mirror of
https://github.com/OpenFOAM/OpenFOAM-6.git
synced 2025-12-08 06:57:46 +00:00
populationBalanceModel: Added Prince and Blanch (1990) coalescence model
Patch contributed by Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden - Rossendorf (HZDR)
This commit is contained in:
Will Bainbridge
@ -21,6 +21,7 @@ populationBalanceModel/coalescenceModels/coalescenceModel/coalescenceModel.C
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populationBalanceModel/coalescenceModels/constantCoalescence/constantCoalescence.C
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populationBalanceModel/coalescenceModels/CoulaloglouTavlaridesCoalescence/CoulaloglouTavlaridesCoalescence.C
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populationBalanceModel/coalescenceModels/hydrodynamic/hydrodynamic.C
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populationBalanceModel/coalescenceModels/PrinceBlanch/PrinceBlanch.C
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populationBalanceModel/binaryBreakupModels/binaryBreakupModel/binaryBreakupModel.C
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populationBalanceModel/binaryBreakupModels/powerLawUniformBinary/powerLawUniformBinary.C
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@ -26,7 +26,6 @@ License
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#include "LaakkonenAlopaeusAittamaa.H"
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#include "addToRunTimeSelectionTable.H"
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#include "phaseCompressibleTurbulenceModel.H"
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#include "phaseSystem.H"
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// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
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@ -80,10 +79,6 @@ Foam::diameterModels::breakupModels::LaakkonenAlopaeusAittamaa::setBreakupRate
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{
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const phaseModel& continuousPhase = popBal_.continuousPhase();
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const sizeGroup& fi = *popBal_.sizeGroups()[i];
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const volScalarField sigma
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(
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popBal_.fluid().sigma(phasePair(fi.phase(), continuousPhase))
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);
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breakupRate =
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C1_*cbrt(continuousTurbulence().epsilon())
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@ -91,7 +86,7 @@ Foam::diameterModels::breakupModels::LaakkonenAlopaeusAittamaa::setBreakupRate
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(
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sqrt
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(
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C2_*sigma
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C2_*popBal_.sigmaWithContinuousPhase(fi.phase())
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/(
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continuousPhase.rho()*pow(fi.d(), 5.0/3.0)
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*pow(continuousTurbulence().epsilon(), 2.0/3.0)
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@ -27,18 +27,18 @@ Class
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Description
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Model of Laakkonen et al. (2006). The total breakup rate is calculated by
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\f[
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C_1 \epsilon_c^{1/3}
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\mathrm{erfc}
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\left(
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\sqrt
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{
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C_2 \frac{\sigma}{\rho_c \epsilon_c^{2/3} (6v_i/\pi)^{5/9}}
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+ C_3 \frac{\mu_c}{\sqrt{\rho_c \rho_d}
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\epsilon_c^{1/3} (6v_i/\pi)^{4/9}}
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}
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\right)
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\f]
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\f[
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C_1 \epsilon_c^{1/3}
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\mathrm{erfc}
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\left(
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\sqrt
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{
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C_2 \frac{\sigma}{\rho_c \epsilon_c^{2/3} (6v_i/\pi)^{5/9}}
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+ C_3 \frac{\mu_c}{\sqrt{\rho_c \rho_d}
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\epsilon_c^{1/3} (6v_i/\pi)^{4/9}}
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}
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\right)
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\f]
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where
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@ -84,7 +84,7 @@ addToCoalescenceRate
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(
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- C2_*continuousPhase.mu()*continuousPhase.rho()
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*continuousTurbulence().epsilon()
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/sqr(sigma(fi.phase().name(), continuousPhase.name()))
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/sqr(popBal_.sigmaWithContinuousPhase(fi.phase()))
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/pow3(1 + popBal_.alphas())
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*pow4(cbrt(fi.x())*cbrt(fj.x())/(cbrt(fi.x()) + cbrt(fj.x())))
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);
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@ -28,18 +28,18 @@ Description
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Model of Coulaloglou and Tavlarides (1977). The coalescence rate is
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calculated by
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\f[
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C_1 (v_i^{2/3} + v_j^{2/3}) (v_i^{2/9} + v_j^{2/9})^{1/2}
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\frac{\epsilon_c^{1/3}}{1 + \alpha_d}
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\text{exp}
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\left[
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- C_2 \frac{\mu_c \rho_c}{\sigma^2}
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\frac{\epsilon_c}{(1 + \alpha_d)^{3}}
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\left(
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\frac{v_i^{1/3} v_j^{1/3}}{v_i^{1/3} + v_j^{1/3}}
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\right)^{4}
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\right]
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\f]
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\f[
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C_1 (v_i^{2/3} + v_j^{2/3}) (v_i^{2/9} + v_j^{2/9})^{1/2}
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\frac{\epsilon_c^{1/3}}{1 + \alpha_d}
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\text{exp}
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\left[
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- C_2 \frac{\mu_c \rho_c}{\sigma^2}
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\frac{\epsilon_c}{(1 + \alpha_d)^{3}}
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\left(
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\frac{v_i^{1/3} v_j^{1/3}}{v_i^{1/3} + v_j^{1/3}}
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\right)^{4}
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\right]
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\f]
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where
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@ -0,0 +1,146 @@
