

A.2 The radiator system test rig A.2.1 Arrangement of the test rig This test rig was constructed in 1998 as part of a project work at the Department of Building Services Systems (Bengtsson and Magnusson, 1998). It was subsequently complemented by a number of pressure measurement points and a temperature sensor for the current work. The diagram below shows the arrangement of the test rig and the positions of the sensors. Radiator valve Temperature sensors

Radiator 1

Return valve

Electric boiler

Integral pump

Radiator 2

Inductive flow meter B

C

A

Balancing and shut-off valve

Pressure measurement point

Figure A18.Schematic diagram of the radiator test rig and positions of sensors. The distribution system to the two radiators in the test rig is arranged as a two-pipe system, i.e. consisting of a supply pipe and a direct return. The radiators and piping system are all mounted on a plywood panel, which is in turn mounted on wheels to enable it to be moved if necessary. The back of the panel, behind the radiators, is clad with thermal insulation in order to prevent the heat from the radiators being lost to the rear. The rig was installed in the Department of Building Services System's experimental laboratories while these measurements were being made. Electric boiler and pump The electric boiler is a CTC Electronic boiler, incorporating an integral 20 litre hot water storage tank and an integral pump. The pump is a three-speed Grundfos UPS 21-40 F, with pump characteristics as shown in Figure A19, which is taken from Grundfos' product catalogue. A-24

APPENDIX A – TEST RIGS

Figure A19.Pump characteristics of the Grundfos UPS 21-40 F pump incorporated in the CTC Electronic boiler. Radiator valves The radiator valves are 20 mm nominal diameter TA TRV 400 valves, without thermostats. They incorporate a special pre-setting facility, which requires a special key to operate, and provides a presetting adjustment range from 0 (fully closed) to 10 (fully open). Figure A20 shows the valve characteristic, as stated by the manufacturer, TA Hydronics.

TRV 400 - Radiator valve 1.0 0.9 kv value [m³/h]

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

1

2

3

4

5

6

7

8

9

10

Pre-setting

Figure A20.Valve characteristic for the TRV 400 radiator valve. Return valves Any adjustment of the TRIM A (DN 20) return valves that may be needed can be carried out using an Allen key. This adjustment has been noted here in the form of the number of A-25

APPENDIX A – TEST RIGS

turns of the key from the closed position. Figure A21 shows the characteristic of the return valves, as stated by the manufacturer, T A Hydronics.

TRIM A - Return valve 1.4

kv value [m³/h]

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Number of turns

Figure A21.Valve characteristic of the TRIM A return valve. Balancing valves The balancing valves (A, B and C in Figure A18) are TA Hydronics' STAD (DN 20) valves. Piping The system piping is of copper. The circulation circuit which passes all three balancing valves has a size according to DN 18, while the branches to the radiators are DN 15. The pipes are insulated with preformed insulation and self-adhesive insulating tape (50 mm wide and 3 mm thick) from NMC (Climaflex). Radiators The two radiators in the rig were supplied by Epicon, with radiator no. 1 being of the type M11 (single panel, with a corrugated convection plate on the rear), while radiator no. 2 is of type M10 (single panel, without a convection plate). Both radiators are 50 x 80 cm in size. A.2.2 The measurement system The measured values in the system have been logged manually, i.e. without using either a data-logger or an instrumentation computer. Figure A22 shows the positions of the sensors in the system, together with a table of information on them.

A-26

APPENDIX A – TEST RIGS

1

Radiator 1

3

2

Radiator 2 4 A

7

H

No. in the figure 1 2 3 4 5 6 7 8 9 10

I

10

9

E

5

I

G

6

8

F

0 B

H

0

K

F

B

Name

Description

Sensor

Tw-1,1 Tw-1,2 Tw-2,1 Tw-2,2 Tw-return Ta-room Vw-1 Vw-2 DP-1 DP-2

Water temperature, radiator 1, inlet Water temperature, radiator 1, return Water temperature, radiator 2, inlet Water temperature, radiator 2, return Water temperature, return Room temperature, 0.9 m above floor level Water flow, radiator 1 Water flow, radiator 2 Differential pressure Differential pressure

Pt-100 (3 mm), in pocket Pt-100 (3 mm), in pocket Pt-100 (3 mm), in pocket Pt-100 (3 mm), in pocket Pt-100 (3 mm), without pocket Huger Clorius Combimeter QN 2,5 Clorius Combimeter QN 2,5 Validyne DP15, membrane 38 (square) Validyne DP103, membrane 38 (round)

Figure A22.Measurement points in the radiator test rig, with a brief description of the sensors. Differential pressure A valve manifold has been used for the various connections needed to measure differential pressure across various points in the radiator test rig, as shown by the circled connections in the diagram above. This is the same manifold as was described in the section describing the instrumentation of the air heater test rig (Section A.1.4). The positions of the four pressure test points are marked in the diagram above, together with indication of the inputs on the manifold (B, F, H and I) to which they were connected by reinforced rubber hose. Water temperature The water temperature was measured at various points in the test rig using five Pt100 sensors. These five points were the inlets to radiators 1 and 2 (numerals 1 and 3 respectively), and their return temperatures (2 and 4 respectively). The total return temperature was also measured before the flow returned to the boiler (5). The first four Pt100 sensors are fitted in thermometer pockets in the rig, while the last one (numeral 5) is in direct contact with the water, i.e. without a thermometer pocket. The reason for this is purely practical. The thermometer pockets for the first four sensors were incorporated A-27

APPENDIX A – TEST RIGS

when the rig was first built, while the final sensor was added to the rig later and was of such a type that no thermometer pocket was needed. However, as the rig is used only for measuring steady-state conditions, and not for dynamic processes, the effect of the thermometer pockets on the measured results can reasonably be presumed to be negligible. The actual registration of the water flow temperatures while the measurements were being made was carried out using a hand-held Technoterm 7300, which shows the temperature directly on a display. The drawback of this method is that it takes a certain time to register each measured value (i.e. to write it down), which means that none of the measurements could be made simultaneously (or even over a very limited period of time). On the other hand, the advantage of the method is that it is undoubtedly simple and requires a minimum of equipment. Room temperature A combination temperature and relative humidity sensor from Huger has been used to measure the room temperature. This is a particularly easy-to-use unit, with a display that shows the temperature and relative humidity. It was mounted 0.9 m above floor level, immediately in front of the radiator test rig and about 2 m from it. Water flow The water flow through the radiators was measured using ISS Clorius Combimeter P inductive flow meters. These meters are fitted with analogue output boards to enable instantaneous flow to be measured. In addition, they incorporate a display that shows the instantaneous value. The display also shows the total volume that has passed through the meter, expressed as m³. This facility has been used by recording the change in total volume over a given period of time, usually ten minutes, which has made it possible to ascertain the mean value of the flows through the two radiators. A.2.3 Uncertainty of measurement Temperature sensors - Pt100 According to their manufacturer (Pentronic) the Pt100 sensors have a maximum uncertainty of measurement when supplied of ± 0.05 °C. This uncertainty was regarded as sufficient for purposes of this work, and so the sensors were not further calibrated in order to improve the uncertainty of measurement. The method of measuring, and the arrangement of the test rig, did not permit any joint calibration of the sensors. Temperature registration - Technoterm 7300 In principle, the hand-held Technoterm 7300 unit measures the resistance of the Pt100 sensors, which varies in proportion to the temperature. The unit was calibrated by connecting it to four different resistors, which in turn had been calibrated at temperatures of 0, 24.9, 54.2 and 76.4 °C by the Monitoring Centre for Energy Research at Chalmers. Calibration of the display unit indicated that, at all temperatures, it was displaying a temperature 0.2 °C lower than the calibrated temperatures of the resistors. Allowance for this difference was therefore made when analysing the results. A-28

