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Chander March 27, 2012 11:59

Grid resolution in porous medium model for heat sink

I am simulating conjugate heat transfer in a heat sink consisting of a number of parallel microchannels.
Since modeling each microchannel is computationally inefficient, I am modeling the heat sink using the porous medium model (this is a well established approach in literature).
Now, if I understand correctly, the porous medium model equations are derived for what is called as the Representative Elementary Volume (REV) that is assumed to be much larger than the average pore size.
In my case the average pore size is of the order of channel width.

So following the above REV assumption, what minimum grid size can I go to while checking for grid Independence? Should I ensure that my average grid size is always much larger than the channel width? If yes, then how much larger it should be than the channel width?

Thanks for your inputs.

ghorrocks March 27, 2012 17:58

You certainly have to be careful as your mesh size approaches the feature size, but often it is OK and you can proceed. Does flow details around the feature contribute a significant amount to the final result in a fashion which is not captured by the porous model? Is grid refinement consistent and converging as it gets smaller than the feature size?

Chander March 30, 2012 05:32

Hi Glen,

Thanks for your reply.
I have repeated the simulations for three grid densities, of average sizes 0.5h, h and 2h where h is nearly equal to the channel width (which represents the pore size in my case).
And the results of three simulations fall on a trend that is typical of a grid independent study. In other words, the results do not change drastically when i refine my grid.
So, is it safe to conclude that the grid size can go below the pore size in porous medium and is independent of the way the differential equations are derived for porous medium?

The channel width does affect the thermal performance of the heat sink. This brings in one more point. I am currently using the equilibrium thermal model for porous medium (i.e. solving one equation for temperature by assuming the temperature of solid same as that of liquid inside porous medium). I am now running the non-equilibrium thermal model for the same cases to see if that causes any difference in results. I will also perform the same grid refinement study as above to see if grid refinement with non-thermal equilibrium model changes the above conclusions or not.

ghorrocks March 30, 2012 05:49

I think you are OK to continue in this case. Turbulence modelling is one case where as the mesh size gets smaller than the turbulent structure size the inherent assumption of the turbulence model starts to fall apart and it does not have sufficient dissipation to keep the turbulent structures out of the "bulk" flow. This is sometimes the cause of problems with mesh refinement with simulations with turbulent models. But there does not seem to be any similar scale related issues with your model, you seem OK.

Chander April 2, 2012 07:10

Thanks Glen for your inputs!
I will come back on this in case I see anything different with the non-equilibrium thermal model for porous medium

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