static COMMAND_FUNC( do_const_alpha )
{
int value;
value=(int)HOW_MANY("value");
CHECK_DPYP("do_const_alpha")
const_alpha(value);
}
void Foam::kineticTheoryModel::solve(const volTensorField& gradUat)
{
if(kineticTheory_)
{
//if (!kineticTheory_)
//{
// return;
//}
//const scalar sqrtPi = sqrt(mathematicalConstant::pi);
if(Berzi_)
{
Info << "Berzi Model is used" << endl;
}
else{
const scalar sqrtPi = sqrt(constant::mathematical::pi);
surfaceScalarField phi = 1.5*rhoa_*phia_*fvc::interpolate(alpha_);
volTensorField dU = gradUat.T();//fvc::grad(Ua_);
volSymmTensorField D = symm(dU);
// NB, drag = K*alpha*beta,
// (the alpha and beta has been extracted from the drag function for
// numerical reasons)
volScalarField Ur = mag(Ua_ - Ub_);
volScalarField betaPrim = alpha_*(1.0 - alpha_)*draga_.K(Ur);
// Calculating the radial distribution function (solid volume fraction is
// limited close to the packing limit, but this needs improvements)
// The solution is higly unstable close to the packing limit.
gs0_ = radialModel_->g0
(
min(max(alpha_, 1e-6), alphaMax_ - 0.01),
alphaMax_
);
// particle pressure - coefficient in front of Theta (Eq. 3.22, p. 45)
volScalarField PsCoeff = granularPressureModel_->granularPressureCoeff
(
alpha_,
gs0_,
rhoa_,
e_
);
// 'thermal' conductivity (Table 3.3, p. 49)
kappa_ = conductivityModel_->kappa(alpha_, Theta_, gs0_, rhoa_, da_, e_);
// particle viscosity (Table 3.2, p.47)
mua_ = viscosityModel_->mua(alpha_, Theta_, gs0_, rhoa_, da_, e_);
dimensionedScalar Tsmall
(
"small",
dimensionSet(0 , 2 ,-2 ,0 , 0, 0, 0),
1.0e-6
);
dimensionedScalar TsmallSqrt = sqrt(Tsmall);
volScalarField ThetaSqrt = sqrt(Theta_);
// dissipation (Eq. 3.24, p.50)
volScalarField gammaCoeff =
12.0*(1.0 - sqr(e_))*sqr(alpha_)*rhoa_*gs0_*(1.0/da_)*ThetaSqrt/sqrtPi;
// Eq. 3.25, p. 50 Js = J1 - J2
volScalarField J1 = 3.0*betaPrim;
volScalarField J2 =
0.25*sqr(betaPrim)*da_*sqr(Ur)
/(max(alpha_, 1e-6)*rhoa_*sqrtPi*(ThetaSqrt + TsmallSqrt));
// bulk viscosity p. 45 (Lun et al. 1984).