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/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | Copyright (C) 2018 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM is free software: you can redistribute it and/or modify it
|
||||
under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation, either version 3 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
|
||||
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
||||
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
||||
for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
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\*---------------------------------------------------------------------------*/
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#include "PrinceBlanch.H"
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#include "addToRunTimeSelectionTable.H"
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#include "mathematicalConstants.H"
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// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
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namespace Foam
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{
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namespace diameterModels
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{
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namespace coalescenceModels
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{
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defineTypeNameAndDebug(PrinceBlanch, 0);
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addToRunTimeSelectionTable
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(
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coalescenceModel,
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PrinceBlanch,
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dictionary
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);
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}
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}
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}
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// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
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Foam::diameterModels::coalescenceModels::PrinceBlanch::
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PrinceBlanch
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(
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const populationBalanceModel& popBal,
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const dictionary& dict
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)
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:
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coalescenceModel(popBal, dict),
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C1_("C1", dimless, dict.lookupOrDefault<scalar>("C1", 0.356)),
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h0_("h0", dimLength, dict.lookupOrDefault<scalar>("h0", 1e-4)),
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hf_("hf", dimLength, dict.lookupOrDefault<scalar>("h0", 1e-8)),
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turbulentCollisions_(dict.lookup("turbulentCollisions")),
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buoyantCollisions_(dict.lookup("buoyantCollisions")),
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laminarShearCollisions_(dict.lookup("laminarShearCollisions"))
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{}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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void
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Foam::diameterModels::coalescenceModels::PrinceBlanch::
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addToCoalescenceRate
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(
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volScalarField& coalescenceRate,
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const label i,
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const label j
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)
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{
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const phaseModel& continuousPhase = popBal_.continuousPhase();
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const sizeGroup& fi = *popBal_.sizeGroups()[i];
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const sizeGroup& fj = *popBal_.sizeGroups()[j];
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scalar pi = constant::mathematical::pi;
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const uniformDimensionedVectorField& g =
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popBal_.mesh().lookupObject<uniformDimensionedVectorField>("g");
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dimensionedScalar rij = 1.0/(1.0/fi.d() + 1.0/fj.d());
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volScalarField collisionEfficiency =
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exp
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(
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- sqrt
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(
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pow3(rij)*continuousPhase.rho()
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/(16.0*popBal_.sigmaWithContinuousPhase(fi.phase()))
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)
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*log(h0_/hf_)
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*cbrt(continuousTurbulence().epsilon())/pow(rij, 2.0/3.0)
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);
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if (turbulentCollisions_)
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{
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coalescenceRate +=
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(
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C1_*pi*sqr(fi.d() + fj.d())
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*cbrt(continuousTurbulence().epsilon())
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*sqrt(pow(fi.d(), 2.0/3.0) + pow(fj.d(), 2.0/3.0))
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)
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*collisionEfficiency;
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}
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if (buoyantCollisions_)
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{
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dimensionedScalar Sij = pi/4.0*sqr(fi.d() + fj.d());
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coalescenceRate +=
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(
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Sij
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*mag
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(
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sqrt
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(
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2.14*popBal_.sigmaWithContinuousPhase(fi.phase())
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/(continuousPhase.rho()*fi.d()) + 0.505*mag(g)*fi.d()
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)
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- sqrt
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(
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2.14*popBal_.sigmaWithContinuousPhase(fi.phase())
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/(continuousPhase.rho()*fj.d()) + 0.505*mag(g)*fj.d()
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)
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)
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)
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*collisionEfficiency;
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}
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if (laminarShearCollisions_)
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{
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FatalErrorInFunction
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<< "Laminar shear collision contribution not implemented for "
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<< this->type() << " coalescence model."
