Week 6: Conjugate Heat Transfer Simulation
Conjugate heat transfer analysis is a kind of heat transfer involving both solids and fluids. For example, if there is a solid that is immersed in water and to this solid heat is supplied externally. This solid heats up and in turn also heats the water it is immersed in. This process in which the heat from a solid is transffered or used to heat any fluid is called conjuagate heat transfer analysis.
In this project, we have simulated a simple case of CHT analysis which involves a fluid flow of air surrounded by aluminium solid wall.
Geometry:
Geometry used for CHT simulation
The above figure shows the geometry used to perform CHT analysis.
The diameter of the outer cylindrical pipe is 0.02m and inner pipe is 0.015m. The air flows through the inner pipe and the thickness between the inner and outer pipe is filled with aluminium solid.
5mm is the thickness of the geometry.
Reynolds number = 7000.
density of air= 1.184kg/m^3 at 300k
dynamic viscosity of air = 1.8e-5 `kg*m/s`
Simulation parameters:
Start time: 0
end time: 0.5s
maximum time step= 1s
minimum time step = 1e-7 and initial time step is 1e-7
The simulation is solved for trasnsient case to observe the temperature distributions with respect to time.
Boundary conditions:
inlet- it is in the air region with temperture of 300k and velocity of 7.04m/s
pressure is zero normal gradient.
The velocity is obtained by the equation
`Re= (rho*v*D)/mu`
where rho is desnity of air, v is velocity at inlet , D is the diameter and mu is the dynamic viscosity of air at 300k.
After calculationg, velocity of air at inlet is 7.04m/s
Outlet: This is also air region with outflow conditon, pressure= 101325 pascal(atmosphere) and velocity is zero normal gradient and backflow temperature is 300k.
Outer wall solid: slip wall boundary condition
temperature - heat flux of -10000W/m2 is given.
wall motion is stationary.
Solid side : This is thermally insulated and hence zero normal gradient for temperature and slip condition.
Interfaces:
Forward region is facing the fluid side and backward region is the one facing solid side.
Supercycling: This technique is used to solve huge and complex conjugate heat transfer simulations. Normally fluid and solid take different times for the solutions to converge since different equations have to be solved for both of them. If this is the case, running normal transient simultion would take too much time.
Hence supercycling is used. In this method, transient case simulation is run for both solid and fluid together and after a certain time, the instantaneous values of heat transfer coefficients and temperatures are averaged and they are stored at the fluid-solid interface. Now at this point of time, the fluid is frozen( solving the fluid equation part) and the steady state analysis of the solid is solved using the values on the interface.
This steady state simulation is done until the value of the solid temperatures are converged and then the fluid part is unfrozen and then solved.
Simulation : The simulation is first run with different base mesh sizes of 0.02, 0.03, 0.04 meters. The three cases were run with a supercycling time interval as 0.01. This was to done to verify the grid dependence of the simulation.
Simulation results:
for mesh size 0.04m:
Temperature contour for mesh size 0.04m
Y+ for the mesh size 0.04m
We used the slip condition for the solid region walls. Normally for a very accurate result with slip condition we need to make sure that the y+ value is less than 10 but in this case the maximum value is 30. This means that the results obtained in this simulation are not 100% accurate and we could further achieve much more accurate results by reducing the y+ to less than 10.
Temperature animation
https://youtu.be/uSxQYgdiRfk
Mesh size 0.03m
Temperature contour for mesh size 0.03m
Y+ for the mesh size 0.03m
Even after further refinement of the mesh we still obtain a y+ value that is greater than 10 hence we need to further refine the mesh to obtain much more accurate results. Since we have used a slip boundary condition, it is important to achieve a y+ of less than 10.
Temperature animation
https://youtu.be/Su5Uxgmehj0
Mesh size 0.02m:
Temperature contour for mesh size 0.02m
y+ for mesh size 0.04m
The y+value is just a little over 10 in this case. The maximum value is 11. We can say that since this value is closer to 10, this result is the most accurate result among all the other mesh size results. If we further refine this mesh to a base mesh size less than 0.02m, we would be able to achieve a y+ value that is less than 10.
This result obtained is the most accurate result among all other mesh size simulations. However the computational time taken to solve for less mesh size is a lot. The mesh size with 0.02m takes the highest time to solve.
Temperature animation
https://youtu.be/C0I-P6QXAV0
Comparision of the fluid temperatures for different grid sizes.
Comparision of the solid temperatures for different grid sizes.
As it can be seen from the above graphs, the fluid temperatures are varying with the mesh sizes. It varies from 323k to 328k. The solid temperature vary from 650k to 710k.
It means that the solution obtained with these mesh and boundary conditions are not very accurate. The accuracy of the solution can further be improved by further reducing the mesh size. After reducing the mesh size to a value which is less than 0.02 would give us the accurate results.
If we further reduce the mesh size values to much lesser values, the solution wont change and the simulation is said to become grid independent in such a situation.
Effect of supercycle stage interval:
The simulation(for both solid and fluid) runs for 0.05s and after that the fluid is frozen and data is collected to perform steady state analysis on the solid domain. It is allowed to converge . Once the solid region achieves convergence, fluid solver is restarted. Now both the fluid and solid solvers runs for another 0.01 seconds and then again the fluid is frozen, data is collected and steady state analysis of solid is performed. This process continues till the end of the simulation time.
Mean fluid temperature for different supercycling time interval
Mean solid temperature for different supercycling time interval
Here the effect of supercycling is done for mesh size 0.04m.
It can be seen that irrespective of the supercycling time, the same values of final temperatures are achieved for both solid and fluid flow regions.
Conclusions:
1) The simulation time for base grid size of 0.04m and supercycle interval 0.01s is 480 seconds.
2) The simulation time for base grid size of 0.03m and supercycle interval 0.01s is 1148 seconds.
3) The simulation time for base grid size of 0.02m and supercycle interval 0.01s is 5139 seconds.
It can be said that as the gird size reduces, simulation time increases significantly.
4) The simulation time for base grid size of 0.04m and supercycle interval 0.02s is 498.82 seconds
5) The simulation time for base grid size of 0.04m and supercycle interval 0.03s is 439 seconds.
There is as such no trend observed in case of varying the supercycle time. The only observation that could be made is that changing the supercycle time gives the same exact results but only the time taken for the simulation to complete varies.