lambda_ = (4.0/3.0)*sqr(alpha_)*rhoa_*da_*gs0_*(1.0+e_)*ThetaSqrt/sqrtPi;
// stress tensor, Definitions, Table 3.1, p. 43
volSymmTensorField tau = 2.0*mua_*D + (lambda_ - (2.0/3.0)*mua_)*tr(D)*I;
if (!equilibrium_)
{
// construct the granular temperature equation (Eq. 3.20, p. 44)
// NB. note that there are two typos in Eq. 3.20
// no grad infront of Ps
// wrong sign infront of laplacian
fvScalarMatrix ThetaEqn
(
fvm::ddt(1.5*alpha_*rhoa_, Theta_)
+ fvm::div(phi, Theta_, "div(phi,Theta)")
==
fvm::SuSp(-((PsCoeff*I) && dU), Theta_)
+ (tau && dU)
+ fvm::laplacian(kappa_, Theta_, "laplacian(kappa,Theta)")
+ fvm::Sp(-gammaCoeff, Theta_)
+ fvm::Sp(-J1, Theta_)
+ fvm::Sp(J2/(Theta_ + Tsmall), Theta_)
);
ThetaEqn.relax();
ThetaEqn.solve();
}
else
{
// equilibrium => dissipation == production
// Eq. 4.14, p.82
volScalarField K1 = 2.0*(1.0 + e_)*rhoa_*gs0_;
volScalarField K3 = 0.5*da_*rhoa_*
(
(sqrtPi/(3.0*(3.0-e_)))
*(1.0 + 0.4*(1.0 + e_)*(3.0*e_ - 1.0)*alpha_*gs0_)
+1.6*alpha_*gs0_*(1.0 + e_)/sqrtPi
);
volScalarField K2 =
4.0*da_*rhoa_*(1.0 + e_)*alpha_*gs0_/(3.0*sqrtPi) - 2.0*K3/3.0;
volScalarField K4 = 12.0*(1.0 - sqr(e_))*rhoa_*gs0_/(da_*sqrtPi);
volScalarField trD = tr(D);
volScalarField tr2D = sqr(trD);
volScalarField trD2 = tr(D & D);
volScalarField t1 = K1*alpha_ + rhoa_;
volScalarField l1 = -t1*trD;
volScalarField l2 = sqr(t1)*tr2D;
volScalarField l3 = 4.0*K4*max(alpha_, 1e-6)*(2.0*K3*trD2 + K2*tr2D);
Theta_ = sqr((l1 + sqrt(l2 + l3))/(2.0*(alpha_ + 1.0e-4)*K4));
}
Theta_.max(1.0e-15);
Theta_.min(1.0e+3);
volScalarField pf = frictionalStressModel_->frictionalPressure
(
alpha_,
alphaMinFriction_,
alphaMax_,
Fr_,
eta_,
p_
);
PsCoeff += pf/(Theta_+Tsmall);
PsCoeff.min(1.0e+10);
PsCoeff.max(-1.0e+10);
// update particle pressure
pa_ = PsCoeff*Theta_;
// frictional shear stress, Eq. 3.30, p. 52
volScalarField muf = frictionalStressModel_->muf
(
alpha_,
alphaMax_,
pf,
D,
phi_
);
// add frictional stress
mua_ += muf;
//-AO Inconsistency of equations
const scalar constSMALL = 0.001; //1.e-06;
mua_ /= (fvc::average(alpha_) + scalar(constSMALL));
lambda_ /= (fvc::average(alpha_) + scalar(constSMALL));
//-AO
mua_.min(1.0e+2);
mua_.max(0.0);
Info<< "kinTheory: max(Theta) = " << max(Theta_).value() << endl;
volScalarField ktn = mua_/rhoa_;
Info<< "kinTheory: min(nua) = " << min(ktn).value()
<< ", max(nua) = " << max(ktn).value() << endl;
Info<< "kinTheory: min(pa) = " << min(pa_).value()
<< ", max(pa) = " << max(pa_).value() << endl;
//}
/*
volScalarField& Foam::kineticTheoryModel::ppMagf(const volScalarField& alphaUpdate)
{
volScalarField alpha = alphaUpdate;
gs0_ = radialModel_->g0(min(alpha, alphaMinFriction_), alphaMax_);
gs0Prime_ = radialModel_->g0prime(min(alpha, alphaMinFriction_), alphaMax_);
// Computing ppMagf
ppMagf_ = Theta_*granularPressureModel_->granularPressureCoeffPrime
(
alpha,
gs0_,
gs0Prime_,
rhoa_,
e_
);
volScalarField ppMagfFriction = frictionalStressModel_->frictionalPressurePrime