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<< exit(FatalError);
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}
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}
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// ************************************************************************* //
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@ -0,0 +1,205 @@
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/*---------------------------------------------------------------------------*\
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||||
========= |
|
||||
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
||||
\\ / O peration |
|
||||
\\ / A nd | Copyright (C) 2018 OpenFOAM Foundation
|
||||
\\/ M anipulation |
|
||||
-------------------------------------------------------------------------------
|
||||
License
|
||||
This file is part of OpenFOAM.
|
||||
|
||||
OpenFOAM is free software: you can redistribute it and/or modify it
|
||||
under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation, either version 3 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
|
||||
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
||||
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
||||
for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
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Class
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Foam::diameterModels::coalescenceModels::PrinceBlanch
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Description
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Model of Prince and Blanch (1990). The coalescence rate is calculated by
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\f[
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\left( \theta_{ij}^{T} + \theta_{ij}^{B} + \theta_{ij}^{LS} \right)
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\lambda_{ij}
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\f]
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with the coalescence efficiency
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\f[
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\lambda_{ij} =
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\mathrm{exp}
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\left(
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- \sqrt{\frac{r_{ij}^3 \rho_c}{16 \sigma}}
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\mathrm{ln} \left(\frac{h_0}{h_f}\right)
|
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\epsilon_c^{1/3}/r_{ij}^{2/3}
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\right)\;,
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\f]
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the turbulent collision rate
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\f[
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\theta_{ij}^{T} =
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C_1 \pi (d_i + d_j)^{2} \epsilon_c^{1/3}
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\sqrt{d_{i}^{2/3} + d_{j}^{2/3}}\;,
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\f]
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and the buoyancy-driven collision rate
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\f[
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\theta_{ij}^{B} = S_{ij} \left| u_{ri} - u_{rj} \right|\;,
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\f]
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where the rise velocity of bubble i is calculated by
|
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|
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\f[
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u_{ri} = \sqrt{2.14 \sigma / \left(\rho_c d_i \right) + 0.505 g d_i}\;,
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\f]
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the equivalent radius by
|
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|
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\f[
|
||||
r_{ij} = \left( \frac{1}{d_i} + \frac{1}{d_j} \right)^{-1}
|
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\f]
|
||||
|
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and the collision cross sectional area by
|
||||
|
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\f[
|
||||
S_{ij} = \frac{\pi}{4} \left(d_i + d_j\right)^{2}\;.
