CFD Simulation of Heat Exchanger Equipment

CCB 3033 ADVANCED TRANSPORT PROCESSES September 2014

GROUP PROJECT Title: CFD Simulation of Heat Exchange Equipment GROUP 4-16 Name

Matric ID

Nelson Yang Soon Kit

16026

Vennesa Johnny Ting

16112

Submission date: 12th December 2014

TABLE OF CONTENT No.

Title

Page

1

Introduction about Heat Exchange Equipment

1

2

Governing Equations

2

2.1 Governing Equations for Laminar Flow in Fluid 2.2 Governing Equations for Non-Isothermal Heat Transfer in Fluid 3

Simulation Method

4

3.1 Modeling Procedure 4

Results and Discussions

6

4.1 Velocity Field Streamline in 2D 4.2 Temperature Profile revolved in 2D & 3D 4.3 Heat View from the Top Part of the Heat Exchanger & Line graph 4.4 Velocity Profile in 3D 4.5 Relationship between Heat Transfer Coefficient and T2 4.6 Trial and Error Process to determine Heat Transfer Coefficient 5

Conclusion

12

6

References

13

1.0 Introduction about Heat Exchange Equipment Heat exchange equipment or more commonly known as heat exchanger is widely used in many large scale industrial plants and has to be an important part of many processes due to its function of heating and cooling in safe manner. Not only that it is used in industrial processes, heat exchanger has more other familiar applications in helping machines and engines to work more efficiently such as car, ship and airplane engines, air-conditioner and refrigerator. (Woodford, 2014) The fundamental principle that lies behind is nothing but heat transfer from one medium to another. Generally, in order for a heat exchanger to work out its principle, there must be the presence of two fluid streams operating at different temperature, either in direct contact or separated by a solid wall to prevent mixing. The medium that separates the two fluids will act as the heat exchange surface while the temperature gradient acts as the driving force in controlling the rate of heat transfer. As aforementioned, the role of a heat exchanger in process plants is of paramount importance to achieve minimum waste of heat and energy. According to Putman (2002), condensers recover some of the heat contained in process discharge streams while heat exchangers recover heat that is recycled from a late stage in the process and use it to preheat a stream that enters at an earlier stage in the process. Thus, it is an ingenious solution to reducing heat loss to the surrounding and at the same time minimizing the cost of utility. The design of heat exchanger varies with the requirements of a process and thus, it can take many forms, ranging from a simple pipe surrounded by a larger pipe, to larger exchangers with hundreds of tubes, multiple pass, floating head etc. Each of these heat exchangers is designed to cope with particular problems. For instance, shell and tube heat exchangers are used for processes operating at a pressure greater than 30bar and temperature greater than 260℃. Plate heat exchangers are designed to give a larger heat transfer surface area and also to ease the cleaning and inspection work. Since the efficiency of a heat exchanger is affected by the heat transfer area and resistance, the overall heat transfer coefficient, ℎ plays a vital role in heat exchanger design. By definition, the overall heat transfer coefficient is a function of the flow geometry, fluid properties and material composition of the heat exchanger. Hence, different geometry and different fluid will result in different overall heat transfer coefficient which then affects the outlet fluid temperature.

1

In this simulation project, the objective is to study the relationship between the overall heat transfer coefficient, ℎ and the outlet fluid temperature, 𝑇2 . By using COMSOL Multiphysics v4.3, heat exchangers with different geometry can be constructed and the overall heat transfer coefficient for a particular outlet fluid temperature can be determined using trial and error method.

2.0 Governing Equations In this project, Computational Fluid Dynamics (CFD) Module and Heat Transfer Module are used. CFD Module includes laminar flow, swirl flow, turbulent flow, non-isothermal flow, high Mach number flow, two-phase flow and fluid-structure interaction (with Structural Mechanics Module) while Heat Transfer Module’s user interfaces and tools are conduction, convection and radiation. Here, the governing equations are used to generate two plots from the non-isothermal laminar flow and heat transfer in the fluid.