(
alpha,
alphaMinFriction_,
alphaMax_,
Fr_,
eta_,
p_
);
// NOTE: this might not be appropriate if J&J model is used (verify)
forAll(alpha, cellI)
{
if(alpha[cellI] >= alphaMinFriction_.value())
{
ppMagf_[cellI] = ppMagfFriction[cellI];
}
}
ppMagf_.correctBoundaryConditions();
return ppMagf_;
}
*/}
}
else if(mofidiedKineticTheoryPU_)
{
//if (!mofidiedKineticTheoryPU_)
//{
// return;
//}
Info << " " << endl;
Info << "Modified kinetic theory model - Chialvo-Sundaresan " << endl;
bool testMKTimp(false);
if(kineticTheoryProperties_.found("testMKTimp"))
{
testMKTimp = true;
Info << "Modified kinetic theory model - testing implementation (chi=1,eEff=e, ksi=1) " << endl;
}
bool diluteCorrection(false);
if(kineticTheoryProperties_.found("diluteCorrection"))
{
testMKTimp = false;
diluteCorrection = true;
Info << "Modified kinetic theory model - Only dilute correction " << endl;
}
bool denseCorrection(false);
if(kineticTheoryProperties_.found("denseCorrection"))
{
testMKTimp = false;
diluteCorrection = false;
denseCorrection = true;
Info << "Modified kinetic theory model - Only dense correction " << endl;
}
bool frictionBlending(false);
if(kineticTheoryProperties_.found("frictionBlending"))
{
frictionBlending = true;
Info << "Modified kinetic theory model - Include Friction Blneding " << endl;
}
if(decomposePp_) Info << "Decompose Pp into Pp - PpStar " << endl;
bool verboseMKT(false);
if(kineticTheoryProperties_.found("verboseMKT")) verboseMKT = true;
const scalar Pi = constant::mathematical::pi;
const scalar sqrtPi = sqrt(constant::mathematical::pi);
const scalar constSMALL = 1.e-06; //1.e-06; 1.e-03;
// Read from dictionary
muFric_ = readScalar(kineticTheoryProperties_.lookup("muFriction"));
eEff_ = e_ - 3.0 / 2.0 * muFric_ * exp(-3.0 * muFric_);
// If only test MKT implementation
if(testMKTimp) eEff_ = e_;
alphaf_ = readScalar(kineticTheoryProperties_.lookup("alphaDiluteInertialUpperLimit"));
alphac_ = readScalar(kineticTheoryProperties_.lookup("alphaCritical"));
alphad_ = readScalar(kineticTheoryProperties_.lookup("alphaDelta"));
upsilons_ = readScalar(kineticTheoryProperties_.lookup("yieldStressRatio"));
// Model parameters
dimensionedScalar I0(0.2); // Table 2, p.15
dimensionedScalar const_alpha(0.36); // Table 2, p.15
dimensionedScalar const_alpha1(0.06); // Table 2, p.15
// Calculating the radial distribution function (solid volume fraction is
// limited close to the packing limit, but this needs improvements)
// The solution is higly unstable close to the packing limit.
gs0_ = radialModel_->g0jamming
(
Ua_.mesh(),
//max(alpha, scalar(constSMALL)),
min(max(alpha_, scalar(constSMALL)),alphaMax_ - 0.01), //changed by YG
alphaMax_,
alphad_, ///changed by YG
alphac_
);
// particle pressure - coefficient in front of T (Eq. 1, p. 3)
volScalarField PsCoeff // -> rho_p * H
(
granularPressureModel_->granularPressureCoeff
(
alpha_,
gs0_,
rhoa_,
e_
)
);
PsCoeff.max(1.0e-15);
