void Foam::SHF::breakupParcel
(
parcel& p,
const scalar deltaT,
const vector& vel,
const liquidMixtureProperties& fuels
) const
{
label cellI = p.cell();
scalar T = p.T();
scalar pc = spray_.p()[cellI];
scalar sigma = fuels.sigma(pc, T, p.X());
scalar rhoLiquid = fuels.rho(pc, T, p.X());
scalar muLiquid = fuels.mu(pc, T, p.X());
scalar rhoGas = spray_.rho()[cellI];
scalar weGas = p.We(vel, rhoGas, sigma);
scalar weLiquid = p.We(vel, rhoLiquid, sigma);
// correct the Reynolds number. Reitz is using radius instead of diameter
scalar reLiquid = p.Re(rhoLiquid, vel, muLiquid);
scalar ohnesorge = sqrt(weLiquid)/(reLiquid + VSMALL);
vector vRel = p.Urel(vel);
scalar weGasCorr = weGas/(1.0 + weCorrCoeff_*ohnesorge);
// droplet deformation characteristic time
scalar tChar = p.d()/mag(vRel)*sqrt(rhoLiquid/rhoGas);
scalar tFirst = cInit_*tChar;
scalar tSecond = 0;
scalar tCharSecond = 0;
// updating the droplet characteristic time
p.ct() += deltaT;
if (weGas > weConst_)
{
if (weGas < weCrit1_)
{
tCharSecond = c1_*pow((weGas - weConst_),cExp1_);
}
else if (weGas >= weCrit1_ && weGas <= weCrit2_)
{
tCharSecond = c2_*pow((weGas - weConst_),cExp2_);
}
else
{
tCharSecond = c3_*pow((weGas - weConst_),cExp3_);
}
}
scalar weC = weBuCrit_*(1.0+ohnCoeffCrit_*pow(ohnesorge, ohnExpCrit_));
scalar weB = weBuBag_*(1.0+ohnCoeffBag_*pow(ohnesorge, ohnExpBag_));
scalar weMM = weBuMM_*(1.0+ohnCoeffMM_*pow(ohnesorge, ohnExpMM_));
bool bag = (weGas > weC && weGas < weB);
bool multimode = (weGas >= weB && weGas <= weMM);
bool shear = (weGas > weMM);
tSecond = tCharSecond*tChar;
scalar tBreakUP = tFirst + tSecond;
if (p.ct() > tBreakUP)
{
scalar d32 =
coeffD_*p.d()*pow(ohnesorge, onExpD_)*pow(weGasCorr, weExpD_);
if (bag || multimode)
{
scalar d05 = d32Coeff_*d32;
scalar x = 0.0;
scalar y = 0.0;
scalar d = 0.0;
scalar px = 0.0;
do
{
x = cDmaxBM_*rndGen_.sample01<scalar>();
d = sqr(x)*d05;
y = rndGen_.sample01<scalar>();
px =
x
/(2.0*sqrt(constant::mathematical::twoPi)*sigma_)
*exp(-0.5*sqr((x-mu_)/sigma_));
} while (y >= px);
p.d() = d;
p.ct() = 0.0;
}
if (shear)
{
scalar dC = weConst_*sigma/(rhoGas*sqr(mag(vRel)));
scalar d32Red = 4.0*(d32*dC)/(5.0*dC - d32);
scalar initMass = p.m();
scalar d05 = d32Coeff_*d32Red;
scalar x = 0.0;
scalar y = 0.0;
scalar d = 0.0;
scalar px = 0.0;
do
{
x = cDmaxS_*rndGen_.sample01<scalar>();
d = sqr(x)*d05;
y = rndGen_.sample01<scalar>();
px =
x
/(2.0*sqrt(constant::mathematical::twoPi)*sigma_)
*exp(-0.5*sqr((x-mu_)/sigma_));
} while (y >= px);
p.d() = dC;
p.m() = corePerc_*initMass;
spray_.addParticle
(
new parcel
(
p.mesh(),
p.position(),
p.cell(),
p.tetFace(),
p.tetPt(),
p.n(),
d,
p.T(),
(1.0 - corePerc_)*initMass,
0.0,
0.0,
0.0,
-GREAT,
p.tTurb(),
0.0,
scalar(p.injector()),
p.U(),
p.Uturb(),
p.X(),
p.fuelNames()
)
);
p.ct() = 0.0;
}
}
}
void reitzDiwakar::breakupParcel
(
parcel& p,
const scalar deltaT,
const vector& vel,
const liquidMixture& fuels
) const
{
/*
These are the default values for this model...
