What is the equation for alphave in Smoluchowski temperature jump BC

[richardliuss]

Hi everybody, I am currently working on the Smoluchowski temperature jump BC, nonEqSmoluchowskiJumpTvMix to be specofic. However, what puzzled me is the equation in the code did not express in the same way as Dr. Daniel Espinoza did in his PhD thesis. I really wondered the expression for the variable palpha. I already found the palpha is actually the value of alphave, but I did not found the defination expression of alphave. Thank you so much!

scalarField C2
(
    pmfp*2.0*pgamma/(pgamma + 1.0)/(pmu/palpha)
  * (2.0 - accommodationCoeff_)/accommodationCoeff_
);

valueFraction() = (1.0/(1.0 + patch().deltaCoeffs()*C2));
refValue() = Twall_;
refGrad() = 0.0;

Many Thanks! Richard

[vincentcasseau]

Hi Richard, palphave is the value of the mixture (for nonEqSmoluchowskiJumpTvMix) vibro-electronic thermal diffusivity at the boundary patch (thus, p for patch).

The definition of the species vibro-electronic thermal conductivity is given in any class present in this folder: src/thermophysicalModels/strath/strathSpecie/transport/speciesTransport/ The relation between modal species thermal conductivity and modal species thermal diffusivity is given in this class: reactionThermo/mixtures/Specie2Mixture/Specie2Mixture.C

Wilke's mixing rule to derive the mixture modal thermal diffusivities is given here: https://github.com/vincentcasseau/hyStrath/blob/master/src/thermophysicalModels/strath/strathSpecie/transport/mixingRules/Wilke/WilkeMR.C

Thanks, Vincent

[richardliuss]

Greetings Dr. Vincent, Thank you for your reply. That helped me alot. As I went through the files you mentioned, it is very interesting to find that in the SutherlandEuckenTransportl.H Line 177 heat conducitvity of translational-rotational mode is defined as followed. For N2, the corresponding Prandtl number of translational-rotational mode (Pr_tr) is usually taken as a value between 0.71-0.75. However, through the code, the Pr_tr is calculated to be around 0.69, which will result in a higher heat flux. I do wonder if there is an empirical formula employed in the code.

template<class Thermo>
inline Foam::scalar Foam::SutherlandEuckenTransport<Thermo>::kappatr
(
    const scalar p,
    const scalar Tt
) const
{
    scalar Cv = this->Cv_t(p, Tt);
    if (Cv > Foam::SMALL)
    {
        return mu(p, Tt)*Cv*(1.32 + 1.77*this->R()/Cv);
    }
    else
    {
        return 0.0;
    }
}

Best regards, Richard

[vincentcasseau]

However, through the code, the Pr_tr is calculated to be around 0.69

At what temperature? This formula can be found here in OF-dev: https://github.com/OpenFOAM/OpenFOAM-dev/blob/master/src/thermophysicalModels/specie/transport/sutherland/sutherlandTransportI.H#L128-L137

[richardliuss]

Hi Dr.Vincent, Assuming the gas is N2 at 300K, R=296.7 as a constant, Cv=5/2R and Cp=7/2R. Take everything into the formula (kappa=mu(p, Tt)Cv(1.32 + 1.77this->R()/Cv)). It turned out to be kappa=muCp/Pr=5.07muR=1.44857mu7/2R=muCp/0.69. Thanks, Richard