// PsCoeff.min(1.0e+10);
// PsCoeff.max(-1.0e+10);
// Solid kinetic+collisional viscosity mua_ = nu_k^star + nu_c^star, Eq. 8,9, p.4
// If Garzo-Dufty viscosity is used (viscosity is dimensionless), there is issue with dimension of mu1
mua_ = viscosityModel_->mua(alpha_, Theta_, gs0_, rhoa_, da_, e_);
// Solid bulk viscosity mua_ = nu_k^star + nu_c^star, Eq. 10, p.4
// If Garzo-Dufty viscosity is used (viscosity is dimensionless), there is issue with dimension of mu1
// Create dimensionedScalar
dimensionedScalar viscDim("zero", dimensionSet(1, -1, -1, 0, 0), 1.0);
lambda_ = viscDim * 384.0 / ( 25.0 * Pi ) * ( 1.0 + e_ ) * alpha_ * alpha_ * gs0_ ;
//lambda_ = (4.0/3.0)*sqr(alpha_)*rhoa_*da_*gs0_*(1.0+e_)*sqrt(Theta_)/sqrtPi;
volScalarField ratioBulkShearVisc(lambda_/(mua_+lambda_));
// J Eq.5, p3
volScalarField J_( 5.0 * sqrtPi / 96.0 * ( mua_ + lambda_ ) / viscDim ); // Dimension issue
// K Eq.6, p3
volScalarField K_(12.0/sqrtPi*alpha_*alpha_*gs0_*(1.0-e_*e_));
// K' Eq.26, p8 modified dissipation due to friction
volScalarField Kmod_(K_*(1.0 - eEff_*eEff_)/(1.0 - e_*e_));
// M Eq.30 p.9
volScalarField M_( max( J_ / max( Kmod_, constSMALL) , const_alpha1 / sqrt( max(alphac_ - alpha_, constSMALL) ) ) );
// Shear stress rate tensor
volTensorField dU(gradUat.T());
volSymmTensorField D(symm(dU));
// Shear stress rate (gammaDot)
volScalarField gammaDot(sqrt(2.*magSqr(D)));
dimensionedScalar gammaDotSmall("gammaDotSmall",dimensionSet(0 , 0 , -1 , 0 , 0, 0, 0), constSMALL);
// Dilute inertia temperature Eq.24, p8
volScalarField ThetaDil_ = ( J_ / max ( Kmod_ , 1e-1 ) ) * ( gammaDot * da_ ) * ( gammaDot * da_ );
// Dense inertia temperature Eq.27, p8
// volScalarField ThetaDense_ = const_alpha1 * ( gammaDot * da_ ) * ( gammaDot * da_ )
// / sqrt( max(alphac_ - alpha_, constSMALL) );
volScalarField ThetaDense_ = const_alpha1 * ( gammaDot * da_ ) * ( gammaDot * da_ )
/ sqrt( max(alphac_ - alpha_, alphad_) )
+ max(alpha_ - (alphac_ - alphad_),0.0) * 0.5 *const_alpha1*( gammaDot * da_ ) * ( gammaDot * da_)*pow(alphad_,-1.5);
// Theta
Theta_ = max(ThetaDil_,ThetaDense_) ;
if(testMKTimp || diluteCorrection) Theta_ = ThetaDil_;
if(denseCorrection) Theta_ = ThetaDense_;
// Limit granular temperature
Theta_.max(1.0e-15);
Theta_.min(1.0e+3);
// Particle pressure
pa_ = PsCoeff * Theta_;
if(frictionBlending)
{
/* volScalarField pf = frictionalStressModel_->frictionalPressure
(
alpha_,
alphaMinFriction_-0.001,
alphaMax_,
Fr_,
eta_,
p_
);
pa_ = pa_ + pf;
*/
// pa_ =pa_ + dimensionedScalar("1e24", dimensionSet(1, -1, -2, 0, 0), Fr_.value())*pow(max(alpha_ - (alphaMinFriction_), scalar(0)), 2/3);
pa_ =pa_ + dimensionedScalar("5810", dimensionSet(1, 0, -2, 0, 0), 581.0)/da_*pow(max(alpha_ - (alphaMinFriction_-0.0), scalar(0)), 2.0/3.0);
// pa_ =pa_ + dimensionedScalar("4.7e9", dimensionSet(1, -1, -2, 0, 0), 4.7e9)*pow(max(alpha_ - (alphaMinFriction_-0.0), scalar(0)), 1.56);
// forAll(alpha_, cellI)
// {
