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RNG k-epsilon model implementation

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Old   July 27, 2011, 08:52
Default RNG k-epsilon model implementation
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Roman Thiele
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Hej,

I was wondering why the implementation of the RNG k-epsilon model in OpenFOAM looks so much different from the implementation of the standard k-epsilon model? Even the k-equation looks different, even though that one should be the same.

k-equation standard k-eps:
Code:
    tmp<fvScalarMatrix> kEqn
    (
        fvm::ddt(k_)
      + fvm::div(phi_, k_)
      - fvm::Sp(fvc::div(phi_), k_) // missing from the k-equation of RNG
      - fvm::laplacian(DkEff(), k_)
     ==
        G
      - fvm::Sp(epsilon_/k_, k_)
    );
k-equation RNG k-eps
Code:
    tmp<fvScalarMatrix> kEqn
    (
        fvm::ddt(k_)
      + fvm::div(phi_, k_)
      - fvm::laplacian(DkEff(), k_)
     ==
        G 
      - fvm::Sp(epsilon_/k_, k_)
    );
The - fvm::Sp(fvc::div(phi_), k_) term is missing. The same is true in the epsilon equation, where instead of the C_eps2 constant the C_eps1 constant is changed, but also not according to literature

eps-equation RNG
Code:
    // Dissipation equation
    tmp<fvScalarMatrix> epsEqn
    (
        fvm::ddt(epsilon_)
      + fvm::div(phi_, epsilon_)
      - fvm::laplacian(DepsilonEff(), epsilon_)
    // I expect another term here
     ==
        (C1_ - R)*G*epsilon_/k_  // why is the term R, which is part of the changed C_eps2 constant subtracted from C_eps1
    //- fvm::SuSp(R*G/k_, epsilon_)
      - fvm::Sp(C2_*epsilon_/k_, epsilon_)  // C2 is a constant here, even though it should be a function of the strain-rate tensor
    );
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Old   November 23, 2011, 09:19
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Vesselin Krastev
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Quote:
Originally Posted by romant View Post
Hej,

I was wondering why the implementation of the RNG k-epsilon model in OpenFOAM looks so much different from the implementation of the standard k-epsilon model? Even the k-equation looks different, even though that one should be the same.

k-equation standard k-eps:
Code:
    tmp<fvScalarMatrix> kEqn
    (
        fvm::ddt(k_)
      + fvm::div(phi_, k_)
      - fvm::Sp(fvc::div(phi_), k_) // missing from the k-equation of RNG
      - fvm::laplacian(DkEff(), k_)
     ==
        G
      - fvm::Sp(epsilon_/k_, k_)
    );
k-equation RNG k-eps
Code:
    tmp<fvScalarMatrix> kEqn
    (
        fvm::ddt(k_)
      + fvm::div(phi_, k_)
      - fvm::laplacian(DkEff(), k_)
     ==
        G 
      - fvm::Sp(epsilon_/k_, k_)
    );
The - fvm::Sp(fvc::div(phi_), k_) term is missing. The same is true in the epsilon equation, where instead of the C_eps2 constant the C_eps1 constant is changed, but also not according to literature

eps-equation RNG
Code:
    // Dissipation equation
    tmp<fvScalarMatrix> epsEqn
    (
        fvm::ddt(epsilon_)
      + fvm::div(phi_, epsilon_)
      - fvm::laplacian(DepsilonEff(), epsilon_)
    // I expect another term here
     ==
        (C1_ - R)*G*epsilon_/k_  // why is the term R, which is part of the changed C_eps2 constant subtracted from C_eps1
    //- fvm::SuSp(R*G/k_, epsilon_)
      - fvm::Sp(C2_*epsilon_/k_, epsilon_)  // C2 is a constant here, even though it should be a function of the strain-rate tensor
    );
The implementation is perfectly consistent with the literature (see for instance "Analysis of an RNG based turbulence model for separated flows", C. G. Speziale and S. Thangam, Int. J. Engng Sci., Vol 30, no 10, pp 1379-1388, 1992). Concerning the missing terms with respect to, for instance, the standard k-epsilon model, though they should not have a significant relevance in an incompressible flow solution (fvc::div(phi) would be exactly equal to zero if the discretized momentum and pressure-correction equations were solved exactly at the current iteration, while using a finite precision it would be simply very very small), to me is also quite a mystery why they are included in some models and they aren't in others...

Best Regards

V.
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