Incorporation of velocity-dependent restitution coefficient and particle surface friction into kinetic theory for modeling granular flow cooling

Duan, Yifei; Feng, Zhi-Gang

doi:10.1103/physreve.96.062907

Incorporation of velocity-dependent restitution coefficient and particle surface friction into kinetic theory for modeling granular flow cooling

Journal Article · Wed Dec 20 00:00:00 EST 2017 · Physical Review E

DOI:https://doi.org/10.1103/physreve.96.062907· OSTI ID:1541207

Duan, Yifei ^[1]; Feng, Zhi-Gang ^[2]

Univ. of Texas at San Antonio, TX (United States). Dept. of Mechanical Engineering; DOE/OSTI
Univ. of Texas at San Antonio, TX (United States). Dept. of Mechanical Engineering

Kinetic theory (KT) has been successfully used to model rapid granular flows in which particle interactions are frictionless and near elastic. However, it fails when particle interactions become frictional and inelastic. For example, the KT is not able to accurately predict the free cooling process of a vibrated granular medium that consists of inelastic frictional particles under microgravity. The main reason that the classical KT fails to model these flows is due to its inability to account for the particle surface friction and its inelastic behavior, which are the two most important factors that need be considered in modeling collisional granular flows. In this study, we have modified the KT model that is able to incorporate these two factors. The inelasticity of a particle is considered by establishing a velocity-dependent expression for the restitution coefficient based on many experimental studies found in the literature, and the particle friction effect is included by using a tangential restitution coefficient that is related to the particle friction coefficient. Theoretical predictions of the free cooling process by the classical KT and the improved KT are compared with the experimental results from a study conducted on an airplane undergoing parabolic flights without the influence of gravity [Y. Grasselli, G. Bossis, and G. Goutallier, Europhys. Lett. 86, 60007 (2009)]. Our results show that both the velocity-dependent restitution coefficient and the particle surface friction are important in predicting the free cooling process of granular flows; the modified KT model that integrates these two factors is able to improve the simulation results and leads to better agreement with the experimental results.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Texas at San Antonio, TX (United States)

Sponsoring Organization:: USDOE; USDOE Office of Fossil Energy (FE)

Grant/Contract Number:: FE0011453

OSTI ID:: 1541207

Alternate ID(s):: OSTI ID: 1414326

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 6 Vol. 96; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (62)