static const scalar Cbag = 6.0;
static const scalar Cb = 0.785;
static const scalar Cstrip = 0.5;
static const scalar Cs = 10.0;
*/
const PtrList<volScalarField>& Y = spray_.composition().Y();
label Ns = Y.size();
label cellI = p.cell();
scalar pressure = spray_.p()[cellI];
scalar temperature = spray_.T()[cellI];
scalar Taverage = p.T() + (temperature - p.T())/3.0;
scalar muAverage = 0.0;
scalar Winv = 0.0;
for(label i=0; i<Ns; i++)
{
Winv += Y[i][cellI]/spray_.gasProperties()[i].W();
muAverage += Y[i][cellI]*spray_.gasProperties()[i].mu(Taverage);
}
scalar R = specie::RR()*Winv;
// ideal gas law to evaluate density
scalar rhoAverage = pressure/R/Taverage;
scalar nuAverage = muAverage/rhoAverage;
scalar sigma = fuels.sigma(pressure, p.T(), p.X());
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
// The We and Re numbers are to be evaluated using the 1/3 rule.
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
scalar WeberNumber = p.We(vel, rhoAverage, sigma);
scalar ReynoldsNumber = p.Re(vel, nuAverage);
scalar sqRey = sqrt(ReynoldsNumber);
if (WeberNumber > Cbag_)
{
if (WeberNumber > Cstrip_*sqRey)
{
scalar dStrip =
pow(2.0*Cstrip_*sigma, 2.0)/
(
rhoAverage
* pow(mag(p.Urel(vel)), 3.0)
* muAverage
);
scalar tauStrip =
Cs_ * p.d()
* sqrt
(
fuels.rho(pressure, p.T(), p.X())
/ rhoAverage
)
/ mag(p.Urel(vel));
scalar fraction = deltaT/tauStrip;
// new droplet diameter, implicit calculation
p.d() = (fraction*dStrip + p.d())/(1.0 + fraction);
}
else
{
scalar dBag =
2.0 * Cbag_ * sigma
/ (
rhoAverage
* pow(mag(p.Urel(vel)), 2.0)
);
scalar tauBag =
Cb_ * p.d()
* sqrt
(
fuels.rho(pressure, p.T(), p.X())
* p.d()
/ sigma
);
scalar fraction = deltaT/tauBag;
// new droplet diameter, implicit calculation
p.d() = (fraction*dBag + p.d())/(1.0 + fraction);
}
}
}
void reitzKHRT::breakupParcel
(
parcel& p,
const scalar deltaT,
const vector& vel,
const liquidMixture& fuels
) const
{
label celli = p.cell();
scalar T = p.T();
scalar r = 0.5*p.d();
scalar pc = spray_.p()[celli];
scalar sigma = fuels.sigma(pc, T, p.X());
scalar rhoLiquid = fuels.rho(pc, T, p.X());
scalar muLiquid = fuels.mu(pc, T, p.X());
scalar rhoGas = spray_.rho()[celli];
scalar Np = p.N(rhoLiquid);
scalar semiMass = Np*pow(p.d(), 3.0);
scalar weGas = p.We(vel, rhoGas, sigma);
scalar weLiquid = p.We(vel, rhoLiquid, sigma);
// correct the Reynolds number. Reitz is using radius instead of diameter
scalar reLiquid = 0.5*p.Re(rhoLiquid, vel, muLiquid);
scalar ohnesorge = sqrt(weLiquid)/(reLiquid + VSMALL);
scalar taylor = ohnesorge*sqrt(weGas);
vector acceleration = p.Urel(vel)/p.tMom();
vector trajectory = p.U()/mag(p.U());
scalar gt = (g_ + acceleration) & trajectory;
// frequency of the fastest growing KH-wave
scalar omegaKH =
(0.34 + 0.38*pow(weGas, 1.5))
/((1 + ohnesorge)*(1 + 1.4*pow(taylor, 0.6)))
*sqrt(sigma/(rhoLiquid*pow(r, 3)));
// corresponding KH wave-length.
