diff --git a/docs/source_docs/refs.bib b/docs/source_docs/refs.bib index 557f0b2dabcac439a391f759d1c9a357b20360c0..63e613739ae4158edfe63f4bc588a6aebcf36ed3 100644 --- a/docs/source_docs/refs.bib +++ b/docs/source_docs/refs.bib @@ -19,21 +19,21 @@ } @article{almgren96, -author = {Almgren, Ann S. and Bell, John B. and Szymczak, William G.}, -title = {A Numerical Method for the Incompressible Navier--Stokes Equations Based on an Approximate Projection}, -year = {1996}, -issue_date = {March 1996}, -publisher = {Society for Industrial and Applied Mathematics}, -address = {USA}, -volume = {17}, -number = {2}, -issn = {1064-8275}, -url = {https://doi.org/10.1137/S1064827593244213}, -doi = {10.1137/S1064827593244213}, -journal = {SIAM Journal on Scientific Computing}, -month = mar, -pages = {358–369}, -numpages = {12}, + author = {Almgren, Ann S. and Bell, John B. and Szymczak, William G.}, + title = {A Numerical Method for the Incompressible Navier--Stokes Equations Based on an Approximate Projection}, + year = {1996}, + issue_date = {March 1996}, + publisher = {Society for Industrial and Applied Mathematics}, + address = {USA}, + volume = {17}, + number = {2}, + issn = {1064-8275}, + url = {https://doi.org/10.1137/S1064827593244213}, + doi = {10.1137/S1064827593244213}, + journal = {SIAM Journal on Scientific Computing}, + month = mar, + pages = {358–369}, + numpages = {12}, } @article{And67, @@ -46,12 +46,12 @@ numpages = {12}, } @article{And96, -author = {Andrews, M. and O'Rourke, P. }, -title = {The multiphase particle-in-cell (MP-PIC) method for dense particulate flows}, -journal = {International Journal of Multiphase Flow}, -year = {1996}, -volume = {22}, -pages = {379-402} + author = {Andrews, M. and O'Rourke, P. }, + title = {The multiphase particle-in-cell (MP-PIC) method for dense particulate flows}, + journal = {International Journal of Multiphase Flow}, + year = {1996}, + volume = {22}, + pages = {379-402} } @article{Ara79, @@ -63,6 +63,15 @@ pages = {379-402} pages = {123-130} } +@article{auton87, + title={The lift force on a spherical body in a rotational flow}, + author={Auton, T. R.}, + journal={Journal of Fluid Mechanics}, + volume={183}, + year={1987}, + pages={199–218} +} + @article{Bee07, author = {Beetstra, R. and van der Hoef, M. A. and Kuipers, J. A.M.}, title = { Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres}, @@ -443,6 +452,17 @@ doi = {https://doi.org/10.1016/j.jcp.2022.111305}, publisher={Cambridge University Press} } +@article{mei92, + title = {An approximate expression for the shear lift force on a spherical particle at finite reynolds number}, + journal = {International Journal of Multiphase Flow}, + volume = {18}, + number = {1}, + pages = {145-147}, + year = {1992}, + issn = {0301-9322}, + author = {R. Mei} +} + @article{nijssen20, author = {Tim M.J. Nijssen and Hans A.M. Kuipers and Jan {van der Stel} and Allert T. Adema and Kay A. Buist}, title = {Complete liquid-solid momentum coupling for unresolved CFD-DEM simulations}, @@ -452,7 +472,6 @@ doi = {https://doi.org/10.1016/j.jcp.2022.111305}, year = {2020} } - @article{Nonaka2018, author = {Andrew Nonaka and Marcus S. Day and John B. Bell}, title = {A conservative, thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration}, @@ -503,6 +522,16 @@ doi = {https://doi.org/10.1016/j.jcp.2022.111305}, pages = {267} } +@article{saffman65, + title={The lift on a small sphere in a slow shear flow}, + volume={22}, + number={2}, + journal={Journal of Fluid Mechanics}, + author={Saffman, P. G.}, + year={1965}, + pages={385–400} +} + @article{sato81, author = {Sato, Y. and Sadatomi, M.