CFD Online Discussion Forums - Prandtl number in compressible laminar boundary layer

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Prandtl number in compressible laminar boundary layer

Hi everybody:
I want to simulate the compressible flow over a flat plate in FLUENT setting the Prandtl number of the air as 1. So, using the equation $\kappa$ = $\mu$ *Cp/Pr, with
$\kappa$ = Thermal Conductivity
Cp= Specific Heat
$\mu$ = Dynamic Viscosity

In order to do that I'm trying to use a variable $\kappa$ using a UDF:

Code:

#include "udf.h"

DEFINE_PROPERTY(thermal_conductivity,c,t)

{

real k_air;       

real tempt = C_T(c,t);

/*Using the Sutherland's law for viscosity*/

k_air= pow(1.716E-5*(273.11+110.56)/(tempt+110.56)*(tempt/273.11),1.5)*1006.43;

return k_air;

}

but the problem I'm facing is I can't get the solution converged. If I use, $\kappa$ constant I can make my solution converge, but with the approach I'm trying to implement now, don't. Can someone help me? Is the approach I'm using correct? Thanks. Regards
Gonzalo
PS: If someone wants the solution settings I'm using, please ask me for that. But first, I want to know if I'm doing things well with my UDF.

I found an error in the thermal conductivity formula, instead of:

Code:

k_air= pow(1.716E-5*(273.11+110.56)/(tempt+110.56)*(tempt/273.11),1.5)*1006.43;

must be:

Code:

k_air= 1.716E-5*(273.11+110.56)/(tempt+110.56)*pow((tempt/273.11),1.5)*1006.43;

I'm looking forward for better results, I'll tell you if I can get them. Regards
Gonzalo