Week 6: Conjugate Heat Transfer Simulation

AIM :- To simulate the conjugate heat transfer problem by using two materials i.e. solid (i.e. Aluminium) and flud (i.e. air).

THEORY AND INTRODUCTION :-

Conjugate heat transfer is a type of heat transfer analysis between solids and fluid. This type of heat transfer include both convection (between fluids) and conductive (between solids) heat transfer, as well as both forced and natural convection. Commen applications and use casses of this thermal simulation type include electronic coolings, heat exchangers, industrial machinery, some AEC casses and more. In order to demonstrate best practices for this application type, an electronics cooling application will be used as an example.

Today, heat transfer problems are often analyzed using a conjugate, coupled, or adjoint
formulation. These three equivalent terms correspond to the problems containing two or more
subdomains with phenomena described by different types of differential equations. If the heat
transfer in a solid body and a neighboring fluid is considered, the first is described by the Laplace
equation and the latter by the Navier–Stokes equations. Thus, heat transfer through solid and fluid
regions can always be considered as a conjugate problem.

Conjugate Heat Transfer is the combination of heat transfer in solids and heat transfer in fluids. In solids, heat transfer takesplace through conduction whereas in fluids it takes place through convection. To simulate conjugate heat transfer using converge studio, the geometry of the pipe was constructed and aluminium was selected as the material of the pipe. The pipe is heated with a constant heat flux of 10,000 W/m2. Apart from running the conjugate heat transfer simulation, grid dependency test was performed by using three different base grid size to demonstrate at what value the outlet temperature converge at for these three casses. A phenomenon known as supercycling was also performed. This is necessary for flows involving for both solid and fluids because the time scale associated with solids. Solid have a high heat capacitance and they take a lot of time to heat up where as gasses which have low specific heat and capacitance undergo a change in temperature easily. In conjugate heat simulation, If the simulation is run at the same time step as a fluid flow then the solid temperature will change slowly. For this reason, supercycling is performed which does steady state simulation of the solid in periodic intervals.

PROCEDURE :-

I adopted the step by step procedure as follows-

1. First off all I created the geometry as- centre-1 = (0,0,0), centre-2 = (0,0,0.2), Radius-1 = 0.015 and radius-2 = 0.015m ......(for small cylinder) Radius-1 = 0.02 and radius-2 = 0.02m........(for bigger cylinder)
2. Then, I created boundary for each edge as follows-
3. Then I setup the case as follows-

1. MATERIAL SELECTION :-

2. GAS SIMULATION :-

3. SOLID SIMULATION :-

4. GLOBAL TRANSPORT PROPARTIES :-

5. SOLID SPECIES :-

6. GAS SPECIES :-

7. RUN PARAMETER :-

8. SIMULATION TIME PARAMETER :-

9. SOLVER PARAMETER FOR NAVIER STROKE SOLVER :-

10. SOLVER PARAMETER FOR MISC. :-

11. BOUNDARY REGION NAME :-

12. INFLOW BOUNDARY :-

13. OUTFLOW BOUNDARY :-

14. SOLID OUTER WALL BOUNDARY :-

15. SOLID THICKNESS BOUNDARY :-

16. INTERFACE BOUNDARY FOR FORWARD SIDE :-

17. INTERFACE BOUNDARY FOR REVERSE SIDE :-

18. REGION AND INITIALIZATION FOR FLUID REGION :-

19. REGION AND INITIALIZATION FOR SOLID REGION :-

20. TURBULENCE MODELLING :-

21. SUPER CYCLE MODELLING :-

22. BASE GRID SIZE :-

23. CELL COUNT ESTIMATER :-

24. POST VARIABLE SELECTION :-

25. OUTPUT FILES :-

26. GEOMETRY WITH SCALING :-

4. Then I export all the files in the propar files.

5. then I run the simulation by using Cygwin64 terminal

6. then I converted the .post file in 3D form for read through paraview

7. then I plotted the graph and animation files by using Paraview and converge studio.

1) Inlet :- 'Inflow' type with pressure set up as Neumann boundary condition. Velocity along the Z-axis was calculated using the Reynold number formula.

Reynold number (Re) = 10000

Charecterastic length (L) = 0.015 m ......(inner diameter)

Density (i.e. rho) (0.77N2 & 0.23O2) = 1.20318 kg/m^3

Viscosity = 1.853e-5 Pa.sec (at 300k)

By using the formula-

Re = (rho*velocity*L)/viscosity

We get the value for velocity is-

Velocity = 10.267236268333 m/s.

2) Outlet :- Outflow type static pressure is 101325 Pa.

3) Solid outer wall :- Type wall with 'slip' condition since it is a solid and heat flux of -10000 W/m^2.

4) Solid side wall :- Type wall with 'Law of wall' boundary condition used.

5) Interface boundary condition :- It's assigned with Forward boundary treated as the fluid domain since that is where the normals are pointed and reverse boundary for the solid domain.

6) Two regions were initialized, one as fluid (stream ID = 0) and the other as solid ( stream ID = 1). The solid regions were initialized to the outer and side wall where as the inlet and outlet were initialized to the fluid region.