APPENDIX A – TEST RIGS

The resolution of the display unit provides an expected error of ± 0.05 °C which, together with the manufacturer's stated uncertainty of measurement for the Pt100 sensors, results in a total uncertainty of measurement of ± 0.07 °C for a coverage factor of 2. Room temperature sensor - Huger The Huger sensor was stated as having an uncertainty of measurement of ± 1 °C over the 0-40 °C temperature range, and of ± 2 °C for temperatures outside this range. As the sensor was used for measuring room temperatures in the 20-25 °C range, it can be assumed that the applicable uncertainty of measurement was ± 1 °C. Water flow meter - Clorius Combimeter The manufacturer of the flow meters, ISS Clorius International A/S, states that the measured error of the meters amounts to 0.17 % at a flow of 250.6 l/h, to 0.51 % at a flow of 44.9 l/h and to 0.51 % at a flow of 7.2 l/h (Bengtsson and Magnusson, 1998). The uncertainty of measurement of calibration was assumed to be the same as previously described (see Section A.1.5), i.e. ± 0.6 %. As the meters were read, and the results calculated, manually, there is also a further opportunity for uncertainty of measurement. Each measurement period takes ten minutes, and reading of the volume change can introduce a maximum error of ± 0.0001 m³, which gives an expected uncertainty of measurement of ± 0.6 l/h. In addition, this method of measuring the flow also means that each flow reading consists of a calculated mean value, and so the estimated uncertainty of measurement can be assumed to be zero. All this says that the total uncertainty of measurement depends partly on the uncertainty of measurement during calibration and partly on the uncertainty of measurement when reading the flow values. The figure below shows how the total uncertainty of measurement varies with the flow. Uncertainty of measurement [% ]

10 8 6 4 2 0 0

50

100

150

200

250

Flow [l/h]

Figure A23.Total uncertainty of measurement of the flow meters in the radiator test rig. A-29

APPENDIX A – TEST RIGS

Differential pressure sensors - Validyne See Section A.1.5 describing the uncertainties of measurement of these pressure sensors as used in the air heater test rig. Calculating the thermal output power The thermal output power can be calculated using equation (A3). The total uncertainty of measurement is estimated in accordance with equation (A5). The maximum uncertainties of density and specific thermal capacity can be estimated as ± 1.0 % and ± 0.3 % respectively (see Section A.1.5). The temperature difference between two identical Pt100 sensors increases the uncertainty of measurement by a factor of √2, to give a total uncertainty of measurement of ± 0.10 °C. The uncertainty of flow measurement is as shown in Figure A23.

Uncertainty of measurement (when calculating the thermal output power) [% ]

As both the flow and the temperature difference vary widely in the radiator measurements, there could be different uncertainties of measurement at the same thermal output powers. For this reason, the diagram below shows the uncertainty of measurement when calculating the thermal output power for different flows and temperature differences. At high temperature differences, it is the uncertainty of determination of the density that predominates, while at low temperature differences it is the uncertainty of measurement of temperature that predominates. At low flows, on the other hand, it is the uncertainty of measurement of the flow that predominates. 7 6 5 4 3

Temperature difference 5 °C

2

7 °C 10 °C 20 °C 50 °C

1 0 0

50

100

150

200

250

Flow [l/h]

Figure A24.Total uncertainty of measurement when calculating thermal output power from the radiator test rig. A-30

APPENDIX B – CALCULATION RELATIONSHIPS

B

CALCULATION RELATIONSHIPS

B.1 The radiator system The analyses of the effects of deviations on a radiator system are based on results from a simple steady-state calculation program derived in Excel. This program is in turn based on a number of different calculation relationships, briefly described below. B.1.1 Room heat balance The calculation of the amount of thermal power emitted by a radiator is based on a thermal balance for the room in which the radiator is installed. The room temperature is also calculated from the information in this heat balance. The following diagram is a schematic representation of a room with a radiator.

& Q ventilation

& Q radiator & Q transmission

troom & Q

tw,in tw,out

int ern

& V w

Figure B1. Heat balance in a room with a radiator. The thermal balance calculations are based on the following equations: Room & +Q & & & Q rad int ern = Q transmission + Q ventilation

(B1)

& Q transmission = UA room ⋅ (t room − t out )

(B2)

& & Q ventilation = ρ a ⋅ Va ⋅ c p ,a ⋅ (t room − t a ,sup ply )

(B3)

Radiator – Room

& = K ⋅ ∆t n = K Q rad rad rad lm

  ⋅  t  ln t 

n

∆t w w ,in − t room

w ,out

− t room

    

B-1

(B4)

APPENDIX B – CALCULATION RELATIONSHIPS

Water – Radiator & = ρ ⋅V & ⋅ c ⋅ (t Q rad w w p,w w ,in − t w ,out ) = C w ⋅ ∆t w & where Q rad & Q

transmission

(B5)

= Thermal power output from the radiator [W] = Thermal power loss from the room by transmission [W]

& Q ventilation & Q

= Thermal power loss from the room by ventilation [W]

UA room ρa & V

= Total coefficient of thermal transmittance of the room [W/°C] = Density of the ventilation air [kg/m³]

int ern

= Thermal power addition from an internal heating source [W]

c p ,a

= Ventilation air flow rate [m³/s] = Specific thermal capacity of the ventilation air [J/kgK]

t room

= Room temperature [°C]

t out

= Outdoor temperature [°C]

t a ,sup ply

= Supply temperature of the incoming ventilation air [°C]

K rad n ∆t lm t w ,in

= = = =

t w ,out

= Water return temperature [°C]

