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src/TurbulenceModels/incompressible/turbulentTransportModels/RAS/kkLOmega: Corrected errors in implementation and from original paper according to

Browse Source 
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.
This commit is contained in:
Henry
2015-01-27 15:06:03 +00:00
parent a9352a19ff
commit 79ec421e55
3 changed files with 158 additions and 113 deletions
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3
src/TurbulenceModels/incompressible/incompressibleTurbulenceModel.H
View File

@ -61,6 +61,9 @@ protected:
geometricOneField rho_;
// Protected member functions
//- ***HGW Temporary function to be removed when the run-time selectable
// thermal transport layer is complete
virtual void correctNut()

227
src/TurbulenceModels/incompressible/turbulentTransportModels/RAS/kkLOmega/kkLOmega.C
View File

@ -56,16 +56,16 @@ tmp<volScalarField> kkLOmega::fINT() const
(
min
(
kl_/(Cint_*(kl_ + kt_ + kMin_)),
kt_/(Cint_*(kl_ + kt_ + kMin_)),
dimensionedScalar("1.0", dimless, 1.0)
)
);
}
tmp<volScalarField> kkLOmega::fSS(const volScalarField& omega) const
tmp<volScalarField> kkLOmega::fSS(const volScalarField& Omega) const
{
return(exp(-sqr(Css_*nu()*omega/(kt_ + kMin_))));
return(exp(-sqr(Css_*nu()*Omega/(kt_ + kMin_))));
}
@ -75,16 +75,17 @@ tmp<volScalarField> kkLOmega::Cmu(const volScalarField& S) const
}
tmp<volScalarField> kkLOmega::BetaTS(const volScalarField& Rew) const
tmp<volScalarField> kkLOmega::BetaTS(const volScalarField& ReOmega) const
{
return(scalar(1) - exp(-sqr(max(Rew - CtsCrit_, scalar(0)))/Ats_));
return(scalar(1) - exp(-sqr(max(ReOmega - CtsCrit_, scalar(0)))/Ats_));
}
tmp<volScalarField> kkLOmega::fTaul
(
const volScalarField& lambdaEff,
const volScalarField& ktL
const volScalarField& ktL,
const volScalarField& Omega
) const
{
return
@ -97,7 +98,7 @@ tmp<volScalarField> kkLOmega::fTaul
(
sqr
(
lambdaEff*omega_
lambdaEff*Omega
+ dimensionedScalar
(
"ROOTVSMALL",
@ -133,8 +134,8 @@ tmp<volScalarField> kkLOmega::fOmega
scalar(1)
- exp
(
-0.41
* pow4
-0.41
*pow4
(
lambdaEff
/ (
@ -152,7 +153,7 @@ tmp<volScalarField> kkLOmega::fOmega
}
tmp<volScalarField> kkLOmega::gammaBP(const volScalarField& omega) const
tmp<volScalarField> kkLOmega::phiBP(const volScalarField& Omega) const
{
return
(
@ -162,11 +163,11 @@ tmp<volScalarField> kkLOmega::gammaBP(const volScalarField& omega) const
(
kt_/nu()
/ (
omega
Omega
+ dimensionedScalar
(
"ROTVSMALL",
omega.dimensions(),
Omega.dimensions(),
ROOTVSMALL
)
)
@ -179,7 +180,7 @@ tmp<volScalarField> kkLOmega::gammaBP(const volScalarField& omega) const
}
tmp<volScalarField> kkLOmega::gammaNAT
tmp<volScalarField> kkLOmega::phiNAT
(
const volScalarField& ReOmega,
const volScalarField& fNatCrit
