An Analytical Model of Spark Ignition Engine for Performance Prediction

AN ANALYTICAL MODEL OF SPARK IGNITION ENGINE FOR PERFORMANCE PREDICTION

MR.SITTHICHOK SITTHIRACHA

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE MASTER OF SCIENCE IN AUTOMOTIVE ENGINEERING SIRINDHORN INTERNATIONAL THAI-GERMAN GRADUATE SCHOOL OF ENGINEERING (TGGS) GRADUATE COLLEGE KING MONGKUT’S INSTITUTE OF TECHNOLOGY NORTH BANGKOK ACADEMIC YEAR 2006 COPYRIGHT OF KING MONGKUT’S INSTITUTE OF TECHNOLOGY NORTH BANGKOK

Name

: Mr. Sitthichok Sitthiracha

Thesis Title

: An Analytical Model of Spark Ignition Engine for Performance Prediction

Major Field

: Automotive Engineering King Mongkut’s Institute of Technology North Bangkok

Thesis Advisors : Assistant Professor Dr.Suthum Patumsawad Assistant Professor Dr.Saiprasit Koetniyom Academic Year : 2006 Abstract The objective of this thesis is to develop a mathematical model of spark ignition engine based on cylinder-by-cylinder engine model which combines both physical formulae, e.g. engine geometries, and empirical formulae, e.g. burning duration. The engine performance, torque and power, can be calculated by integrating the pressure inside cylinder within one engine cycle. The model is verified by data from 8 engine models. It can capture torque and power characteristics very well. The overall errors are in between -6% to 4%. The model is used for simulating in order to predict the burning duration of the alternative fuels. Furthermore, the model indicates the effects on ηv when using these alternative fuels too. (Total 60 pages)

Keywords : Spark ignition engine, Gasoline engine, Engine modeling, Cylinder-bycylinder engine model, Engine simulation ______________________________________________________________Advisor ii

ชื่อ ชื่อวิทยานิพนธ์

: นายสิ ทธิโชค สิ ทธิราชา : แบบจําลองวิเคราะห์สาํ หรับการทํานายสมรรถนะของเครื่ องยนต์ จุดระเบิดด้วยประกายไฟ สาขาวิชา : วิศวกรรมยานยนต์ สถาบันเทคโนโลยีพระจอมเกล้าพระนครเหนือ ที่ปรึ กษาวิทยานิพนธ์ : ผูช้ ่วยศาสตราจารย์ ดร.สุ ธรรม ปทุมสวัสดิ ิ ยม ผูช้ ่วยศาสตราจารย์ ดร.สายประสิ ทธิ เกดนิ ปี การศึกษา : 2549 บทคัดย่ อ วัตถุประสงค์ของวิทยานิพนธ์น้ ีคือ เพื่อพัฒนาแบบจําลองทางคณิ ตศาสตร์ของเครื่ องยนต์จุด ่ บ ซึ่งรวมเอาทั้ งทฤษฎี ระเบิดด้วยประกายไฟบนพื้นฐานของแบบจําลองเครื่ องยนต์แบบสู บตอสู ทางกายภาพ เป็ นต้นวา่ เรขาคณิ ตของเครื่ องยนต์ และทฤษฎีที่ได้จากการสังเกต เป็ นต้นวา่ ํ ง สามารถคํานวณได้โดย ระยะเวลาการเผาไหม้ สมรรถนะของเครื่ องยนต์อนั ได้แก่ แรงบิดและกาลั การอินทีเกรตความดันในกระบอกสู บภายใต้หนึ่งรอบการหมุนของเครื่ องยนต์ แบบจําลองได้ ่ ั ่ องยนต์ 8 รุ่ น พบวา่ สามารถทํานายลักษณะกราฟสมรรถนะของ ทดสอบเปรี ยบเทียบคากบเครื ่ โดยมีคาผิ ่ ดพลาดโดยรวมอยูร่ ะหวาง ่ -6% ถึง 4% เครื่ องยนต์ได้เป็ นอยางดี แบบจําลองนี้ ได้จาํ ลองสถานการณ์ เพื่อที่จะทํานายระยะเวลาในการเผาไหม้ของเชื้ อเพลิง ่ ยิ่ง กวานั ่ ้ น แบบจํา ลองยัง สามารถที่ จ ะอธิ บ ายผลกระทบของการใช้เ ชื้ อ เพลิ ง ทางเลื อ กตางๆ ทางเลือกที่มีต่อประสิ ทธิภาพเชิงปริ มาตรได้อีกด้วย (วิทยานิ พนธ์มีจาํ นวนทั้ งสิ้ น 60 หน้า)

คําสําคัญ : เครื่ องยนต์จุดระเบิดด้วยประกายไฟ, เครื่ องยนต์เบนซิน, แบบจําลองเครื่ องยนต์, ่ บ, การจําลองเครื่ องยนต์ แบบจําลองเครื่ องยนต์แบบสูบตอสู ________________________________________________อาจารย์ที่ปรึ กษาวิทยานิ พนธ์ iii

ACKNOWLEDGEMENTS I would like to express my sincere gratitude to Professor Dr.Gyeung-Ho Choi of Power Train Laboratory, Keimyung University, Republic of Korea and Assistant Professor Dr.Noppavan Chananpanich of King Mongkut’s Institute of Technology North Bangkok who are initiators of this story. My colleague and I had a chance to have internship in the Power Train Laboratory under their allowance. This laboratory brought me to the engine technology field. Until Associate Professor Dr.Suwat Kuntanapreeda and Dr.Boonchai Watjatrakul went to visit us in South Korea. They advised me to undertake this topic for my thesis. This thesis has been developed since that point. After I came back to Thailand, this thesis is strengthened by many precious comments and suggestions from Assistant Professor Dr.Suthum Patumsawad and Assistant Professor Dr.Saiprasit

Koetniyom. Thanks to all persons who are

mentioned here. And also the staffs of the Power Train Laboratory who took care of us along 4 months of our visit in South Korea.

Sitthichok Sitthiracha

iv

TABLE OF CONTENTS Page Abstract (in English)

ii

Abstract (in Thai)

iii

Acknowledgement

iv

List of Tables

viii

List of Figures

ix

List of Abbreviations and Symbols

xii

Chapter 1 Introduction

1

1.1 Background

1

1.2 Objectives

1

1.3 Approach

1

1.4 Scope

1

1.5 Assumptions

2

1.6 Impacts or Benefits from Research

2

1.7 Thesis Outline

2 3

Chapter 2 Literature Review 2.1 Spark Ignition Engine

3

2.2 Modeling

5

2.2.1 Mean Value vs. Cylinder-by-cylinder Models

5

2.2.2 Limit of Physical Properties

5

Chapter 3 The Model

6

3.1 Model Overview

6

3.2 Crank Slider Model

8

3.3 Cylinder Pressure Model

8

3.4 Wiebe Function

9

3.4.1 Burning Duration

9

3.5 Heat Input

10

3.6 Air/Fuel Ratio

10

3.7 Heat Transfer

11

3.7.1 Heat Transfer Coefficient Correlations

v

11

TABLE OF CONTENTS (CONTINUED) Page 3.8 Volumetric Efficiency

12

3.8.1 Flow through Valves

15

3.8.2 Valve Lift

16

3.8.3 Discharge Coefficient

17

3.8.4 Frictional Losses

17

3.8.5 Charge Heating

19

3.9 Residual Gas

19

3.10 Friction

21

3.11 Torque & Power

21

3.12 Minimum Spark Advance for Best Torque

21

3.13 Simulation conditions

22

3.14 Alternative Fuels

22

3.14.1 Ethanol-blended Gasoline or Gasohol

23

3.14.2 Ethanol

24

3.14.3 Compressed Natural Gas

24

3.14.4 Liquefied Petroleum Gas

25

Chapter 4 Model Validation and Sensitivity Analysis

26

4.1 Performance Validation

26

4.2 Sensitivity Analysis

31

4.2.1 Burning Duration

31

4.2.2 Discharge Coefficient

32

4.2.3 Frictional Losses

33

4.2.4 Charge Heating

34

4.2.5 Exhaust Gas Temperature

34

4.3 Combustion Duration of Alternative Fuels

35

4.3.1 Ethanol-blended Gasoline or Gasohol

35

4.3.2 Ethanol

37

4.3.3 Compressed Natural Gas

38

4.3.4 Liquefied Petroleum Gas

39

vi

TABLE OF CONTENTS (CONTINUED) Page Chapter 5 Conclusions and Suggestions

41

5.1 Conclusions

41

5.2 Suggestions

41

References

43

Appendix A Engine Specifications

45

Appendix B Matlab/Simulink Block Diagrams

50

Biography

60

vii

LIST OF TABLES Table

Page

3-1 Air/fuel ratios of many substances

11

3-2 Parameters for simulation

22

3-3 Summaries of major properties of gasoline, ethanol, E10 and E20

23

3-4 Summaries of major properties of methane, ethane, and natural gas

24

3-5 Summaries of major properties of propane, butane, and LPG

25

viii

LIST OF FIGURES Figure

Page

2-1 Schematic of gasoline engine

6

2-2 Basic four stroke cycle

3

2-3 Pressure-volume diagram of Otto cycle

3

3-1 Model overview

6

3-2 Model overview (continued)

7

3-3 Piston cylinder and geometries

8

3-4 Burned mass fraction characteristic

9

3-5 Effect of engine speed on flame-development angle

10

3-6 Comparison of surface-averaged heat flux variations predicted by CFD calculations and empirical correlations

12

3-7 Volumetric efficiency versus mean piston speed for a four-cylinder indirect-injection diesel and a six-cylinder spark-ignition engine

13

3-8 Effect on volumetric efficiency of different phenomena which affect the air flow rate as a function of speed. Solid line is final volumetric efficiency versus speed curve

14

3-9 Discharge coefficient of typical inlet poppet valve

17

3-10 Pressure losses in the intake system of a four-stroke cycle spark-ignition engine determined under steady flow conditions

18

3-11 Assumption of remaining pressure after subtracted by pressure losses

18

3-12 Assumption of temperature inside manifold

19

3-13 Measured cylinder pressure pc, calculated cylinder-gas temperature Tc, exhaust mass flow rate m& e , and measured gas temperature at exhaust port exit Tp, for single-cylinder spark ignition engine at speed = 1000 rpm 3-14 Assumption of exhaust gas temperature

20 20

3-15 Cylinder pressure versus crank angle for over-advanced spark timing (50°), MBT timing (30°), and retarded timing (10°) and Effect of spark advance on brake torque at constant speed and air/fuel ratio, at wide open throttle 4-1 Simulation results of Mercedes-Benz 250SE

ix

22 26

LIST OF FIGURES (CONTINUED) Figure

Page

4-2 Simulation results of Mercedes-Benz 250E/8

27

4-3 Simulation results of Mercedes-Benz 250SL

27

4-4 Simulation results of Mercedes-Benz 280SE/8

28

4-5 Simulation results of Mercedes-Benz 280SL/8

28

4-6 Simulation results of Mercedes-Benz 300SEL/8

29

4-7 Simulation results of Mercedes-Benz 300SEL

29

4-8 Simulation results of Mercedes-Benz 600

30

4-9 Summarized relative errors from simulation results of 8 engines

30

4-10 Comparison between gasoline and +/-10 modified combustion range without spark advanced adjusting