∆t w

= Temperature drop of the water flow through the radiator (= t w ,in − t w ,ut ) [°C]

ρw & V

= Density of the water [kg/m³]

a

w

cw Cw

Radiator constant [W/°C] Radiator exponent [-] Logarithmic mean temperature difference [°C] Water inlet (supply) temperature [°C]

= Water flow [m³/s] = Specific thermal capacity of the water [J/kg°C] & ⋅ c ) [W/°C] = Thermal capacity flow of the water (= ρ w ⋅ V w w

All calculations are made by either analytical or iterative solution of the equations, or combinations thereof. B.1.2 Distribution system The total water flow through the system depends on the total flow resistance of the system and on the pump characteristic. However, the flow resistance varies with the flow rate, depending on whether the flow is laminar or turbulent, which means that the flow calculations must be performed by iteration. Calculation of the flow in all parts of the systems is based on the equations described below. Pump The pump characteristic is expressed in the form of a polynomial equation:

B-2

APPENDIX B – CALCULATION RELATIONSHIPS

2   & &     V V w w ∆p =  A + B ⋅  + D  + C ⋅  + D   ⋅ F   E   E   

(B6)

where A, B, C, D, E and F are constants. In addition, the pump characteristic can be modified by speed control, in accordance with the affinity laws (Abel et. al, 1997): & n2 V = 2 & n1 V 1

(B7) 2

n 2 ∆p 2 = n 1 ∆p1 2 where: n 1 n2 & V 1 & V2 ∆p1 ∆p 2

= = = = = =

(B8)

Original speed [r/min] New speed [r/min] Original flow in accordance with the original characteristic [m³/s] New flow in accordance with the new characteristic [m³/s] Original pump pressure in accordance with the original characteristic [m³/s] New pump pressure in accordance with the new characteristic [m³/s]

Piping Wadmark's empirical relationship (Abel et. al, 1997) is used to calculate the coefficient of friction of the pipes for turbulent flow:  5.6 − 37 ⋅ k d    kd λ =  − 2 ⋅ log +   Re 0.9  3.7065   where: λ k d Re

−2

(B9)

= Coefficient of friction [-] = Roughness of the pipe [mm] = Hydraulic diameter (internal diameter) of the pipe [m] = Reynolds Number [-]

The coefficient of friction with laminar flow can be calculated from the following relationship (Abel et. al, 1997): λ=

64 Re

(B10)

When the coefficient of friction has been determined, the pressure drop can be calculated from the following equation (Abel et. al, 1997):

B-3

APPENDIX B – CALCULATION RELATIONSHIPS

∆p = λ ⋅ where: ∆p L ρ c

L ρ ⋅ c2 ⋅ d 2

(B11)

= Pressure drop in the pipe [Pa] = Length of the pipe [m] = Density of the water in the pipe [kg/m³] = Velocity of the water in the pipe [m/s]

It is assumed that the flow is laminar up to Re < 4000 (Abel et. al, 1997). In order to prevent a sudden jump in calculation of the coefficient of friction when Re = 4000 is passed, the value of the coefficient of friction changes between the laminar value and the turbulent value via a transition zone, the size of which can be arbitrarily selected in the program, but which in these calculations was set as 4000 < Re < 4500. Reynolds Number is calculated in accordance with the following equation (Abel et al, 1997): Re = where ν

c⋅d ν

(B12)

= Kinematic viscosity of the water [m²/s]

The flow resistance is calculated from the following simple equation: k= where k

∆p &2 V

(B13)

= Coefficient of flow resistance [Pa/(m³/s)2]

It should again be pointed out that the coefficient of flow resistance is not a constant value, but changes with the flow. Valve The capacity of the valve is expressed by: kv =

where k v & V ∆p ∆p 0 ρ ρ0

& V

(B14)

∆p ρ 0 ⋅ ∆p 0 ρ = The capacity of the valve [m³/h] = = = = =

Water flow through the valve [m³/h] Differential pressure across the valve [bar] Reference differential pressure = 1 bar Density of the water [kg/m³] Reference density = 1000 kg/m³

B-4

APPENDIX B – CALCULATION RELATIONSHIPS

The coefficient of flow resistance of the valve can be calculated from its capacity, using the following equation: k valve =

1 2 kv

(B15)

where k valve = Coefficient of flow resistance of the valve [Pa/(m³/s)2] Series connection of flow resistances

k1

k2

=

ktot

Figure B2. Series connection of flow resistances. The total flow resistance is obtained from: k tot = k 1 + k 2 or, more generally: n

k tot = ∑ k i

(B16)

i =1

Parallel connection of flow resistances

k1

= k2

Figure B3. Parallel connection of flow resistances. The total flow resistance can be expressed as: k tot =

1  1 1   +  k k 2   1

2

or, more generally:

B-5

ktot

APPENDIX B – CALCULATION RELATIONSHIPS

k tot =

1  n 1  ∑   i =1 k  i  

(B17)

2

Total flow resistance The combination of the system's series connections and parallel connections provides a total coefficient of flow resistance for the system. With this, the system characteristic can be expressed as follows: &2 ∆p system = k system ⋅ V system

(B18)

where ∆p system = Total pressure drop in the system [Pa] k system & V

system

= Total coefficient of flow resistance in the system [Pa/(m³/s)2] = Total flow in the system [m³/s]

Having calculated the total flow resistance of the system, the pump operating point can be determined using the equations for both the system and the pump characteristics. This provides a new total flow and a new total pressure drop. The flow distribution can be calculated from the calculated values of coefficients of flow resistance for each part of the system, using Equation B13. This gives new values of coefficients of flow resistance, and so on. When the calculations have clearly converged (with a tolerance of 0.001), the system can be regarded as being in equilibrium in terms of flow and pressure drop. B.1.3 Thermostatic radiator valves The thermostatic radiator valves as used in the program are “ideal” valves, which means that the model does not allow for effects such as hysteresis, temperature sensitivity, differential pressure sensitivity or dynamic aspects. The program allows the P-band of the thermostatic valve to be set either as a constant or as a function that is determined by the balancing of the valve. In the latter case, the relationship between the P-band and the balancing setting is assumed to be linear, which represents some simplification of real conditions, in accordance with the following equation. P − band = P − band max ⋅ where P − band P − band max H balanced H max

H balanced H max

(B19)

= The current P-band width of the valve [°C] = The maximum P-band width of the valve (when fully open) [°C] = The balanced valve opening of the valve [%] = The maximum valve opening of the valve (= 100 %)