Boundary conditions for collisional granular flows of frictional and rotational particles at flat walls Zhao, Yunhua; Zhong, Yingjie; He, Yurong AIChE Journal, Vol. 60, Issue 12 https://doi.org/10.1002/aic.14596	journal	August 2014
A bubbling fluidization model using kinetic theory of granular flow Ding, Jianmin; Gidaspow, Dimitri AIChE Journal, Vol. 36, Issue 4 https://doi.org/10.1002/aic.690360404	journal	April 1990
The Coefficient of Restitution of Ice Particles in Glancing Collisions: Experimental Results for Unfrosted Surfaces Supulver, K. Icarus, Vol. 113, Issue 1 https://doi.org/10.1006/icar.1995.1015	journal	January 1995
The effects of an impact velocity dependent coefficient of restitution on stresses developed by sheared granular materials Lun, C. K. K.; Savage, S. B. Acta Mechanica, Vol. 63, Issue 1-4 https://doi.org/10.1007/BF01182538	journal	November 1986
Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy Herbst, Olaf; Huthmann, Martin; Zippelius, Annette Granular Matter, Vol. 2, Issue 4 https://doi.org/10.1007/PL00010915	journal	October 2000
Solutions of the kinetic theory for bounded collisional granular flows Xu, H.; Louge, M.; Reeves, A. Continuum Mechanics and Thermodynamics, Vol. 15, Issue 4 https://doi.org/10.1007/s00161-003-0116-6	journal	August 2003
Some experiments on anelastic rebound Lifshitz, J. M.; Kolsky, H. Journal of the Mechanics and Physics of Solids, Vol. 12, Issue 1 https://doi.org/10.1016/0022-5096(64)90005-5	journal	February 1964
A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres Thornton, Colin; Ning, Zemin Powder Technology, Vol. 99, Issue 2 https://doi.org/10.1016/S0032-5910(98)00099-0	journal	September 1998
Computational fluid dynamics for dense gas–solid fluidized beds: a multi-scale modeling strategy van der Hoef, M. A.; van Sint Annaland, M.; Kuipers, J. A. M. Chemical Engineering Science, Vol. 59, Issue 22-23 https://doi.org/10.1016/j.ces.2004.07.013	journal	November 2004
Euler–Euler modeling of a gas–solid bubbling fluidized bed with kinetic theory of rough particles Zhao, Yunhua; Lu, Bing; Zhong, Yingjie Chemical Engineering Science, Vol. 104 https://doi.org/10.1016/j.ces.2013.10.001	journal	December 2013
Modification of kinetic theory of granular flow for frictional spheres, Part I: Two-fluid model derivation and numerical implementation Yang, L. (Lei); Padding, J. T. (Johan); Kuipers, J. A. M. (Hans) Chemical Engineering Science, Vol. 152 https://doi.org/10.1016/j.ces.2016.05.031	journal	October 2016
Modification of kinetic theory of granular flow for frictional spheres, part II: Model validation Yang, L. (Lei); Padding, J. T. (Johan); Kuipers, J. A. M. (Hans) Chemical Engineering Science, Vol. 152 https://doi.org/10.1016/j.ces.2016.06.015	journal	October 2016
Microgravity experiments on the collisional behavior of saturnian ring particles Heißelmann, Daniel; Blum, Jürgen; Fraser, Helen J. Icarus, Vol. 206, Issue 2 https://doi.org/10.1016/j.icarus.2009.08.009	journal	April 2010
Influence of collisional parameters for rough particles on simulation of a gas-fluidized bed using a two-fluid model Zhao, Yunhua; Lu, Bing; Zhong, Yingjie International Journal of Multiphase Flow, Vol. 71 https://doi.org/10.1016/j.ijmultiphaseflow.2014.12.002	journal	May 2015
A comparison for different wall-boundary conditions for kinetic theory based two-fluid models Soleimani, Afsaneh; Schneiderbauer, Simon; Pirker, Stefan International Journal of Multiphase Flow, Vol. 71 https://doi.org/10.1016/j.ijmultiphaseflow.2014.12.008	journal	May 2015
High apparent adhesion energy in the breakdown of normal restitution for binary impacts of small spheres at low speed Sorace, C. M.; Louge, M. Y.; Crozier, M. D. Mechanics Research Communications, Vol. 36, Issue 3 https://doi.org/10.1016/j.mechrescom.2008.10.009	journal	April 2009
Open-source MFIX-DEM software for gas-solids flows: Part II — Validation studies Li, Tingwen; Garg, Rahul; Galvin, Janine Powder Technology, Vol. 220 https://doi.org/10.1016/j.powtec.2011.09.020	journal	April 2012
A modified cohesion model for CFD–DEM simulations of fluidization Gu, Yile; Ozel, Ali; Sundaresan, Sankaran Powder Technology, Vol. 296 https://doi.org/10.1016/j.powtec.2015.09.037	journal	August 2016
Computational fluid dynamics for dense gas-solid fluidized beds: a multi-scale modeling strategy van der Hoef, M. A.; van Sint Annaland, M.; Kuipers, J. A. M. China Particuology, Vol. 3, Issue 1-2 https://doi.org/10.1016/s1672-2515(07)60169-9	journal	April 2005
Experimental study on the kinetics of granular gases under microgravity Tatsumi, Soichi; Murayama, Yoshihiro; Hayakawa, Hisao Journal of Fluid Mechanics, Vol. 641 https://doi.org/10.1017/S002211200999231X	journal	December 2009
A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles Jenkins, J. T.; Savage, S. B. Journal of Fluid Mechanics, Vol. 130, Issue -1 https://doi.org/10.1017/S0022112083001044	journal	May 1983
Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield Lun, C. K. K.; Savage, S. B.; Jeffrey, D. J. Journal of Fluid Mechanics, Vol. 140 https://doi.org/10.1017/S0022112084000586	journal	March 1984
Numerical simulation of inelastic frictional spheres in simple shear flow Lun, C. K. K.; Bent, A. A. Journal of Fluid Mechanics, Vol. 258 https://doi.org/10.1017/S0022112094003356	journal	January 1994
Structure, stability and evolution of Saturn's rings Bridges, Frank G.; Hatzes, A.; Lin, D. N. C. Nature, Vol. 309, Issue 5966 https://doi.org/10.1038/309333a0	journal	May 1984
Kinetic theory for identical, frictional, nearly elastic spheres Jenkins, James T.; Zhang, Chao Physics of Fluids, Vol. 14, Issue 3 https://doi.org/10.1063/1.1449466	journal	March 2002
Equation of State for Nonattracting Rigid Spheres Carnahan, Norman F.; Starling, Kenneth E. The Journal of Chemical Physics, Vol. 51, Issue 2 https://doi.org/10.1063/1.1672048	journal	July 1969
Transport Properties of Polyatomic Fluids. IV. The Kinetic Theory of a Dense Gas of Perfectly Rough Spheres McCoy, Benjamin J.; Sandler, Stanley I.; Dahler, John S. The Journal of Chemical Physics, Vol. 45, Issue 10 https://doi.org/10.1063/1.1727365	journal	November 1966
Kinetic theory for identical, frictional, nearly elastic disks Yoon, David K.; Jenkins, James T. Physics of Fluids, Vol. 17, Issue 8 https://doi.org/10.1063/1.2000768	journal	August 2005
A driven two-dimensional granular gas with Coulomb friction Herbst, Olaf; Cafiero, Raffaele; Zippelius, Annette Physics of Fluids, Vol. 17, Issue 10 https://doi.org/10.1063/1.2049277	journal	January 2005
A modified kinetic theory for frictional granular flows in dense and dilute regimes Chialvo, Sebastian; Sundaresan, Sankaran Physics of Fluids, Vol. 25, Issue 7 https://doi.org/10.1063/1.4812804	journal	July 2013
Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations Vescovi, D.; Berzi, D.; Richard, P. Physics of Fluids, Vol. 26, Issue 5 https://doi.org/10.1063/1.4879267	journal	May 2014
Modified kinetic theory applied to the shear flows of granular materials Duan, Yifei; Feng, Zhi-Gang; Michaelides, Efstathios E. Physics of Fluids, Vol. 29, Issue 4 https://doi.org/10.1063/1.4979632	journal	April 2017
Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks Jenkins, J. T.; Richman, M. W. Physics of Fluids, Vol. 28, Issue 12 https://doi.org/10.1063/1.865302	journal	January 1985
Measurements of the collision properties of small spheres Foerster, Samuel F.; Louge, Michel Y.; Chang, Hongder Physics of Fluids, Vol. 6, Issue 3 https://doi.org/10.1063/1.868282	journal	March 1994
Introduction to discrete element methods: Basic of contact force models and how to perform the micro-macro transition to continuum theory Luding, Stefan European Journal of Environmental and Civil Engineering, Vol. 12, Issue 7-8 https://doi.org/10.1080/19648189.2008.9693050	journal	August 2008
Collisional properties of ice spheres at low impact velocities Hatzes, A. P.; Bridges, F. G.; Lin, D. N. C. Monthly Notices of the Royal Astronomical Society, Vol. 231, Issue 4 https://doi.org/10.1093/mnras/231.4.1091	journal	April 1988
Surface Energy and the Contact of Elastic Solids Johnson, K. L.; Kendall, K.; Roberts, A. D. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 324, Issue 1558 https://doi.org/10.1098/rspa.1971.0141	journal	September 1971
Model for collisions in granular gases Brilliantov, Nikolai V.; Spahn, Frank; Hertzsch, Jan-Martin Physical Review E, Vol. 53, Issue 5 https://doi.org/10.1103/PhysRevE.53.5382	journal	May 1996
Measurements of collisional properties of spheres using high-speed video analysis Labous, Laurent; Rosato, Anthony D.; Dave, Rajesh N. Physical Review E, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevE.56.5717	journal	November 1997
Homogeneous cooling of rough, dissipative particles: Theory and simulations Luding, S.; Huthmann, M.; McNamara, S. Physical Review E, Vol. 58, Issue 3 https://doi.org/10.1103/PhysRevE.58.3416	journal	September 1998
Simulations of vibrated granular medium with impact-velocity-dependent restitution coefficient McNamara, Sean; Falcon, Eric Physical Review E, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevE.71.031302	journal	March 2005
Evolution of enduring contacts and stress relaxation in a dense granular medium Zhang, Duan Z. Physical Review E, Vol. 71, Issue 4 https://doi.org/10.1103/PhysRevE.71.041303	journal	April 2005
Rheology of a granular gas under a plane shear Saitoh, Kuniyasu; Hayakawa, Hisao Physical Review E, Vol. 75, Issue 2 https://doi.org/10.1103/PhysRevE.75.021302	journal	February 2007
Collision dynamics of granular particles with adhesion Brilliantov, Nikolai V.; Albers, Nicole; Spahn, Frank Physical Review E, Vol. 76, Issue 5 https://doi.org/10.1103/PhysRevE.76.051302	journal	November 2007
Role of roughness on the hydrodynamic homogeneous base state of inelastic spheres Reyes, Francisco Vega; Santos, Andrés; Kremer, Gilberto M. Physical Review E, Vol. 89, Issue 2 https://doi.org/10.1103/PhysRevE.89.020202	journal	February 2014
Transient Structures in a Granular Gas Brilliantov, Nikolai; Salueña, Clara; Schwager, Thomas Physical Review Letters, Vol. 93, Issue 13 https://doi.org/10.1103/PhysRevLett.93.134301	journal	September 2004
Translations and Rotations Are Correlated in Granular Gases Brilliantov, N. V.; Pöschel, T.; Kranz, W. T. Physical Review Letters, Vol. 98, Issue 12 https://doi.org/10.1103/PhysRevLett.98.128001	journal	March 2007
Boundary Conditions for Rapid Granular Flow: Flat, Frictional Walls Jenkins, J. T. Journal of Applied Mechanics, Vol. 59, Issue 1 https://doi.org/10.1115/1.2899416	journal	March 1992
A Simple Kinetic Theory for Granular Flow of Rough, Inelastic, Spherical Particles Lun, C. K. K.; Savage, S. B. Journal of Applied Mechanics, Vol. 54, Issue 1 https://doi.org/10.1115/1.3172993	journal	March 1987
Impact: The Theory and Physical Behavior of Colliding Solids Goldsmith, Werner; Frasier, J. T. Journal of Applied Mechanics, Vol. 28, Issue 4 https://doi.org/10.1115/1.3641808	journal	December 1961
Stress relaxation in dense and slow granular flows Zhang, D. Z.; Rauenzahn, R. M. Journal of Rheology, Vol. 44, Issue 5 https://doi.org/10.1122/1.1287287	journal	September 2000
A viscoelastic model for dense granular flows Zhang, D. Z.; Rauenzahn, R. M. Journal of Rheology, Vol. 41, Issue 6 https://doi.org/10.1122/1.550844	journal	November 1997
Coefficient of tangential restitution for viscoelastic spheres Schwager, T.; Becker, V.; Pöschel, T. The European Physical Journal E, Vol. 27, Issue 1 https://doi.org/10.1140/epje/i2007-10356-3	journal	August 2008
Numerical Simulation of Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy van der Hoef, M. A.; van Sint Annaland, M.; Deen, N. G. Annual Review of Fluid Mechanics, Vol. 40, Issue 1 https://doi.org/10.1146/annurev.fluid.40.111406.102130	journal	January 2008
Velocity-dependent restitution coefficient and granular cooling in microgravity Grasselli, Y.; Bossis, G.; Goutallier, G. EPL (Europhysics Letters), Vol. 86, Issue 6 https://doi.org/10.1209/0295-5075/86/60007	journal	June 2009
Microgravity experiments on the collisional behavior of Saturnian ring particles Heißelmann, Daniel; Blum, Jürgen; Fraser, Helen J. arXiv https://doi.org/10.48550/arxiv.0908.3424	text	January 2009
Role of roughness on the hydrodynamic homogeneous base state of inelastic spheres Reyes, F. Vega; Santos, A.; Kremer, G. M. arXiv https://doi.org/10.48550/arxiv.1309.2369	text	January 2013
Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations Vescovi, Dalila; Berzi, Diego; Richard, Patrick arXiv https://doi.org/10.48550/arxiv.1406.0475	text	January 2014
A driven two-dimensional granular gas with Coulomb friction Herbst, Olaf; Cafiero, Raffaele; Zippelius, Annette arXiv https://doi.org/10.48550/arxiv.cond-mat/0501223	text	January 2005
Simulations of vibrated granular medium with impact velocity dependent restitution coefficient Mcnamara, Sean; Falcon, Eric arXiv https://doi.org/10.48550/arxiv.cond-mat/0502172	text	January 2005
Homogeneous cooling of rough, dissipative particles: Theory and simulations Luding, S.; Huthmann, M.; McNamara, S. arXiv https://doi.org/10.48550/arxiv.cond-mat/9804003	text	January 1998
Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy Herbst, Olaf; Huthmann, Martin; Zippelius, Annette arXiv https://doi.org/10.48550/arxiv.cond-mat/9911306	preprint	January 1999

