Capturing the dynamics of a two orifice silo with the μ(I) model and extensions

Advanced Powder Technology - Tập 34 - Trang 104044 - 2023
Samuel K. Irvine1, Luke A. Fullard1, Daniel J. Holland2, Daniel A. Clarke3, Thomasin A. Lynch1, Pierre-Yves Lagrée4
1School of Mathematical and Computational Sciences, Massey University, Palmerston North, New Zealand
2Department of Chemical and Process Engineering, University of Canterbury, Christchurch, New Zealand
3School of Chemical and Physical Sciences, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand
4Sorbonne Université, Institut Jean Le Rond d’Alembert, CNRS, UMR7190, Paris 75005, France

Tài liệu tham khảo

Cheng, 2018, Inter-orifice distance dependence of flow rate in a quasi-two-dimensional hopper with dual outlets, Powder Technol., 328, 7, 10.1016/j.powtec.2018.01.019 Fullard, 2019, The dynamics of granular flow from a silo with two symmetric openings, Proc. Roy. Soc. A, 475, 20180462, 10.1098/rspa.2018.0462 Melo, 2007, On drawbody shapes: from bergmark–roos to kinematic models, Int. J. Rock Mech. Min. Sci., 44, 77, 10.1016/j.ijrmms.2006.04.010 Melo, 2008, Kinematic model for quasi static granular displacements in block caving: Dilatancy effects on drawbody shapes, Int. J. Rock Mech. Min. Sci., 45, 248, 10.1016/j.ijrmms.2007.07.005 PA Cundall. A computer model for rock mass behavior using interactive graphics for the input and output of geometrical data. A Report Prepared under Contract Number DACW 45–74-C-006, for the Missouri River Division, 1974. Zhang, 2016, Investigation of flow rate in a quasi-2d hopper with two symmetric outlets, Phys. Lett. A, 380, 1301, 10.1016/j.physleta.2016.01.046 MiDi, 2004, On dense granular flows, Eur. Phys. J. E, 14, 341, 10.1140/epje/i2003-10153-0 Jop, 2006, A constitutive law for dense granular flows, Nature, 441, 727, 10.1038/nature04801 Holyoake, 2012, High-speed granular chute flows, J. Fluid Mech., 710, 35, 10.1017/jfm.2012.331 Staron, 2012, The granular silo as a continuum plastic flow: The hour-glass vs the clepsydra, Phys. Fluids, 24, 103301, 10.1063/1.4757390 Staron, 2014, Continuum simulation of the discharge of the granular silo, Eur. Phys. J. E, 37, 1, 10.1140/epje/i2014-14005-6 Z Zou, Pierre Ruyer, P-Y. Lagrée, Pascale Aussillous, Discharge of a silo through a lateral orifice: Role of the bottom inclination versus friction. Phys. Rev. E, 102(5):052902, 2020. Fullard, 2019, Pierre-Yves Lagrée, Stéphane Popinet. Quantifying silo flow using mri velocimetry for testing granular flow models, Phys. Rev. Fluids, 4, 074302, 10.1103/PhysRevFluids.4.074302 Zhou, 2017, Experiments on, and discrete and continuum simulations of, the discharge of granular media from silos with a lateral orifice, J. Fluid Mech., 829, 459, 10.1017/jfm.2017.543 Reynolds, 1885, Lvii. on the dilatancy of media composed of rigid particles in contact. with experimental illustrations, The London, Edinburgh, and Dublin Philos. Magaz. J. Sci., 20, 469, 10.1080/14786448508627791 Guilherme Salvador-Vieira, Lydie Staron, Stéphane Popinet, Stéphanie Deboeuf, Pierre-Yves Lagrée, Modeling flow arrest using a non-local rheology? in: EPJ Web of Conferences, volume 140, page 03045. EDP Sciences, 2017. David L. Henann, Ken Kamrin, A predictive, size-dependent continuum model for dense granular flows, Proc. Natl. Acad. Sci., 110(17), 6730–6735, 2013. Kamrin, 2012, Nonlocal constitutive relation for steady granular flow, Phys. Rev. Lett., 108, 178301, 10.1103/PhysRevLett.108.178301 Bouzid, 2015, Non-local rheology in dense granular flows, Eur. Phys. J. E, 38, 1, 10.1140/epje/i2015-15125-1 Barker, 2015, Well-posed and ill-posed behaviour of the-rheology for granular flow, J. Fluid Mech., 779, 