@ -200,12 +201,19 @@ tmp<volScalarField> kkLOmega::gammaNAT
}
tmp<volScalarField> kkLOmega::D(const volScalarField& k) const
{
return nu()*magSqr(fvc::grad(sqrt(k)));
}
// * * * * * * * * * * * * Protected Member Functions * * * * * * * * * * * //
void kkLOmega::correctNut()
{
nut_ = kt_/omega_;
nut_.correctBoundaryConditions();
// Currently this function is not implemented due to the complexity of
// evaluating nut. Better calculate nut at the end of correct()
notImplemented("kkLOmega::correctNut()");
}
@ -490,18 +498,6 @@ kkLOmega::kkLOmega
),
mesh_
),
omega_
(
IOobject
(
IOobject::groupName("omega", U.group()),
runTime_.timeName(),
mesh_,
IOobject::MUST_READ,
IOobject::AUTO_WRITE
),
mesh_
),
kl_
(
IOobject
@ -514,17 +510,38 @@ kkLOmega::kkLOmega
),
mesh_
),
y_(wallDist::New(mesh_).y())
omega_
(
IOobject
(
IOobject::groupName("omega", U.group()),
runTime_.timeName(),
mesh_,
IOobject::MUST_READ,
IOobject::AUTO_WRITE
),
mesh_
),
epsilon_
(
IOobject
(
"epsilon",
runTime_.timeName(),
mesh_
),
kt_*omega_ + D(kl_) + D(kt_)
), y_(wallDist::New(mesh_).y())
{
bound(kt_, kMin_);
bound(kl_, kMin_);
bound(omega_, omegaMin_);
bound(epsilon_, epsilonMin_);
if (type == typeName)
{
// This is only an approximate nut, so only good for initialization
// not restart
// correctNut();
// Evaluating nut_ is complex so start from the field read from file
nut_.correctBoundaryConditions();
printCoeffs(type);
}
@ -584,22 +601,28 @@ void kkLOmega::correct()
return;
}
const volScalarField lambdaT(sqrt(kt_)/(omega_ + omegaMin_));
const volScalarField kT(kt_ + kl_);
const volScalarField lambdaT(sqrt(kT)/(omega_ + omegaMin_));
const volScalarField lambdaEff(min(Clambda_*y_, lambdaT));
const volScalarField fw
(
lambdaEff/(lambdaT + dimensionedScalar("SMALL", dimLength, ROOTVSMALL))
pow
(
lambdaEff
/(lambdaT + dimensionedScalar("SMALL", dimLength, ROOTVSMALL)),
2.0/3.0
)
);
const volTensorField gradU(fvc::grad(U_));
const volScalarField omega(sqrt(2.0)*mag(skew(gradU)));
const volScalarField S2(2.0*magSqr(symm(gradU)));
tmp<volTensorField> tgradU(fvc::grad(U_));
const volTensorField& gradU = tgradU();
const volScalarField ktS(fSS(omega)*fw*kt_);
const volScalarField Omega(sqrt(2.0)*mag(skew(gradU)));
const volScalarField S2(2.0*magSqr(dev(symm(gradU))));
const volScalarField ktS(fSS(Omega)*fw*kt_);
const volScalarField nuts
(
@ -607,20 +630,19 @@ void kkLOmega::correct()
*fINT()
*Cmu(sqrt(S2))*sqrt(ktS)*lambdaEff
);
const volScalarField Pkt(nuts*S2);
const volScalarField ktL(kt_ - ktS);
const volScalarField ReOmega(sqr(y_)*omega/nu());
const volScalarField ReOmega(sqr(y_)*Omega/nu());
const volScalarField nutl
(
min
(
C11_*fTaul(lambdaEff, ktL)*omega*sqr(lambdaEff)
* sqrt(ktL)*lambdaEff/nu()
+ C12_*BetaTS(ReOmega)*ReOmega*sqr(y_)*omega
,
0.5*(kl_ + ktL)/sqrt(S2)