scalar lambdaKH =
9.02
*r
*(1.0 + 0.45*sqrt(ohnesorge))
*(1.0 + 0.4*pow(taylor, 0.7))
/pow(1.0 + 0.865*pow(weGas, 1.67), 0.6);
// characteristic Kelvin-Helmholtz breakup time
scalar tauKH = 3.726*b1_*r/(omegaKH*lambdaKH);
// stable KH diameter
scalar dc = 2.0*b0_*lambdaKH;
// the frequency of the fastest growing RT wavelength.
scalar helpVariable = mag(gt*(rhoLiquid - rhoGas));
scalar omegaRT = sqrt
(
2.0*pow(helpVariable, 1.5)
/(3.0*sqrt(3.0*sigma)*(rhoGas + rhoLiquid))
);
// RT wave number
scalar KRT = sqrt(helpVariable/(3.0*sigma + VSMALL));
// wavelength of the fastest growing RT frequency
scalar lambdaRT = 2.0*mathematicalConstant::pi*cRT_/(KRT + VSMALL);
// if lambdaRT < diameter, then RT waves are growing on the surface
// and we start to keep track of how long they have been growing
if ((p.ct() > 0) || (lambdaRT < p.d()))
{
p.ct() += deltaT;
}
// characteristic RT breakup time
scalar tauRT = cTau_/(omegaRT + VSMALL);
// check if we have RT breakup
if ((p.ct() > tauRT) && (lambdaRT < p.d()))
{
// the RT breakup creates diameter/lambdaRT new droplets
p.ct() = -GREAT;
scalar multiplier = p.d()/lambdaRT;
scalar nDrops = multiplier*Np;
p.d() = cbrt(semiMass/nDrops);
}
// otherwise check for KH breakup
else if (dc < p.d())
{
// no breakup below Weber = 12
if (weGas > weberLimit_)
{
label injector = label(p.injector());
scalar fraction = deltaT/tauKH;
// reduce the diameter according to the rate-equation
p.d() = (fraction*dc + p.d())/(1.0 + fraction);
scalar ms = rhoLiquid*Np*pow3(dc)*mathematicalConstant::pi/6.0;
p.ms() += ms;
// Total number of parcels for the whole injection event
label nParcels =
spray_.injectors()[injector].properties()->nParcelsToInject
(
spray_.injectors()[injector].properties()->tsoi(),
spray_.injectors()[injector].properties()->teoi()
);
scalar averageParcelMass =
spray_.injectors()[injector].properties()->mass()/nParcels;
if (p.ms()/averageParcelMass > msLimit_)
{
// set the initial ms value to -GREAT. This prevents
// new droplets from being formed from the child droplet
// from the KH instability
// mass of stripped child parcel
scalar mc = p.ms();
// Prevent child parcel from taking too much mass
if (mc > 0.5*p.m())
{
mc = 0.5*p.m();
}
spray_.addParticle
(
new parcel
(
spray_,
p.position(),
p.cell(),
p.n(),
dc,
p.T(),
mc,
0.0,
0.0,
0.0,
-GREAT,
p.tTurb(),
0.0,
p.injector(),
p.U(),
p.Uturb(),
p.X(),
p.fuelNames()
)
);
p.m() -= mc;
p.ms() = 0.0;
}
}
}
}