2.1 Governing Equations for Laminar Flow in Fluid 𝑞𝑙𝑜𝑠𝑡 = 𝑞𝑔𝑎𝑖𝑛 𝑞𝑙𝑜𝑠𝑡 𝑜𝑟 𝑔𝑎𝑖𝑛 = 𝑈𝑖 𝐴𝑖 ∆𝑇𝑙𝑚 = (𝑚𝑐𝑝)(𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡 )|𝑠ℎ𝑒𝑙𝑙 = (𝑚𝑐𝑝)(𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡 )|𝑡𝑢𝑏𝑒 Where, 𝐴𝑖 = inside tube area 𝑈𝑖 = overall heat transfer coefficient, based on inside area ∆𝑇𝑙𝑚 = LMTD (Log Mean Temperature Difference) =

∆𝑇1 −∆𝑇2 𝑙𝑛

∆𝑇1 ∆𝑇2

𝑞0 = ℎ(𝑇𝑒𝑥𝑡 − 𝑇) Where, 𝑞0 = heating flux 𝑇𝑒𝑥𝑡 = external temperature For laminar flow (𝑅𝑒𝑓 < 2100) ℎ0 (

𝜇𝑓 2 𝑘𝑓 3 𝜌𝑓 2 𝑔

1/3

)

= 1.47 (

4𝑇′ ) 𝜇𝑓

−1/3

2

ℎ0 = 0.943 (

𝑘𝑓 3 𝜌𝑓 2 𝑔𝜆 (𝑇𝑐𝑜𝑛𝑑𝑒𝑛𝑠𝑖𝑛𝑔 𝑠𝑡𝑒𝑎𝑚 − 𝑇𝑤𝑎𝑙𝑙 )𝐿𝜇𝑓

0.25

)

Where, 𝑘𝑓 = conductivity coefficient 𝐿 = length of tube

2.2 Governing Equations for Non-Isothermal Heat Transfer in Fluid For conductive and convective heat transfer ∇. (−𝑘∇𝑇) = 𝑄 − 𝜌𝐶𝑝 𝑢. ∇𝑇 Where, 𝐶𝑝 = specific heat capacity (J/(kg.K)) 𝑘 = thermal conductivity (W/(m.K)) 𝑢 = velocity vector (m/s) 𝑄 = sink or source term (in which it is set to zero as there is no production or consumption of heat in the device) For hot stream, 𝑟 2 𝑣 = 𝑣𝑚𝑎𝑥 (1 − ( ) ) 𝑅 Where, 𝑣𝑚𝑎𝑥 = maximum velocity (m/s) 𝑟 = distance from center of the channel (m) 𝑅 = channel radius (m) For cold stream, 𝑟 2 𝑣 = −𝑣𝑚𝑎𝑥 (1 − ( ) ) 𝑅 For non-isothermal flow interface, 𝜌 = 𝜌𝑚 (1 −

𝑇 − 𝑇𝑚 ) 𝑇𝑚

Where, 𝜌𝑚 = mean density (kg/𝑚3 ) 𝑇𝑚 = (𝑇𝑐𝑜𝑙𝑑 + 𝑇ℎ𝑜𝑡 )/2 is the mean fluid temperature

−𝑘∇𝑇. 𝑛 = 0

3

3.0 Simulation Method Start

Problem Identification

Model Sketching

Model Drawing using CFD

Simulation using CFD

Specify Heat Flux

Data Computation for Outlet Temperature

No

Yes Contour and capture of relevant 2D plot for surface and iso-surface velocity and temperature

2D Line graph is plotted for temperature vs. heat transfer coefficient

End

3.1 Modeling Procedure MODEL WIZARD 1. In the Space Dimension window, 2D axisymmetric is selected. 2. In the Add Physics window, Non-Isothermal Flow>Laminar Flow is selected 3. Under Study Type, stationary is selected. GEOMETRY

4

1. In the Model Builder window>Geometry I, the geometry is built using 2 rectangles, 2 squares and 4 circles. (Take note of the coordinates of each geometry) MATERIALS 1. In the Material Browser window, Built-In>Water is added to the entire model. NON-ISOTHERMAL FLOW 1. In the Model Builder window, Model I>Non-Isothermal Flow is expanded. 

