From eab0a11079e80965214c4038ff7e41e94771e52c Mon Sep 17 00:00:00 2001 From: Kutalmis Bercin Date: Tue, 2 Nov 2021 16:52:11 +0000 Subject: [PATCH] DOC: DragForce: improve header file documentation --- .../DistortedSphereDragForce.H | 86 ++++++++++++- .../Drag/ErgunWenYuDrag/ErgunWenYuDragForce.H | 108 +++++++++++++++- .../Drag/NonSphereDrag/NonSphereDragForce.H | 118 +++++++++++++++--- .../PlessisMasliyahDragForce.H | 81 +++++++++++- .../Drag/SphereDrag/SphereDragForce.H | 85 ++++++++++++- .../Drag/WenYuDrag/WenYuDragForce.H | 98 ++++++++++++++- 6 files changed, 547 insertions(+), 29 deletions(-) diff --git a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/DistortedSphereDrag/DistortedSphereDragForce.H b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/DistortedSphereDrag/DistortedSphereDragForce.H index 1ce2b2fde4..7cdfba6116 100644 --- a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/DistortedSphereDrag/DistortedSphereDragForce.H +++ b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/DistortedSphereDrag/DistortedSphereDragForce.H @@ -6,6 +6,7 @@ \\/ M anipulation | ------------------------------------------------------------------------------- Copyright (C) 2014-2017 OpenFOAM Foundation + Copyright (C) 2021 OpenCFD Ltd. ------------------------------------------------------------------------------- License This file is part of OpenFOAM. @@ -30,16 +31,89 @@ Group grpLagrangianIntermediateForceSubModels Description - Drag model based on assumption of distorted spheres according to: + Particle-drag model wherein drag forces (per unit carrier-fluid velocity) + are dynamically computed by using \c sphereDrag model; however, are + corrected for particle distortion by linearly varying the drag between of + a sphere (i.e. \c sphereDrag) and a value of 1.54 corresponding to a disk. + \f[ + \mathrm{F}_\mathrm{D} = + \frac{3}{4} + \frac{\mu_c\,\mathrm{C}_\mathrm{D}\,\mathrm{Re}_p}{\rho_p \, d_p^2} + \f] + with + + \f[ + \mathrm{C}_\mathrm{D} = + \mathrm{C}_{\mathrm{D, sphere}} \left( 1 + 2.632 y \right) + \f] + + where + \vartable + \mathrm{F}_\mathrm{D} | Drag force per carrier-fluid velocity [kg/s] + \mathrm{C}_\mathrm{D} | Particle drag coefficient + \mathrm{C}_{\mathrm{D, sphere}} | Sphere drag coefficient + \mathrm{Re}_p | Particle Reynolds number + \rho_p | Particle mass density + d_p | Particle diameter + y | Level of distortion determined by other models internally + \endvartable + + Constraints: + - Applicable to particles with a spatially homogeneous distribution. + - \f$ 1 \geq y \geq 0 \f$ + + References: \verbatim - "Effects of Drop Drag and Breakup on Fuel Sprays" - Liu, A.B., Mather, D., Reitz, R.D., - SAE Paper 930072, - SAE Transactions, Vol. 102, Section 3, Journal of Engines, 1993, - pp. 63-95 + Standard model: + Putnam, A. (1961). + Integratable form of droplet drag coefficient. + ARS Journal, 31(10), 1467-1468. + + Standard model (tag:AOB): + Amsden, A. A., O'Rourke, P. J., & Butler, T. D. (1989). + KIVA-II: A computer program for chemically + reactive flows with sprays (No. LA-11560-MS). + Los Alamos National Lab.(LANL), Los Alamos, NM (United States). + DOI:10.2172/6228444 + + Expression correcting drag for particle distortion (tag:LMR): + Liu, A. B., Mather, D., & Reitz, R. D. (1993). + Modeling the effects of drop drag + and breakup on fuel sprays. + SAE Transactions, 83-95. + DOI:10.4271/930072 \endverbatim +Usage + Minimal example by using \c constant/\: + \verbatim + subModels + { + particleForces + { + distortedSphereDrag; + } + } + \endverbatim + + where the entries mean: + \table + Property | Description | Type | Reqd | Deflt + type | Type name: distortedSphereDrag | word | yes | - + \endtable + +Note + - \f$\mathrm{F}_\mathrm{D}\f$ is weighted with the particle mass + at the stage of a function return, so that it can later be normalised + with the effective mass, if necessary (e.g. when using virtual-mass forces). + +See also + - Foam::SphereDragForce + +SourceFiles + DistortedSphereDragForce.C + \*---------------------------------------------------------------------------*/ #ifndef DistortedSphereDragForce_H diff --git a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/ErgunWenYuDrag/ErgunWenYuDragForce.H b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/ErgunWenYuDrag/ErgunWenYuDragForce.H index 6b12970c87..41cc8eb897 100644 --- a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/ErgunWenYuDrag/ErgunWenYuDragForce.H +++ b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/ErgunWenYuDrag/ErgunWenYuDragForce.H @@ -6,6 +6,7 @@ \\/ M anipulation | ------------------------------------------------------------------------------- Copyright (C) 2013-2017 OpenFOAM Foundation + Copyright (C) 2021 OpenCFD Ltd. ------------------------------------------------------------------------------- License This file is part of OpenFOAM. @@ -30,7 +31,112 @@ Group grpLagrangianIntermediateForceSubModels Description - Ergun-Wen-Yu drag model for solid spheres. + Particle-drag model wherein drag forces (per unit carrier-fluid + velocity) are dynamically computed based on the Gidaspow drag model + which is a switch-like combination of the Wen-Yu and Ergun drag models. + + \f[ + \mathrm{F}_{\mathrm{D}, Wen-Yu} = + \frac{3}{4} + \frac{(1 - \alpha_c) \, \mu_c \, \alpha_c \, \mathrm{Re}_p }{d_p^2} + \mathrm{C}_\mathrm{D} \, \alpha_c^{-2.65} + \f] + + \f[ + \mathrm{F}_{\mathrm{D}, Ergun} = + \left(150 \frac{1-\alpha_c}{\alpha_c} + 1.75 \mathrm{Re}_p \right) + \frac{(1-\alpha_c) \, \mu_c}{d_p^2} + \f] + + \f[ + \mathrm{F}_\mathrm{D} = \mathrm{F}_{\mathrm{D}, Wen-Yu} + \quad \mathrm{if} \quad \alpha_c \geq 0.8 + \f] + + \f[ + \mathrm{F}_\mathrm{D} = \mathrm{F}_{\mathrm{D}, Ergun} + \quad \mathrm{if} \quad \alpha_c < 0.8 + \f] + with + + \f[ + \mathrm{Re}_p = + \frac{\rho_c \, | \mathbf{u}_\mathrm{rel} | \, d_p}{\mu_c} + \f] + + where + \vartable + \mathrm{F}_\mathrm{D} | Drag force per carrier-fluid velocity [kg/s] + \mathrm{C}_\mathrm{D} | Particle drag coefficient + \mathrm{Re}_p | Particle Reynolds number + \mu_c | Dynamic viscosity of carrier at the cell occupying particle + d_p | Particle diameter + \rho_c | Density of carrier at the cell occupying particle + \mathbf{u}_\mathrm{rel} | Relative velocity between particle and carrier + \alpha_c | Volume fraction of carrier fluid + \endvartable + + References: + \verbatim + Standard model (tag:G): + Gidaspow, D. (1994). + Multiphase flow and fluidization: + continuum and kinetic theory descriptions. + Academic press. + + Drag-coefficient model: + Schiller, L., & Naumann, A. (1935). + Über die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. + Z. Ver. Dtsch. Ing., 77: 318–326. + + Expressions (tags:ZZB, GLSLR), (Eq.16-18, Table 3): + Zhou, L., Zhang, L., Bai, L., Shi, W., + Li, W., Wang, C., & Agarwal, R. (2017). + Experimental study and transient CFD/DEM simulation in + a fluidized bed based on different drag models. + RSC advances, 7(21), 12764-12774. + DOI:10.1039/C6RA28615A + + Gao, X., Li, T., Sarkar, A., Lu, L., & Rogers, W. A. (2018). + Development and validation of an enhanced filtered drag model + for simulating gas-solid fluidization of Geldart A particles + in all flow regimes. + Chemical Engineering Science, 184, 33-51. + DOI:10.1016/j.ces.2018.03.038 + \endverbatim + +Usage + Minimal example by using \c constant/\: + \verbatim + subModels + { + particleForces + { + ErgunWenYuDrag + { + alphac ; // e.g. alpha.air + } + } + } + \endverbatim + + where the entries mean: + \table + Property | Description | Type | Reqd | Deflt + type | Type name: ErgunWenYuDrag | word | yes | - + alphac | Name of carrier fluid | word | yes | - + \endtable + +Note + - \f$\mathrm{F}_\mathrm{D}\f$ is weighted with the particle mass/density + at the stage of a function return, so that it can later be normalised + with the effective mass, if necessary (e.g. when using virtual-mass forces). + +See also + - Foam::WenYuDragForce + +SourceFiles + ErgunWenYuDragForce.C \*---------------------------------------------------------------------------*/ diff --git a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/NonSphereDrag/NonSphereDragForce.H b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/NonSphereDrag/NonSphereDragForce.H index 779cbf0208..2d5a791232 100644 --- a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/NonSphereDrag/NonSphereDragForce.H +++ b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/NonSphereDrag/NonSphereDragForce.H @@ -6,6 +6,7 @@ \\/ M anipulation | ------------------------------------------------------------------------------- Copyright (C) 2011-2017 OpenFOAM Foundation + Copyright (C) 2021 OpenCFD Ltd. ------------------------------------------------------------------------------- License This file is part of OpenFOAM. @@ -30,35 +31,114 @@ Group grpLagrangianIntermediateForceSubModels Description - Drag model for non-spherical particles. + Particle-drag model wherein drag forces (per unit carrier-fluid + velocity) are dynamically computed based on empirical expressions using + a four-parameter general drag correlation for non-spherical particles. - Takes the form of + \f[ + \mathrm{F}_\mathrm{D} = + \frac{3}{4} + \frac{\mu_c\,\mathrm{C}_\mathrm{D}\,\mathrm{Re}_p}{\rho_p \, d_p^2} + \f] + with - 24.0/Re*(1.0 + a_*pow(Re, b_)) + Re*c_/(Re + d_); + \f[ + \mathrm{C}_\mathrm{D} = + \frac{24}{\mathrm{Re}_p} \left( 1 + A \, \mathrm{Re}_p^B \right) + + \frac{C \, \mathrm{Re}_p}{D + \mathrm{Re}_p} + \f] + where - Where a(phi), b(phi), c(phi) and d(phi) are model coefficients, with phi - defined as: + \f[ + A = \exp(2.3288 - 6.4581\phi + 2.4486 \phi^2) + \f] - area of sphere with same volume as particle - phi = ------------------------------------------- - actual particle area + \f[ + B = 0.0964 + 0.5565\phi + \f] - Equation used is Eqn (11) of reference below - good to within 2 to 4 % of - RMS values from experiment. + \f[ + C = \exp(4.9050 - 13.8944\phi + 18.4222\phi^2 - 10.2599 \phi^3) + \f] - H and L also give a simplified model with greater error compared to - results from experiment - Eqn 12 - but since phi is presumed - constant, it offers little benefit. + \f[ + D = \exp(1.4681 + 12.2584\phi - 20.7322\phi^2 + 15.8855\phi^3) + \f] - Reference: + \f[ + \phi = \frac{A_p}{A_a} + \f] + + \f[ + \mathrm{Re}_p = + \frac{\rho_c \, | \mathbf{u}_\mathrm{rel} | \, d_p}{\mu_c} + \f] + + where + \vartable + \mathrm{F}_\mathrm{D} | Drag force per carrier-fluid velocity [kg/s] + \mathrm{C}_\mathrm{D} | Particle drag coefficient + \mathrm{Re}_p | Particle Reynolds number + \rho_p | Particle mass density + \mu_c | Dynamic viscosity of carrier at the cell occupying particle + d_p | Particle diameter + \rho_c | Density of carrier at the cell occupying particle + \mathbf{u}_\mathrm{rel} | Relative velocity between particle and carrier + A_p | Surface area of sphere with the same volume as the particle + A_a | Actual surface area of the particle + \phi | Ratio of surface areas + \endvartable + + Constraints: + - Applicable to particles with a spatially homogeneous distribution. + - \f$ 1 \geq \phi > 