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||||
\f]
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|
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Note that in equation 2, the bubble radius has been substituted by the
|
||||
bubble diameter. Also the expression for the equivalent radius r_ij
|
||||
(equation 19 in the paper of Prince and Blanch (1990)) was corrected.
|
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The collision rate contribution due to laminar shear in the continuous phase
|
||||
is currently neglected.
|
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|
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\vartable
|
||||
\theta_{ij}^{T} | Turbulent collision rate [m3/s]
|
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\theta_{ij}^{B} | Buoyancy-driven collision rate [m3/s]
|
||||
\theta_{ij}^{LS} | Laminar shear collision rate [m3/s]
|
||||
\lambda_{ij} | Coalescence efficiency [-]
|
||||
r_{ij} | Equivalent radius [m]
|
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\rho_c | Density of continous phase [kg/m3]
|
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\sigma | Surface tension [N/m]
|
||||
h_0 | Initial film thickness [m]
|
||||
h_f | Critical film thickness [m]
|
||||
\epsilon_c | Continuous phase turbulent dissipation rate [m2/s3]
|
||||
d_i | Diameter of bubble i [m]
|
||||
d_j | Diameter of bubble j [m]
|
||||
u_{ri} | Rise velocity of bubble i [m/s]
|
||||
S_{ij} | Collision cross sectional area [m2]
|
||||
g | Gravitational constant [m/s2]
|
||||
\endvartable
|
||||
|
||||
References:
|
||||
\verbatim
|
||||
"Bubble Coalescence and Break-Up in Air-Sparged Bubble-Columns"
|
||||
Prince, M.J., Blanch, H.W.
|
||||
AIChE Journal, Vol. 36, Issue 10, 1990, pp. 1485-1499
|
||||
\endverbatim
|
||||
|
||||
Usage
|
||||
\table
|
||||
Property | Description | Required | Default value
|
||||
C1 | Coefficient C1 | no | 0.089
|
||||
\endtable
|
||||
|
||||
SourceFiles
|
||||
PrinceBlanch.C
|
||||
|
||||
\*---------------------------------------------------------------------------*/
|
||||
|
||||
#ifndef PrinceBlanch_H
|
||||
#define PrinceBlanch_H
|
||||
|
||||
#include "coalescenceModel.H"
|
||||
|
||||
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
||||
|
||||
namespace Foam
|
||||
{
|
||||
namespace diameterModels
|
||||
{
|
||||
namespace coalescenceModels
|
||||
{
|
||||
|
||||
/*---------------------------------------------------------------------------*\
|
||||
Class PrinceBlanch Declaration
|
||||
\*---------------------------------------------------------------------------*/
|
||||
|
||||
class PrinceBlanch
|
||||
:
|
||||
public coalescenceModel
|
||||
{
|
||||
// Private data
|
||||
|
||||
//- Optional coefficient C1, defaults to 0.089
|
||||
dimensionedScalar C1_;
|
||||
|
||||
//- Initial film thickness, defaults to 1e-4m
|
||||
dimensionedScalar h0_;
|
||||
|
||||
//- Critical film thickness, defaults to 1e-8m
|
||||
dimensionedScalar hf_;
|
||||
|
||||
//- Switch for considering turbulent collisions
|
||||
Switch turbulentCollisions_;
|
||||
|
||||
//- Switch for considering buoyancy-induced collisions
|
||||
Switch buoyantCollisions_;
|
||||
|
||||
//- Switch for considering buoyancy-induced collisions
|
||||
Switch laminarShearCollisions_;
|
||||
|
||||
|
||||
public:
|
||||
|
||||
//- Runtime type information
|
||||
TypeName("PrinceBlanch");
|
||||
|
||||
// Constructor
|
||||
|
||||
PrinceBlanch
|
||||
(
|
||||
const populationBalanceModel& popBal,
|
||||
const dictionary& dict
|
||||
);
|
||||