31

4-11 Relative errors of before and after adjusting the spark timing

32

4-12 Comparison between normal CD and +/-10% changing

32

4-13 Comparison between using and non-using Cf

33

4-14 Comparison between using and non-using Cheat

34

4-15 Comparison between normal and +/-50 K exhaust gas temperature

35

4-16 Effect of ethanol-blended fuel on volumetric efficiency

35

4-17 Combustion duration of gasoline, E10, and E20

29

4-18 Comparison between gasoline, E10, and E20 when using with unmodified engine

36

4-19 Effect of ethanol as a fuel on volumetric efficiency

37

4-20 Combustion duration of gasoline, E10, E20, and E100

37

4-21 Effect of ethanol as a fuel on volumetric efficiency

38

4-22 Combustion duration of gasoline and CNG

38

4-23 Effect of ethanol as a fuel on volumetric efficiency

39

4-24 Combustion duration of gasoline and LPG

39

A-1 Performance curve of Mercedes-Benz 250SE

46

A-2 Performance curve of Mercedes-Benz 250SL

46

A-3 Performance curve of Mercedes-Benz 250E/8

47

A-4 Performance curve of Mercedes-Benz 280SE/8

47

x

LIST OF FIGURES (CONTINUED) Figure

Page

A-5 Performance curve of Mercedes-Benz 280SL/8

48

A-6 Performance curve of Mercedes-Benz 300SEL/8

48

A-7 Performance curve of Mercedes-Benz 300SEL

49

A-8 Performance curve of Mercedes-Benz 600

49

B-1 Main model

51

B-2 Cm block details

52

B-3 Engine geometry block details

52

B-4 Engine geometry/Vd block details

52

B-5 Engine geometry/A(CA) block details

52

B-6 Engine geometry/Crank geometry block details

53

B-7 Engine geometry/V(CA),Vc block details

53

B-8 Wiebe fn block details

53

B-9 Burn duration block details

53

B-10 P block details

54

B-11 P/Pratio block details

55

B-12 P/Lv fn block details

55

B-13 P/Cd block details

55

B-14 P/mdot block details

56

B-15 P/Cheat factor block details

56

B-16 P/Cf factor block details

56

B-17 Mw block details

57

B-18 Residual mass block details

57

B-19 T block details

57

B-20 Heat tran block details

57

B-21 h block details

58

B-22 Work&Power block details

58

B-23 Work&Power/Work block details

58

B-24 Work&Power/FMEP block details

59

B-25 Work&Power/Effective power block details

59

xi

LIST OF ABBREVIATIONS AND SYMBOLS Abbreviations BDC

Bottom Dead Center

CFD

Computational Fluid Dynamic

CNG

Compressed Natural Gas

CO

Carbon Monoxide

DIN

Deutschland Industrial Norm

ECU

Engine Control Unit

EGR

Exhaust Gas Recirculation

HC

Hydrocarbon

HHV

High Heating Value

HP

Horsepower

LPG

Liquefied Petroleum Gas

MBT

Maximum Brake Torque

MWF

Modified Wall Function

rpm

Round per Minute

SAE

Society of Automotive Engineers

SWF

Standard Wall Function

TDC

Top Dead Center

WOT

Wide Open Throttle

Symbols a

Crank Radius

A

Exposed Combustion Chamber Surface Area

AR

Reference Area

b

Cylinder Bore

CD

Discharge Coefficient

Cf

Frictional Loss Factor

Cheat

Charge Heating Factor

Cm

Mean Piston Speed

xii

LIST OF ABBREVIATIONS AND SYMBOLS (CONTINUED) Div

Inlet Valve Diameter

Dv

Valve Diameter

f

Fraction of Heat Added

h

Convection Heat Transfer Coefficient

HV

Heating Value of Fuel

IVC

Inlet Valve Close Angle After BDC

IVO

Inlet Valve Open angle Before TDC

k

Specific Heat Ratio

l

Connecting Rod Length

Liv,max

Maximum Inlet Valve Lift

Lv

Valve Lift Function

mair,stoich Theoretical Amount of Air Requirement m&

Mass Flow Rate

ma

Air Mass

N

Engine Speed

pf

Friction Mean Effective Pressure

pme

Brake Mean Effective Pressure

pmi

Indicated Mean Effective Pressure

pT

Pressure at Restriction

p0

Upstream Stagnation Pressure

P

Pressure Inside Cylinder

Pe

Effective Power

Q

Heat Addition

Qin

Overall Heat Input

Qloss

Heat Transfer

R

Gas Constant

s

Stroke

Tg

Temperature of Cylinder Gas

Texh

Exhaust Gas Temperature

Tw

Cylinder Wall Temperature xiii

LIST OF ABBREVIATIONS AND SYMBOLS (CONTINUED) T0

Stagnation Temperature

V

Cylinder Volume

Vd

Displacement Volume

Δθ

Duration of Heat Addition

ε

Compression Ratio

ηv

Volumetric Efficiency

θ

Crank Angle

θ0

Angle of Start of Heat Addition

ρa

Air Density

xiv

CHAPTER 1 INTRODUCTION 1.1 Background Four-stroke spark ignition engine was developed by Otto in 1876. This engine provided power output 3 HP. Since that point, the engine developing has been done continuously over 100 years. Even now, some engines can provide power output more than 1,000 HP. However, developments of spark ignition engine along 100 years has been conducting very slow due to lots of parameter, such as physical geometries (bore, stroke, crank radius, compression ratio), ignition advanced, valve timing, combustion characteristic etc., influencing the performances. Many studies on effects of each parameter were done by experiments. But this approach spent lots of expenses and time such as building test engine, setting up laboratory, etc. Another approach is simulation method that allows engine designer to change and test many different parameters without building real parts or even real engines. The engine model can be used in various ways including designing engine control system or ECU, designing transmission, etc. Although the computational model is unable to obtain the exact characteristics because there are no perfect models and there are many complex phenomena taking place in the engine, it simply estimates the trend of those characteristics and effects with very low cost and less time consumption that is very helpful for speeding up the engine development process before making real one. 1.2 Objectives 1.2.1 Develop a physically based, cylinder-by-cylinder spark ignition engine model for predicting torque and power characteristics in order to study effects of parameters such as engine geometries, fuel properties, valve timing layout, etc. 1.2.2 Predict the burning duration of alternative fuels such as Liquefied Petroleum Gas (LPG), Compressed Natural Gas (CNG) and gasohol which are needed information for simulation. 1.3 Approach The engine model is developed under MatLab/Simulink which describes the torque and power characteristics of the engine. The parameters, engine geometries and valve timing layout, from existed gasoline engines are used. The model is evaluated and compared with test data in order to determine the accuracy. 1.4 Scope 1.4.1 Use Matlab/Simulink for developing the engine model. 1.4.2 Gasoline is used for developing the model. 1.4.3 Outputs of the model are torque and power characteristics under full load or wide open throttle (WOT) condition. For the alternative fuels, output is burning durations.

2 1.5 Assumptions 1.5.1 The model will be derived from the spark ignition engine without turbo or super charger and Exhaust Gas Recirculation (EGR) system. 1.5.2 The engine uses multi-port injection system for adding fuels. 1.5.3 Fuel evaporates to be gas phase completely. 1.5.4 Fuel and air mix together perfectly. 1.5.5 Fuel-air mixture is assumed to be an ideal gas all the time. 1.5.6 There is no any effect of combustion chamber design. 1.5.7 Combustion chamber wall temperature is set at 400 Kelvin. 1.5.8 There is no effect of throttle body or there is no pressure drop at throttle body due to WOT condition. 1.5.9 There are no effect of exhaust stroke and exhaust system. 1.6 Impacts or Benefits from Research The model which is developed under this thesis can be used for many purposes. It can be used as an engineering tool in the development of the spark ignition engines. The simulation can reduce the time consumption and costly tests needed in laboratory. And also the model can be used for teaching a tool in the internal combustion engine course. 1.7 Thesis Outline The details of this thesis are shown as following Chapter 1 Introduction Chapter 2 This chapter explains of fundamental of spark ignition engine and engine processes, review previous researches and theory of engine modeling Chapter 3 Focusing on the performance prediction, this chapter describes the model and theory of each component in details and explanations of the alternative fuels Chapter 4 Model validation by comparing to performance data from vehicle manufacturer, analyze sensitivity when changing parameters, and find out combustion duration of the alternative fuels Chapter 5 Conclusions and suggestions

CHAPTER 2 LITERATURE REVIEW 2.1 Spark Ignition Engine The spark ignition engines are used in different applications, such as cars, boats and small power generators. Depending on the field of application, the spark ignition engine has certain structure and components which may differ from field to field. A basic spark ignition engine used within the automotive industry has the following structure and components as shown in Fig.2-1.

FIGURE 2-1 Schematic of gasoline engine [1] The basic operation of a four stroke engine involves intake, compression, expansion (or power), and exhaust strokes as shown in Fig.2-2. The piston starts at the top, the intake valve opens, and the piston moves down to let the engine take in a cylinder-full of air and gasoline. This is the intake stroke. Only the tiniest drop of gasoline needs to be mixed into the air for this to work. Then the piston moves back up to compress this fuel/air mixture. Compression makes the explosion more powerful. When the piston reaches almost the top of its stroke, the spark plug emits a spark to ignite mixture. The power generates from combustion and driving the piston down. Once the piston hits the bottom of its stroke, the exhaust valve opens and the exhaust leaves the cylinder to go out the exhaust pipe.

4

FIGURE 2-2 Basic four stroke cycle With models for each of these processes, a simulation of complete engine cycle can be built up and be analyzed to provide information on engine performances. These ideal models that describe characteristic of each process are proposed. However the calculation needs information from each state as shown in Fig.2-3a which sometime could not obtain from real condition as shown in Fig.2-3b.

