[Shenan]

The momentum equation for settlingFoam is different in OpenFOAM 2.2.1 and FOAM-extend 3.1. The term

-(fvc::grad(U) & fvc::grad(muEff))

is missing in FE 3.1.

In OF 2.2, the momentum equation is:

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:

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:

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:

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:

- fvm::laplacian(muEff, U, "laplacian(muEff,U)") 
- (fvc::grad(U) & fvc::grad(muEff))

and

turbulence->divDevRhoReff(U)

.

If so, please can you tell me the relationship between

(fvc::grad(U) & fvc::grad(muEff))

and

fvc::div(muEff*dev(T(fvc::grad(U))))

?

Thank you.