src/turbulenceModels/incompressible/RAS/kkLOmega/kkLOmega: Corrected errors in implementation and from original paper according to
Furst, J. (2013). Numerical simulation of transitional flows with laminar kinetic energy. Engineering MECHANICS, 20(5), 379-388. Thanks to Jan-Niklas Klatt for analysing problems with and correcting the implementation and testing corrections to the model proposed by Furst.
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2 changed files with 128 additions and 88 deletions
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@ -2,7 +2,7 @@
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | Copyright (C) 2011-2012 OpenFOAM Foundation
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\\ / A nd | Copyright (C) 2011-2015 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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@ -56,7 +56,7 @@ tmp<volScalarField> kkLOmega::fINT() const
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(
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min
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(
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kl_/(Cint_*(kl_ + kt_ + kMin_)),
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kt_/(Cint_*(kl_ + kt_ + kMin_)),
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dimensionedScalar("1.0", dimless, 1.0)
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)
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);
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@ -75,16 +75,17 @@ tmp<volScalarField> kkLOmega::Cmu(const volScalarField& S) const
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}
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tmp<volScalarField> kkLOmega::BetaTS(const volScalarField& Rew) const
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tmp<volScalarField> kkLOmega::BetaTS(const volScalarField& ReOmega) const
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{
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return(scalar(1) - exp(-sqr(max(Rew - CtsCrit_, scalar(0)))/Ats_));
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return(scalar(1) - exp(-sqr(max(ReOmega - CtsCrit_, scalar(0)))/Ats_));
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}
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tmp<volScalarField> kkLOmega::fTaul
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(
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const volScalarField& lambdaEff,
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const volScalarField& ktL
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const volScalarField& ktL,
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const volScalarField& omega
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) const
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{
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return
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@ -97,7 +98,7 @@ tmp<volScalarField> kkLOmega::fTaul
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(
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sqr
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(
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lambdaEff*omega_
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lambdaEff*omega
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+ dimensionedScalar
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(
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"ROOTVSMALL",
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@ -133,8 +134,8 @@ tmp<volScalarField> kkLOmega::fOmega
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scalar(1)
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- exp
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(
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-0.41
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* pow4
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-0.41
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*pow4
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(
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lambdaEff
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/ (
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@ -152,7 +153,7 @@ tmp<volScalarField> kkLOmega::fOmega
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}
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tmp<volScalarField> kkLOmega::gammaBP(const volScalarField& omega) const
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tmp<volScalarField> kkLOmega::phiBP(const volScalarField& omega) const
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{
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return
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(
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@ -179,7 +180,7 @@ tmp<volScalarField> kkLOmega::gammaBP(const volScalarField& omega) const
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}
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tmp<volScalarField> kkLOmega::gammaNAT
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tmp<volScalarField> kkLOmega::phiNAT
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(
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const volScalarField& ReOmega,
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const volScalarField& fNatCrit
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@ -533,7 +534,7 @@ tmp<volSymmTensorField> kkLOmega::R() const
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IOobject::NO_READ,
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IOobject::NO_WRITE
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),
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((2.0/3.0)*I)*(kt_) - nut_*twoSymm(fvc::grad(U_)),
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((2.0/3.0)*I)*(kt_ + kl_) - nut_*twoSymm(fvc::grad(U_)),
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kt_.boundaryField().types()
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)
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);
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@ -643,16 +644,18 @@ void kkLOmega::correct()
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y_.boundaryField() = max(y_.boundaryField(), VSMALL);
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}
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const volScalarField kT(kt_ + kl_);
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const volScalarField lambdaT(sqrt(kT)/(omega_ + omegaMin_));
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const volScalarField lambdaT(sqrt(kt_)/(omega_ + omegaMin_));
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const volScalarField lambdaEff(min(Clambda_*y_, lambdaT));
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const volScalarField fw
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(
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lambdaEff/(lambdaT + dimensionedScalar("SMALL", dimLength, ROOTVSMALL))
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pow
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(
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lambdaEff
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/(lambdaT + dimensionedScalar("SMALL", dimLength, ROOTVSMALL)),
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2.0/3.0
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)
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);
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const volTensorField gradU(fvc::grad(U_));
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@ -665,7 +668,10 @@ void kkLOmega::correct()
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const volScalarField nuts
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(
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fv(sqr(fw)*kt_/nu()/(omega_ + omegaMin_))
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fv
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(
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sqr(fw)*kt_/nu()/(omega_ + omegaMin_)
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)
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*fINT()
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*Cmu(sqrt(S2))*sqrt(ktS)*lambdaEff
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);
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@ -677,8 +683,8 @@ void kkLOmega::correct()
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(
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min