(a) (b) FIGURE 2-3 Pressure-volume diagram of Otto cycle: (a) ideal; (b) real Overall engine work can be determined by integrating the area under the pressure-volume diagram. So many previous works concerned mainly prediction the pressure inside the combustion chamber [2, 3, 4]. But the pressure and volume are influenced by engine geometries during variation of crank angle. So the pressure and displacement volume are needed to convert as functions of crank angle. Kuo [3] and Kirkpatrick [5] proposed the method that can calculate the pressure and volume at any crank angle. The combustion process can be described by simple correlation, Wiebe function [6]. The results from Kuo [3] and Zeng et al [4] indicated that heat transfer from inside the cylinder to engine cooling water had much influences on the pressure inside the cylinder. So the heat transfer function is needed to take into account in the model. Many researches reported that the mass of mixture that flows into the cylinder during intake stroke is a very importance parameter [1, 2, 3], [6] because it affects amount of fuel which mixes with the air. This mass can be determined by combining the ideal gas law and volumetric efficiency. However it is very difficult to evaluate because they are affected by many factors, such as manifold geometries and valve timing [6]. So Eriksson et al [2] and Kuo [3] assumed that the pressure inside

5 manifold and inside the cylinder are the same, and neglect effect of volumetric efficiency. But Kuo [3] used corrective equation from real experiment to compensate the errors. While Zeng et al [1] took the effect of volumetric efficiency into account. However the data were obtained from the real experiment and stored in a 3-dimension table by relation between engine speed and intake manifold pressure. It can say that combining of those methods that are mentioned above can predict the engine performances precisely only if some testing data are known, mainly the volumetric efficiency. So this thesis tries to use the one-dimension flow model to predict the volumetric efficiency in order to reduce the testing data dependence. 2.2 Modeling There are numerous ways of describing reality through a model [7, 8]. Some are more complex than others and the different approaches may differ in both structure and accuracy. Choosing the model depends on the particular situation and especially the field of application. The model classifications are summarized follow. 2.2.1 Mean Value vs. Cylinder-by-cylinder Approaches When considering the cylinder, two main approaches can be found. The most common use is mean value engine method. The mean value method defines number of cylinders as one which occupies whole displacement volume. The fluctuating flow through the inlet port is modeled by average value over a cycle. The dynamics of speed, engine torque, pressure build-up in the inlet and exhaust manifolds are the aspects of most interest in this approach. Another method to the mean method is the cylinder-by-cylinder engine approach. Unlike the mean method, it describes each cylinder individually and generates for example a torque signal with each individual combustion pulse present. Normally the mean model is sufficient enough for use in processes such as control system design. But in engine performance development aspect, the cylinder-bycylinder method is better because this method derives from engine geometries, which is very useful for improving and optimizing the engine in the future. 2.2.2 Limit of Physical Properties There are a number of approaches available when deciding on the basis of a model. Physical equation theoretically describing the system is the most common method since it creates a general model working for many operating areas. Its drawback is that reality might be difficult to describe correctly in theory. Another common approach bases on the model entirely on measurements. The measured data is stored as a table of two or more dimensions in a so called black box depending on input signals. This approach often provides an accurate result since it is based directly on empirical formulation. However it is only defined for a limited region. A combination of both approaches is commonly used. The main basis of the model rests on physical equations. And empirical equations are used to model certain complexities.

CHAPTER 3 THE MODEL In this chapter the model is described in detail. The engine to be modeled is a gasoline engine which has no EGR and turbo system. The chosen model bases on the pressure inside the cylinder prediction. There are two main approaches to consider; mean value and cylinder-by-cylinder models. Since the objective of this thesis intends to develop the model which can describe effects of each parameter on the engine performance, the cylinder-by-cylinder approach is used in order to achieve this goal. Another consideration for model selection is limited by physical properties. Since there are no perfect equations which can describe phenomena in the engine, both physical and empirical formulae are used in the model. 3.1 Model Overview Start RPM

Stroke

Bore

Conn. Rod

Comp.Ratio

Spark Angle

IVC

IVO

k

Conn. Rod

A/F Ratio

Heating Value

Liv

Div

Tw

No. Cylinder

θ = -360

No Find displacement volume

Find exposed combustion chamber surface area, Eq.3-2

Find compression volume

Find total heat input, Eq.3-7 Wiebe Function, Eq.3-4 B

Find residual mass C

Heat release, Eq.3-5

Find pressure inside cylinder by integrating

End

D

A

Find exhaust gas temperature, Eq.3-21

Yes

θ = 180

Find cylinder volume, Eq.3-1

Find Temperature of gas in cylinder

Find mean piston speed

Find heat transfer coefficient, Eq.3-10

Find pressure increment, Eq.3-3

FIGURE 3-1 Model overview

Find total heat transfer, Eq.3-8

7

A

Find valve lift function, Eq.3-16

Find valve curtain area, Eq.3-14 Find discharge coefficient, Eq.3-18

Find frictional loss factor, Eq.3-19 Find charge heating factor, Eq.3-20

Find flow-in mass, Eq.3-15

Find total flow-in mass by integrating Find pressure that belong to flow-in mass

pT ⎡ 2 ⎤ = ⎢ p0 ⎣ k + 1⎥⎦

pT p = T p0 p0

C

Yes

⎛ pT ⎞ ⎡ 2 ⎤ ⎟⎟ ⎜⎜ ≥⎢ ⎥ ⎝ p0 ⎠ Critic ⎣ k + 1⎦

k /( k −1)

B

Find indicated mean pressure, Eq.3-23 Find friction loss, Eq.3-22

Find effective pressure, Eq.3-24 Find effective power, Eq.3-25 Pe

θ=θ+1 D FIGURE 3-2 (CONTINUED)

No

k /( k −1)

8 Fig.3-1 and Fig.3-2 shows the overview of the model. Engine geometries, such as bore, stroke, compression ratio, etc., are calculated to obtain physical information such as displacement volume, area and volume variation as function of crank angle, etc. That information will be used for cylinder pressure prediction with another line of information about heat input. Heat energy needs data from amount of flow in mass and burn characteristic which is described by Wiebe function. Predicted pressure will be used to determine temperature inside cylinder and also heat transfer from cylinder to wall chamber. Rate of heat loss will be fed back to the pressure prediction function. Resulted pressure will be converted to indicated mean effective pressure subtracted by mean friction, then work and power will be known finally. The Matlab/Simulink block diagrams of the model are shown in Appendix B. The details of each module are described in following section. 3.2 Crank Slider Model The volume of the piston cylinder can be determined as a function of crank angle from the compression ratio (ε), the stroke (s), bore (b) and connecting rod length (a). The geometric parameters of the piston cylinder can be described by the crank slider model which is represented in Fig.3-3.

FIGURE 3-3 Piston cylinder and geometries

The equations of volume and area that relate to crank angle are described as following equation [5]: 2

1 Vd Vd l ⎛l⎞ 2 V (θ ) = + [ + 1 − cos θ − (⎜ ⎟ − sin θ ) 2 ] ε-1 2 a ⎝a⎠ 2

A(θ ) =

Eq.3-1 1

π 2 s l ⎛l⎞ b + πb [ + 1 − cos θ + (⎜ ⎟ − sin 2 θ ) 2 ] 2 2 a ⎝a⎠

Eq.3-2

3.3 Cylinder Pressure Model This model is derived from the first law of thermodynamics. The pressure is derived as a function of crank angle also [5].

dP k − 1 ⎛ ∂Q P dV ⎞ = − Qloss ⎟ − k ⎜ dθ V ⎝ dθ V dθ ⎠

Eq.3-3

9

dV can be determined from Eq.3-1 by taking derivative with respect to the dθ ∂Q . crank angle (θ). The Wiebe function for the burn fraction is used for dθ 3.4 Wiebe Function (f) The mass fraction burned profiles as a function of crank angle in each individual cycle shown in Fig.3-4. It has a characteristic S-Shape. The rate at which fuel-air mixture burns increases from a low value intermediately following the spark discharge to a maximum about halfway through the burning process and then decreases to a close to zero as the combustion process ends.

FIGURE 3-4 Burned mass fraction characteristic

A functional form often used to represent the mass fraction burned versus crank angle curve is the Wiebe function:

⎡ ⎛ θ − θ0 ⎞3 ⎤ f (θ ) = 1 − exp ⎢− 5⎜ ⎟ ⎥ ⎢⎣ ⎝ Δθ ⎠ ⎥⎦

Eq.3-4

The heat release ( ∂Q ) over the crank angle change (Δθ) is:

∂Q df = Qin dθ dθ

Eq.3-5

Then take the derivative of the heat release function (f(θ)), with respect to crank df from Eq.3-4. angle, being dθ 3.4.1 Burning Duration (Δθ) Mixture burning rate is influenced by engine speed. It is well established that the duration of combustion in crank angle degrees only increases slowly with increasing engine speed. Fig.3-5 shows how intervals of burning characteristics are. The burning rate throughout the combustion process does not increase linearly as engine speed. Additionally, increasing in-cylinder gas velocities (e.g. with intake generated swirl) increases the burning rate. Increasing engine speed and introducing swirl both increase the levels of turbulence in the engine cylinder.

Mass Burn (×100) %

10

(a) (b) FIGURE 3-5 Effect of engine speed on flame-development angle (a) 10% and 90% burn [6] and (b) 100% burn [9] However, the swirl characteristic is not able to determine easily depending on manifold geometries and piston head design. Therefore, the results in Fig.3-5a, which obtained from experiment, are used to estimate the burning duration (Δθ) for gasoline.

Δθ = −1.6189(

N 2 N ) + 19.886( ) + 39.951 1000 1000

for 1000 ≤ N ≤ 6000

Eq.3-6

3.5 Heat Input Overall heat input can be determined by using heating value of fuel and amount of mass which is drawn into cylinder. IVC

HV Qin =

∫ m(θ )dθ

IVO

1 + mair , stoich

Eq.3-7

Values of final mass fraction burned usually are in the range 93% to 98% due to the fact that not all of the fuel is burned [6]. Kuo [3] used 95%. So this value is applied to Qin. 3.6 Air/Fuel Ratio In internal combustion engines, the air-fuel ratio refers to the proportion of air and fuel present during combustion. The chemically optimal point at which this happens is the stoichiometric ratio. Examples are shown in Table 3-1. For gasoline fuel, the stoichiometric air/fuel mixture is approximately 14.6 times the mass of air to fuel. This is the mixture that modern engine management systems employing fuel injection attempt to achieve in light load cruise situations. Any mixture less than 14.6 to 1 is considered to be a rich mixture, any more than 14.6 to 1 is a lean mixture.

11 TABLE 3-1 Air/fuel ratios of many substances

3.7 Heat Transfer Generally there are three modes of heat transfer in the combustion engine. Conduction - Conduction in solid matter is caused by molecular movement. The driving physical characteristic is the thermal conductivity. The heat flow in the combustion chamber walls occurs through heat conduction. Convection - Convection is a term for heat transfer occurring in a moving fluid. The exchange of heat between the coolant or combustion gas and the combustion chamber wall occurs through convection. The velocity and the degree of turbulence of the moving fluid determine the degree of heat transfer via the convection. Radiation - Heat transfer through occurs in the form of electromagnetic waves. The energy of the radiation is proportional to T4. Radiation is only relevant in the combustion chamber and only short period of time during and after combustion when high gas temperatures are present. In spark ignition engines, the primary heat transfer mechanism from the cylinder gases to the wall is convection, with only 5% from radiation. Using a Newtonian model, the heat loss to the wall is given by:

Qloss = hA(Tg-Tw)

Eq.3-8

When determining the heat release term ( ∂Q ) the heat loss to the walls has to dθ

be taken into account. Substitute Eq.3-5 and Eq.3-8 in Eq.3-3, the pressure over crank angle now becomes: dP k − 1 ⎡ df hA P dV ⎤ = − (Tg − Tw )⎥ − k Qin ⎢ dθ V ⎣ dθ 6 N V dθ ⎦

Eq.3-9

3.7.1 Heat Transfer Coefficient Correlations (h) The heat transfer coefficient is needed in order to calculate heat loss from the cylinder in Eq.3-8. For design purposes, simplified analyzes are often performed using empirical heat transfer correlations such as Annand, Woschni and Hohenberg. These give at most estimates of the surface-averaged heat transfer coefficient, which are defined in terms of the bulk gas temperature and used with this to calculate surface-averaged or total heat flux. Annand assumed a constant characteristic gas velocity equal to the mean piston speed, while Woschni assumed that the average gas velocity should be proportional to the mean piston speed. Hohenberg examined Woschni’s formula and made changes to give better predictions.