Inlet 1 assigned to boundary 2 (𝑈0 = 0.1𝑚/𝑠)



Outlet 1 assigned to boundary 9 (𝑃0 = 0𝑃𝑎)



Temperature 1 assigned to boundary 2 (𝑇0 = 293.15𝐾)



Outflow assigned to boundary 9



Heat flux assigned to boundaries 19 to 30. Inward heat flux is selected (𝑞0 = ℎ(𝑇𝑒𝑥𝑡 − 𝑇))

2. The value of heat transfer coefficient is specified. MESH 1. In the Model Builder window, Model I>Mesh>Free Triangular with the following setting: 

Maximum element size = 0.0137m



Minimum element size= 3.3e-4



Maximum element growth rate=1.3



Resolution of curvature=0.3



Resolution of narrow region=1

2. The boundary selected is the entire geometry excluding the 2 circles and 2 semi-circles. RESULT 1. In the Model Builder window, a cut line 2D is constructed with the following setting: Point 1 Point 2

𝑥 0 0.05

𝑦 1.05 1.05

STUDY 1. In the Model Builder window, Compute button is clicked. RESULT 1. Back to Result again, Derived Values>Line Average>Evaluate

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2. This step is repeated for trial and error in order to get the desired value of heat transfer coefficient.

4.0 Results and Discussions 4.1 Velocity field streamline in 2D

Figure (a1)

Figure (a2)

X=0.14

X=0.1

Y=0.1

Y=0.14

In both of the graphs above, Figure (a1) and Figure (a2) there are differences in terms of velocity flow line as the dimensions for both the heat exchanger varies respectively. In figure (a1), the length of y (0.1) which is much shorter compared to the y length (0.14) in figure (a2) causes the velocity stream of water in both heat exchanger varies respectively. As observed, there are more dead zones in figure (a1) as the differences in dimensions causes more dead zones towards the output nozzle as compared to figure (a2). The reason behind the existence of the dead zones are due to more stagnation of water being formed in figure (a1) compared to figure (a2). Apart from that, there are also more dead zones in figure (a1) compared to figure (a2) at the input zones respectively. The heating coils in figure (a1) which is slightly placed higher in the y axis compared to figure (a2) causes the streamline of the water to be obstructed. The phenomenon of Vena Contracta actually occurs in the flows of water for both heat exchangers. This causes more water to be stagnant; forming more dead zones as there will be a pocket or region where it is protected from the flow of water. In short, the velocity flow of water in heat exchanger, figure (a2) is much more efficient as there are less dead zones and the function of heat transfer would be more efficient. This is due to the dimension of y which is shorter allowing more spaces for water to flow more efficiently. 6

4.2 Temperature profile in revolve- 2D & 3D

Figure (b1) X=0.14 Y=0.1

Figure (c1) X=0.1 Y=0.14

In both figure (b1) and figure (c1), the heat flows through the heat exchanger in almost a similar manner. Undoubtedly, as shown in both the figures, as the water firstly enters the input respectively, the brightness of the red is dull showing that a low temperature of water is being measured. As it proceeds towards the output of the heat exchangers respectively, the temperature increases as water will be heated to carry out heat transfer purposes. This is proven as the brightness of the red color increase in both the figures when the water travels toward the output of the nozzle in both figures. However, the difference in dimensions of x and y in figure (c1) and figure (b1) clearly affects the distribution of the heat flux in a minority. As observed on the mid-section of the heat section in figure (c1), the redness appears to be brighter indicating more heat are being transferred through from the coil as compared to figure (b1). This can be explained as we observe the length as shown by the arrow in the picture. The length in figure (c1) is longer allowing more heated water to flow through towards the output as compared to figure (b1). Hence, more heat is being transferred.