B-6

APPENDIX B – CALCULATION RELATIONSHIPS

If thermostatic radiator valves are used - and they can be applied arbitrarily for each radiator - the valve opening of the radiator valve is determined by the following equation: H=

t room − t room ,design P − band

⋅ (H max − H balanced ) + H balanced

(B20)

where H = Current valve opening of the valve [%] t rum = Current room temperature [°C] t rum ,önskad = Desired (design) room temperature [°C] Naturally, the valve opening of the valve is restricted to a value between 0 and 100 %. B.1.4 Media data The program calculates the density of the water, its specific thermal capacity and its kinematic viscosity for each case. Density and specific thermal capacity are included in calculation of the heat release from the radiators, and are temperature-dependent. For this reason, it is the mean value of the supply and return temperature that is used in these calculations. The kinematic viscosity, which is also temperature-dependent, is used in calculation of Reynolds Number, which is calculated for each section of supply and return pipe together (to maintain mass flow balance). The following diagrams show how the density, specific thermal capacity and kinematic viscosity change with water temperature, being values taken from “Data and Diagrams” (1989). Curve matching, in the form of a polynomial equation, has been applied in each diagram. It is these equations that are used in the calculations. Density of water 1005 1000

Density [kg/m³]

995 990 985 980 975 970 965 y = 1.5954E-05x 3 - 5.9682E-03x 2 + 2.2423E-02x + 9.9995E+02

960 955 0

10

20

30

40

50

60

70

80

90

Temperature [°C]

Figure B4. Relationship between water density and temperature.

B-7

100

APPENDIX B – CALCULATION RELATIONSHIPS

Specific thermal capacity of water Specific thermal capacity [J/kg/°C]

4230 y = -6.0996E-08x 5 + 1.8698E-05x 4 - 2.2299E-03x 3 + 1.3776E-01x 2 4.2227E+00x + 4.2246E+03

4220 4210 4200 4190 4180 4170 0

10

20

30

40

50

60

70

80

90

100

Temperature [°C]

Figure B5. Relationship between water thermal capacity and temperature. Kinematic viscosity of water 2.0E-06

Kinematic viscosity [m²/s]

1.8E-06

y = 3.4081E-14x 4 - 9.4201E-12x 3 + 1.0094E-09x 2 - 5.5632E-08x + 1.7818E-06

1.6E-06 1.4E-06 1.2E-06 1.0E-06 8.0E-07 6.0E-07 4.0E-07 2.0E-07 0.0E+00 0

10

20

30

40

50

60

70

80

90

100

Temperature [°C]

Figure B6. Relationship between water kinematic viscosity and temperature. B.1.5 Limitations Only simple equations for the equilibrium conditions have been used, in order not to exaggerate the scope of the model. The following notes describe the program limitations.

B-8

APPENDIX B – CALCULATION RELATIONSHIPS

- The room description is limited to the UA value, ventilation air flow rate, ventilation air supply temperature and internal heat release. Although these parameters provide quite a lot of information and control, they are not really suited to dealing with effects such as the results of the use of additional insulation or the opening of windows. In addition, there is no allowance for heat exchange with neighbouring rooms. - The design of the distribution system is not capable of modification in terms of re-routing or rearranging the pipes. However, the pipe sizes, lengths and materials can be selected as required. The program is also capable of dealing only with a traditional two-pipe system. It cannot deal with bends or T-pieces, although their effects can instead be incorporated by treating them as additional lengths of pipe. The maximum number of radiators is 20, and the pressure drop through the radiators and their connection pipes is ignored. There is no allowance for possible heat losses from the pipes, and the consequence of this is further discussed below. - As far as the radiators themselves are concerned, the radiator exponent (n) is a critical parameter, as it is based on a mathematical model that attempts to describe reality, with which it is perhaps not always completely successful. However, the reason for continuing to use the model is because of its simplicity and because it is accepted for the purposes of most radiator contexts. In addition, it is sufficiently accurate for its purposes under steady-state conditions, as has been shown in this work. However, it could not be considered for dynamic applications. - The model is not capable of simulating time-dependent processes, as its calculations are based on steady-state thermal balances. This means that it is not possible to investigate what happens between two steady-state conditions. It also means that it is not possible to investigate the effect of thermal energy storage in the building structure. - Although density and specific thermal capacity are calculated for each case, their values are based on the mean value of system supply and return temperatures. In principle, the water temperature can vary between 0 °C and 90 °C, which indicates a maximum possible (but unlikely) error of about 1.8 % in density, and 0.6 % in specific thermal capacity, which combine to give a maximum possible error of just under 2 % in the thermal output power of the radiators. The effect of heat losses from the pipes The simulations have not made any allowance for a possible drop in the temperature of the radiator supply water resulting from heat losses from the distribution system. In reality, of course, this has some effect. There are fears that this effect would be greatest in low-flow systems, partly because the supply temperature of such systems is higher, which would result in higher heat losses, and partly because the flow rate is lower, which would provide more time for the higher heat losses to abstract heat. However, this could also be countered by the fact that the flow in the pipes is lower, which would mean that the coefficient of thermal transmittance would also be lower, and particularly if the flow was laminar. However, Andersson and Sandberg (1989) have shown that the lower flow does not adversely affect the total coefficient of thermal transmittance of the pipes. They also present calculations of temperature drops in a 20 mm diameter pipe, both for a high-flow case and for a low-flow case. After 10 m, the temperature has

B-9

APPENDIX B – CALCULATION RELATIONSHIPS

fallen from 65 ºC to 63.1 ºC in the high-flow case, and from 80 ºC to 67.6 ºC in the low-flow case. Although this is, admittedly, a considerable difference, it must be borne in mind that the low-flow rate is only one-fifth of the high-flow rate, which partly accounts for the high temperature drop in the low-flow case. The following diagram shows how the heat loss from uninsulated radiator pipes is affected by the pipe size and temperature. The values in the diagram are taken from a Wirsbo product brochure (1998). 60 Pipe size [mm] ⇒ 28

Heat release [W/m]

50

22 18 15 12

40 30 20 10 0 0

10

20

30

40

50

60

70

80

Temperature difference (water - room) [°C]

Figure B7. Heat losses from radiator pipes (Wirsbo product brochure). The above diagram can be used to illustrate the difference in heat losses from high-flow system pipes and low-flow system pipes, by providing data to show how the water temperature falls as a function of length and flow rate for a particular pipe size.

Water temperature [°C]

80 70

21.8 l/h

109 l/h

43.6 l/h

218 l/h

60 50 40 30

Pipe size = 12 mm 20 0

5

10

15

20

25

30

Pipe length [m]

Figure B8. The effect of flow and pipe length on water temperature for a 12 mm diameter pipe.