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(
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C11_*fTaul(lambdaEff, ktL)*omega*sqr(lambdaEff)
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* sqrt(ktL)*lambdaEff/nu()
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C11_*fTaul(lambdaEff, ktL, omega)*omega*sqr(lambdaEff)
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*sqrt(ktL)*lambdaEff/nu()
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+ C12_*BetaTS(ReOmega)*ReOmega*sqr(y_)*omega
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,
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0.5*(kl_ + ktL)/sqrt(S2)
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@ -698,17 +704,69 @@ void kkLOmega::correct()
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const volScalarField Rbp
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(
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CR_*(1.0 - exp(-gammaBP(omega)()/Abp_))*omega_
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/ (fw + fwMin)
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CR_*(1.0 - exp(-phiBP(omega)()/Abp_))*omega_
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/(fw + fwMin)
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);
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const volScalarField fNatCrit(1.0 - exp(-Cnc_*sqrt(kl_)*y_/nu()));
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// Natural source term divided by kl_
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const volScalarField Rnat
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(
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CrNat_*(1.0 - exp(-gammaNAT(ReOmega, fNatCrit)/Anat_))*omega
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CrNat_*(1.0 - exp(-phiNAT(ReOmega, fNatCrit)/Anat_))*omega
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);
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omega_.boundaryField().updateCoeffs();
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// Turbulence specific dissipation rate equation
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tmp<fvScalarMatrix> omegaEqn
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(
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fvm::ddt(omega_)
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+ fvm::div(phi_, omega_)
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- fvm::laplacian(DomegaEff(alphaTEff), omega_)
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==
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Cw1_*Pkt*omega_/(kt_ + kMin_)
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+ fvm::SuSp
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(
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(CwR_/(fw + fwMin) - 1.0)*kl_*(Rbp + Rnat)/(kt_ + kMin_)
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, omega_
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)
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- fvm::Sp(Cw2_*sqr(fw)*omega_, omega_)
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+ (
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Cw3_*fOmega(lambdaEff, lambdaT)*alphaTEff*sqr(fw)*sqrt(kt_)
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)().dimensionedInternalField()/pow3(y_.dimensionedInternalField())
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);
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omegaEqn().relax();
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omegaEqn().boundaryManipulate(omega_.boundaryField());
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solve(omegaEqn);
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bound(omega_, omegaMin_);
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const volScalarField Dl(nu()*magSqr(fvc::grad(sqrt(kl_))));
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// Laminar kinetic energy equation
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tmp<fvScalarMatrix> klEqn
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(
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fvm::ddt(kl_)
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+ fvm::div(phi_, kl_)
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- fvm::laplacian(nu(), kl_)
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==
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Pkl
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- fvm::Sp(Rbp, kl_)
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- fvm::Sp(Rnat, kl_)
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- fvm::Sp(Dl/max(kl_, kMin_), kl_)
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);
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klEqn().relax();
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klEqn().boundaryManipulate(kl_.boundaryField());
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solve(klEqn);
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bound(kl_, kMin_);
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const volScalarField Dt(nu()*magSqr(fvc::grad(sqrt(kt_))));
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// Turbulent kinetic energy equation
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@ -716,11 +774,11 @@ void kkLOmega::correct()
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(
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fvm::ddt(kt_)
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+ fvm::div(phi_, kt_)
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- fvm::laplacian(DkEff(alphaTEff), kt_, "laplacian(alphaTEff,kt)")
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- fvm::laplacian(DkEff(alphaTEff), kt_)
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==
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Pkt
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+ (Rbp + Rnat)*kl_
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- Dt
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- fvm::Sp(Dt/max(kt_, kMin_), kt_)
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- fvm::Sp(omega_, kt_)
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);
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@ -731,59 +789,7 @@ void kkLOmega::correct()
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bound(kt_, kMin_);
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const volScalarField Dl(nu()*magSqr(fvc::grad(sqrt(kl_))));
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// Laminar kinetic energy equation
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tmp<fvScalarMatrix> klEqn
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(
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fvm::ddt(kl_)
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+ fvm::div(phi_, kl_)
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- fvm::laplacian(nu(), kl_, "laplacian(nu,kl)")
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==
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Pkl
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- fvm::Sp(Rbp, kl_)
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- fvm::Sp(Rnat, kl_)
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- Dl
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);
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klEqn().relax();
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klEqn().boundaryManipulate(kl_.boundaryField());
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solve(klEqn);
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bound(kl_, kMin_);
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omega_.boundaryField().updateCoeffs();
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// Turbulence specific dissipation rate equation
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tmp<fvScalarMatrix> omegaEqn
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(
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fvm::ddt(omega_)
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+ fvm::div(phi_, omega_)
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- fvm::laplacian
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(
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DomegaEff(alphaTEff),
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omega_,
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"laplacian(alphaTEff,omega)"
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)
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==
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Cw1_*Pkt*omega_/(kt_ + kMin_)