12 Kleeman et al [10] compared these empirical correlations with Computational Fluid Dynamic (CFD) prediction by using Standard Wall Function (SWF) and Modified Wall Function (MWF) methods. Both SWF and MWF are boundary layer models which have been employed to calculate wall shear and heat transfer in CFD. SWF derives the near-wall velocity and temperature profiles from a Couette flow analysis, assuming steady one dimensional flow and ignore the variation within the layer of the fluid thermophysical properties (e.g. density, viscosity, thermal conductivity). The use of SWF in CFD calculation of engine heat transfer generally leads to underprediction of the wall heat flux. So MWF is developed further for using in engine simulation by taking the fluid thermophysical properties into account. The results are shown in Fig.3-6.

FIGURE 3-6 Comparison of surface-averaged heat flux variations predicted by CFD calculations and empirical correlations [10]

The results from [10] showed that the MWF method gave the most accurate results. So using these simple correlations will introduce some errors. However MWF can only be obtained from CFD because the CFD program can calculate the instantaneous local heat fluxes which are not uniform throughout the combustion chamber, while this thesis assumes the charge are burned completely throughout the cylinder at the same time. According to the results in Fig.3-6, the Hohenberg correlation is selected because it is closest to MWF and also there is no empirical form for MWF. The Hohenberg correlation is following equation [4]. h = 130V −0.06 P 0.8Tg−0.4 (C m + 1.4) 0.8

Eq.3-10

3.8 Volumetric Efficiency (ηv) The intake system – the air filter, carburetor, and throttle plate (in a spark ignition engine), intake manifold, intake port, intake valve – restricts the amount of air which an engine of given displacement can induct. The parameter used to measure the effectiveness of an engine’s induction process is the volumetric efficiency (ηv).

13 Volumetric efficiency is only used with four-stroke engines which have distinct induction process. It is defined as the volume of air which is drawn into the intake system divided by the volume which is displaced by the piston, Eq.3-11. Typical maximum values of volumetric efficiency for naturally aspirated engines are in the range 80 to 90%. The volumetric efficiency for diesels is somewhat higher than the spark ignition engines as shown in Fig.3-7.

ηv =

ma ρ aV d

Eq.3-11

FIGURE 3-7 Volumetric efficiency versus mean piston speed for a four-cylinder indirect-injection diesel and a six-cylinder spark-ignition engine [6]

According to Fig.3-7, there are no such a model can predict the trend of the volumetric efficiency exactly because it is affected by the following fuel, engine design and engine operating variables: 1. Fuel type, air/fuel ratio, fraction of fuel vaporized in the intake system, and fuel heat of vaporization 2. Mixture temperature as influenced by heat transfer 3. Ratio of exhaust to inlet manifold pressures 4. Compression ratio 5. Engine speed 6. Intake and exhaust manifold and port design 7. Intake and exhaust valve geometry, size, lift and timings The manifold and valve geometry design has great effects on the volumetric efficiency since the designs of each engine model have never been the same. So this thesis tries to develop the model in order to predict ηv caused by the different valve design.

14

FIGURE 3-8 Effect on volumetric efficiency of different phenomena which affect the air flow rate as a function of speed. Solid line is final volumetric efficiency versus speed curve [6]

The shape of volumetric efficiency can be explained by Fig.3-8. It is affected by many different phenomena. Non-speed-dependent effects (such as fuel vapor pressure) drop the volumetric efficiency below 100% (curve A). Charge heating in the manifold and cylinder drops curve A to curve B. It has greater effect at low engine speeds due to longer gas residence time. Frictional flow losses increase as the square of engine speed, and drop curve B to curve C. At higher engine speeds, the flow into the engine during at least part of intake process becomes choked. Once this occurs, further increases in speed do not increase the flow rate significantly so volumetric efficiency decreases sharply (curve C to D). The induction ram effect at higher engine speeds which occurs from inertia of mixture raises curve D to curve E. Late inlet valve closing, which allows advantage to be taken of increased charging at higher speeds, results in a decrease in the volumetric efficiency at low engine speeds due to backflow (curve C and D to F). Finally, intake and/or exhaust tuning can increase the volumetric efficiency (often by substantial amount) over part of the engine speed range, curve F to G. The terms which appear in Fig.3-8 are described as following. Frictional losses – During the intake stroke, the pressure in the cylinder is less than atmospheric pressure due to friction in each part of the intake system. This total pressure drop is the sum of the pressure loss in each component of the intake system: air filter, carburetor and throttle, manifold, inlet port, and inlet valve. Ram effect – The pressure in the inlet manifold varies during each cylinder’s intake process due to the piston velocity variation, valve open area variation, and the unsteady gas-flow effects that result from geometric variations. At high engine speeds, the inertia of the gas in the intake system as the intake valve is closing increases the pressure in the port and continue charging process when the piston slow down around BDC and starts the compression stroke. This effect becomes progressively greater as engine speed is increased.

15

Back flow – Because the inlet valve closes after the start of the compression stroke, a reverse flow of fresh charge from the cylinder back into the intake can occur as the cylinder pressure rises due to piston motion toward TDC. This reverse flow is largest at the lowest engine speeds. This phenomenon cannot be avoided due to choosing the inlet valve closing time for taking advantage of the ram effect at high speeds. Tuning – The time-varying inlet flow to the cylinder causes expansion waves to be propagated back into the inlet manifold. These expansion waves can be reflected at the open end of the manifold (at the plenum) causing positive pressure waves to be propagated toward the cylinder. If the timing of these waves is appropriately arranged, the positive pressure wave will cause raising the pressure at the inlet valve above the nominal at the end of intake process. This will increase the inducted air mass and be described as tuned. This phenomenon can occur in exhaust system also. Charge Heating - According to the conduction heat transfer, the heat inside the cylinder transfers to inlet manifold via connecting ports and intake valves. This heat is absorbed by air/fuel mixture directly and makes the mixture expand its volume due to increasing of temperature. Finally, the volumetric efficiency decreases automatically. Generally, the residence times, length of inlet manifold and manifold geometries are the main factors which influence how much heat can be transferred to the mixture. Choking - Choked flow of a fluid is caused by the Venturi effect. When a flowing fluid at a certain pressure and temperature flows through a restriction (such as the hole in an orifice plate or a valve in a pipe) into a lower pressure environment, under the conservation of mass the fluid velocity must increase for initially subsonic upstream conditions as it flows through the smaller cross-sectional area of the restriction. At the same time, the Venturi effect causes the pressure to decrease. Choked flow is a limiting condition which occurs when the mass flow rate will not increase with a further decrease in the downstream pressure environment. 3.8.1 Flow through Valves The valve is usually the most important flow restriction in the intake and the exhaust system of four-stroke cycle engines. In this thesis considers only the intake valve in order to determine ηv. The mass flow rate through a poppet valve is usually described by the equation for compressible flow through a flow restriction, Eq.3-12. This equation is derived from a one-dimensional isentropic flow analysis, and real gas flow effects are included by means of an experimentally determined discharge coefficient (CD). m& =

C D AR p 0 ( RT0 ) 0.5

⎛ pT ⎞ ⎜⎜ ⎟⎟ p ⎝ 0⎠

1/ k

⎧⎪ 2k ⎡ ⎛ p ⎞ ( k −1) / k ⎤ ⎫⎪ ⎢1 − ⎜⎜ T ⎟⎟ ⎥⎬ ⎨ ⎥⎦ ⎪⎭ ⎪⎩ k − 1 ⎢⎣ ⎝ p 0 ⎠

When the flow is choked, the pressure ratio (

0.5

Eq.3-12

pT ) will not lower than the p0

following value so called critical pressure ratio. ⎛ pT ⎞ ⎡ 2 ⎤ ⎟⎟ ⎜⎜ =⎢ ⎥ ⎝ p 0 ⎠ Critic ⎣ k + 1⎦

k /( k −1)

Eq.3-13

16

For the mass flow of the mixture into the cylinder through the intake valve, p0 is ambient pressure, and pT is the cylinder pressure [6], [11]. T0 is ambient temperature. For AR, the most convenient reference area in practice is the so called valve curtain area since it varies linearly with valve lift and is simple to determine [5, 6]. AR = πDv Lv

Eq.3-14

Eq.3-12 should be converted into a function of crank angle also by dividing with 6N same as Eq.3-9. C D AR p 0 dm = dθ 6 N ( RT0 ) 0.5

⎛ pT ⎞ ⎟⎟ ⎜⎜ ⎝ p0 ⎠

1/ k

⎧⎪ 2k ⎡ ⎛ p ⎞ ( k −1) / k ⎤ ⎫⎪ ⎢1 − ⎜⎜ T ⎟⎟ ⎥⎬ ⎨ k p 1 − ⎢ ⎥⎦ ⎪⎭ 0 ⎠ ⎝ ⎪⎩ ⎣

0.5

Eq.3-15

Eq.3-9 doesn’t consider about mass flow into cylinder. It determines pressure different based on pressure at previous crank angle. But the pressure inside cylinder is influenced not only by volume variation, incoming mass also. So Eq.3-15 is integrated to obtain amount of mass over a crank angle degree and then finding the pressure of mixture inside cylinder by using ideal gas equation of state, PV = mRT . The pressure is added with integrated pressure from Eq.3-9 to obtain pT in Eq.3-15. 3.8.2 Valve Lift The fundamental the valve lift design is to satisfy an engine breathing requirement at the design speeds. However, it is philosophies and secrecies of each carmaker. One of the valve lift design uses polynomial function, for example, Hermann, McCartan and Blair (HMB) technique [12] uses up to 11th order polynomial functions. The alternative approach is the G. P. Blair (GPB) method [12] which considers jerk characteristic of valve motion. Which method is employed depends on how smooth of the lift and/or acceleration diagrams are otherwise the forces and impacts on the cam follower mechanism will be considered. In other words, a good mathematical smoothing technique within the valve lift design process is absolutely essential, may be degree by degree level. So this thesis assumes to use cosine function for valve lift instead in order to reduce complexity as following equation: Lv (θ ) =

ϕ=

Liv ,max (1 + cos ϕ ) 2

π ( IVO − IVC + 2θ + 540) IVO + IVC + 180

Eq.3-16

Eq.3-17

17 3.8.3 Discharge Coefficient (CD) Fig.3-9 shows the results of steady state flow tests on a typical inlet valve configuration with a sharp-cornered valve seat. The discharge coefficient based on valve curtain area is a discontinuous function of the valve-lift/diameter ratio. The three segments shown correspond to different flow regimes as indicated. At very low lifts, the flow remains attached to the valve head and seat, giving high values for the discharge coefficient. At intermediate lifts, the flow separates from the valve head at the inner edge of the valve seat as shown. An abrupt decrease in discharge coefficient occurs at this point. The discharge coefficient then increases with increasing lift since the size of separated region remains approximately constant while the minimum flow area is increasing. At high lifts, the flow separates from the inner edge of the valve seat as well. Typical maximum values of valve-lift/diameter ratio are 0.25. Although the flow through valve is dynamic behavior, it has been shown that over the normal engine speed range, steady flow discharge coefficient results can be used to predict dynamic performance with reasonable precision. The averaged equation which obtained from the results in Fig.3-9 is shown as Eq.3-18.