B-10

APPENDIX B – CALCULATION RELATIONSHIPS

The flow of 43.6 l/h in the diagram is equivalent to the flow through a radiator in the simulated high-flow system, while that of 21.8 l/h corresponds to the flow through a radiator on the low-flow system. The dotted lines show the flow in the branch (i.e. to five radiators) for the respective systems. The pipe size used in the diagram is 12 mm, regardless of system type. After 25 m, the water temperatures in both systems are the same if the pipe carries the supply to only one radiator. At higher flow rates, the temperature reduction is considerably less. It can be seen from the diagram that the low-flow system is more sensitive to heat loss from the pipe. Although the temperature loss from the pipes contributed to increasing the magnitude of effects caused by deviations, it can be asked by how much the heat emissions and return temperatures are affected by these reduction in the supply temperature? The following diagrams show this effect for the high-flow and low-flow systems. 1000

Heat release [W]

900

Low-flow system

800 High-flow system 700 600 Outdoor temperature = - 15 °C

500 -20

-15

-10

-5

0

Change in inlet water temperature [°C]

Figure B9. The effect of inlet water temperature reduction on heat emission from a radiator.

B-11

APPENDIX B – CALCULATION RELATIONSHIPS

40 Return temperature [°C]

38 36 High-flow system

34 32 30 28

Low-flow system

26 24 22

Outdoor temperature = - 15 °C

20 -20

-15

-10

-5

0

Change in inlet water temperature [°C]

Figure B10.The effect of inlet water temperature reduction on the return temperature from a radiator. The diagrams show that it is in the high-flow system that both the thermal output power and the return temperature are most affected by a reduction in the inlet temperature. However, the reduction in inlet water temperature was seen to be greatest in the low-flow system. A calculation of the reduction of the inlet temperature in the high-flow system under design conditions shows that the inlet temperature to the radiator at the farthest end of the system (BII5) is approximately 53 ºC, i.e. 7 °C below the design temperature. In the case of the low-flow system, the corresponding supply temperature is about 55 ºC, which represents a reduction of more than 18 ºC. These calculations are based on an ambient temperature of 20 ºC. Further calculation indicates that the thermal output power of radiator BII5 would be about 900 W in the high-flow system, and about 700 W in the low-flow system, with respective return temperatures of about 35 ºC and 25 ºC. From this, it can be seen that the effect of pipe heat losses is greatest in the low-flow system. Unless it has been considered, this represents a substantial deviation. However, it is not necessarily the case that the room temperature will fall by corresponding amounts as, in one way or another, the heat losses from the pipes will benefit the room. However, this heat release is uncontrolled, and can therefore contribute to the scatter of the room temperatures. As it is the radiators furthest from the heat source that receive the lowest supply temperatures, and as they also have the lowest differential pressure across them, it is most likely that the low room temperatures will occur in these rooms. If the problem is dealt with by raising the supply temperature from the heat source, the effect will be to increase the mean temperature in the building and also to increase the return temperature. The only way in which the problem can properly be dealt with is to balance the system, with proper allowance for the reduction in supply temperature. For this reason, careful balancing is presumably important, particularly in low-flow systems.

B-12

APPENDIX B – CALCULATION RELATIONSHIPS

B.2 Single-pipe, two-pipe and three-pipe systems Chapter 6 included a simple comparison of three different radiator system structures: one-pipe, two-pipe and three-pipe systems. The calculations for these systems have been limited to a small system consisting of only five radiators. B.2.1 Thermal balance in the room The room model, containing one radiator, is the same as that already described in B.1.1. B.2.2 Distribution system The calculations of pressure and flows in the systems are made in the same way as previously described in B.1.2, but with one important exception. The calculations are simplified, to the extent that flows are assumed to be fully turbulent. This means that the coefficients of flow resistance of the pipes can therefore be assumed to be constant, calculated in accordance with the following well-known equation: &2 ∆p = k pipe ⋅ V

(B21)

B.2.3 Limitations All the limitations described in B.1.5 for the model of the radiator system also apply in connection with the calculations for the one-pipe, two-pipe and three-pipe systems. In addition, there are three further important limitations: - The number of radiators is fixed, at five. - All flow is assumed to be turbulent. - The media data is constant, with an assumed value of 4180 J/kg°C for the specific thermal capacity, and 1000 kg/m³ for the density. These parameter values result in maximum respective errors of 3 % and 0.3 %, with a total error of just below 3 % for the calculated thermal output power.

B.3 The district heating substation radiator heat exchanger Chapter 6 also included a consideration of the effect of the heat exchanger used between the district heating system and the radiator system. Calculation of its performance is carried out iteratively, as the media data for heat transfer depend on the temperature conditions, which cannot be calculated unless details of the heat transfer are known. The schematic diagram below represents the heat exchanger.

B-13

APPENDIX B – CALCULATION RELATIONSHIPS

treturn,rad

tsupply,rad & Q

treturn,dh

tsupply,dh

Figure B11.The heat exchanger between the district heating water and the radiator water (a flat plate heat exchanger). B.3.1 Thermal balance The thermal power transfer can be calculated from the following general relationships for a heat exchanger (Abel et. al, 1997): & = UA ⋅ ∆t Q lm & where Q UA ∆t lm

(B22)

= Thermal power transferred by the heat exchanger [W] = Coefficient of thermal transmittance of the heat exchanger [W/°C] = Logarithmic mean temperature difference [°C]

The logarithmic mean temperature difference (for counter-flow connection) can be calculated from: ∆t lm =

(t

sup ply ,dh

− t sup ply,rad ) − (t return ,dh − t return ,rad )  t sup ply,dh − t sup ply,rad ln  t return ,dh − t return ,rad

   

(B23)

where t sup ply,dh = Supply temperature on the district heating side [°C] t sup ply,rad = Supply temperature on the radiator side [°C] t return ,dh

= Return temperature on the district heating side [°C]

t return ,rad = Return temperature on the radiator side [°C] The thermal power from the district heating side can be calculated from: & = ρ ⋅V & ⋅ c ⋅ (t Q dh dh dh dh sup ply ,dh − t return ,dh ) & = Thermal power from the district heating side [W] where Q dh ρ dh = Density of the district heating water [kg/m³] & = District heating water flow through the heat exchanger [m³/s] V dh c dh = Specific thermal capacity of the district heating water [J/kg°C] The thermal power picked up on the radiator water side can be expressed as: B-14

(B24)

APPENDIX B – CALCULATION RELATIONSHIPS

& = ρ ⋅V & ⋅ c ⋅ (t Q rad rad rad rad sup ply , rad − t return , rad )

(B25)

& = Thermal power input to the radiator water [W] where Q rad ρ rad = Density of the radiator water [kg/m³] & = Radiator water flow through the heat exchanger [m³/s] V rad c rad = Specific thermal capacity of the radiator water [J/kg°C] The following relationship applies under equilibrium conditions, and if there are no heat losses to the surroundings: & =Q & =Q & Q dh rad