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+ fvm::SuSp
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(
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(CwR_/(fw + fwMin) - 1.0)*kl_*(Rbp + Rnat)/(kt_ + kMin_)
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, omega_
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)
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- fvm::Sp(Cw2_*omega_, omega_)
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+ Cw3_*fOmega(lambdaEff, lambdaT)*alphaTEff*sqr(fw)*sqrt(kt_)/pow3(y_)
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);
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omegaEqn().relax();
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omegaEqn().boundaryManipulate(omega_.boundaryField());
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solve(omegaEqn);
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bound(omega_, omegaMin_);
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// Re-calculate viscosity
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// Re-calculate turbulent viscosity
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nut_ = nuts + nutl;
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nut_.correctBoundaryConditions();
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}
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@ -2,7 +2,7 @@
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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||||
\\ / O peration |
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\\ / A nd | Copyright (C) 2011-2012 OpenFOAM Foundation
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\\ / A nd | Copyright (C) 2011-2015 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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@ -31,14 +31,26 @@ Description
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Low Reynolds-number k-kl-omega turbulence model for
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incompressible flows.
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Turbulence model described in:
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This turbulence model is described in:
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\verbatim
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D. Keith Walters, Davor Cokljat
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"A Three-Equation Eddy-Viscosity Model for Reynold-Averaged
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Navier-Stokes Simulations of Transitional Flow"
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Walters, D. K., & Cokljat, D. (2008).
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A three-equation eddy-viscosity model for Reynolds-averaged
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Navier–Stokes simulations of transitional flow.
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Journal of Fluids Engineering, 130(12), 121401.
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\endverbatim
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The default model coefficients correspond to the following:
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however the paper contains several errors which must be corrected for the
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model to operation correctly as explained in
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\verbatim
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Furst, J. (2013).
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Numerical simulation of transitional flows with laminar kinetic energy.
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Engineering MECHANICS, 20(5), 379-388.
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\endverbatim
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All these corrections and updates are included in this implementation.
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The default model coefficients are
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\verbatim
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kkLOmegaCoeffs
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{
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@ -110,12 +122,13 @@ class kkLOmega
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tmp<volScalarField> Cmu(const volScalarField& S) const;
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tmp<volScalarField> BetaTS(const volScalarField& Rew) const;
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tmp<volScalarField> BetaTS(const volScalarField& ReOmega) const;
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tmp<volScalarField> fTaul
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(
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const volScalarField& lambdaEff,
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const volScalarField& ktL
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const volScalarField& ktL,
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const volScalarField& omega
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) const;
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tmp<volScalarField> alphaT
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@ -131,9 +144,9 @@ class kkLOmega
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const volScalarField& lambdaT
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) const;
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tmp<volScalarField> gammaBP(const volScalarField& omega) const;
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tmp<volScalarField> phiBP(const volScalarField& omega) const;
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tmp<volScalarField> gammaNAT
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tmp<volScalarField> phiNAT
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(
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const volScalarField& ReOmega,
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const volScalarField& fNatCrit
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@ -181,6 +194,8 @@ protected:
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volScalarField omega_;
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volScalarField kl_;
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volScalarField nut_;
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//- Wall distance
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wallDist y_;
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@ -240,11 +255,30 @@ public:
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}
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//- Return the turbulence kinetic energy
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virtual tmp<volScalarField> k() const
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virtual tmp<volScalarField> kt() const
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{
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return kt_;
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}
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//- Return the total fluctuation kinetic energy
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virtual tmp<volScalarField> k() const
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{
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return tmp<volScalarField>
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(
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new volScalarField
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(
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IOobject
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(
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"k",
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mesh_.time().timeName(),
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mesh_
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),
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kt_ + kl_,
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omega_.boundaryField().types()
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)
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);
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}
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//- Return the turbulence specific dissipation rate
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virtual tmp<volScalarField> omega() const
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{
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