Average

FIGURE 3-9 Discharge coefficient of typical inlet poppet valve [6] C D = 190.47(

Lv 4 L L L ) − 143.13( v ) 3 + 31.248( v ) 2 − 2.5999( v ) + 0.6913 Div Div Div Div

Eq.3-18

3.8.4 Frictional Losses Takizawa et al [13] made an experiment to measure pressure losses due to friction across the air cleaner, carburetor, throttle and manifold plenum of a standard four-cylinder automotive engine intake system. The results are shown in Fig.3-10. However, the parameters which are used to calculate the pressure losses still unknown, mainly frictional factor for each component. So a frictional loss factor (Cf) is introduced to adjust p0 in Eq.3-15. The products of Cf and p0 are assumed as shown in Fig.3-11. The basis of Cf is assumed to be a function of engine speed linearly in order to reduce complexity as following equation.

18 C f = −0.019738(

N ) + 0.986923 1000

for 1000 ≤ N ≤ 6000

Eq.3-19

FIGURE 3-10 Pressure losses in the intake system of a four-stroke cycle sparkignition engine determined under steady flow conditions [13]

Remaining Pressure, kPa

100 98 96 94 92 90 88 86 0

1000

2000

3000

4000

5000

6000

7000

Engine Speed, RPM

FIGURE 3-11 Assumption of remaining pressure after subtracted by pressure losses

19 3.8.5 Charge Heating As mentioned in Sec.3.8, the residence times, length of inlet manifold and manifold geometries are the main factors which influence how much heat can be transferred to the mixture. However, the length and geometries of manifold cannot be determined easily and the mixture velocity is dynamic behavior. So a charge heating factor (Cheat) is introduced to apply with T0 in Eq.3-15. The assumption is defined that temperatures inside manifold are in between cylinder wall temperature and ambient temperature. The products of Cheat and T0 are assumed as shown in Fig.3-12, 373 K at 1000 rpm and 308 K at 6000 rpm. The basis of Cheat is assumed to be a function of engine speed linearly in order to reduce complexity as following.

Temperature Inside Manifold, K

C heat = −0.043624(

N ) + 1.2953 1000

for 1000 ≤ N ≤ 6000

Eq.3-20

380 360 340 320 300 280 260 0

1000

2000

3000

4000

5000

6000

7000

Engine Speed, RPM

FIGURE 3-12 Assumption of temperature inside manifold 3.9 Residual Gas The residual gas affects volumetric efficiency and engine performance directly, and efficiency and emissions through its effect on working fluid thermodynamic properties [6]. The residual gas is primarily a function of inlet and exhaust pressure, speed, compression ratio, valve timing, and exhaust system dynamics. However, the equation which can describe the magnitude of residual gas is still unknown. So this thesis assumes that the amount of residual gas can be determined by using the ideal gas equation of state, PV = mRT at TDC which is a function of exhaust pressure, compressed volume, exhaust gas molecular weight, and exhaust gas temperature. The exhaust pressure is between 1 and 1.5 atm [3]. So it is selected at 1.5 atm. The exhaust gas molecular weight is 30.4 g/mol. Caton and Heywood [14] measured cylinder pressure, calculated cylinder gas temperature and exhaust mass flow rate, and measured gas temperature at the exhaust port exit for a single-cylinder spark ignition engine at 1000 rpm. The results of [14] are shown in Fig.3-13. According to Fig.3-13, the exhaust gas temperature at 1000 rpm can be assumed starting at 900 K. The exhaust temperatures along other engine speeds are calculated at point 4 in Fig.2-3a under ideal process. The increments of temperature at point 4 on each engine speed are added to 900 K as shown in Fig.3-14. And the exhaust gas temperature equation is obtained from those results as following.

20 Texh = 3.3955(

N 3 N 2 N ) − 51.9( ) + 279.49( ) + 676.21 1000 1000 1000

for 1000 ≤ N ≤ 6000 Eq.3-21

FIGURE 3-13 Measured cylinder pressure pc, calculated cylinder-gas temperature Tc, exhaust mass flow rate m& e , and measured gas temperature at exhaust port exit Tp, for single-cylinder spark ignition engine at speed = 1000 rpm [14]

Exhaust Gas Temperature, K

1400 1200 1000 800 600 400 200 0 0

1

2

3 4 Engine Speed, RPM

5

6

FIGURE 3-14 Assumption of temperature inside manifold

7

21 3.10 Friction Friction losses influence the indicated power and useful output, the brake power. Barnes-Moss [15] tested several four-stroke cycle four cylinder SI engines between 845 and 2000 cm3 displacement at wide-open throttle. The total friction work per cycle (and thus the friction mean effective pressure) for a given engine geometry will vary with the engine speed as following equation.

N 2 N p f = 0.05( ) + 0.15( ) + 0.97 1000 1000

for 1000 ≤ N ≤ 6000

Eq.3-22

3.11 Torque & Power To determine the overall performance, indicated mean effective pressure is used [16]. The indicated mean effective pressure represents the work per combustion cycle normalized by the displacement volume also called specific work. This value indicates amount of maximum available power that can generate from single cylinder.

p mi =

∫ PdV Vd

Eq.3-23

The engine has to overcome the friction loss. So the available output becomes:

p me = p mi − p f

Eq.3-24

Effective power can be determined by following equation.

Pe = 0.5 N ⋅ p me ⋅ Vd

Eq.3-25

Finally, torque can be determined by following relation.

Pe =

πNT 30

Eq.3-26

3.12 Minimum Spark Advance for Best Torque (MBT) The charge of the air/fuel is burned by a flame-front beginning at the spark plug. The flame starts a kernel with a rather slow rate of expansion, but once a small percentage of the charge is ignited, the combustion process accelerates at a faster rate. Due to the very slow initial reaction rates, ignition must occur before TDC. This is the "advance" in ignition and is measured in degrees of crankshaft rotation. The best advance depends on design and operating conditions. This value is called “Minimum Spark Advance” which will produce the maximum torque at a given operating condition of speed and load of a given engine combination. In most cases the spark advance curve can be advanced several degrees before torque begins to drop off. If "knock" occurs, advance can be determined. The advance is referred to as "knock limits". The fuel octane, camshaft profile and/or the compression ratio will need to be addressed before maximum output can be achieved.

22

(a) (b) FIGURE 3-15 (a) Cylinder pressure versus crank angle for over-advanced spark timing (50°), MBT timing (30°), and retarded timing (10°). (b) Effect of spark advance on brake torque at constant speed and air/fuel ratio, at wide open throttle [6] 3.13 Simulation conditions The conditions for simulation are summarized in Table 3-2. TABLE 3-2 Parameters for simulation Parameters Ambient Pressure Ambient Temperature Mean cylinder wall temperature Specific heat ratio (k) Air molecular weight Air density Gasoline molecular weight Gasoline heating value Gasoline air/fuel ratio

Value 1 atm 298 K 400 K [11, 17] 1.3 [3, 6] 28.97 g/mol 1.2 kg/m3 114 g/mol 44,000 kJ/kg 14.6:1

In real engine test (SAE, DIN standard), the performance of engine is measured with all accessories and standard intake and exhaust systems. All parameters which affect to the volumetric efficiency due to using those systems are taken into account as well. Although the temperature inside manifold is varied from 308 to 373 Kelvin due to the heat transfer from cylinder (Sec.3.8.4) which affects to density of air, the air density is still kept constantly at 1.2 because the volumetric efficiency is measured comparing to the ambient condition. 3.14 Alternative Fuels By researches of many scientists, quantity of petroleum in the world has a limit and it cannot be renewed. 70% of petroleum is consumed in transportation and it is increasing every year. With this rate, the petroleum will deplete from the world one day in the near future. So many countries are searching the other sources of energy to replace the petroleum in long run. Furthermore, improvement of air quality is another objective too.

23 Many road-tests on the alternative fuels are done to prove these potentials. However, there are a few on analytical studies. So this thesis would like to study the alternative fuels in analytical aspect. This section is going to mention about the alternative fuels, such as LPG, CNG and alcohol-blended gasoline in details and how the model is applied to study these fuels. The model needs lots of parameter which are distinguished as shown in Fig.3-2, engine geometries, valve geometries, fuel properties, and engine operating condition, in order to predict the performance. However, the alternative fuel properties in details are still unknown, mainly the combustion duration. So the studies are set to predict the combustion range of these alternative fuels by comparing between the output performances and simulated values which the data are obtained from previous researches. The model is used to explain the volumetric efficiency in order to determine effects of using those alternative fuels too. The previous researches are selected under specific condition. They have to study the using both gasoline and one of alternative fuels on the same engine in order to compare the information. The gasoline engine model which is developed under this thesis uses parameters of the engine in order to determine the spark advanced angle. With additional information of specific spark advanced setting on each alternative fuels, the burning duration can be determined. 3.14.1 Ethanol-blended Gasoline or Gasohol Ethanol (ethyl alcohol) and methanol (methyl alcohol) are two types of alcohol fuels. The use of pure alcohols in internal combustion engines is only possible if the engine is designed or modified for that purpose. However, in their anhydrous or pure forms, they can be mixed with gasoline in various ratios for use in unmodified automobile engines. Typically, only ethanol is used widely in this manner, particularly since methanol is toxic. E10, also frequently called gasohol, is a fuel mixture of 10% ethanol and 90% gasoline by volume that can be used in the internal combustion engines of most modern automobiles. However, not enough scientific tests have been done to determine if E10 is harmful to older cars' fuel systems. It has been introduced nationwide in Denmark and Thailand, and will replace high octane pure gasoline in Thailand by 2007. E20 contains 20% ethanol and 80% gasoline. This fuel is not yet widely used in the world. Since February 2006, this is the standard ethanol-gasoline mixture sold in Brazil, where concerns with the alcohol supply resulted in a drop in the ethanol percentage, previously at 25%. Flexible-fuel cars are set up to run with gasoline in such concentration range and few will work properly with lower concentrations of ethanol. The properties of E10 and E20 are compared in Table 3-3. TABLE 3-3 Summaries of major properties of gasoline, ethanol, E10 and E20 [18] Properties Gasoline Ethanol E10 E20 Heating value (kJ/kg) 44,000 27,000 41,900 40,000 Stoichiometric air/fuel ratio 14.6 9 14 13.5

24 Al-Farayedhi et al [19] investigated the effect of using unleaded gasoline– ethanol blends on typical SI engine performance in order to replace leaded gasoline. He founded that using of ethanol-blended fuel increase spark timing by average -1 degree for E10 and -6 degree for E20 when comparing to gasoline. And also the engine brake thermal efficiency is improved when compared to the leaded fuel. 3.14.2 Ethanol Ethanol fuel is an alternative to gasoline. Anhydrous ethanol or ethanol without water can be blended with gasoline in any concentration up to pure ethanol (E100) to reduce the consumption of petroleum fuels, as well as to reduce air pollution. In Brazil, ethanol-powered and flexible-fuel vehicles are manufactured to be capable of operation by burning hydrated ethanol. In addition, flexible-fuel vehicles can run on any mixture of hydrated ethanol and gasoline, as long as there is at least 20% of ethanol. A few flexible-fuel systems, like the Hi-Flex, used by Renault and Fiat, can also run with pure gasoline. Renault Clio is one of many vehicle models which are sold in Brazil. It is equipped by Hi-Flex technology which allows using pure ethanol as fuel with full efficiency due to the automatic adjustment on engine system. The power curve of Clio increases only 1 horsepower throughout engine speed range when using ethanol. And also, information from [20] indicates that the proper timing for an ethanol engine is five to eight degrees advanced from the optimum gasoline setting. 3.14.3 Compressed Natural Gas (CNG) CNG is a substitute for gasoline or diesel fuel. It is considered to be an environmentally "clean" alternative to those fuels. It comprises mainly methane (CH4) and ethane (C2H6). It is stored and distributed in hard containers, usually cylinders, and keeped under high pressure. In response to high fuel prices and environmental concerns, compressed natural gas is starting to be used in light-duty passenger vehicles and pickup trucks, medium-duty delivery trucks, and in transit and school buses. The properties of natural gas are shown in Table 3-4 TABLE 3-4 Summaries of major properties of methane, ethane, and natural gas [21] Natural Gas Properties Methane Ethane (C2H6) (CH3.76) [20] (CH4) Heating value (kJ/kg) 50,100 47,400 49,500 Stoichiometric air/fuel ratio 17.16 16 16.9

Mello et al [21] evaluated the maximum horsepower in many vehicles which were converted to use both natural gas and gasoline, so called “bi-fuel vehicle”. They founded that there is substantial drop in horsepower 13-17% when using the natural gas with electronically lambda control. However, emissions are reduced dramatically. The drop of power came from using of gas mixer which restricts air flow through manifold. And also the natural gas is gaseous fuel which occupies a larger volume than liquid fuel. It causes reduction of ηv. Not only that, spark advanced angle is needed to increase about 21-25 degree in order to obtain the maximum output due to low burning rate.