(B26)

The thermal power transfer depends on the UA value of the heat exchanger, the flows and the temperature levels. The U-value changes with flow and temperature, as indicated by the following equation (Abel et. al, 1997): dp 1 1 1 = + + U α dh λ p α rad where U α dh

(B27)

α rad dp

= Coefficient of thermal transmittance [W/°Cm²] = Coefficient of thermal transmittance on the district heating side [W/°Cm²] = Coefficient of thermal transmittance on the radiator side [W/°Cm²] = Metal thickness between the water flows in the heat exchanger [m]

λp

= Thermal conductivity of the metal [W/°Cm]

The coefficients of thermal transmittance can be calculated using Nusselts Number (Hjorthol, 1990): Nu = where Nu α d λ Re Pr C m n

α⋅d = C ⋅ Re n ⋅ Pr m λ = = = = = = = = =

(B28)

Nusselts Number [-] Coefficient of thermal transmittance [W/°Cm²] Characteristic length [m] Thermal conductivity [W/°Cm] Reynolds Number [-] Prandtls Number [-] Constant coefficient (= 0.2) Constant exponent (= 0.67) Constant exponent (= 0.4)

Prandtls Number can be calculated from:

B-15

APPENDIX B – CALCULATION RELATIONSHIPS

Pr =

ν ⋅ ρ ⋅ cp

(B29)

λ

The model divides the flat plate heat exchanger up into a freely selectable number of layers, defined by the number of plates. In addition, it requires the dimensions of the plates, the distance between them and their thickness to be specified. Two different sizes of heat exchangers have been considered in the calculations: one for the high-flow system, and one for the low-flow system. They differ only in the number of plates, with the former having 10 plates and the latter having 30 plates. B.3.2 Media data Media data has been taken from “Data and Diagrams” (1989). Polynomial equations have been developed to match the curves, for use in the calculations. Those for density, specific thermal capacity and kinematic viscosity were shown above in B.1.4. The diagram below show the corresponding curve for the thermal conductivity of the water. Thermal conductivity of water

Thermal conductivity [W/m°C]

0.8 0.7 0.6 0.5

y = -1.0746E-05x 2 + 2.3310E-03x + 5.5643E-01

0.4 0.3 0.2 0.1 0.0 0

10

20

30

40

50

60

70

80

90

100

Temperature [°C]

Figure B12 Temperature dependence of the thermal conductivity of the water. B.3.3 Limitations The most important limitations of the model are that: - only static calculations are possible. - all flow is assumed to be turbulent. - flow distribution and flow patterns in the heat exchanger are assumed to be homogeneous.

B-16

APPENDIX B – CALCULATION RELATIONSHIPS

B.4 Derivation of radiator sensitivity The sensitivity of the radiator to a flow change can be approximately expressed by the following equation: D Q& V& ≈

2 ⋅ (t w ,in

n ⋅ ∆t w − t room ) − (2 − n ) ⋅ ∆t w

(B30)

n ∆t w

& dQ & Q = The sensitivity of the radiator to a flow deviation [-] = & dV δ & V = Radiator exponent, that depends on the size and shape of the radiator [-] = t w ,in − t w ,ut = The water temperature drop through the radiator [ºC]

t w ,in

= The inlet (supply) water temperature [ºC]

t rum

= The room temperature [ºC]

δ

where D Q& V&

Equation (B30) describes the relative change in thermal output power from a radiator in response to a relative change in flow. The value of D Q& V& varies between 0 (for infinitely high flow) and 1 (which is the maximum value, and which occurs when the flow through the radiator is just above zero). In fairly general terms, this would mean that a sensitivity of, for example, 0.5, would mean that a 1 % change in the flow would result in a change of 0.5 % in the thermal output power. B.4.1 Basic relationships The relationship (B30) has been derived from the following equations, which describe the radiator thermal output power as a function of its size, type and flow: & = K ⋅ ∆t n Q rad m

(B31)

& = c⋅ρ⋅V & ⋅ (t Q w ,in − t w ,out ) = C ⋅ ∆t w

(B32)

& where Q K rad ∆t m & V ρ c C

= Thermal output power from the radiator [W] = Radiator constant that depends on the type and size of the radiator [W/°Cn] = Mean temperature difference between the radiator and the room [°C] = Water flow through the radiator [m³/s] = Density of the water [kg/m³] = Specific thermal capacity of the water [J/kg°C] & ) [W/°C] = Thermal capacity flow (= c ⋅ ρ ⋅ V

The mean temperature difference can be approximately expressed by (from “Data och Diagram”, 1989):

B-17

APPENDIX B – CALCULATION RELATIONSHIPS

∆t m ≈

(t

w ,in

− t room ) ⋅ (t w ,out − t room ) = ∆t max ⋅ (∆t max − ∆t w )

(B33)

where t room = Room temperature [ºC] ∆t max = Maximum temperature difference (= t w ,in − t room ) [ºC] B.4.2 The effect of the flow on the temperature drop First a relationship is required to be obtained that describes how the temperature drop through the radiator changes with the flow. Equation (B31), together with (B32) and (B33), gives: & ⋅ ∆t ≈ K ⋅ (∆t ⋅ (∆t − ∆t ))n 2 c⋅ρ⋅V w rad max max w

(B34)

& in the flow produces a small change in temperature drop of A small change of dV d∆t w : & + dV & ) ⋅ (∆t + d∆t ) ≈ K ⋅ (∆t ⋅ (∆t − (∆t + d∆t ))) c ⋅ ρ ⋅ (V w w rad max max w w

n 2

(B35)

After simplification, dividing (B35) by (B34) gives:   &   d∆t w    dV d∆t w 1  ≈ 1 − 1 +  ⋅ 1 + ⋅ &  ∆t max ∆t w   ∆t w V   −1  ∆t w  Differentiating

& V

n 2

(B36)

& d∆t w dV with respect to gives: & ∆t w V

d∆t w ∆t w = ≈ & dV ∂ & V ∂

D ∆t w

     

For low values of

1+

& dV & V

    & n 1 1 dV   − ⋅ ⋅ 1− ⋅  &  ∆t max 2 ∆t max V −1  −1  ∆t w ∆t w  

(B37)

n −1 2

 d∆t w − 1 + ∆t w 

  

& d∆t w dV (≈ 0) and (≈ 0), expression (B37) can be approximated to: & ∆t w V

B-18

APPENDIX B – CALCULATION RELATIONSHIPS

D ∆t w

& V

≈

1 n 1 − ⋅ 2 ∆t max −1 ∆t w

=−

∆t max − ∆t w  n ∆t max − 1 −  ⋅ ∆t w  2

(B38)