794, 10.1017/jfm.2015.412 Joris Heyman, 2017, Compressibility regularizes the μ (i)-rheology for dense granular flows, J. Fluid Mech., 830, 553, 10.1017/jfm.2017.612 Irvine, 2016, The effect of heaped and sloped powder layers on ejection times and the residence-time distribution of a conical mass-flow hopper, 175 Ronald Midgley Nedderman et al, 1992, volume 352 Jaehyuk Choi, Arshad Kudrolli, Martin Z. Bazant, Velocity profile of granular flows inside silos and hoppers, J. Phys.: Condensed Matter, 17(24):S2533, 2005. Nedderman, 1979, A kinematic model for the flow of granular materials, Powder Technol., 22, 243, 10.1016/0032-5910(79)80030-3 Kenneth Norman Kamrin, 2008 Ken Kamrin, A hierarchy of granular continuum models: Why flowing grains are both simple and complex, in: EPJ Web of Conferences, volume 140, page 01007. EDP Sciences, 2017. Popinet, 2003, Gerris: a tree-based adaptive solver for the incompressible euler equations in complex geometries, J. Comput. Phys., 190, 572, 10.1016/S0021-9991(03)00298-5 Lagrée, 2011, The granular column collapse as a continuum: validity of a two-dimensional navier–stokes model with a <texmath type=”inline”>mu </texmath> (i)-rheology, J. Fluid Mech., 686, 378, 10.1017/jfm.2011.335 Stéphane Popinet and collaborators. Basilisk. http://basilisk.fr, 2015. López-Herrera, 2015, Electrokinetic effects in the breakup of electrified jets: A volume-of-fluid numerical study, Int. J. Multiph. Flow, 71, 14, 10.1016/j.ijmultiphaseflow.2014.12.005 P-P Cortet, Daniel Bonamy, François Daviaud, Olivier Dauchot, Bérengère Dubrulle, Mathieu Renouf, Relevance of visco-plastic theory in a multi-directional inhomogeneous granular flow, EPL (Europhys. Lett.), 88(1):14001, 2009. J. Antoon Van Hooft, Stéphane Popinet, Chiel C. Van Heerwaarden, Steven J.A. Van der Linden, Stephan R. de Roode, Bas J.H. Van de Wiel, Towards adaptive grids for atmospheric boundary-layer simulations, Bound.-layer Meteorol., 167(3):421–443, 2018. Zhou, 2016 Shafaei, 2016, Analytical study of friction coefficients of pomegranate seed as essential parameters in design of post-harvest equipment, Inform. Process. Agric., 3, 133 Andreotti, 2013 Thomas Barker, 2017, Well-posed continuum equations for granular flow with compressibility and μ (I)-rheology, Proc. Roy. Soc. A: Math., Phys. Eng. Sci., 473, 20160846, 10.1098/rspa.2016.0846 Pailha, 2009, A two-phase flow description of the initiation of underwater granular avalanches, J. Fluid Mech., 633, 115, 10.1017/S0022112009007460 Bouchut, 2021, Dilatancy in dry granular flows with a compressible μ(I) rheology, J. Comput. Phys., 429, 110013, 10.1016/j.jcp.2020.110013 Hurley, 2015, Friction in inertial granular flows: competition between dilation and grain-scale dissipation rates, Granular Matter, 17, 287, 10.1007/s10035-015-0564-2 Robinson, 2021, Evidence of a non-local ø(I) response. In EPJ Web of Conferences, EDP Sci., 249, page 03028 Pouliquen, 2009, A non-local rheology for dense granular flows, Philos. Trans. Royal Soc.A: Math., Phys. Eng. Sci., 367, 5091, 10.1098/rsta.2009.0171 Dorian Faroux, Kimiaki Washino, Takuya Tsuji, Toshitsugu Tanaka, Coupling non-local rheology and volume of fluid (vof) method: a finite volume method (fvm) implementation. In EPJ Web of Conferences, volume 249, page 03025. EDP Sciences, 2021. Kamrin, 2019, Non-locality in granular flow: Phenomenology and modeling approaches, Front. Phys., 7, 116, 10.3389/fphy.2019.00116 Wim A. Beverloo, Hendrik Antonie Leniger, J. Van de Velde, The flow of granular solids through orifices, Chem. Eng. Sci., 15(3-4):260–269, 1961. Mankoc, 2007, The flow rate of granular materials through an orifice, Granular Matter, 9, 407, 10.1007/s10035-007-0062-2