Error or Different Meaning of alpha in eEqu and hEqu of compressible solver?
 

In compressible flow solvers, eEqu and hEqu share the same parameter "thermal diffusivity", or turbulence->alphaEff() in the following equations. However, my understanding of the meaning of thermal diffusivity should be different in these equaitons, i.e. , (for a laminar flow),

In eEqu, alpha = K / (Cv rho), where Cv, k and rho are heat capacity at constant volume, theremal conductivity and density, respectively.

while, in hEqu, alpha = k / ( Cp rho), where Cp, k and rho are heat capacity at constant pressure, theremal conductivity and density, respectively.

My questions are:

1, my understanding about alpha is right or wrong?
2, if i am right, is openFoam wrong ?, or there is specific application inside openfoam dealing with this issue?

========================================
In sonicFoam eEqu is

solve
(
fvm::ddt(rho, e)
+ fvm::div(phi, e)
- fvm::laplacian(turbulence->alphaEff(), e)
==
- p*fvc::div(phi/fvc::interpolate(rho))
);

========================================
In rhoPisoFoam hEqu is

fvScalarMatrix hEqn
(
fvm::ddt(rho, h)
+ fvm::div(phi, h)
- fvm::laplacian(turbulence->alphaEff(), h)
==
DpDt
);

compare with rhoFurbFoam
 

Hi yu
you are not wrong in understanding but you have compare similar solvers like rhoTurbFoam in 1.5 and sonicFoam in 1.6.

iam working on both the slovers and i feel both are same (Unsteady Turbulent compressible solvers).

try to analyze with rhoTurbFoam that will clear your doubt.