Enthalpy equation for multicomponent mixtures
I would like to write a laminar, steady-state solver for multicomponent, reacting mixtures. I have some questions about the enthalpy equation which is used in several solvers for multicomponent mixtures (in steady state conditions, SIMPLE algorithm):
- fvm::Sp(fvc::div(phi), h)
- fvm::laplacian(turbulence->alphaEff(), h)
1. Thermal diffusivity
In laminar conditions the turbulence->alphaEff() term should become k/Cp (where k is the thermal conductivity). Is it correct?
2. Pressure term
I cannot understand why the term associated to the pressure is written as:
I expected just the first term:
3. Temperature gradient
In the enthalpy equation the div(k grad(T)) term is written as laplacian(k/Cp grad(h)) since grad(h)=Cp grad(T) .
However for multicomponent mixtures we have:
grad(h)=Cp grad(T) + sum h_i grad(Y_i)
where i is the species index and the sum is over all the species.Therefore:
grad(T) = 1/Cp ( grad(h) - sum h_i grad(Y_i) )
So, I expected this term in the enthalpy equation:
- fvm::laplacian(k/Cp, h - sum ( h_i grad(Y_i) ) )
Thank you very much.
Concerning your second point:
Isn't basically phi=rho*U at the faces?
Then I would understand to be phi/rho = U at the faces.
Then p*div(phi/rho) = p* div(U) which would be the effect of compression...
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