C11_*fTaul(lambdaEff, ktL, Omega)*Omega*sqr(lambdaEff)
*sqrt(ktL)*lambdaEff/nu()
+ C12_*BetaTS(ReOmega)*ReOmega*sqr(y_)*Omega
,
0.5*(kl_ + ktL)/(sqrt(S2) + omegaMin_)
)
);
@ -637,60 +659,18 @@ void kkLOmega::correct()
const volScalarField Rbp
(
CR_*(1.0 - exp(-gammaBP(omega)()/Abp_))*omega_
/ (fw + fwMin)
CR_*(1.0 - exp(-phiBP(Omega)()/Abp_))*omega_
/(fw + fwMin)
);
const volScalarField fNatCrit(1.0 - exp(-Cnc_*sqrt(kl_)*y_/nu()));
// Natural source term divided by kl_
const volScalarField Rnat
(
CrNat_*(1.0 - exp(-gammaNAT(ReOmega, fNatCrit)/Anat_))*omega
CrNat_*(1.0 - exp(-phiNAT(ReOmega, fNatCrit)/Anat_))*Omega
);
const volScalarField Dt(nu()*magSqr(fvc::grad(sqrt(kt_))));
// Turbulent kinetic energy equation
tmp<fvScalarMatrix> ktEqn
(
fvm::ddt(kt_)
+ fvm::div(phi_, kt_)
- fvm::laplacian(DkEff(alphaTEff), kt_, "laplacian(alphaTEff,kt)")
==
Pkt
+ (Rbp + Rnat)*kl_
- Dt
- fvm::Sp(omega_, kt_)
);
ktEqn().relax();
ktEqn().boundaryManipulate(kt_.boundaryField());
solve(ktEqn);
bound(kt_, kMin_);
const volScalarField Dl(nu()*magSqr(fvc::grad(sqrt(kl_))));
// Laminar kinetic energy equation
tmp<fvScalarMatrix> klEqn
(
fvm::ddt(kl_)
+ fvm::div(phi_, kl_)
- fvm::laplacian(nu(), kl_, "laplacian(nu,kl)")
==
Pkl
- fvm::Sp(Rbp, kl_)
- fvm::Sp(Rnat, kl_)
- Dl
);
klEqn().relax();
klEqn().boundaryManipulate(kl_.boundaryField());
solve(klEqn);
bound(kl_, kMin_);
omega_.boundaryField().updateCoeffs();
@ -699,33 +679,74 @@ void kkLOmega::correct()
(
fvm::ddt(omega_)
+ fvm::div(phi_, omega_)
- fvm::laplacian
(
DomegaEff(alphaTEff),
omega_,
"laplacian(alphaTEff,omega)"
)
- fvm::laplacian(DomegaEff(alphaTEff), omega_)
==
Cw1_*Pkt*omega_/(kt_ + kMin_)
+ fvm::SuSp
- fvm::SuSp
(
(CwR_/(fw + fwMin) - 1.0)*kl_*(Rbp + Rnat)/(kt_ + kMin_)
(1.0 - CwR_/(fw + fwMin))*kl_*(Rbp + Rnat)/(kt_ + kMin_)
, omega_
)
- fvm::Sp(Cw2_*omega_, omega_)
- fvm::Sp(Cw2_*sqr(fw)*omega_, omega_)
+ (
Cw3_*fOmega(lambdaEff, lambdaT)*alphaTEff*sqr(fw)*sqrt(kt_)
)().dimensionedInternalField()/pow3(y_.dimensionedInternalField())
);
omegaEqn().relax();
omegaEqn().boundaryManipulate(omega_.boundaryField());
solve(omegaEqn);
bound(omega_, omegaMin_);
// Re-calculate viscosity
const volScalarField Dl(D(kl_));
// Laminar kinetic energy equation
tmp<fvScalarMatrix> klEqn
(
fvm::ddt(kl_)
+ fvm::div(phi_, kl_)
- fvm::laplacian(nu(), kl_)
==
Pkl
- fvm::Sp(Rbp + Rnat + Dl/(kl_ + kMin_), kl_)
);
klEqn().relax();
klEqn().boundaryManipulate(kl_.boundaryField());
solve(klEqn);
bound(kl_, kMin_);
const volScalarField Dt(D(kt_));
// Turbulent kinetic energy equation
tmp<fvScalarMatrix> ktEqn
(
fvm::ddt(kt_)
+ fvm::div(phi_, kt_)
- fvm::laplacian(DkEff(alphaTEff), kt_)
==
Pkt
+ (Rbp + Rnat)*kl_
- fvm::Sp(omega_ + Dt/(kt_+ kMin_), kt_)
);
ktEqn().relax();
ktEqn().boundaryManipulate(kt_.boundaryField());
