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foam-extend4.1-coherent-io/applications/solvers/combustion/XiFoam/bEqn.H

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if (ign.ignited())
{
// progress variable
// ~~~~~~~~~~~~~~~~~
volScalarField c = scalar(1) - b;
// Unburnt gas density
// ~~~~~~~~~~~~~~~~~~~
volScalarField rhou = thermo->rhou();
// Calculate flame normal etc.
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~
volVectorField n = fvc::grad(b);
volScalarField mgb = mag(n);
dimensionedScalar dMgb = 1.0e-3*
(b*c*mgb)().weightedAverage(mesh.V())
/((b*c)().weightedAverage(mesh.V()) + SMALL)
+ dimensionedScalar("ddMgb", mgb.dimensions(), SMALL);
mgb += dMgb;
surfaceVectorField SfHat = mesh.Sf()/mesh.magSf();
surfaceVectorField nfVec = fvc::interpolate(n);
nfVec += SfHat*(fvc::snGrad(b) - (SfHat & nfVec));
nfVec /= (mag(nfVec) + dMgb);
surfaceScalarField nf = (mesh.Sf() & nfVec);
n /= mgb;
# include "StCorr.H"
// Calculate turbulent flame speed flux
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
surfaceScalarField phiSt = fvc::interpolate(rhou*StCorr*Su*Xi)*nf;
scalar StCoNum = max
(
mesh.surfaceInterpolation::deltaCoeffs()
*mag(phiSt)/(fvc::interpolate(rho)*mesh.magSf())
).value()*runTime.deltaT().value();
Info<< "Max St-Courant Number = " << StCoNum << endl;
// Create b equation
// ~~~~~~~~~~~~~~~~~
fvScalarMatrix bEqn
(
fvm::ddt(rho, b)
+ mvConvection->fvmDiv(phi, b)
+ fvm::div(phiSt, b, "div(phiSt,b)")
- fvm::Sp(fvc::div(phiSt), b)
- fvm::laplacian(turbulence->muEff(), b)
);
// Add ignition cell contribution to b-equation
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# include "ignite.H"
// Solve for b
// ~~~~~~~~~~~
bEqn.solve();
Info<< "min(b) = " << min(b).value() << endl;
// Calculate coefficients for Gulder's flame speed correlation
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
volScalarField up = uPrimeCoef*sqrt((2.0/3.0)*turbulence->k());
//volScalarField up = sqrt(mag(diag(n * n) & diag(turbulence->r())));
volScalarField epsilon = pow(uPrimeCoef, 3)*turbulence->epsilon();
volScalarField tauEta = sqrt(thermo->muu()/(rhou*epsilon));
volScalarField Reta = up/
(
sqrt(epsilon*tauEta) + dimensionedScalar("1e-8", up.dimensions(), 1e-8)
);
//volScalarField l = 0.337*k*sqrt(k)/epsilon;
//Reta *= max((l - dimensionedScalar("dl", dimLength, 1.5e-3))/l, 0.0);
// Calculate Xi flux
// ~~~~~~~~~~~~~~~~~
surfaceScalarField phiXi =
phiSt
- fvc::interpolate(fvc::laplacian(turbulence->muEff(), b)/mgb)*nf
+ fvc::interpolate(rho)*fvc::interpolate(Su*(1.0/Xi - Xi))*nf;
// Calculate mean and turbulent strain rates
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
volVectorField Ut = U + Su*Xi*n;
volScalarField sigmat = (n & n)*fvc::div(Ut) - (n & fvc::grad(Ut) & n);
volScalarField sigmas =
((n & n)*fvc::div(U) - (n & fvc::grad(U) & n))/Xi
+ (
(n & n)*fvc::div(Su*n)
- (n & fvc::grad(Su*n) & n)
)*(Xi + scalar(1))/(2*Xi);
// Calculate the unstrained laminar flame speed
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
volScalarField Su0 = unstrainedLaminarFlameSpeed()();
// Calculate the laminar flame speed in equilibrium with the applied strain
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
volScalarField SuInf = Su0*max(scalar(1) - sigmas/sigmaExt, scalar(0.01));
if (SuModel == "unstrained")
{
Su == Su0;
}
else if (SuModel == "equilibrium")
{
Su == SuInf;
}
else if (SuModel == "transport")
{
// Solve for the strained laminar flame speed
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
volScalarField Rc =
(sigmas*SuInf*(Su0 - SuInf) + sqr(SuMin)*sigmaExt)
/(sqr(Su0 - SuInf) + sqr(SuMin));
solve
(
fvm::ddt(rho, Su)
+ fvm::div(phi + phiXi, Su, "div(phiXi,Su)")
- fvm::Sp(fvc::div(phiXi), Su)
==
- fvm::SuSp(-rho*Rc*Su0/Su, Su)
- fvm::SuSp(rho*(sigmas + Rc), Su)
);
// Limit the maximum Su
// ~~~~~~~~~~~~~~~~~~~~
Su.min(SuMax);
Su.max(SuMin);
}
else
{
FatalError
<< args.executable() << " : Unknown Su model " << SuModel
<< abort(FatalError);
}
// Calculate Xi according to the selected flame wrinkling model
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if (XiModel == "fixed")
{
// Do nothing, Xi is fixed!
}
else if (XiModel == "algebraic")
{
// Simple algebraic model for Xi based on Gulders correlation
// with a linear correction function to give a plausible profile for Xi
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Xi == scalar(1) +
(scalar(1) + (2*XiShapeCoef)*(scalar(0.5) - b))
*XiCoef*sqrt(up/(Su + SuMin))*Reta;
}
else if (XiModel == "transport")
{
// Calculate Xi transport coefficients based on Gulders correlation
// and DNS data for the rate of generation
// with a linear correction function to give a plausible profile for Xi
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
volScalarField XiEqStar =
scalar(1.001) + XiCoef*sqrt(up/(Su + SuMin))*Reta;
volScalarField XiEq =
scalar(1.001)
+ (scalar(1) + (2*XiShapeCoef)*(scalar(0.5) - b))
*(XiEqStar - scalar(1.001));
volScalarField Gstar = 0.28/tauEta;
volScalarField R = Gstar*XiEqStar/(XiEqStar - scalar(1));
volScalarField G = R*(XiEq - scalar(1.001))/XiEq;
//R *= (Gstar + 2*mag(dev(symm(fvc::grad(U)))))/Gstar;
// Solve for the flame wrinkling
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
solve
(
fvm::ddt(rho, Xi)
+ fvm::div(phi + phiXi, Xi, "div(phiXi,Xi)")
- fvm::Sp(fvc::div(phiXi), Xi)
==
rho*R
- fvm::Sp(rho*(R - G), Xi)
- fvm::Sp
(
rho*max
(
sigmat - sigmas,
dimensionedScalar("0", sigmat.dimensions(), 0)
),
Xi
)
);
// Correct boundedness of Xi
// ~~~~~~~~~~~~~~~~~~~~~~~~~
Xi.max(1.0);
Info<< "max(Xi) = " << max(Xi).value() << endl;
Info<< "max(XiEq) = " << max(XiEq).value() << endl;
}
else
{
FatalError
<< args.executable() << " : Unknown Xi model " << XiModel
<< abort(FatalError);
}
Info<< "Combustion progress = "
<< 100*(scalar(1) - b)().weightedAverage(mesh.V()).value() << "%"
<< endl;
St = Xi*Su;
}