25 3.14.4 Liquefied Petroleum Gas (LPG) LPG comprises primarily propane (C3H8) and mixed by butane (C4H10). LPG is mainly used in household, industries and transportation respectively. LPG can be produced from crude oil and natural gas. However, the composition between propane and butane depends on the sources. The characteristics of LPG are summarized in Table 3-5. TABLE 3-5 Summaries of major properties of propane, butane, and LPG [22] Properties Propane Butane LPG (C3H8) (C4H10) (97.6%C3H8) [21] Heating value (kJ/kg) 46,000 45,400 45,900 Stoichiometric air/fuel ratio 15.6 15.4 15.6

Caton et al [22] developed a dedicated LPG fueled engine from production car. They founded that torque drops about 10-12% when using LPG without any enhanced modification. The reason of performance reduction came from using the gaseous fuel which decreases ηv. For spark timing, LPG needs an advanced spark timing usually around +10 degree due to slower burning rate [23].

CHAPTER 4 MODEL VALIDATION AND SENSITIVITY ANALYSIS This chapter presents and describes results acquired through simulations made with the model. The results are compared to data which appear in vehicle technical manual in order to prove the accuracy.

120

300

100

250

80

200

60

150

40

Power

Torque, Nm

Power, kW

4.1 Performance Validation This section shows the results of simulation comparing to test data from 8 engines. All engine geometries are obtained from Mercedes-Benz model year 1969 which are summarized in Appendix A. The model is simulated between 1,000 to 6,000 rpm of engine speed range.

100

Power(Sim) Torque

20

50

Torque(Sim) 0 1000

2000

3000

4000

5000

0 6000

Engine Speed, RPM

FIGURE 4-1 Simulation results of Mercedes-Benz 250SE

27

120

350 300

100

Power, kW

200 60 150 40

Power Power(Sim) Torque

20

Torque(Sim) 0 1000

2000

3000

4000

5000

Torque, Nm

250

80

100 50 0 6000

Engine Speed, RPM

FIGURE 4-2 Simulation results of Mercedes-Benz 250SL 400

120

350

100

Power, kW

80

250

60

200 150

40

Power Power(Sim)

100

Torque

20

Torque(Sim) 0 1000

Torque, Nm

300

2000

3000

4000

5000

50 0 6000

Engine Speed, RPM

FIGURE 4-3 Simulation results of Mercedes-Benz 250E/8

28

140

400

120

350

Power, kW

250 80 200 60 150 Power

40

Power(Sim)

100

Torque

20 0 1000

Torque, Nm

300

100

Torque(Sim)

2000

3000

4000

5000

50 0 6000

Engine Speed, RPM

150

400

120

320

90

240

60

160

Torque, Nm

Power, kW

FIGURE 4-4 Simulation results of Mercedes-Benz 280SE/8

Power Power(Sim) 30

Torque

80

Torque(Sim) 0 1000

2000

3000

4000

5000

0 6000

Engine Speed, RPM

FIGURE 4-5 Simulation results of Mercedes-Benz 280SL/8

150

400

120

320

90

240

60

160

Torque, Nm

Power, kW

29

Power Power(Sim) 30

Torque

80

Torque(Sim) 0 1000

2000

3000

4000

5000

0 6000

Engine Speed, RPM

150

400

120

320

90

240

60

160

Torque, Nm

Power, kW

FIGURE 4-6 Simulation results of Mercedes-Benz 300SEL/8

Power Power(Sim) 30

Torque

80

Torque(Sim) 0 1000

2000

3000

4000

5000

0 6000

Engine Speed, RPM

FIGURE 4-7 Simulation results of Mercedes-Benz 300SEL

30 800

200

160

120 400 80 Power

200

Power(Sim)

40

Torque, Nm

Power, kW

600

Torque Torque(Sim)

0 1000

2000

3000

4000

5000

0 6000

Engine Speed, RPM

FIGURE 4-8 Simulation results of Mercedes-Benz 600

According to the results from Fig.4-1 to Fig.4-8, torque and power characteristics at low and high speed are almost the same to reference data for all cases. There are some cases greater at high speed. But all graphs are lower at mid range. When considering relative errors which are summarized from simulation results of 8 engines in Fig.4-9, overall errors are in between -6% to 4%. But at low and high engine speed, the error values are in positive side. While the error values in negative side occur in mid engine speed. 10 8 6 4

%

2 0 -2 -4 -6 -8 -10 0

1000

2000

3000

4000

5000

6000

7000

Engine Speed (RPM)

FIGURE 4-9 Summarized relative errors from simulation results of 8 engines

31 According to the results, the model can interpret the output engine performance very well. The errors might come from inadequate information which has to be assumed such as pressure losses in the intake system, temperature inside manifold, exhaust gas temperature, etc. And also some effects which are not included in the model such as tuning, ram effect, exhaust stroke, and exhaust valve. However, the next section is going to determine the effects of each parameter in order to find which parameter has to be studied seriously in the future. 4.2 Sensitivity Analysis This section is going to determine the sensitivity of the model affected by each parameter. 4.2.1 Burning Duration This section is going to determine the effects of changing the gasoline burning duration from Eq.3-6 by increasing and decreasing 10 degree of burning duration while keeping the optimum gasoline spark advanced setting. 1.5

120

1

100

0.5 0 %

Power, kW

80

60

-10 deg

-1

40

-1.5

Gasoline +10 deg -10 deg

20

0 1000

+10 deg

-0.5

2000

3000

4000

5000

Engine Speed, RPM

-2

6000

-2.5 1000

2000

3000

4000

5000

6000

Engine Speed, RPM

(a) (b) FIGURE 4-10 Comparison between gasoline and +/-10 degree modified combustion range without spark advanced adjusting (a) output power; (b) relative power gain Results from Fig.4-10a indicate that power curves are almost the same when increasing and decreasing 10 degree of combustion range. When considering the relative power gain in Fig.4-10b, 10 degree increasing reduces power gradually from 1.4% to 2.0%, while 10 degree decreasing raises power gradually up to 0.9% maximum except at low speed. These results roughly indicate that shorter combustion time brings better performance to engine. The wave-liked curves cause from inappropriate spark advanced timing. So adjusting the spark timing is the next thing to study.

32 2 1.5 1 0.5 +10 deg

%

0

-10 deg

-0.5

+10 deg optimum -10 deg optimum

-1 -1.5 -2 -2.5 1000

2000

3000

4000

5000

6000

Engine Speed, RPM

FIGURE 4-11 Relative errors of before and after adjusting the spark timing

According to Fig.4-11, adjusting the optimum spark timing increases power in both cases. For 10 degree increasing, power shifts up average 0.5% due to more 5 degree advanced adjusting. And 10 degree decreasing case, power shifts up average 0.7% due to less 5 degree advanced adjusting. It can conclude that changing of combustion duration affects to the output performance. But it does not affect much and also it has no any effect to ηv. Only one thing affected is the spark advanced angle. 4.2.2 Discharge coefficient This section is going to determine the effects of changing the discharge coefficient from Eq.3-18 by increasing and decreasing 10%. 140

10 8

120

6 4 2

80

%

Power, kW

100

60

0 -2

40

-4

Normal +10% Cd -10% Cd

20 0 1000

2000

3000

4000

5000

Engine Speed, RPM

+10% Cd

-6

-10% Cd

-8 6000

-10 1000

2000

3000

4000

5000

Engine Speed, RPM

(a) (b) FIGURE 4-12 Comparison between normal CD and +/-10% changing (a) output power; (b) relative power gain

6000

33 According to Fig.4-12a, output powers do not look different much at low and mid engine speed. But at high engine speed, less CD value causes lower power than normal, while greater CD value causes greater power than normal. When considering relative power gain in Fig.4-12b, less CD value causes more power a bit at low and mid engine speed, while greater CD value causes less power. For high engine speed, the results are explicitly the same as in Fig.4-12a. When considering Eq.3-15, less CD value causes less pT due to less mass flow into the cylinder during intake stroke. With this reason, total mass flow in is increased a bit at the end of intake process. But at high speed, lesser magnitude of pT does not affect to mass flow rate any more due to choking which limits the mass flow rate. So less CD value limits mass flow into the cylinder itself. The greater CD value gives opposite results to the explanations above. However, changing of CD alters the output performance very much only at high engine speed about +/-10%. 4.2.3 Frictional Losses This section is going to determine the effect of non-applying frictional loss factor (Cf) in Eq.3-15. p0 is kept at 1 atm constantly. Changing of p0 affects ηv mainly. So ηv graph is considered in order to explain the effect. 160

110

140 100

90

100 80

nv, %

Power, kW

120

80

60 70

40

With Cf

20

Without Cf

0 1000

2000

3000

4000

5000

Engine Speed, RPM

Without Cf With Cf 60

6000

50 0

1000

2000

3000

4000

5000

6000

7000

Engine speed, rpm

(a) (b) FIGURE 4-13 Comparison between using and non-using Cf (a) output power; (b) ηv The using of ambient pressure gives the maximum possible power and maximum ηv to the engine. It is clearly that non-applying of the frictional losses causes more power according to Fig.4-13a. When considering Fig.4-13b, ηv curve is increased also. The difference of ηv increases gradually throughout the engine speed range due to the assumption which defines more pressure drop for more speed. However, ηv increases up to 100.8% which might cause from accumulative sum of error. The lower values of ηv are still under interferences of charge heating, back flow effect at low speed, and choking effect at high speed. So Cf applying in Eq.3-15 is reasonable.