}, title = {Momentum and heat transfer in two-phase bubble flow - I. Theory}, @@ -589,6 +618,16 @@ doi = {https://doi.org/10.1016/j.jcp.2022.111305}, doi = {https://doi.org/10.1016/j.ijmultiphaseflow.2011.05.010}, } +@article{tomiyama02, + title = {Transverse migration of single bubbles in simple shear flows}, + author = {Akio Tomiyama and Hidesada Tamai and Iztok Zun and Shigeo Hosokawa}, + journal = {Chemical Engineering Science}, + volume = {57}, + number = {11}, + pages = {1849-1858}, + year = {2002} +} + @article{vanleer79, author = "Bram [van Leer]", title = "Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method", @@ -678,7 +717,6 @@ doi = {https://doi.org/10.1016/j.jcp.2022.111305}, year = {1964} } - @article{zhou1999, title={Rolling friction in the dynamic simulation of sandpile formation}, author={Zhou, YC and Wright, BD and Yang, RY and Xu, Bao Hua and Yu, Ai-Bing}, diff --git a/docs/source_docs/user_guide/inputs/model_options.rst b/docs/source_docs/user_guide/inputs/model_options.rst index fe32454aaaec3a00760846dbdaa10c146eb73048..f9d71ed860a2ad220dc165062a17db33bbbbc4ab 100644 --- a/docs/source_docs/user_guide/inputs/model_options.rst +++ b/docs/source_docs/user_guide/inputs/model_options.rst @@ -192,53 +192,109 @@ Drag coefficient The following input is defined using the prefix ``mfix.drag``: -.. |VirtualMass_Eq| replace:: :math:`\mathbf{F}_p,vm = -C_{p,vm} \rho_f \left(\frac{D\mathbf{u}_f}{Dt} - \frac{d\mathbf{u}_p}{dt}\right)\mathcal{V}_p` +.. |VirtualMass_Eq| replace:: :math:`\mathbf{F}_{p,vm} = -C_{p,vm} \rho_f \left(\frac{D\mathbf{u}_f}{Dt} - \frac{d\mathbf{u}_p}{dt}\right)\mathcal{V}_p` .. |VM_Zuber_Eq| replace:: :math:`C_{p,vm} = (\frac{1}{2})\frac{(1+2\varepsilon_p)}{(1-\varepsilon_p)}` .. |VM_Nijssen_Eq| replace:: :math:`C_{p,vm} = C_{0,vm} + \sum_{k=1}^3 \left\{ \left[a_{k,0} + a_{k,1} \ln\left(\frac{\rho_p}{\rho_f}\right)\right] \varepsilon_p^k \right\}` - -+--------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ -| | Description | Type | Default | -+==========================+===========================================================================================+===========+===========+ -| model | Fluid-particle drag model. Options: | String | None | -| | | | | -| | * ``WenYu``- Wen-Yu :cite:p:`Wen66` | | | -| | * ``Gidaspow`` :cite:p:`ding90,Lat00` | | | -| | * ``BVK2`` - Beetstra, van der Hoef, and Kuipers :cite:p:`Bee07,Bee071,tenneti11,tang15` | | | -| | * ``SyamOBrien`` - Syamlal-O'Brien :cite:p:`syam88` | | | -| | * ``UserDrag`` - User-supplied drag model | | | -| | | | | -| | | | | -+--------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ -| model.SyamOBrien.c1 | Fitting parameters for ``SyamOBrien`` drag model | Real | None | -| model.SyamOBrien.d1 | | | | -+--------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ -| virtual_mass | Include virtual mass force in fluid-particle momentum transfer. | String | None | -| | The virtual mass force is not included by default. | | | -| | | | | -| | |VirtualMass_Eq| | | | -| | | | | -| | Options: | | | -| | | | | -| | * ``None`` - virtual mass force calculation is skipped | | | -| | * ``Null`` - zero virtual mass coefficient, :math:`C_p,vm = 0` (for testing) | | | -| | * ``Constant`` - specified constant coefficient | | | -| | * ``Zuber`` - :cite:p:`zuber64` | | | -| | | | | -| | |VM_Zuber_Eq| | | | -| | | | | -| | * ``Nijssen`` - :cite:p:`nijssen20` | | | -| | | | | -| | |VM_Nijssen_Eq| | | | -+--------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ -| virtual_mass.constant | Constant virtual-mass coefficient. | Real | 0.5 | -+--------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ -| include_divtau | Interpolate the fluid shear stress to particles and include in the | Int | 0 | -| | fluid-particle drag force. The force is applied to the fluid by | | | -| | multiplying the shear stress by fluid volume fraction. | | | -+--------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +.. |Lift_Force_Eq| replace:: :math:`\mathbf{F}_{p,lift} = C_{p,L} \rho_f \left[ ( \mathbf{u}_f - \mathbf{u}_p) \times \omega \right] \mathcal{V}_p` + + +.. |LF_Tomiyama_Eq| replace:: :math:`C_L = \left\{ \begin{array}{ll} \min(0.288\tanh(0.121 \mathrm{Re}_p),f(\mathrm{Eo}_d^\ast)) & \mathrm{Eo}_d < 4 \\ f(\mathrm{Eo}_d^\ast) & 4 \le \mathrm{Eo}_d \le 10.7 \end{array} \right.