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Different momentum equation in different versions of settlingFoam

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Old   April 15, 2015, 14:09
Default Different momentum equation in different versions of settlingFoam
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Shenan
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The momentum equation for settlingFoam is different in OpenFOAM 2.2.1 and FOAM-extend 3.1. The term
Code:
-(fvc::grad(U) & fvc::grad(muEff))
is missing in FE 3.1.

In OF 2.2, the momentum equation is:

Code:
fvVectorMatrix UEqn
(
    fvm::ddt(rho, U)
  + fvm::div(phi, U)
  + fvc::div
    (
        (Alpha/(scalar(1.001) - Alpha))*(sqr(rhoc)/rho)*Vdj*Vdj,
        "div(phiVdj,Vdj)"
    )
  - fvm::laplacian(muEff, U, "laplacian(muEff,U)")
  - (fvc::grad(U) & fvc::grad(muEff))
);
In FE 3.1, the momentum equation is:

Code:
fvVectorMatrix UEqn
(
    fvm::ddt(rho, U)
  + fvm::div(phi, U)
  + fvc::div
    (
        (Alpha/(scalar(1.001) - Alpha))*(sqr(rhoc)/rho)*Vdj*Vdj,
        "div(phiVdj,Vdj)"
    )
  - fvm::laplacian(mu, U, "laplacian(muEff,U)")
);
The equations are based on the mixture momentum equation in Dan Brennan's thesis (2001, p86). Are both equations correct?

In OF 2.3.1, settlingFoam has been replaced with driftFluxFoam. Its momentum equation is:

Code:
fvVectorMatrix UEqn
(
    fvm::ddt(rho, U)
  + fvm::div(rhoPhi, U)
  + fvc::div(UdmModel.tauDm())
  + turbulence->divDevRhoReff(U)
 ==
    fvOptions(rho, U)
);
divDevRhoReff is defined in kEpsilon.C as:

Code:
tmp<fvVectorMatrix> kEpsilon::divDevRhoReff
(
    const volScalarField& rho,
    volVectorField& U
) const
{
    volScalarField muEff("muEff", rho*nuEff());

    return
    (
      - fvm::laplacian(muEff, U)
      - fvc::div(muEff*dev(T(fvc::grad(U))))
    );
}
Hence, in OF 2.* there appears to be a connection between:
Code:
- fvm::laplacian(muEff, U, "laplacian(muEff,U)") 
- (fvc::grad(U) & fvc::grad(muEff))
and
Code:
turbulence->divDevRhoReff(U)
.

If so, please can you tell me the relationship between
Code:
(fvc::grad(U) & fvc::grad(muEff))
and
Code:
fvc::div(muEff*dev(T(fvc::grad(U))))
?

Thank you.

Last edited by Shenan; April 15, 2015 at 14:15. Reason: ease of reading code
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drift flux model, settlingfoam


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