B.4.3 The effect of the flow on the thermal output power & results in a small change in temperature drop of d∆t . A small change of flow of dV w & This results in a small change of dQ in the thermal output power. Inserting these values in equation (B32) gives the following expression:

(

)

& + dQ & = c⋅ρ⋅ V & + dV & ⋅ (∆t + d∆t ) Q w w

(B39)

Dividing by equation (B32) gives: 1+

&  dV &   d∆t w dQ  ⋅ 1 + = 1 + & & ∆t w V Q   

Differentiating

  

(B40)

& & dQ dV with respect to gives the radiator sensitivity: & & V Q

& dQ & & d∆t w  dV Q ⋅D = = 1+ + 1 + & &  ∆t w ∆t w  dV V ∂ & V ∂

D Q& V&

For low values of

& V

(B41)

& d∆t w dV (≈ 0) and (≈ 0), expression (B41) can be approximated to: & ∆t w V

D Q& V& ≈ 1 + D ∆t w

(B42)

& V

Finally, inserting equation (B38) in (B42) gives: D Q& V& ≈

n ⋅ ∆t w 2 ⋅ ∆t max − (2 − n ) ⋅ ∆t w

(B30)

B.4.4 Limitations Following limitations must be considered: -

Equations (B31) and (B33) are approximate. The specific thermal capacity and the density are assumed to be constant. All equations presuppose that the system is in equilibrium. Relative changes in flow and temperature drop are assumed to be negligible.

B-19

APPENDIX B – CALCULATION RELATIONSHIPS

B.5 Optimum valve characteristic The work has involved deriving an optimum valve characteristic for the control valve in some of the system configurations. This has been done by iteration, i.e. progressive adjustment of the characteristic until the desired results have been achieved, which is quite time-consuming. The process is described below in a simplified manner. B.5.1 Necessary static characteristic The purpose of employing an optimum valve characteristic is to ensure that the necessary P-band width remains as constant as possible, which also has the effect of the maximum necessary P-band width being as narrow as possible. The most difficult stage when arriving at an optimum valve characteristic is determination of the necessary static characteristic of the system, as needed to achieve this constant requisite necessary P-band width. This requires good knowledge of all aspects of the system. The necessary P-band width is defined by: Pnec =

Td ⋅ KS Tk

(B43)

where Pnec = Necessary P-band width [ºC] Td = Dead time [s] Tk = Time constant [s]

∆t [ºC] ∆H ∆t = Change in outgoing air temperature for a ... ∆H = ... change in the valve opening of the control valve K S = System gain (for a given valve opening) =

The static characteristic defines how the gain changes with the valve opening. If dynamic processes are ignored, the necessary P-band width is the same as the gain, which must then be constant if a constant P-band width is to be obtained. This means that the necessary static characteristic will be a straight line, as shown in the diagram below: ∆ta / ∆ta,max [-] 1

0

0

1

H [-]

Figure B13.Necessary static characteristic if the effects of system dynamics are ignored.

B-20

APPENDIX B – CALCULATION RELATIONSHIPS

The axes are referred to their maximum values, which means that the rise in air temperature across the air heater (the y axis) is related to the design temperature rise. If allowance is made for the dynamics, the change in the dead time and the time constant as the valve opening of the control valve changes will affect the necessary static characteristic. The way in which this occurs depends on the design of the system. Grindal (1994) has previously shown that the system dead time is relatively constant, and this has been confirmed by the measurements made in the work of this project. Changing the dead time requires the velocity of the temperature wavefront to be changed, which can be linked to the flow. The flow in a valve group having a recirculation connection is relatively constant, and so the dead time hardly changes at all. Although, in a direct connection arrangement, the flow does change, the design is such that the dead time does not change with the flow. This means that it is the change in the system time constant that affects the appearance of the necessary characteristic, with this time constant being made up of three elements: - The air heater - The air duct - The valve group The time constant of the air heater depends on the design of the heater, and varies with varying water and air flows as shown in the following equation (Jensen, 1978), (which ignores the mass of air in the air heater): Tk ,H = where Tk ,H Mm Mw UA Ca Cw

(M m + M w ) ⋅ (UA + C a ) UA ⋅ (C w + C a ) + C w ⋅ C a

(B44)

= The air heater time constant [s] = = = = =

Thermal capacity of the metal in the air heater [J/ºC] Thermal capacity of the water in the air heater [J/ºC] Coefficient of thermal transmittance of the air heater [W/ºC] Thermal capacity flow on the air side [W/ºC] Thermal capacity flow on the water side [W/ºC]

Constant water and air flows result in a constant time constant. The higher the water flow rate, the shorter the air heater's time constant. If the thermal capacity of the air in the ventilation duct is ignored, we obtain the following time constant for the duct (Jensen, 1978): Tk ,a =

M k ⋅ (C a + α k ⋅ A k ) Ca ⋅ α k ⋅ A k

(B45)

where Tk ,a = Time constant of the air duct [s] M k = Thermal capacity of the air duct (its metal parts) [J/ºC] B-21

APPENDIX B – CALCULATION RELATIONSHIPS

C a = Thermal capacity flow of the air [W/ºC] α k = Coefficient of thermal transmittance of the internal surface of the duct [W/m²ºC] A k = Surface area of the duct [m²] The time constant of the valve group depends largely on the amount of recirculation, and can be described by the following equation (Børresen, 1985): Tk ,s = −

τ

(B46)

ln ((1 − η w ) ⋅ (1 − ϕ))

where Tk ,s = The time constant of the valve group [s] τ ηw ϕ

= The time for the temperature wave to pass through the entire recirculation circuit [s] = The air heater efficiency on the water side [-] = The proportion of flow passing through the control valve in relation to the circulation flow [-]

The greater the valve opening of the control valve, the greater the value of ϕ and the shorter the time constant. The longer the pipe, and the lower the flow velocity, the longer it takes for the temperature wave to complete a turn of the recirculation circuit, and so the longer the time constant. When the control valve is fully open, the time constant is zero for the valve group. It must also be pointed out that the thermal capacities of the pipes affect the temperature front in the valve group, which increases the system time constant (Grindal, 1984). This can be described by Equation B45, modified to apply to pipes filled with water. The total system time constant depends on the values of the constituent parts, but to different degrees. If the distance between the air heater and the temperature sensor in the air duct that controls it is long, this element can dominate the total system time constant. A constant air flow therefore results in a control circuit time constant that is more or less independent of the valve opening of the control valve. This has the effect of making the necessary static characteristic more or less linear. However, Grindal (1984) has shown that, in most cases, the dominating time constant is determined by the recirculation connection (where one is used). In these cases, the valve opening of a control valve definitely affects the time constant. However, for a direct connection, it is the air heater time constant that dominates, as there is no recirculation. The diagram below shows examples of how the relationship between dead time and time constant varies with the flow (related to design flow) for a number of different system arrangements. The values are taken from the measurements made in this work.

