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Old   July 14, 2012, 20:25
Default A question about UEqn sonicFoam
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Luis Felipe Gutierrez Marcantoni
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Hi, I have a question about the UEqn implemented into sonicFoam, the code of the UEqn is:

Code:
fvVectorMatrix UEqn
(
    fvm::ddt(rho, U)
    + fvm::div(phi, U)
    + turbulence->divDevRhoReff(U)
);
My question is about the term that is computed from the turbulence model, i.e if K-epsilon model is selected, this term results:

Code:
tmp<fvVectorMatrix> kEpsilon::divDevRhoReff(volVectorField& U) const
{
    return
    (
      - fvm::laplacian(muEff(), U)
      - fvc::div(muEff()*dev2(fvc::grad(U)().T()))
    );
}
Initially I thought that it corresponded to

\nabla \cdot \left( \widetilde{\tau}-\bar{\rho}\widetilde{u^{''}u^{''}} \right) =
2\mu\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) 
+\left( 2\mu_{t}\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) -
\frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I}
\right) (1)

but after examining the definition of dev2 in src/OpenFOAM/primitives/Tensor/TensorI.H

I found the following:

dev2(u)=u-\frac{2}{3}tr\left(u\right)

S is the rate-of-strain tensor given by

S=\frac{1}{2}\left(\nabla u + \left(\nabla u \right)^\mathrm{T} \right)

but according to the definition of DivDevRhoReff

divDevRhoReff = -\nabla^{2}\left(\mu_{eff} U\right)
-\nabla \cdot \left( dev2 \left(\mu_{eff}\left(\nabla U \right)^{\mathrm{T}}\right)\right)

And manipulating the expression (1) I conclude that the term

Code:
     + turbulence->divDevRhoReff(U)
does not correspond to (1).

If someone can help me with my confusion about this term, I was very thankful
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Felipe G

Last edited by lfgmarc; July 15, 2012 at 14:34.
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Old   January 24, 2013, 13:26
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Quote:
Originally Posted by lfgmarc View Post
Hi, I have a question about the UEqn implemented into sonicFoam, the code of the UEqn is:

Code:
fvVectorMatrix UEqn
(
    fvm::ddt(rho, U)
    + fvm::div(phi, U)
    + turbulence->divDevRhoReff(U)
);
My question is about the term that is computed from the turbulence model, i.e if K-epsilon model is selected, this term results:

Code:
tmp<fvVectorMatrix> kEpsilon::divDevRhoReff(volVectorField& U) const
{
    return
    (
      - fvm::laplacian(muEff(), U)
      - fvc::div(muEff()*dev2(fvc::grad(U)().T()))
    );
}
Initially I thought that it corresponded to

\nabla \cdot \left( \widetilde{\tau}-\bar{\rho}\widetilde{u^{''}u^{''}} \right) =
2\mu\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) 
+\left( 2\mu_{t}\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) -
\frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I}
\right) (1)

but after examining the definition of dev2 in src/OpenFOAM/primitives/Tensor/TensorI.H

I found the following:

dev2(u)=u-\frac{2}{3}tr\left(u\right)

S is the rate-of-strain tensor given by

S=\frac{1}{2}\left(\nabla u + \left(\nabla u \right)^\mathrm{T} \right)

but according to the definition of DivDevRhoReff

divDevRhoReff = -\nabla^{2}\left(\mu_{eff} U\right)
-\nabla \cdot \left( dev2 \left(\mu_{eff}\left(\nabla U \right)^{\mathrm{T}}\right)\right)

And manipulating the expression (1) I conclude that the term

Code:
     + turbulence->divDevRhoReff(U)
does not correspond to (1).

If someone can help me with my confusion about this term, I was very thankful
Indeed, I was thinking it should be dev instead of dev2 as well if the explanation by poplar in Calculating divDevReff is correct.

I hope I can find out what is wrong.
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Old   February 15, 2013, 10:07
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Jens Klostermann
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Hi,

the term

\nabla\cdot\left[2\mu\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) 
+\left( 2\mu_{t}\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right)
\right)\right]
is equal to
divDevRhoReff = -\nabla \cdot \left(\mu_{eff} \nabla U\right)
-\nabla \cdot \left( dev2 \left(\mu_{eff}\left(\nabla U \right)^{\mathrm{T}}\right)\right)


But I miss the term
\left(-
\frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I}
\right)

in
Code:
turbulence->divDevRhoReff(U)
maybe someone can comment on this hidden term?

Jens
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Old   June 14, 2013, 15:36
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Sasan Ghomi
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Hi jens
Did you find this term ? I have a similar problem .
\left(-
\frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I}
\right)

Thanks
Sasan.
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Old   June 17, 2013, 09:57
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Jens Klostermann
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No, I didn't habe time to work further on this problem.
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Old   December 24, 2014, 16:48
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Dongyue Li
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Quote:
Originally Posted by jens_klostermann View Post
No, I didn't habe time to work further on this problem.
I found a similar thing on this: sqr(Ct)*k is missing in twoPhaseEulerFoam 2.2.x?
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Old   February 1, 2015, 17:49
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Panagiotis Giannatselis
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Reading Calculating divDevReff I concluded that this term is zero if the fluid is incompressible and near convergence it doesn't concern us. The term remains for stability reasons when we are still far from the solution. If somebody more experienced confirms my thinking, the problem is solved.

I don't feel able to tell you that my point is 100% correct.
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