34 4.2.4 Charge Heating This section is going to determine the effect of non-applying charge heating factor (Cheat) in Eq.3-15. T0 is kept at 298 K constantly. Changing of T0 affects ηv mainly. So ηv graph is considered in order to explain the effect. 140

110

120 100

100

nv, %

Power, kW

90

80 60

80

70

40 With Cheat 20 0 1000

Without Cheat

Without Cheat

2000

3000

4000

Engine Speed, RPM

5000

With Cheat

60

6000

50 0

1000

2000

3000

4000

5000

6000

7000

Engine speed, rpm

(a) (b) FIGURE 4-14 Comparison between using and non-using Cheat (a) output power; (b) ηv The using of ambient temperature gives the maximum possible power and maximum ηv to the engine. It is clearly that non-applying of the charge heating causes more power according to Fig.4-14a. When considering Fig.4-14b, ηv curve is increased also. The difference of ηv reduces gradually throughout the engine speed range due to the assumption which defines less heat transfer for more speed. However, ηv increases up to 101.6% which might cause from accumulative sum of error. The lower values of ηv are still under interferences of frictional losses, back flow effect at low speed, and choking effect at high speed. So Cheat applying in Eq.315 is reasonable. 4.2.5 Exhaust Gas Temperature The exhaust gas temperature, Eq.3-21, is used to determine the residual mass which is affected to ηv as mentioned in Sec.3.9. This section is going to determine the effects of changing the exhaust gas temperature (Texh) by increasing and decreasing temperature 50 K.

35 140

0.1

120 0.05 100

%

Power, kW

0 80 60

-0.05

-0.1

40

Normal +50 K Texh -50 K Texh

20 0 1000

2000

3000

4000

5000

+50 K Texh

-0.15

6000

Engine Speed, RPM

-0.2 1000

-50 K Texh

2000

3000

4000

5000

6000

Engine Speed, RPM

(a) (b) FIGURE 4-15 Comparison between normal and +/-50 K exhaust gas temperature (a) output power; (b) relative power gain According to Fig.4-15a, output powers are almost the same in both cases. When considering Fig.4-15b, Increasing of Texh raises power up to 0.85%, while reduction of Texh reduces power up to 0.14%. Increasing of Texh reduces the residual mass according to ideal gas equation of state, PV = mRT , and increases ηv. While reduction of Texh gives opposite results. These results agree with explanations in [6]. 4.3 Combustion Duration of Alternative fuels This section is going to interpret the results of simulation in order to determine the combustion duration of the alternative fuels. 4.3.1 Ethanol-blended Gasoline or Gasohol 90

85

nv, %

80

75

70

Gasoline E10 E20

65

60 0

1000

2000

3000

4000

5000

Engine speed, rpm

FIGURE 4-16 Effect of ethanol-blended fuel on volumetric efficiency

36

Combustion Duration, deg

120 100 80 60 Gasoline

40

E10 E20

20 0 0

1000

2000

3000

4000

5000

FIGURE 4-17 Combustion duration of gasoline, E10, and E20

Using of ethanol-blended gasoline introduces increasing of ηv by average 2.7% for E10 and 4.3% for E20 as results in Fig.4-16. The results agree with [19]. Increasing of ηv can compensate reduction of heating value and cause toque and power gain. However, conditions of air/fuel ratio in [19] are rich mixture in all cases which increase ηv greater than stoich condition due to the excess fuel. So ηv might be lower than simulation results around 0.5-1% at stoich condition. According to information of spark timing, it’s clear that combustion duration increases in parallel as percentage of ethanol increase throughout engine speed range as shown in Fig.4-17. The equations of combustion duration are shown below. For E10

N 2 N ) + 20.479( ) + 41.271 1000 1000

for 1000 ≤ N ≤ 6000 Eq.4-1

N 2 N ) + 21.443( ) + 50.343 1000 1000

for 1000 ≤ N ≤ 6000 Eq.4-2

Δθ = −1.6429( For E20

Δθ = −1.8571( 110

3

100 2.5

90

E10 E20

2

70 60

%

Power, kW

80

1.5

50 Gasoline

40

1

E10

30

0.5

E20

20 10 1000

2000

3000

4000

5000

Engine Speed, RPM

6000

0 1000

2000

3000

4000

5000

6000

Engine Speed, RPM

(a) (b) FIGURE 4-18 Comparison between gasoline, E10, and E20 when using with unmodified engine (a) output power; (b) relative power gain

37

In Thailand, the gasohol is introduced through nation for a while. However, the effects of using gasohol are still questioned. So the scenario is set to determine effect of using E10 and E20 with unmodified spark ignition engine. The results are shown in Fig.4-18. According to Fig.4-18a, the output powers seem to be almost the same. But when considering in details, using gasohol brings more power both E10 and E20 as shown in Fig.4-18b. The maximum power gains are about 2% for E10 and 2.5% for E20 at low engine speed and gradually reduce through high engine speed. According to the results, E10 and E20 can replace gasoline immediately in aspect of performance. Nevertheless, the maximum efficiency cannot be achieved. However, real experiments are needed to confirm the simulation results because the condition of scenario is set to run under stoich condition which the ECU might not handle much different air/fuel ratio of E20. This effect occurs also in transient driving. Many drivers may feel that their vehicles have less acceleration when using E10. It causes from ECU of feedback fuel control system getting “hesitation”. So if the ECU is not designed to be smart enough, this problem might appear even steady state running. 4.3.2 Ethanol 100

90

nv, %

80

70

60 Gasoline E100 50

40 0

1000

2000

3000

4000

5000

6000

7000

Engine speed, rpm

FIGURE 4-19 Effect of ethanol as a fuel on volumetric efficiency

Combustion Duration, deg

120 100 80 60 Gasoline

40

E10 E20

20

E100

0 0

1000

2000

3000

4000

5000

FIGURE 4-20 Combustion duration of gasoline, E10, E20, and E100

38 Using of ethanol as a fuel increases ηv by average 7.2% as results in Fig.4-19. Although increasing of ηv can compensate reduction of heating value, the power and torque do not take advantages much due to very low heating value and low combustion rate when comparing to gasoline. According to the results in Fig.4-20, the combustion duration of ethanol does not much difference to E20. It might conclude that the combustion lengths of E20 to E100 are almost the same. Only stoichiometric air/fuel ratio is different which can be controlled by the Flex-fuel technology. The equation of combustion duration is shown below. For E100

Δθ = −1.6843(

N 2 N ) + 21.178( ) + 52.787 for 1000 ≤ N ≤ 6000 1000 1000

4.3.3 Compressed Natural Gas (CNG) 90

85

nv, %

80

75

70

65 Gasoline CNG 60 2500

3500

4500

5500

Engine speed, rpm

FIGURE 4-21 Effect of CNG as a fuel on volumetric efficiency 160 Combustion Duration, deg

140 120 100 80 60

Gasoline

40

CNG

20 0 0

1000

2000

3000

4000

5000

FIGURE 4-22 Combustion duration of gasoline and CNG

Eq.4-3

39 According to Fig.4-21, it’s clear that using of gaseous fuel and gas mixer introduce ηv reduction as mentioned in [21]. It decreases about average 6.9%. Fig.422 shows the combustion duration of CNG comparing to gasoline. The combustion range of CNG is almost twice time of the gasoline. So when considering to use CNG in both bi-fuel and dedicated system, spark timing adjusting is recommended. For bifuel system, electronic control box is needed to control the spark timing during using of CNG. The equation of CNG combustion duration is shown below. For CNG

Δθ = −2.4286(

N 2 N ) + 27.976( ) + 72.405 for 1000 ≤ N ≤ 6000 1000 1000

4.3.4 Liquefied Petroleum Gas (LPG) 90

85

nv, %

80

75

70 Gasoline LPG 65

60 0

1000

2000

3000

4000

5000

Engine speed, rpm

FIGURE 4-23 Effect of ethanol as a fuel on volumetric efficiency

Combustion Duration, deg

140 120 100 80 60 Gasoline

40

LPG

20 0 0

1000

2000

3000

4000

5000

FIGURE 4-24 Combustion duration of gasoline and LPG

Eq.4-4

40 The results agree as mentioned in [22] when using gaseous fuel. ηv decreases about 3% average as shown in Fig.4-23. Caton et al [22] used sequential LPG gas injection system for delivering fuel which sacrifices some performance due to the ηv reduction. Combustion duration of LPG is greater than gasoline in Fig.4-24 and still less than CNG. Nevertheless, using of LPG needs electronic control box in order to adjust the spark timing as well. The equation of LPG combustion duration is shown below. For LPG

Δθ = −1.8095(

N 2 N ) + 21.762( ) + 58.571 1000 1000

for 1000 ≤ N ≤ 6000 Eq.4-5

CHAPTER 5 CONCLUSIONS AND SUGGESTIONS 5.1 Conclusions An analytical model of spark ignition engine has been constructed based on cylinder-by-cylinder engine model which combines both physical formulae, e.g. engine geometries, and empirical formulae, e.g. burning duration. The engine performance, torque and power, can be calculated by integrating the pressure inside cylinder within one engine cycle. In engine modeling, the model needs design parameters from real engine. It is the same as 3-D engine model which needs the perfect 3-D geometry of combustion chamber, valves, and ports in order to achieve the accuracy. The parameters which are usually provided by commercial brochures are not enough for engine modeling. The model is verified by data from 8 engine models. It can capture torque and power characteristics very well. The overall errors are in between -6% to 4%. But the error values at low engine speed occur in positive side, while most of error values occur in negative side at mid and high engine speed. These errors might cause from calculation itself, many assumptions and unknown phenomena which are not considered yet such as the tuning, ram effect, exhaust stroke, and exhaust valve, etc. There are significant changes to the performance curves when changing the parameters which affect ηv, for example, pressure and temperature. So ηv affects dominantly to the performance shapes because it represents how much the fuel is drawn into the cylinder. But the prediction of ηv is still very difficult. It is combined result from a lot of parameters and many phenomena. If those phenomena can be realized, the accuracy can be achieved. The simulations in order to predict the burning duration of the alternative fuels express many interesting information. All alternative fuels in this thesis have greater combustion durations when compare to gasoline. Furthermore, the model indicates the effects on ηv when using these alternative fuels. Using of ethanol and ethanol blended fuel can increase ηv due to high latent heat value of ethanol itself. While using LPG and CNG reduce ηv due to gaseous fuels. 5.2 Suggestions Eq.3-3, which is used for predicting the pressure inside cylinder, is derived from close cycle. Kirkpatrick [5] made assumptions that compression and power strokes are close system due to all valves closing and neglecting effects of incoming mixture which is drawn into cylinder. Only Qin is considered as input for Eq.3-3. But Qin can be determined only if mixture mass is known. Therefore, 1-D mass flow model, Eq.312, is applied by comparing between ambient pressure and pressure inside cylinder. Then pressure is determined to by amount of flow-in mass and fed back to pressure comparing loop. However, the ambient pressure and also the ambient temperature are influenced by frictional losses and charge heating respectively. So both topics should be studied more in order to make better assumptions. For residual mass, the assumption should include other parameters as described in [6].

42 For part load condition, the throttle body model is needed to integrate into the engine model. However, the real geometries of the throttle body, e.g. close angle, maximum angle, inside throttle body diameter, are needed also in order to calculate the mass flow through the throttle itself. All equations which describe the combustion range of the alternative fuels should be verified by experiment in order to prove model prediction accuracy. However, the results from experiments may deviate from the predictions caused by proportion of fuel mixture and also testing conditions. In order to predict the output performance of engines which use the alternative fuels, the model is needed to be revised due to the different technique of fuel dispensing system, e.g. gas mixer, gas injector.