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Figure (b2)

Figure (c2)

X=0.14

X=0.1

Y=0.1

Y=0. 14

Figure (b3) X=0.14 Y=0.1 In both Iso-surface figures, the distribution of the heat flux is the same as indicated by the intensity of the blue color increases from the input section towards the output sections in both figures. However, the highlight here is again emphasized towards the mid-section of the heat exchanger in figure (c2) as compared to figure (b2). The distribution of heat in the mid-section of figure (c2) projected to be longer and more concentrated towards the output nozzle. However, in figure (b2) the distribution of heat slims down towards the output indicating less heat to be transferred through due to the difference in dimensions. The explanation is the same for both in contour in the heat exchanger for the two respective dimensions as shown above. More heat is shown to be distributed in figure (c3) compared to figure (b3). 8

4.3 Heat View from the Top Part of the Heat Exchanger & Line graph

This is the results obtain from both heat exchanger respectively. As observed from the top the middle or the core of the circle represents the outlet of the heat exchanger from the top view. This is where the heater water from the coil of the heat exchanger flows out. Therefore, the red color indicated the highest temperature; as it decreases towards the outer layer of the circle. The outer layer of the circle is blue in color indicating a lower temperature value. This is because heat is loss to the surrounding atmosphere from the core of the heat exchanger itself. The graph also shows as the arc length of the reactor increases the heat decreases with is acceptable as explained as above.

4.4 Velocity Profile in 3D

Figure (d1)

Figure (e1)

X=0.14

X=0.1

Y=0.1

Y=0. 14

9

Figure (d2) X=0.14 Y=0.1

Figure (e2) X=0.1 Y=0. 14 Figure (b2)

In all the figures shown, it is shown that the velocity of water will increase as it flows from the input X=0.14

section of the heat exchangers towards the output section of the heat exchanger. However, the debate Y=0.1

here focuses on the difference in velocity of water flowing through respective 14 heat exchangers. As indicated, in figure (d1) and figure (d2) the water flows through faster; resulting in a brighter blue intensity in color as compared to figure (e1) and figure (e2). This is cause by the opening in figure (d1) and figure (d2) in the heat exchanger which is smaller, or in other words, the length of y which is shorter compare to figure (e1) and figure (e2). We can relate this behind the theory of Bernoulli’s Principle which states that the flow of a con-conductive fluid, an increase of fluid occurs whenever there is a sudden decrease in pressure due to the change in amount of space for fluid to flow. As it flows through a smaller opening it will results in a greater decrease of pressure drop; hence water would flow faster as shown in figure (d1) and figure (d2). Apart from that, the phenomenon of Vena Contracta also occurs for both heat exchangers respectively. Vena contracta is the point in a fluid stream where the diameter of the stream is the least, and fluid velocity is at its maximum, such as in the case of a stream issuing out of a nozzle, (orifice). (Evangelista Torricelli, 1643). It is a place where the cross section area is minimum. Therefore, the smaller diameter in figure (d1) and figure (d2) will oozes out the water at a higher velocity compare to the other heat exchanger. As a result, the velocity profile in heat exchanger (figure d) will be much faster compared to the other.

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4.5 Relationship between heat transfer coefficient and T2 80 70

Nelson

60

venessa

50

Nelson X=0.1 Y=0.14

Average outlet T2

40 30 20

Vennesa X=0.14

10 0 0

100

200

300

400

500

600

700

800Heat 900 Transfer1000 Coefficient

The respective values are plotted according to the axis and compared for both heat exchangers with different dimensions. As shown in the graph, the heat transfer coefficient is directly proportional to the average outlet, T2 which indicates the increase in heat transfer coefficient the higher the temperature we would obtain.