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APPENDIX B – CALCULATION RELATIONSHIPS

1.0

V341-4,H,D

0.9 0.8

V341-4,L,D

Td/Tk [-]

0.7 0.6

V341-4,H,DH

0.5 V341-4,L,DH

0.4 0.3

V341-4,H,SABO

0.2 0.1

V341-4,L,SABO

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Flow (per-unit) [-] (Flow through control valve related to design flow)

Figure B14.Measured values of the quotient of dead time and time constant for a number of different systems, according to the flow per-unit. The dead time in the directly connected systems is considerably less than in the other systems, which means that the quotient of dead time and time constant in these systems is low. In systems having a valve group, a low-flow balanced system results in a higher quotient in general (as compared with a high-flow balanced system), which means that the value of the requisite P-band width in such systems is also higher. It can be seen from the diagram that the quotient of dead time and time constant changes with the flow through the control valve, such that it is low with low flow and high with high flow. This means that the system gain must be higher at low flows than at high flows, which therefore introduces a bend into the necessary static characteristic, as shown in the following diagram. The three curves in the diagram correspond to different cases, where the dominating time constant can be related to: the valve group (refer to systems with a circulation circuit), the air heater (refer to direct connection systems) and the air duct. Apart from the straight line, which symbolises the necessary static characteristic when the quotient of dead time and time constant does not change with the valve opening, the values used in the diagram are taken from the simulations in this work.

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APPENDIX B – CALCULATION RELATIONSHIPS

1.0 Temperature rise (per-unit) ( ta/ ta,m ax) [-]

0.9 0.8

Dominating time constant can be related to:

0.7 0.6

Valve group

0.5

Air heater

0.4

Air duct

0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Valve opening [-]

Figure B15.Necessary static characteristic related to different kind of systems. B.5.2 Valve group characteristic In order to be able to apply the necessary static characteristic to an optimum valve characteristic, there needs to be a relationship between the temperature rise across the air heater and the corresponding necessary flow rate. This relationship consists of the total efficiency of the valve group on the air side, as expressed below: η a ,s =

where η a ,s ηa

1 1 1 1  + ⋅  − 1 ηa R  ϕ 

=

∆t a t w ,sup ply − t a ,in

= The total efficiency of the valve group (with the air heater) on the air side [-] = The air heater efficiency on the air side [-]

C

CR [-] CH η C = w = a [-] ηw Ca = The air heater efficiency on the water side [-] & ⋅ρ⋅c = Thermal capacity flow = V p

CR CH Ca Cw

= = = =

∆t a

= Temperature rise across the air heater on the air side [°C]

ϕ R ηw

(B47)

=

Thermal capacity flow through the control valve [W/K] Thermal capacity flow through the air heater [W/K] Thermal capacity flow of the air through the air heater [W/K] C H = Thermal capacity flow of the water through the air heater [W/K]

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APPENDIX B – CALCULATION RELATIONSHIPS

t w ,sup ply = Water supply temperature [ºC] t a ,in

= Temperature of the entry air to the air heater [°C]

If this is expressed as a per-unit function of the valve group efficiency when the control valve is fully open (ϕ = 1), we obtain: η a ,s η a ,max

1

= η a ,max

 1 1  1  ⋅  + ⋅  − 1   ηa R  ϕ  

=

∆t a ∆t a ,max

(B48)

where η a ,max = Maximum efficiency (which is the same value for the air heater and the valve group at fully open control valve) [-] ∆t a ,max = Maximum temperature rise across the air heater (at fully open control valve) [°C] For a valve group having a recirculation connection, the flow through the air heater is more or less constant, which means that ηa is equal to ηa,max. For a direct connection, ϕ is always equal to 1. this gives the following two equations: For a valve group with recirculation:

∆t a = ∆t a ,max

For direct connection:

∆t a ηa = ∆t a ,max η a ,max

1 1  1 + η w ⋅  − 1 ϕ 

(B49)

(B50)

With a direct connection, the efficiency on the air side depends on the flow. If the flow is expressed as a per-unit value of the maximum value (i.e. with a fully open control valve), we obtain the following diagram which shows how the per-unit temperature rise across the air heater varies with the flow. Values have been taken from the simulations in this work.

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APPENDIX B – CALCULATION RELATIONSHIPS

1.0 Temperature rise (per-unit) ( ta/ ta,m ax) [-]

0.9 0.8 0.7

System configuration

0.6

H, Direct

0.5

H, Shunt

0.4

L, Direct L, Shunt

0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Flow (per-unit) (ϕ ) [-]

Figure B16.The effect of flow on the air temperature rise across the air heater, depending on system configuration. “H” = High flow, “L” = Low flow, “Direct” = Direct connection and “Shunt” = Valve group with recirculation circuit. B.5.3 Valve authority The last step in arriving at the optimum valve characteristic involves consideration of the valve authority, which links the necessary flow through the control valve with the required kv value. An example of this is shown in the following figure, the values in which have been taken from the simulations. 1.0 Relative kv value (kv/kvs ) [-]

0.9 0.8 0.7

Valve authority

0.6

0.05 0.30 0.72

0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Flow (per-unit) (ϕ ) [-]

Figure B17.The effect of the valve authority on the relationship between the flow through the control valve and its kv value. B-26

APPENDIX B – CALCULATION RELATIONSHIPS

B.5.4 Nomogram The way in which the three elements - the necessary static characteristic - the total efficiency of the valve group - the valve authority interact to give an impression of the necessary optimum valve characteristic can be illustrated by a nomogram, as shown below. Temperature rise (per-unit) (∆ta/∆ta,max) [-] 1

Static characteristic

1

1

Valve authority

Valve opening [-]

Flow (per-unit) (ϕ) [-]

Total efficiency of the valve group

Valve characteristic

1 Relative kv value (kv/kvs) [-] Figure B18.Nomogram to produce the valve characteristic from the valve authority, total efficiency of the valve group and system static characteristic. The dotted line in the nomogram above illustrates the procedure for arriving at an optimum valve characteristic, with the starting point for each point on the curve

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APPENDIX B – CALCULATION RELATIONSHIPS

(indicated by rings) being some arbitrary valve opening. The simplification in this method of presentation lies in the application of a constant requisite static characteristic: in fact, this changes with the valve characteristic, which means that it is actually necessary to arrive at the optimum characteristic by iteration, which is done in the simulations in this work.

B-28