Hello,

While solving the enthalpy eqn for mixture (multiphase flows), what is the best way to compute the mixture Cp and mixture density.

Using a linear combination

rhomix = alpha*rhol + (1-alpha)*rhog

cpmix = (alpha1*rho1*cp1+alpha2*rho2*cp2)/(rhomix)

results in a cp very very sensitive to alpha. I have problems with high temperatures since i solve enthalpy eqn and get T = h/cpmix due to this strong dependency.

is there a better stable evaluation of mixture cp,density and hence the mixture fluxes?

what could be done to avoid the dependency of cp,density on alpha ?

Thanks,

CFDtoy

I am not sure what your alpha's are. I will use mass fractions instead (which you may later convert to you alpha's, if you wish).

Let Yk be the mass fraction of the k-th species.

Using Cp's expressed in per-mass units, and assuming Cp,k is the value of the k-th species, the mixture Cp (denoted Cp,mix) is

Cp,mix = (sum on all species k of) {Cp,k*Yk}

For the mixture density (denoted rho,mix) relation to the species densities (dented rho,k), the relation is

rho,mix = 1 / [ (sum on all species k of) {Yk/rho,k} ]

The reference I used is the CHEMKIN manual. You may find similar expressions in textbooks as well.