multiphaseEulerFoam: LaakkonenAlopaeusAittamaa: Updated to a more recent reference
The former implementation of the daughterSizeDistributionModel based on Laakkonen et al. (2006) had the issue of not conserving the total particle number and volume properly, except when the coefficient C4 is set to a value of 2. The issue is solved by following the work of Laakkonen et al. (2007). The default coefficients in both the breakupModel and the daughterSizeDistributionModel were updated as well according to the suggestions of the authors. Patch contributed by Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden - Rossendorf (HZDR) and VTT Technical Research Centre of Finland Ltd.
This commit is contained in:
Will Bainbridge
@ -64,7 +64,7 @@ LaakkonenAlopaeusAittamaa
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"C1",
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dict,
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dimensionSet(0, -2.0/3.0, 0, 0, 0),
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6.0
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2.25
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)
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),
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C2_(dimensionedScalar::lookupOrDefault("C2", dict, dimless, 0.04)),
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@ -2,7 +2,7 @@
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration | Website: https://openfoam.org
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\\ / A nd | Copyright (C) 2018-2020 OpenFOAM Foundation
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\\ / A nd | Copyright (C) 2018-2021 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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@ -25,7 +25,7 @@ Class
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Foam::diameterModels::breakupModels::LaakkonenAlopaeusAittamaa
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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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Model of Laakkonen et al. (2007). 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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@ -44,7 +44,7 @@ Description
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\vartable
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\sigma | Surface tension [N/m]
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v_i | Volume of mother bubble i [m]
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v_i | Volume of mother bubble i [m3]
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\epsilon_c | Turbulent dissipation rate of continuous phase [m^2/s^3]
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\mu_c | Molecular dynamic viscosity of liquid phase [Pa s]
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\rho_c | Density of continuous phase [kg/m^3]
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@ -53,17 +53,15 @@ Description
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References:
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\verbatim
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Laakkonen, M., Alopaeus, V., & Aittamaa, J. (2006).
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Validation of bubble breakage, coalescence and mass transfer models for
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gas-liquid dispersion in agitated vessel.
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Chemical engineering science, 61(1), 218-228.
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Eq. 2-3, p. 220.
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Laakkonen, M., Moilanen, P., Alopaeus, V., & Aittamaa, J. (2007).
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Modelling local bubble size distributions in agitated vessels.
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Chemical Engineering Science, 62, 721–740.
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\endverbatim
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Usage
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\table
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Property | Description | Required | Default value
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C1 | coefficient C1 | no | 6.0
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C1 | coefficient C1 | no | 2.25
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C2 | coefficient C2 | no | 0.04
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C3 | coefficient C3 | no | 0.01
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daughterSizeDistributionModel | inh. from breakupModel | inherited |
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@ -98,7 +96,7 @@ class LaakkonenAlopaeusAittamaa
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{
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// Private Data
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//- Optional coefficient C1, defaults to 6.0
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//- Optional coefficient C1, defaults to 2.25
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dimensionedScalar C1_;
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//- Optional coefficient C2, defaults to 0.04
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@ -2,7 +2,7 @@
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration | Website: https://openfoam.org
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\\ / A nd | Copyright (C) 2018-2020 OpenFOAM Foundation
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\\ / A nd | Copyright (C) 2018-2021 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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@ -57,7 +57,7 @@ LaakkonenAlopaeusAittamaaDsd::LaakkonenAlopaeusAittamaaDsd
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)
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:
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daughterSizeDistributionModel(breakup, dict),
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C4_(dimensionedScalar::lookupOrDefault("C4", dict, dimless, 4.3))
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C4_(dimensionedScalar::lookupOrDefault("C4", dict, dimless, 18.25))
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{}
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@ -81,12 +81,18 @@ LaakkonenAlopaeusAittamaaDsd::antiderivative
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) const
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{
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return
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(
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pow(xk, -C4_ - 3)*pow(xk - v, C4_)*(v - xk)*((C4_ + 1)*(C4_ + 2)
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*(C4_ + 3)*pow3(v) - (C4_ + 1)*(C4_ + 2)*(bndr*(C4_ + 4) - 3.0*xk)
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*sqr(v) - 2.0*xk*(C4_ + 1)*(bndr*(C4_ + 4) - 3.0*xk)*v - 2.0*bndr
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*sqr(xk)*C4_ + 6.0*pow3(xk) - 8.0*bndr*sqr(xk))
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)/(2.0*(range)*(C4_ + 4));
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(4.0/3.0 + C4_/3)
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*(
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pow(xk, -C4_ - 3)*pow(xk - v, C4_)*(v - xk)
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*(
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(C4_ + 1)*(C4_ + 2)*(C4_ + 3)*pow3(v)
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- (C4_ + 1)*(C4_ + 2)*(bndr*(C4_ + 4) - 3*xk)*sqr(v)
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- 2*v*xk*(C4_ + 1)*(bndr*(C4_ + 4) - 3*xk)
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- 2*bndr*C4_*sqr(xk)
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+ 6*pow3(xk)
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- 8*bndr*sqr(xk)
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)
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)/(2*range*(C4_ + 4));
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}
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@ -26,12 +26,12 @@ Class
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LaakkonenAlopaeusAittamaaDsd
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Description
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Daughter size distribution model used by Laakkonen et al. (2006). Note that
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the diameters in the original expression was substituted by bubble volumes
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Daughter size distribution model of Laakkonen et al. (2007). Note that the
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diameters in the original expression were substituted by bubble volumes
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giving
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\f[
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\left(9 + \frac{33}{2}C_4 + 9C_4^2 + \frac{3}{2}C_4^3\right)
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(1 + C_4)(2 + C_4)(3 + C_4)(4 + C_4)
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\times \left(\frac{1}{3}\right) \left(\frac{1}{v_j}\right)
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\left(\frac{v_i}{v_j}\right)^{2} \left(1 - \frac{v_i}{v_j}\right)^{C_4}
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\f]
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@ -39,23 +39,28 @@ Description
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where
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\vartable
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v_i | Volume of daughter bubble i [m]
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v_j | Volume of mother bubble j [m]
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v_i | Volume of daughter bubble i [m3]
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v_j | Volume of mother bubble j [m3]
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\endvartable
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The total number of daughter bubbles generated depends on C4 and evaluates
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to
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\f[
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\frac{4}{3} + \frac{C_4}{3}
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\f]
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References:
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\verbatim
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Laakkonen, M., Alopaeus, V., & Aittamaa, J. (2006).
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Validation of bubble breakage, coalescence and mass transfer models for
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gas-liquid dispersion in agitated vessel.
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Chemical engineering science, 61(1), 218-228.
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Eq. 3, p. 220.
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Laakkonen, M., Moilanen, P., Alopaeus, V., & Aittamaa, J. (2007).
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Modelling local bubble size distributions in agitated vessels.
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Chemical Engineering Science, 62, 721–740.
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\endverbatim
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Usage
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\table
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Property | Description | Required | Default value
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C4 | Coefficient C4 | no | 4.3
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C4 | Coefficient C4 | no | 18.25
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\endtable
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SourceFiles
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@ -87,7 +92,7 @@ class LaakkonenAlopaeusAittamaaDsd
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{
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// Private Data
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//- Optional coefficient C4, defaults to 4.3
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//- Optional coefficient C4, defaults to 18.25
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dimensionedScalar C4_;
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