4.6 Trial and error process to determine heat transfer coefficient 18 16

nelson

14

venessa

12

Nelson X=0.1 Y=0.14

T avg outlet - T2

10 8

Vennesa X=0.14 Y=0.1

6 4 2

Heat Transfer Coefficient

0 0

200

400

600

800

1000

11

Using the trial and error, we have finally found the heat transfer coefficient needed to operate both the heat exchanger that has its own respective dimensions as stated in the graph. For Nelson’s results the optimum heat transfer coefficient is found to be 540 W/(m2K) for the heat exchanger to operate while for Vanessa’s results, the optimum heat transfer coefficient is found to be 647 W/(m2K).

5.0 Conclusion In this project, we learned that by changing the dimensions of the heat exchanger, the heat transfer coefficient changes. This shows that the heat transfer coefficient is directly affected by the width of the slit and the diameter of the tube. The heat transfer coefficient needed for a process can be estimated when the outlet fluid temperature is given. This can be done by the simulation of Non-Isothermal Laminar Flow package in COMSOL Multiphysics with trial and error method. The outcome of this project is that we are able to compare the velocity and temperature profile of heat exchange with different dimensions (Nelson’s x=0.1, y=0.14; Vennesa’s x=0.14, y=0.1) at an outlet fluid temperature of 58℃. In the comparison for velocity field streamline in 2D, it is found that the velocity flow of water in the heat exchanger is more efficient when the length of y is longer as there are less dead zones which then allow more spaces for water to flow more. As for the velocity profile in 3D, the phenomena Vena Contracta is observed to have occurred in both heat exchangers. In this case, smaller diameter of the heat exchanger will oozes out the water at a higher velocity. Then, the comparison for temperature profile in revolved 2D and 3D also shows that the longer length of Y enables more heat to be supplied to the flow through the output. In iso-surface comparison, it can be seen that the heat flux for both heat exchangers are the same. However, a slight change can be observed from the middle of the heat exchanger onwards. The distribution of heat is observed to be longer and more concentrated towards the output nozzle. Here, it is again shown that the width of the slit y affects the heat distribution in the heat exchanger. A line graph of temperature plotted using COMSOL Multiphysics enables us to study the heat exchanger from its top view. It is observed that the outer layer of the heat exchanger is mostly in blue colour while the inner part towards the core is red in colour. This is due to heat loss to the surrounding atmosphere from the core of the heat exchanger itself. The graph also shows that as arc length of the reactor increases, heat decreases.

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Lastly, the relationship between the heat transfer coefficient and the outlet fluid temperature is studied. From the graph, we learned that the heat transfer coefficient is directly proportional to the average outlet temperature which indicates that increase in heat transfer coefficient increases the outlet temperature. Using the trial and error method, the heat transfer coefficient determined for (x=0.14, y=0.1) is 540𝑊/(𝑚2 𝐾) and 647𝑊/(𝑚2 𝐾) for the dimension (x=0.1, y=0.14).

References McCabe, Warren L., Julian C. Smith and Peter Harriot, Unit Operations of Chemical Engineering, 5th ed., New York, McGraw-Hill Book Company (1993). Welty, James R,; Wicks, Charles E.; Wilson, Robert E.; Rorrer, Gregory. (2001). Fundamentals of Momentum, Heat, and Mass Transfer, John Wiley William M. (1998), Analysis of Transport Phenomenam Oxford University Press Blocken, B., Cualtieri, C. 2012. Ten iterative steps for model development and evaluation applied to Computational Fluid Dynamics for Environmental Fluid Mechanics. Environmental Modelling & Software 33:1-22. Joel.L. 9 (2004), Tranport Phenomena Fundamentals, Chemical Industries Series, CRC Press, pp.1, 2, 3. Esionwu, C. (2014). Further Aerodynamics and Finite Volume Discretization Basics. Retrieved from http://www.dicat.uniqe.it/querrero/of2013/fvmpdf Howes, D.J. & Sanders, B.F. (2013) Velocity Contour Weighting Method. Retrieved from http://digitalcommons.calpoly.edu/cgi/viewcontent/cgi?article=1104&context=bae_fac

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