Cited By (3)

Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres Megías, Alberto; Santos, Andrés Granular Matter, Vol. 21, Issue 3 https://doi.org/10.1007/s10035-019-0901-y	journal	June 2019
A new kinetic theory model of granular flows that incorporates particle stiffness Duan, Yifei; Feng, Zhi-Gang Physics of Fluids, Vol. 31, Issue 1 https://doi.org/10.1063/1.5051034	journal	January 2019
Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres Megías, Alberto; Santos, Andrés arXiv https://doi.org/10.48550/arxiv.1901.11307	text	January 2019

Similar Records

Modified kinetic theory applied to the shear flows of granular materials

Journal Article · Mon Apr 10 20:00:00 EDT 2017 · Physics of Fluids · OSTI ID:1347615

Measurement of flow properties coupled to experimental and numerical analyses of dense, granular flows for solar thermal energy storage

Journal Article · Mon Jun 29 20:00:00 EDT 2020 · Solar Energy · OSTI ID:1633772

Brownian motion in granular gases of viscoelastic particles

Journal Article · Mon Dec 14 23:00:00 EST 2009 · Journal of Experimental and Theoretical Physics · OSTI ID:21443648

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Incorporation of velocity-dependent restitution coefficient and particle surface friction into kinetic theory for modeling granular flow cooling

Citation Formats

References (62)

Cited By (3)

Similar Records

Related Subjects