# Enthalpy equation for multicomponent mixtures

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 September 16, 2009, 05:11 Enthalpy equation for multicomponent mixtures #1 New Member   Alberto Cuoci Join Date: Aug 2009 Posts: 3 Rep Power: 9 Hello everybody, 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::div(phi, h) - fvm::Sp(fvc::div(phi), h) - fvm::laplacian(turbulence->alphaEff(), h) == fvc::div(phi/fvc::interpolate(rho)*fvc::interpolate(p, "div(U,p)")) - p*fvc::div(phi/fvc::interpolate(rho)) 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: div(p*phi/rho)-p*div(phi/rho) I expected just the first term: div(p*phi/rho) 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. Alberto

 October 8, 2009, 10:59 #2 New Member   Dominik Christ Join Date: Mar 2009 Posts: 28 Rep Power: 9 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... Regards Dominik

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