` + +.. |LF_Tomiyama_Eq_fEo| replace:: :math:`f(\mathrm{Eo}_d^\ast) = 0.00105 \, {\mathrm{Eo}^\ast_d}^3 - 0.0159\, {\mathrm{Eo}^\ast_d}^2 - 0.0204\, {\mathrm{Eo}^\ast_d} + 0.474` + +.. |LF_Tomiyama_Eq_Eo_ast| replace:: :math:`\mathrm{Eo}^\ast_d = \min\left\{ \mathrm{Eo}_d, 10.7 \right\}` + +.. |LF_Saffman_Eq| replace:: :math:`C_L = \frac{1.61 d_p^2}{\mathcal{V}_p} \sqrt{\frac{\mu_f}{\rho_f \|\omega\|}}` + + +.. |LF_SaffmanMei_Eq| replace:: :math:`C_L = C_L^{\mathrm{Saffman}} J(\mathrm{Re}_p,\epsilon)` + +.. |LF_SaffmanMei_Eq_J_Re_le_4| replace:: :math:`J = \left\{ \begin{array}{ll} 0.0524 \sqrt{\mathrm{Re}_\omega} & \epsilon \le 20 \\ 1 - 0.287/\epsilon^2 & \epsilon \gt 20 \end{array} \right.` + +.. |LF_SaffmanMei_Eq_J_Re_gt_4| replace:: :math:`J = (1−0.3314 \sqrt{\epsilon / 2}) \exp{(-\mathrm{Re}_p/10)} + 0.3314 \sqrt{\epsilon / 2}` + ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +| | Description | Type | Default | ++===============================+===========================================================================================+===========+===========+ +| model | Fluid-particle drag model. Options: | String | None | +| | | | | +| | * ``WenYu``- Wen-Yu :cite:p:`Wen66` | | | +| | * ``Gidaspow`` :cite:p:`ding90,Lat00` | | | +| | * ``BVK2`` - Beetstra, van der Hoef, and Kuipers :cite:p:`Bee07,Bee071,tenneti11,tang15` | | | +| | * ``SyamOBrien`` - Syamlal-O'Brien :cite:p:`syam88` | | | +| | * ``UserDrag`` - User-supplied drag model | | | +| | | | | +| | | | | ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +| model.SyamOBrien.c1 | Fitting parameters for ``SyamOBrien`` drag model | Real | None | +| model.SyamOBrien.d1 | | | | ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +| virtual_mass | Include virtual mass force in fluid-particle momentum transfer. | String | None | +| | The virtual mass force is not included by default. | | | +| | | | | +| | |VirtualMass_Eq| | | | +| | | | | +| | Options: | | | +| | | | | +| | * ``None`` - virtual mass force calculation is skipped | | | +| | * ``Null`` - zero virtual mass coefficient, :math:`C_p,vm = 0` (for testing) | | | +| | * ``Constant`` - specified constant coefficient | | | +| | * ``Zuber`` - :cite:p:`zuber64` | | | +| | | | | +| | |VM_Zuber_Eq| | | | +| | | | | +| | * ``Nijssen`` - :cite:p:`nijssen20` | | | +| | | | | +| | |VM_Nijssen_Eq| | | | ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +| virtual_mass.constant | Constant virtual-mass coefficient. | Real | 0.5 | ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +| include_divtau | Interpolate the fluid shear stress to particles and include in the | Int | 0 | +| | fluid-particle drag force. The force is applied to the fluid by | | | +| | multiplying the shear stress by fluid volume fraction. | | | ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +| lift.model | Include lift force in fluid-particle momentum transfer. | String | None | +| | | | | +| | |Lift_Force_Eq| where :math:`\omega = \nabla \times \mathbf{u}_f` | | | +| | | | | +| | Options: | | | +| | | | | +| | * ``None`` - No lift force | | | +| | * ``Null`` - zero lift force, :math:`C_{p,L} = 0` (for testing) | | | +| | * ``Auton`` - specified constant coefficient :cite:p:`auton87` | | | +| | * ``Tomiyama`` - :cite:p:`tomiyama02` | | | +| | | | | +| | |LF_Tomiyama_Eq| | | | +| | | | | +| | where |LF_Tomiyama_Eq_Eo_ast| and |LF_Tomiyama_Eq_fEo| | | | +| | | | | +| | * ``Saffman`` - :cite:p:`saffman65` | | | +| | | | | +| | |LF_Saffman_Eq| | | | +| | | | | +| | * ``Saffman-Mei`` - :cite:p:`mei92` | | | +| | | | | +| | |LF_SaffmanMei_Eq| | | | +| | | | | +| | For Re :math:`\le 4`: | | | +| | | | | +| | |LF_SaffmanMei_Eq_J_Re_le_4| | | | +| | | | | +| | For Re :math:`\gt 4`: | | | +| | | | | +| | |LF_SaffmanMei_Eq_J_Re_gt_4| | | | +| | | | | +| | where :math:`\epsilon = \mathrm{Re}_\omega / \mathrm{Re}_p` and | | | +| | :math:`\mathrm{Re}_\omega = {\rho_f \|\omega\| d_p^2}/\mu_f` | | | +| | | | | ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +| lift.Auton.coeff | Constant coefficient for Auton lift force model. | Real | 0.5 | ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ +| lift.Tomiyama.surface_tension | Surface tension in Tomiyama lift force model. | Real | None | ++-------------------------------+-------------------------------------------------------------------------------------------+-----------+-----------+ .. note::