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CFDtoy January 28, 2008 11:13

Specific heat, density evaluation in mixture eqn
 
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


Rami January 29, 2008 03:08

Re: Specific heat, density evaluation in mixture e
 
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.



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