# Are two simulations equivalent if they have the same Grassof and Reynolds?

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 November 10, 2017, 12:01 Are two simulations equivalent if they have the same Grassof and Reynolds? #1 Senior Member   Hector Redal Join Date: Aug 2010 Location: Madrid, Spain Posts: 197 Rep Power: 9 Hi, I would like to know if two simulations that have the same Reynolds and Grassof number are thermally equivalent? I am trying to simulate the problem described in the following article: http://heattransfer.asmedigitalcolle...icleid=1438948 I am supposing air with Pr = 0.71. When I double the viscosity, doubling the inlet velocity (keeping reynolds number), and doubling the temperature difference in the formula for calculating the Grashof number, the results I am obtaining are different. I have always understood that non-dimensional number allow comparison between different simulations/experiments that show same behaviour. May I am missing something? As thermal coefficient expansion (beta) for the Grashof number I am using 1/T, being T the low temperature in the problem. Should I use any other value for the temperature (i.e., the high temperature)? The middle temperature in the range? Any comment is welcome. Best regards, Hector.

 November 10, 2017, 12:10 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,641 Rep Power: 41 You can easily answer by looking at the governing equations in non-dimensional form. If you have the same non dimensional parameters the two non-dimensional solutions must be the same.

November 10, 2017, 20:26
#3
Senior Member

Hector Redal
Join Date: Aug 2010
Posts: 197
Rep Power: 9
Quote:
 Originally Posted by FMDenaro You can easily answer by looking at the governing equations in non-dimensional form. If you have the same non dimensional parameters the two non-dimensional solutions must be the same.
This was also my understanding, but what I am observing is not this.
The non-dimensional solution differ by almost 5%.

 November 11, 2017, 04:27 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,641 Rep Power: 41 There is a difference in the two simulation, maybe different iteration accuracy

November 13, 2017, 12:32
#5
Senior Member

Hector Redal
Join Date: Aug 2010
Posts: 197
Rep Power: 9
Quote:
 Originally Posted by FMDenaro There is a difference in the two simulation, maybe different iteration accuracy
If I run a simulation without solving the energy equation, the difference between two solution having the same non-dimensional numbers (but using different values for velocity, or density, or viscosity, etc.) is almost zero.

I only observe this discrepancy when trying to solve a problem with energy equation coupled. The difference between both solutions is more ore less 5%. No more.
For me, it's more than can be justified by the accuracy iteration. Maybe I am wrong.

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