0 \f$ + + References: \verbatim - "Drag coefficient and terminal velocity of spherical and nonspherical - particles" - A. Haider and O. Levenspiel, - Powder Technology - Volume 58, Issue 1, May 1989, Pages 63-70 + Standard model (tag:HL), (Eq. 4,10-11): + Haider, A., & Levenspiel, O. (1989). + Drag coefficient and terminal velocity of + spherical and nonspherical particles. + Powder technology, 58(1), 63-70. + DOI:10.1016/0032-5910(89)80008-7 \endverbatim +Usage + Minimal example by using \c constant/\: + \verbatim + subModels + { + particleForces + { + nonSphereDrag + { + phi ; + } + } + } + \endverbatim + + where the entries mean: + \table + Property | Description | Type | Reqd | Deflt + type | Type name: nonSphereDrag | word | yes | - + phi | Ratio of surface area of sphere having same volume as particle to actual surface area of particle | scalar | yes | - + \endtable + +Note + - The drag coefficient model in (HL:Eq. 11) is good to within + 2 to 4 \% of RMS values from the corresponding experiment. + - (HL:Eq. 12) also give a simplified model with greater error + compared to results from the experiment, but since \c phi is + presumed constant, Eq. 12 offers little benefit. + - \f$\mathrm{F}_\mathrm{D}\f$ is weighted with the particle mass + at the stage of a function return, so that it can later be normalised + with the effective mass, if necessary (e.g. when using virtual-mass forces). + +SourceFiles + NonSphereDragForce.C \*---------------------------------------------------------------------------*/ diff --git a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/PlessisMasliyahDrag/PlessisMasliyahDragForce.H b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/PlessisMasliyahDrag/PlessisMasliyahDragForce.H index 7fd2575c13..da24387aea 100644 --- a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/PlessisMasliyahDrag/PlessisMasliyahDragForce.H +++ b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/PlessisMasliyahDrag/PlessisMasliyahDragForce.H @@ -31,7 +31,86 @@ Group grpLagrangianIntermediateForceSubModels Description - PlessisMasliyahDragForce drag model for solid spheres. + Particle-drag model wherein drag forces (per unit carrier-fluid + velocity) are dynamically computed based on the Du Plessis-Masliyah + drag model. + + \f[ + \mathrm{F}_\mathrm{D} = + \left(\mathrm{A}\, (1-\alpha_c) + \mathrm{B}\, \mathrm{Re}\right) + \frac{(1-\alpha_c)\, \mu_c}{\alpha_c^2\, d_p^2} + \f] + with + + \f[ + A = \frac{26.8\, \alpha_c^2} + { + \alpha_p^{2/3} + (1 - \alpha_p^{1/3}) + (1 - \alpha_p^{2/3}) + } + \f] + + \f[ + \mathrm{B} = \frac{\alpha_c^2}{\left( 1 - \alpha_p^{2/3} \right)^2} + \f] + + \f[ + \mathrm{Re}_p = + \frac{\rho_c \, | \mathbf{u}_\mathrm{rel} | \, d_p}{\mu_c} + \f] + + where + \vartable + \mathrm{F}_\mathrm{D} | Drag force per carrier-fluid velocity [kg/s] + \mathrm{Re}_p | Particle Reynolds number + \mu_c | Dynamic viscosity of carrier at the cell occupying particle + d_p | Particle diameter + \rho_c | Density of carrier at the cell occupying particle + \mathbf{u}_\mathrm{rel} | Relative velocity between particle and carrier + \alpha_c | Volume fraction of carrier fluid + \alpha_p | Volume fraction of particles + \endvartable + + References: + \verbatim + Standard model (tag:P), (Eq. 34-36): + Du Plessis, J. P. (1994). + Analytical quantification of coefficients in the + Ergun equation for fluid friction in a packed bed. + Transport in porous media, 16(2), 189-207. + DOI:10.1007/BF00617551 + \endverbatim + +Usage + Minimal example by using \c constant/\: + \verbatim + subModels + { + particleForces + { + PlessisMasliyahDrag + { + alphac ; // e.g. alpha.air + } + } + } + \endverbatim + + where the entries