solve(ktEqn);
bound(kt_, kMin_);
// Update total fluctuation kinetic energy dissipation rate
epsilon_ = kt_*omega_ + Dl + Dt;
bound(epsilon_, epsilonMin_);
// Re-calculate turbulent viscosity
nut_ = nuts + nutl;
nut_.correctBoundaryConditions();
}

41
src/TurbulenceModels/incompressible/turbulentTransportModels/RAS/kkLOmega/kkLOmega.H
View File

@ -31,7 +31,7 @@ Description
Low Reynolds-number k-kl-omega turbulence model for
incompressible flows.
Turbulence model described in:
This turbulence model is described in:
\verbatim
Walters, D. K., & Cokljat, D. (2008).
A three-equation eddy-viscosity model for Reynolds-averaged
@ -39,6 +39,17 @@ Description
Journal of Fluids Engineering, 130(12), 121401.
\endverbatim
however the paper contains several errors which must be corrected for the
model to operation correctly as explained in
\verbatim
Furst, J. (2013).
Numerical simulation of transitional flows with laminar kinetic energy.
Engineering MECHANICS, 20(5), 379-388.
\endverbatim
All these corrections and updates are included in this implementation.
The default model coefficients are
\verbatim
kkLOmegaCoeffs
@ -116,7 +127,8 @@ class kkLOmega
tmp<volScalarField> fTaul
(
const volScalarField& lambdaEff,
const volScalarField& ktL
const volScalarField& ktL,
const volScalarField& omega
) const;
tmp<volScalarField> alphaT
@ -132,14 +144,16 @@ class kkLOmega
const volScalarField& lambdaT
) const;
tmp<volScalarField> gammaBP(const volScalarField& omega) const;
tmp<volScalarField> phiBP(const volScalarField& omega) const;
tmp<volScalarField> gammaNAT
tmp<volScalarField> phiNAT
(
const volScalarField& ReOmega,
const volScalarField& fNatCrit
) const;
tmp<volScalarField> D(const volScalarField& k) const;
protected:
@ -179,8 +193,9 @@ protected:
// Fields
volScalarField kt_;
volScalarField omega_;
volScalarField kl_;
volScalarField omega_;
volScalarField epsilon_;
//- Wall distance
// Note: different to wall distance in parent RASModel
@ -250,7 +265,7 @@ public:
}
//- Return the turbulence kinetic energy
virtual tmp<volScalarField> k() const
virtual tmp<volScalarField> kt() const
{
return kt_;
}
@ -261,8 +276,8 @@ public:
return omega_;
}
//- Return the turbulence kinetic energy dissipation rate
virtual tmp<volScalarField> epsilon() const
//- Return the total fluctuation kinetic energy
virtual tmp<volScalarField> k() const
{
return tmp<volScalarField>
(
@ -270,16 +285,22 @@ public:
(
IOobject
(
"epsilon",
"k",
mesh_.time().timeName(),
mesh_
),
kt_*omega_,
kt_ + kl_,
omega_.boundaryField().types()
)
);
}
//- Return the total fluctuation kinetic energy dissipation rate
virtual tmp<volScalarField> epsilon() const
{
return epsilon_;
}
//- Solve the turbulence equations and correct the turbulence viscosity
virtual void correct();
};