void Foam::DCPP::correct()
{
// Velocity gradient tensor
volTensorField L = fvc::grad(U());
// Upper convected derivate term
volTensorField Cupper = S_ & L;
// Lower convected derivate term
volTensorField Clower = L & S_;
// Twice the rate of deformation tensor
volSymmTensorField twoD = twoSymm(L);
// Evolution of orientation
fvSymmTensorMatrix SEqn
(
fvm::ddt(S_)
+ fvm::div(phi(), S_)
==
(1 - zeta_/2)*twoSymm(Cupper)
- (zeta_/2)*twoSymm(Clower)
- (1 - zeta_)*fvm::Sp((twoD && S_), S_)
- fvm::Sp(1/lambdaOb_/Foam::sqr(Lambda_), S_)
+ 1/lambdaOb_/Foam::sqr(Lambda_)/3*I_
);
SEqn.relax();
SEqn.solve();
// Evolution of the backbone stretch
fvScalarMatrix lambdaEqn
(
fvm::ddt(Lambda_)
+ fvm::div(phi(), Lambda_)
==
fvm::Sp((twoD && S_)/2 , Lambda_)
- fvm::Sp(Foam::exp(2/q_*(Lambda_ - 1))/lambdaOs_ , Lambda_)
+ Foam::exp( 2/q_*(Lambda_ - 1))/lambdaOs_
);
lambdaEqn.relax();
lambdaEqn.solve();
// Viscoelastic stress
tau_ = etaP_/lambdaOb_/(1 - zeta_) * (3*Foam::sqr(Lambda_)*S_ - I_);
}
void thixotropicViscosity::correct
(
const volScalarField& p,
const volScalarField& T
)
{
const kinematicSingleLayer& film = filmType<kinematicSingleLayer>();
// references to film fields
const volVectorField& U = film.U();
const volVectorField& Uw = film.Uw();
const volScalarField& delta = film.delta();
const volScalarField& deltaRho = film.deltaRho();
const surfaceScalarField& phi = film.phi();
// gamma-dot (shear rate) raised to the power d
volScalarField gDotPowD
(
"gDotPowD",
pow(mag(U - Uw)/(delta + film.deltaSmall()), d_)
);
dimensionedScalar c0("SMALL", dimMass/sqr(dimLength)/dimTime, SMALL);
volScalarField coeff(-deltaRho*c_*gDotPowD + c0);
fvScalarMatrix lambdaEqn
(
fvm::ddt(deltaRho, lambda_)
+ fvm::div(phi, lambda_)
- fvm::Sp(fvc::div(phi), lambda_)
==
deltaRho*a_*pow((1.0 - lambda_), b_)
+ fvm::SuSp(coeff, lambda_)
);
lambdaEqn.relax();
lambdaEqn.solve();
lambda_.min(1.0);
lambda_.max(0.0);
updateMu();
}
void thixotropicViscosity::correct
(
const volScalarField& p,
const volScalarField& T
)
{
const kinematicSingleLayer& film = filmType<kinematicSingleLayer>();
const volVectorField& U = film.U();
const volVectorField& Uw = film.Uw();
const volScalarField& delta = film.delta();
const volScalarField& deltaRho = film.deltaRho();
const surfaceScalarField& phi = film.phi();
const volScalarField& alpha = film.alpha();
const Time& runTime = this->film().regionMesh().time();
// Shear rate
const volScalarField gDot
(
"gDot",
alpha*mag(U - Uw)/(delta + film.deltaSmall())
);
if (debug && runTime.writeTime())
{
gDot.write();
}
const dimensionedScalar deltaRho0
(
"deltaRho0",
deltaRho.dimensions(),
rootVSmall
);
const surfaceScalarField phiU(phi/fvc::interpolate(deltaRho + deltaRho0));
const dimensionedScalar c0("c0", dimless/dimTime, rootVSmall);
const volScalarField coeff("coeff", -c_*pow(gDot, d_) + c0);
fvScalarMatrix lambdaEqn
(
fvm::ddt(lambda_)
+ fvm::div(phiU, lambda_)
- fvm::Sp(fvc::div(phiU), lambda_)
==
a_*pow((1 - lambda_), b_)
+ fvm::SuSp(coeff, lambda_)
// Include the effect of the impinging droplets added with lambda = 0
- fvm::Sp
(
max
(
-film.rhoSp(),
dimensionedScalar(film.rhoSp().dimensions(), 0)
)/(deltaRho + deltaRho0),
lambda_
)
);
lambdaEqn.relax();
lambdaEqn.solve();
lambda_.min(1);
lambda_.max(0);
mu_ = muInf_/(sqr(1 - K_*lambda_) + rootVSmall);
mu_.correctBoundaryConditions();
}
void thixotropicViscosity::correct
(
const volScalarField& p,
const volScalarField& T
)
{
const kinematicSingleLayer& film = filmType<kinematicSingleLayer>();
// references to film fields
const volVectorField& U = film.U();
const volVectorField& Uw = film.Uw();
const volScalarField& delta = film.delta();
const volScalarField& deltaRho = film.deltaRho();
const surfaceScalarField& phi = film.phi();
const volScalarField& alpha = film.alpha();
const Time& runTime = this->owner().regionMesh().time();
// Shear rate
volScalarField gDot("gDot", alpha*mag(U - Uw)/(delta + film.deltaSmall()));
if (debug && runTime.outputTime())
{
gDot.write();
}
dimensionedScalar deltaRho0("deltaRho0", deltaRho.dimensions(), ROOTVSMALL);
surfaceScalarField phiU(phi/fvc::interpolate(deltaRho + deltaRho0));
dimensionedScalar c0("c0", dimless/dimTime, ROOTVSMALL);
volScalarField coeff("coeff", -c_*pow(gDot, d_) + c0);
// Limit the filmMass and deltaMass to calculate the effect of the added
// droplets with lambda = 0 to the film
const volScalarField filmMass
(
"thixotropicViscosity:filmMass",
film.netMass() + dimensionedScalar("SMALL", dimMass, ROOTVSMALL)
);
const volScalarField deltaMass
(
"thixotropicViscosity:deltaMass",
max(dimensionedScalar("zero", dimMass, 0), film.deltaMass())
);
fvScalarMatrix lambdaEqn
(
fvm::ddt(lambda_)
+ fvm::div(phiU, lambda_)
- fvm::Sp(fvc::div(phiU), lambda_)
==
a_*pow((1.0 - lambda_), b_)
+ fvm::SuSp(coeff, lambda_)
- fvm::Sp(deltaMass/(runTime.deltaT()*filmMass), lambda_)
);
lambdaEqn.relax();
lambdaEqn.solve();
lambda_.min(1.0);
lambda_.max(0.0);
mu_ = muInf_/(sqr(1.0 - K_*lambda_) + ROOTVSMALL);
mu_.correctBoundaryConditions();
}