|
||||
|
||||
//- Destructor
|
||||
virtual ~PrinceBlanch()
|
||||
{}
|
||||
|
||||
|
||||
// Member Functions
|
||||
|
||||
//- Add to coalescenceRate
|
||||
virtual void addToCoalescenceRate
|
||||
(
|
||||
volScalarField& coalescenceRate,
|
||||
const label i,
|
||||
const label j
|
||||
);
|
||||
};
|
||||
|
||||
|
||||
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
||||
|
||||
} // End namespace coalescenceModels
|
||||
} // End namespace diameterModels
|
||||
} // End namespace Foam
|
||||
|
||||
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
||||
|
||||
#endif
|
||||
|
||||
// ************************************************************************* //
|
||||
@ -24,7 +24,6 @@ License
|
||||
\*---------------------------------------------------------------------------*/
|
||||
|
||||
#include "coalescenceModel.H"
|
||||
#include "phaseSystem.H"
|
||||
|
||||
// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
|
||||
|
||||
@ -38,25 +37,6 @@ namespace diameterModels
|
||||
}
|
||||
|
||||
|
||||
// * * * * * * * * * * * * Protected Member Functions * * * * * * * * * * * //
|
||||
|
||||
const Foam::tmp<Foam::volScalarField>
|
||||
Foam::diameterModels::coalescenceModel::sigma
|
||||
(
|
||||
const word& phase1,
|
||||
const word& phase2
|
||||
) const
|
||||
{
|
||||
const phasePairKey key
|
||||
(
|
||||
phase1,
|
||||
phase2
|
||||
);
|
||||
|
||||
return popBal_.fluid().sigma(key);
|
||||
}
|
||||
|
||||
|
||||
// * * * * * * * * * * * * * * * * Selector * * * * * * * * * * * * * * * * //
|
||||
|
||||
Foam::autoPtr<Foam::diameterModels::coalescenceModel>
|
||||
|
||||
@ -59,16 +59,6 @@ protected:
|
||||
const populationBalanceModel& popBal_;
|
||||
|
||||
|
||||
// Protected member functions
|
||||
|
||||
//- Return the surface tension coefficient
|
||||
const tmp<volScalarField> sigma
|
||||
(
|
||||
const word& phase1,
|
||||
const word& phase2
|
||||
) const;
|
||||
|
||||
|
||||
public:
|
||||
|
||||
//- Runtime type information
|
||||
|
||||
@ -32,10 +32,10 @@ Description
|
||||
mass conservation following Kumar and Ramkrishna (1996). Also the internal
|
||||
coordinate was changed to particle volume, which gives
|
||||
|
||||
\f[
|
||||
\frac{60}{v_j} \left(\frac{v_i}{v_j}\right)^{2}
|
||||
\left(1 - \frac{v_i}{v_j}\right)^{2}
|
||||
\f]
|
||||
\f[
|
||||
\frac{60}{v_j} \left(\frac{v_i}{v_j}\right)^{2}
|
||||
\left(1 - \frac{v_i}{v_j}\right)^{2}
|
||||
\f]
|
||||
|
||||
where
|
||||
|
||||
|
||||
@ -1145,6 +1145,22 @@ Foam::diameterModels::populationBalanceModel::gamma
|
||||
}
|
||||
|
||||
|
||||
const Foam::tmp<Foam::volScalarField>
|
||||
Foam::diameterModels::populationBalanceModel::sigmaWithContinuousPhase
|
||||
(
|
||||
const phaseModel& dispersedPhase
|
||||
) const
|
||||
{
|
||||
const phasePairKey key
|
||||
(
|
||||
dispersedPhase.name(),
|
||||
continuousPhase_.name()
|
||||
);
|
||||
|
||||
return fluid_.sigma(key);
|
||||
}
|
||||
|
||||
|
||||
void Foam::diameterModels::populationBalanceModel::solve()
|
||||
{
|
||||
const dictionary& solutionControls = mesh_.solverDict(name_);
|
||||
|
||||
@ -412,6 +412,13 @@ public:
|
||||
const dimensionedScalar& v
|
||||
) const;
|
||||
|
||||
//- Return the surface tension coefficient between a given dispersed
|
||||
// and the continuous phase
|
||||
const tmp<volScalarField> sigmaWithContinuousPhase
|
||||
(
|
||||
const phaseModel& dispersedPhase
|
||||
) const;
|
||||
|
||||
//- Solve the population balance equation
|
||||
void solve();
|
||||
};
|
||||
|
||||
Reference in New Issue
Block a user