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lfgmarc October 25, 2011 10:57

HsEqn ReactingFoam Hypothesis?
Hi, I'm a little confuse with the assumptions under HsEqn implemented in reactingFoam, the energy equation in terms of the sensible enthalpy, can be written as:

\dfrac{D}{Dt}\left(\bar{\rho}\widetilde{h_{s}}\right)=\overline{\dfrac{DP}{Dt}}+\dfrac{\partial}{\partial x_{i}}\left(\overline{\lambda\dfrac{\partial T}{\partial x_{i}}}-\rho u_{i}^{''}h_{s}^{''}\right)+\overline{\tau_{ij}\dfrac{\partial u_{i}}{\partial x_{j}}}-\dfrac{\partial}{\partial x_{i}}\left(\overline{\rho{\displaystyle \sum V_{k,i}Y_{k}h_{s,k}}}\right)+\overline{\dot{W}_{T}}

My confusion is with two terms:

1. the term associated with the species diffusion:

\dfrac{\partial}{\partial x_{i}}\left(\overline{\rho{\displaystyle \sum V_{k,i}Y_{k}h_{s,k}}}\right)

2, the term associated with the energy dissipation by viscous effects:

\overline{\tau_{ij}\dfrac{\partial u_{i}}{\partial x_{j}}}

The implementation of this equation in reactingFoam is:


    fvm::ddt(rho, hs)
      + mvConvection->fvmDiv(phi, hs)
      - fvm::laplacian(turbulence->alphaEff(), hs)
//      - fvm::laplacian(turbulence->muEff(), hs)  // unit lewis no.
      + chemistrySh

In this implementation I see that is neglected the viscous dissipation, but I don't understand very well why? i think that may be under the hypothesis of an Brinkman number<<1?

On the other hand it is clear that the species diffusion term was neglected, but reviewed bibliography I see that this term ussually is neglected if :

a) if mixture contains only one specie

b) if all species have the same sensible enthalpy.

c) sometimes is set to zero because it is usually negligible compared with


The first assumption in this case is not suitable, I'm confused with the second one, it is applicable in this case or simply is considered the third hypothesis?

if someone could shed some light on this I'll be very grateful

Thanks in advance


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