// if(alpha_[cellI] >= (alphaMinFriction_.value()-0.00001))
// {
// pa_[cellI] = pa_[cellI] + 581.0/da_.value()*pow(alpha_[cellI] - (alphaMinFriction_.value()-0.00001), 2.0/3.0);
// }
// }
}
// Psi Eq.32, p.12
dimensionedScalar psi(1.0 + 3.0/10.0*pow((1.0-e_*e_),-1.5)*(1.0-exp(-8.0*muFric_)));
if(testMKTimp) psi = 1.0;
// Shear stress ratio in dilute regime, Eq.33, p.12
dimensionedScalar paSmall("paSmall",dimensionSet(1, -1, -2, 0, 0), constSMALL);
volScalarField inertiaNumber( gammaDot * da_ / sqrt( (pa_ + paSmall) / rhoa_ ) );
// Modified inertia number Eq.35, p.13
volScalarField modInertiaNumber( inertiaNumber / max( alpha_, constSMALL ) );
// Model parameters
volScalarField chi( 1.0 / ( pow( I0 / max( modInertiaNumber,constSMALL ) , 1.5 ) + 1.0 ));
if(testMKTimp || diluteCorrection) chi = max( modInertiaNumber,constSMALL ) / max( modInertiaNumber,constSMALL ) ;
if(denseCorrection) chi= modInertiaNumber - modInertiaNumber;
// Beta + Sigma_tau Eq.49 p.14
volScalarField beta(alpha_ * psi * J_ * sqrt( K_ /( max ( (Kmod_ * ( PsCoeff / rhoa_)), constSMALL ) ) ) );
volScalarField sigmaTau( const_alpha / max( beta, constSMALL ) + ( 1 - const_alpha / max( beta, constSMALL ) ) * chi);
// Sigma_gamma Eq.51 p.14
volScalarField sigmaGamma( beta * sqrt( PsCoeff/rhoa_ ) / max( ( Kmod_ * M_ ), constSMALL ) * sigmaTau);
// dissipation
volScalarField gammaCoeff
(
// van Wachem (Eq. 3.24, p.50) 12.0*(1.0 - sqr(e_))*sqr(alpha_)*rhoa_*gs0_*(1.0/da_)*ThetaSqrt/sqrtPi
// Chialvo & Sundaresan Eq.50 p.14
//rhoa_ / da_ * Kmod_ * Theta_ * sqrt(Theta_) * sigmaGamma
rhoa_ / da_ * Kmod_ * sqrt(Theta_) * sigmaGamma
);
// Blending function
volScalarField func_B( const_alpha + ( beta-const_alpha ) * chi );
// Shear stress ratio
upsilon_ = upsilons_ * (1 - chi) + func_B * modInertiaNumber;
// Shear stress
volSymmTensorField S( D - 1./3.*tr(D)*I );
volSymmTensorField hatS( 2. * S / max( gammaDot, gammaDotSmall ) );
// Shear stress based on pressure and ratio
tau_ = pa_ * upsilon_ * hatS;
// Viscosity
mua_ = ( pa_ * upsilon_ ) / (max( gammaDot, gammaDotSmall )) ;
// Divide by alpha (to be consistent with OpenFOAM implementation)
/* mua_ /= (fvc::average(alpha_) + scalar(0.001));
tau_ /= (fvc::average(alpha_) + scalar(0.001));
lambda_ /= (fvc::average(alpha_) + scalar(0.001)); */
mua_ /= max(alpha_, scalar(constSMALL));
// Limit mua
mua_.min(3e+02);
mua_.max(0.0);
// Limit lambda
lambda_ = mua_ * ratioBulkShearVisc;
// Limit shear stress
tau_ = mua_ * gammaDot * hatS;
// tau_ /= max(alpha_, scalar(constSMALL));
// lambda_ /= max(alpha_, scalar(constSMALL));
//mua_ /= max(alpha_, scalar(constSMALL));
//tau_ /= max(alpha_, scalar(constSMALL));
//lambda_ /= max(alpha_, scalar(constSMALL));
if(verboseMKT)
{
#include "verboseMKT.H"
}
//-AO, YG - Decompose particle pressure, Sundar's idea
if(decomposePp_)
{
pa_ /= (fvc::average(alpha_) + scalar(0.001));
//pa_.correctBoundaryConditions();
pa_.max(1.0e-15);
}
}
else
{
return;
}
}