REFERENCES

1. Zeng, P. and Assanis, D. N. “The Development of a Computer-Based Teaching Tool for Internal Combustion Engine Courses.” Proceedings of IMECE 2004. (2004). 2. Eriksson, L. and Andersson, I. “An Analytic Model for Cylinder Pressure in a Four Stroke SI Engine.” SAE 2002 Transactions Journal of Engines. (2002) : 726-733. 3. Kuo, P. S. “Cylinder Pressure in a Spark Ignition Engine: A Computational Model.” Journal of Undergraduate Science. (1996) : 141-145. 4. Zeng, P., et al. “Reconstructing Cylinder Pressure of a Spark-Ignition Engine for Heat Transfer and Heat Release Analyses.” Proceedings of ASME ICEF 2004. (2004). 5. Kirkpatrick, Allan. Internal Combustion Engine Thermodynamic. Available from: http://www.engr.colostate.edu/~allan/thermo/page6/page6.html [2005, November]. 6. Heywood, J. B. Internal Combustion Engine Fundamentals. International edition. Singapore, McGraw-Hill Book Company, c1988. 7. Ramstedt, Magnus. Cylinder-by-Cylinder Diesel Engine Modelling - A Torquebased Approach. Master thesis, Dept. of Electrical Engineering, Linkopings universitet, 2004. 8. Silverlind, Daniel. Mean Value Engine Modeling with Modelica. Master thesis, Dept. of Electrical Engineering, Linkopings universitet, 2001. 9. Tatschl, R., Wieser K. and Reitbauer, R. “Multidimensional Simulation of Flow Evolution, Mixer Preparation and Combustion in a 4-Valve SI Engine.” Proceedings of COMODIA. (1994) : 139-149. 10. Kleemann, A. P., Gosmany A. D. and Binder, K. B. “Heat Transfer in Diesel Engines: A CFD Evaluation Study.” Proceedings of COMODIA. (2001) : 123-131. 11. Shaver, G. M., Roelle, M. and Gerdes, J. C. “Modeling Cycle-to-Cycle Coupling in HCCI Engines Utilizing Variable Valve Actuation.” Proceedings of the 1st IFAC Symposium on Advances in Automotive Control. (2004) : 244249. 12. Blair, G. P., McCartan, C. and Hermann, H. “The right lift.” Race Engine Technology Magazine. Issues 009 (2005) : 44-52. 13. Takizawa, M., Uno, T., Oue, T., and Yura, T. “A Study of Gas Exchange Process Simulation of an Automotive Multi-Cylinder Internal Combustion Engine.” SAE Transaction. vol. 91 (1982). 14. Caton, J. A., and Heywood, J. B. “An Experiment and Analytical Study of Heat Transfer in an Engine Exhaust Port.” Int. J. Heat Mass Transfer. vol 24, no. 4 (1981) : 581-595. 15. Barnes-Moss, H. W. “A designer’s viewpoint.” Proceedings of Conference on Passenger Car Engines. (1975) : 133-147. 16. Pischinger, S. and Backer, H. Internal Combustion Engine Volume I. RWTH Aachen, c2002.

44 17. Klein, M. and Eriksson, L. “Models, methods and performance when estimating the compression ratio based on the cylinder pressure.” Proceedings of CCSSE. (2002). 18. Orbital Engine Company. A literature review based assessment on the impacts of a 10% and 20% ethanol gasoline fuel blend on non-automotive engines. Available from: http://www.deh.gov.au/atmosphere/fuelquality/publications/review-nonautomotive/pubs/review.pdf [2006, November]. 19. Al-Farayedhi, A. A., Al-Dawood, A. M. and Gandhidasan, P. “Experimental investigation of SI engine performance using oxygenated fuel.” Journal of Engineering for Gas Turbines and Power. Vol. 126 (2004) : 178-191. Available from: 20. Converting gasoline engines to run on alcohol. http://running_on_alcohol.tripod.com/id26.html [2006, December]. 21. Mello, P., et al. “Evaluation of the maximum horsepower of vehicles converted for use with natural gas fuel.” Fuel. Vol. 85, Issues 14-15 (2006) : 21802186. 22. Caton, J. A., McDermott, M. and Chona, R. “Development of a dedicated LPGfueled spark-ignition engine and vehicle for the 1996 propane vehicle challenge.” SAE Transactions - Journal of Fuels and Lubricants. Section 4, Vol. 106 (1998) : 792–805. 23. RPi Engineering Ltd. V8 Rover LPG information. Available from: http://www.v8dualfuel.com/pdf/LPG_Info_2003.pdf [2006, December]

APPENDIX A Engine Specifications

46 This appendix summarizes all engine specifications which are used for simulation in this thesis A.1 Mercedes-Benz 250SE (Model Year 1969) No. of Cylinders No. of Valves per Cylinder Displacement (cc.) Bore × Stroke (mm.) Compression Ratio Intake Valve Open before TDC (degree) Intake Valve Close after BDC (degree) Maximum Valve Lift (mm.) Inlet Valve Diameter (mm.)

FIGURE A-1

6 2 2,500 82 × 78.8 9.3 : 1 11° 53° 8 41.2

Performance curve of Mercedes-Benz 250SE

A.2 Mercedes-Benz 250SL (Model Year 1969) No. of Cylinders No. of Valves per Cylinder Displacement (cc.) Bore × Stroke (mm.) Compression Ratio Intake Valve Open before TDC (degree) Intake Valve Close after BDC (degree) Maximum Valve Lift (mm.) Inlet Valve Diameter (mm.)

FIGURE A-2

: : : : : : : : :

: : : : : : : : :

6 2 2,500 82 × 78.8 9.5 : 1 11° 53° 8 41.2

Performance curve of Mercedes-Benz 250SL

47 A.3 Mercedes-Benz 250E/8 (Model Year 1969) No. of Cylinders No. of Valves per Cylinder Displacement (cc.) Bore × Stroke (mm.) Compression Ratio Intake Valve Open before TDC (degree) Intake Valve Close after BDC (degree) Maximum Valve Lift (mm.) Inlet Valve Diameter (mm.)

FIGURE A-3

6 2 2,500 82 × 78.8 9.5 : 1 16° 46° 8.5 41.2

Performance curve of Mercedes-Benz 250E/8

A.4 Mercedes-Benz 280SE/8 (Model Year 1969) No. of Cylinders No. of Valves per Cylinder Displacement (cc.) Bore × Stroke (mm.) Compression Ratio Intake Valve Open before TDC (degree) Intake Valve Close after BDC (degree) Maximum Valve Lift (mm.) Inlet Valve Diameter (mm.)

FIGURE A-4

: : : : : : : : :

: : : : : : : : :

6 2 2,800 86.5 × 78.8 9.5 : 1 11° 47° 8.5 41.2

Performance curve of Mercedes-Benz 280SE/8

48 A.5 Mercedes-Benz 280SL/8 (Model Year 1969) No. of Cylinders No. of Valves per Cylinder Displacement (cc.) Bore × Stroke (mm.) Compression Ratio Intake Valve Open before TDC (degree) Intake Valve Close after BDC (degree) Maximum Valve Lift (mm.) Inlet Valve Diameter (mm.)

FIGURE A-5

6 2 2,800 86.5 × 78.8 9.5 : 1 12° 56° 9 41.2

Performance curve of Mercedes-Benz 280SL/8

A.6 Mercedes-Benz 300SEL/8 (Model Year 1969) No. of Cylinders No. of Valves per Cylinder Displacement (cc.) Bore × Stroke (mm.) Compression Ratio Intake Valve Open before TDC (degree) Intake Valve Close after BDC (degree) Maximum Valve Lift (mm.) Inlet Valve Diameter (mm.)

FIGURE A-6

: : : : : : : : :

: : : : : : : : :

6 2 2,800 86.5 × 78.8 9.5 : 1 12° 56° 9 41.2

Performance curve of Mercedes-Benz 300SEL/8

49 A.7 Mercedes-Benz 300SEL (Model Year 1969) No. of Cylinders No. of Valves per Cylinder Displacement (cc.) Bore × Stroke (mm.) Compression Ratio Intake Valve Open before TDC (degree) Intake Valve Close after BDC (degree) Maximum Valve Lift (mm.) Inlet Valve Diameter (mm.)

FIGURE A-7

6 2 3,000 85 × 88 8.8 : 1 18° 58° 7 49

Performance curve of Mercedes-Benz 300SEL

A.8 Mercedes-Benz 600 (Model Year 1969) No. of Cylinders No. of Valves per Cylinder Displacement (cc.) Bore × Stroke (mm.) Compression Ratio Intake Valve Open before TDC (degree) Intake Valve Close after BDC (degree) Maximum Valve Lift (mm.) Inlet Valve Diameter (mm.)

FIGURE A-8

: : : : : : : : :

: : : : : : : : :

8 2 6,300 103 × 95 9:1 2.5° 52.5° 7 48.95

Performance curve of Mercedes-Benz 600

APPENDIX B Matlab/Simulink Block Diagrams

FIGURE B-1 Main model

51

52

FIGURE B-2 Cm block details

FIGURE B-3 Engine geometry block details

FIGURE B-4 Engine geometry/Vd block details

FIGURE B-5 Engine geometry/A(CA) block details

53

FIGURE B-6 Engine geometry/Crank geometry block details

FIGURE B-7 Engine geometry/V(CA),Vc block details

FIGURE B-8 Wiebe fn block details

FIGURE B-9 Burn duration block details

FIGURE B-10 P block

54

55

FIGURE B-11 P/Pratio block details

FIGURE B-12 P/Lv fn block details

FIGURE B-13 P/Cd block details

56

FIGURE B-14 P/mdot block details

FIGURE B-15 P/Cheat factor block details

FIGURE B-16 P/Cf factor block details

57

FIGURE B-17 Mw block details

FIGURE B-18 Residual mass block details

FIGURE B-19 T block details

FIGURE B-20 Heat tran block details

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FIGURE B-21 h block details

FIGURE B-22 Work&Power block details

FIGURE B-23 Work&Power/Work block details

59

FIGURE B-24 Work&Power/FMEP block details

FIGURE B-25 Work&Power/Effective power block details

60 BIOGRAPHY

Name

: Mr.Sitthichok Sitthiracha

Thesis Title : An Analytical Model of Spark Ignition Engine for Performance Prediction Major Field : Automotive Engineering Biography Mr.Sitthichok

Sitthiracha has studied in King Mongkut's Institute of

Technology North Bangkok (KMITNB) since vocational school. It was first time for him studying automotive vehicle. After that he studied Mechanical Engineering in KMITNB. As undergraduate, he joined the cooperative education program which gave chance to him for working in automotive industry about one year. Along the one year program, he worked in many positions such as manufacturing & process engineer, product engineer, and quality engineer. Then he got a bachelor degree in Mechanical Engineering in 2003. After one year of graduate, he decided to study Master degree in Automotive Engineering in KMITNB also. He was selected to have an internship in South Korea about LPG retrofit on heavy duty truck engines and engine testing for 4 months. He earned many experiences about engine technology through practicalities which become the inspiration for this thesis.