I created here total 9-casses, 3 for supercycle stage interval by changing griding size for each supercycle stage.

GRID DEPENDENCY TEST :-

CASE-1 :-

Base grid size = 0.001m

Total number of cells = 343612

A. supercycle stage interval = 0.01 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Velocity vector along X-axis :-

17. Y-plus contour :-

18. Y-plus plot :-

19. Pressure animation :-

20. Temperature animation :-

21. Velocity animation :-

B. supercycle stage interval = 0.02 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Y-plus contour :-

17. Y-plus plot :-

18. Pressure animation :-

19. Temperature animation :-

20. Velocity animation :-

C. supercycle stage interval = 0.03 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Y-plus contour :-

17. Pressure animation :-

18. Temperature animation :-

19. Velocity animation :-

CASE-2 :-

Base grid size = 0.002m

Total number of cells = 42951

A. supercycle stage interval = 0.01 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Y-plus contour :-

17. Pressure animation :-

18. Temperature animation :-

19. Velocity animation :-

B. supercycle stage interval = 0.02 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Y-plus contour :-

17. Pressure animation :-

18. Temperature animation :-

19. Velocity animation :-

C. supercycle stage interval = 0.03 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Y-plus contour :-

17. Pressure animation :-

18. Temperature animation :-

19. Velocity animation :-

CASE-3 :-

Base grid size = 0.003m

Total number of cells = 12726

A. supercycle stage interval = 0.01 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Y-plus contour :-

17. Pressure animation :-

18. Temperature animation :-

19. Velocity animation :-

B. supercycle stage interval = 0.02 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Y-plus contour :-

17. Pressure animation :-

18. Temperature animation :-

19. Velocity animation :-

C. supercycle stage interval = 0.03 sec

1. Cell count for fluid region :-

2. Cell count for solid region :-

3. Mass flow rate for inlet :-

4. Mass flow rate for outlet :-

5. Mean temperature for fluid region :-

6. Mean temperature for solid region :-

7. Pressure contour for surface with edge :-

8. Pressure contour for surface :-

9. Pressure plot :-

10. Temperature contour for surface with edge :-

11. Temperature contour for surface :-

12. Temperature plot :-

13. Velocity contour for surface with edge :-

14. Velocity contour for surface :-

15. Velocity magnitude plot :-

16. Y-plus contour :-

17. Pressure animation :-

18. Temperature animation :-

19. Velocity animation :-

RESULTS :-

From the above casses I conclude the following points-

1. Cell count for solid region and fluid region is depends upon grid size not on supercycle stage interval, as grid size increases cell count for solid region and fluid region decreases.
2. Mass flow rate for inlet is depends upon grid size and not on supercycle stage interval, as grid size increases mass flow rate for inlet decreases.
3. Mass flow rate for outlet is depends upon both base grid size and supercycle stage interval, as supercycle stage interval increases, mass flow rate increases less frequently and due to base grid size increasing range of mass flow rate increases with respect to time.
4. Mean temperature for fluid region and solid region is depends upon base grid size not on supercycle stage interval, as base grid size increases the temperature range also increases and vice versa.
5. Pressure contour and pressure plot is depends upon supercycle stage interval as supercycle stage interval increases the value of pressure increases at inlet and at outlet it constant and minimum for all casses.
6. Temperature contour and temperature plot is depends on supercycle stage interval and not on base grid size because heat transfer takesplace inside the fluid, as supercycle stage interval decreases the temperature effect also decreases and then increases.
7. Velocity contour and velocity plot is depends upon supercycle stage interval and not on base grid cycle, as supercycle stage interval increases velocity range decreases by small value and vice versa.
8. Yplus value is depends upon base grid size and not on supercycle stage interval, as base grid size increases Yplus value increases because due to increasing base size value mesh will coarse and for coarser mesh Yplus value is more.

Effect of supercycle stage interval :-

The simulation was run for three different supercycle stage intervals of 0.01, 0.02 and 0.03 seconds to see the effects it has on the total simulation time and the convergence of supercycle temperature.

As the stage interval was increased, the simulation time decreased conversely. In all the three casses the temperature converges to a steady state value.

CONCLUSIONS :-

From above plots and results we can conclude that-

• As grid size decreases the simulation time increases due to finer mesh.
• Supercycle stage interval required only for there, where solid and fluid contacts are occured.
• Pressure, temperature and velocity are depends upon supercycle stage interval because it's the result of contact between two layers.
• Mass flow rate and Yplus value are depends upon base grid size because it depends on quality of mesh.
• As the mesh gets finer the difference between the mean temperature of the solid region and the super cycled temperature becomes larger.
• The range of Y+ value becomes smaller as the mesh becomes finer.

Simulation time for 0.01 seconds = 381.414044 sec

Simulation time for 0.02 seconds = 364.2277 sec

Simulation time for 0.03 seconds = 346.54 seconds

In this way I check the grid dependency test and effect of base grid size and supercycle stage interval and write the detailed report for that. Here we use two material i.e. solid and liquid and according to that I calculate inlet velocity and calculate overall results.