mean: + \table + Property | Description | Type | Reqd | Deflt + type | Type name: PlessisMasliyahDrag | word | yes | - + alphac | Name of carrier fluid | word | yes | - + \endtable + +Note + - \f$\mathrm{F}_\mathrm{D}\f$ is weighted with the particle mass/density + at the stage of a function return, so that it can later be normalised + with the effective mass, if necessary (e.g. when using virtual-mass forces). + +SourceFiles + PlessisMasliyahDragForce.C \*---------------------------------------------------------------------------*/ diff --git a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/SphereDrag/SphereDragForce.H b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/SphereDrag/SphereDragForce.H index 3618b8fc00..1fd0bb0772 100644 --- a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/SphereDrag/SphereDragForce.H +++ b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/SphereDrag/SphereDragForce.H @@ -6,6 +6,7 @@ \\/ M anipulation | ------------------------------------------------------------------------------- Copyright (C) 2011-2017 OpenFOAM Foundation + Copyright (C) 2021 OpenCFD Ltd. ------------------------------------------------------------------------------- License This file is part of OpenFOAM. @@ -30,7 +31,89 @@ Group grpLagrangianIntermediateForceSubModels Description - Drag model based on assumption of solid spheres + Particle-drag model wherein drag forces (per unit carrier-fluid + velocity) are dynamically computed based on empirical expressions. + + \f[ + \mathrm{F}_\mathrm{D} = + \frac{3}{4} + \frac{\mu_c\,\mathrm{C}_\mathrm{D}\,\mathrm{Re}_p}{\rho_p \, d_p^2} + \f] + with + + \f[ + \mathrm{C}_\mathrm{D} = + \frac{24}{\mathrm{Re}_p} + \left(1 + \frac{1}{6}\mathrm{Re}_p^{2/3} \right) + \quad \mathrm{if} \quad \mathrm{Re}_p \leq 1000 + \f] + \f[ + \mathrm{C}_\mathrm{D} = + 0.424 \quad \mathrm{if} \quad \mathrm{Re}_p > 1000 + \f] + and + \f[ + \mathrm{Re}_p = + \frac{\rho_c \, | \mathbf{u}_\mathrm{rel} | \, d_p}{\mu_c} + \f] + + where + \vartable + \mathrm{F}_\mathrm{D} | Drag force per carrier-fluid velocity [kg/s] + \mathrm{C}_\mathrm{D} | Particle drag coefficient + \mathrm{Re}_p | Particle Reynolds number + \rho_p | Particle mass density + \mu_c | Dynamic viscosity of carrier at the cell occupying particle + d_p | Particle diameter + \rho_c | Density of carrier at the cell occupying particle + \mathbf{u}_\mathrm{rel} | Relative velocity between particle and carrier + \endvartable + + Constraints: + - Particles remain spherical throughout the force + computation, hence no particle distortion. + - Applicable to particles with a spatially homogeneous distribution. + + References: + \verbatim + Standard model: + Putnam, A. (1961). + Integratable form of droplet drag coefficient. + ARS Journal, 31(10), 1467-1468. + + Expressions (tag:AOB), (Eq. 34-35): + Amsden, A. A., O'Rourke, P. J., & Butler, T. D. (1989). + KIVA-II: A computer program for chemically + reactive flows with sprays (No. LA-11560-MS). + Los Alamos National Lab.(LANL), Los Alamos, NM (United States). + DOI:10.2172/6228444 + \endverbatim + +Usage + Minimal example by using \c constant/\: + \verbatim + subModels + { + particleForces + { + sphereDrag; + } + } + \endverbatim + + where the entries mean: + \table + Property | Description | Type | Reqd | Deflt + type | Type name: sphereDrag | word | yes | - + \endtable + +Note + - \f$\mathrm{F}_\mathrm{D}\f$ is weighted with the particle mass/density + at the stage of a function return, so that it can later be normalised + with the effective mass, if necessary (e.g. when using virtual-mass forces). + +SourceFiles + SphereDragForce.C \*---------------------------------------------------------------------------*/ diff --git a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/WenYuDrag/WenYuDragForce.H b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/WenYuDrag/WenYuDragForce.H index 90a8cfa560..dd3dd88575 100644 --- a/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/WenYuDrag/WenYuDragForce.H +++ b/src/lagrangian/intermediate/submodels/Kinematic/ParticleForces/Drag/WenYuDrag/WenYuDragForce.H @@ -6,6 +6,7 @@ \\/ M anipulation | ------------------------------------------------------------------------------- Copyright (C) 2013-2017 OpenFOAM Foundation + Copyright (C) 2021 OpenCFD Ltd. ------------------------------------------------------------------------------- License This file is part of OpenFOAM. @@ -30,7 +31,102 @@ Group grpLagrangianIntermediateForceSubModels Description - Wen-Yu drag model for solid spheres. + Particle-drag model wherein drag forces (per unit carrier-fluid + velocity) are dynamically computed based on the Wen-Yu drag model. + + \f[ + \mathrm{F}_\mathrm{D} = + \frac{3}{4} + \frac{(1 - \alpha_c) \, \mu_c \, \alpha_c \, \mathrm{Re}_p }{d_p^2} + \mathrm{C}_\mathrm{D} \, \alpha_c^{-2.65} + \f] + with + + \f[ + \mathrm{C}_\mathrm{D} = + \frac{24}{\alpha_c \, \mathrm{Re}_p} + \left(1 + \frac{1}{6}(\alpha_c \, \mathrm{Re}_p)^{2/3} \right) + \quad \mathrm{if} \quad \alpha_c \, \mathrm{Re}_p < 1000 + \f] + \f[ + \mathrm{C}_\mathrm{D} = + 0.44 \quad \mathrm{if} \quad \alpha_c \, \mathrm{Re}_p \geq 1000 + \f] + and + \f[ + \mathrm{Re}_p = + \frac{\rho_c \, | \mathbf{u}_\mathrm{rel} | \, d_p}{\mu_c} + \f] + + where + \vartable + \mathrm{F}_\mathrm{D} | Drag force per carrier-fluid velocity [kg/s] + \mathrm{C}_\mathrm{D} | Particle drag coefficient + \mathrm{Re}_p | Particle Reynolds number + \mu_c | Dynamic viscosity of carrier at the cell occupying particle + d_p | Particle diameter + \rho_c | Density of carrier at the cell occupying particle + \mathbf{u}_\mathrm{rel} | Relative velocity between particle and carrier + \alpha_c | Volume fraction of the carrier fluid + \endvartable + + References: + \verbatim + Standard model: + Wen, C. Y., & Yu, Y. H., (1966). + Mechanics of fluidization. + Chem. Eng. Prog. Symp. Ser. 62, 100-111. + + Drag-coefficient model: + Schiller, L., & Naumann, A. (1935). + Über die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. + Z. Ver. Dtsch. Ing., 77: 318–326. + + Expressions (tags:ZZB, GLSLR), (Eq.13-14, Table 3): + Zhou, L., Zhang, L., Bai, L., Shi, W., + Li, W., Wang, C., & Agarwal, R. (2017). + Experimental study and transient CFD/DEM simulation in + a fluidized bed based on different drag models. + RSC advances, 7(21), 12764-12774. + DOI:10.1039/C6RA28615A + + Gao, X., Li, T., Sarkar, A., Lu, L., & Rogers, W. A. (2018). + Development and validation of an enhanced filtered drag model + for simulating gas-solid fluidization of Geldart A particles + in all flow regimes. + Chemical Engineering Science, 184, 33-51. + DOI:10.1016/j.ces.2018.03.038 + \endverbatim + +Usage + Minimal example by using \c constant/\: + \verbatim + subModels + { + particleForces + { + WenYuDrag + { + alphac ; // e.g. alpha.air + } + } + } + \endverbatim + + where the entries mean: + \table + Property | Description | Type | Reqd | Deflt + type | Type name: WenYuDrag | word | yes | - + alphac | Name of carrier fluid | word | yes | - + \endtable + +Note + - \f$\mathrm{F}_\mathrm{D}\f$ is weighted with the particle mass/density + at the stage of a function return, so that it can later be normalised + with the effective mass, if necessary (e.g. when using virtual-mass forces). + +SourceFiles + WenYuDragForce.C \*---------------------------------------------------------------------------*/