Modified kinetic theory applied to the shear flows of granular materials
Abstract
Here, granular materials are characterized by large collections of discrete particles, where the particle-particle interactions are significantly more important than the particle-fluid interactions. The current kinetic theory captures fairly accurately the granular flow behavior in the dilute case, when only binary interactions are significant, but is not accurate at all in the dense flow regime, where multi-particle interactions and contacts must be modeled. To improve the kinetic theory results for granular flows in the dense flow regime, we propose a Modified Kinetic Theory (MKT) model that utilizes the contact duration or cut-off time to account for the complex particle-particle interactions in the dense regime. The contact duration model, also called TC model, is originally proposed by Luding and McNamara to solve the inelastic collapse issue existing in the Inelastic Hard Sphere (IHS) model. This model defines a cut-off time tc such that dissipation is not counted if the time between two consecutive contacts is less than tc. As shown in their study, the use of a cut-off time tc can also reduce the dissipation during multi-particle contacts. In this paper we relate the TC model with the Discrete Element Method (DEM) by choosing the cut-off time tc to be themore »
- Authors:
-
- Univ. of Texas at San Antonio, San Antonio, TX (United States)
- Texas Christian Univ., Fort Worth, TX (United States)
- Univ. of Texas at El Paso, El Paso, TX (United States)
- Publication Date:
- Research Org.:
- Univ. of Texas at San Antonio, San Antonio, TX (United States)
- Sponsoring Org.:
- USDOE Office of Fossil Energy (FE)
- OSTI Identifier:
- 1347615
- Alternate Identifier(s):
- OSTI ID: 1361806
- Grant/Contract Number:
- FE0011453
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Fluids
- Additional Journal Information:
- Journal Volume: 29; Journal Issue: 4; Journal ID: ISSN 1070-6631
- Publisher:
- American Institute of Physics
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; kinetic theory; granular flows modeling; discrete element method
Citation Formats
Duan, Yifei, Feng, Zhi -Gang, Michaelides, Efstathios E., and Mao, Shaolin. Modified kinetic theory applied to the shear flows of granular materials. United States: N. p., 2017.
Web. doi:10.1063/1.4979632.
Duan, Yifei, Feng, Zhi -Gang, Michaelides, Efstathios E., & Mao, Shaolin. Modified kinetic theory applied to the shear flows of granular materials. United States. https://doi.org/10.1063/1.4979632
Duan, Yifei, Feng, Zhi -Gang, Michaelides, Efstathios E., and Mao, Shaolin. Tue .
"Modified kinetic theory applied to the shear flows of granular materials". United States. https://doi.org/10.1063/1.4979632. https://www.osti.gov/servlets/purl/1347615.
@article{osti_1347615,
title = {Modified kinetic theory applied to the shear flows of granular materials},
author = {Duan, Yifei and Feng, Zhi -Gang and Michaelides, Efstathios E. and Mao, Shaolin},
abstractNote = {Here, granular materials are characterized by large collections of discrete particles, where the particle-particle interactions are significantly more important than the particle-fluid interactions. The current kinetic theory captures fairly accurately the granular flow behavior in the dilute case, when only binary interactions are significant, but is not accurate at all in the dense flow regime, where multi-particle interactions and contacts must be modeled. To improve the kinetic theory results for granular flows in the dense flow regime, we propose a Modified Kinetic Theory (MKT) model that utilizes the contact duration or cut-off time to account for the complex particle-particle interactions in the dense regime. The contact duration model, also called TC model, is originally proposed by Luding and McNamara to solve the inelastic collapse issue existing in the Inelastic Hard Sphere (IHS) model. This model defines a cut-off time tc such that dissipation is not counted if the time between two consecutive contacts is less than tc. As shown in their study, the use of a cut-off time tc can also reduce the dissipation during multi-particle contacts. In this paper we relate the TC model with the Discrete Element Method (DEM) by choosing the cut-off time tc to be the duration of contact calculated from the linear-spring-dashpot soft-sphere model of the DEM. We examine two types of granular flows: simple shear flow and the plane shear flow, and compare the results of the classical Kinetic Theory (KT) model, the present MKT model, and the DEM model. Here, we show that the MKT model entails a significant improvement over the KT model for simple shear flows at inertial regimes. With the MKT model the calculations are close to the DEM results at solid fractions as high as 0.57. Even for the plane shear flows, where shear rate and solid fraction are inhomogeneous, the results of the MKT model agree very well with the DEM results.},
doi = {10.1063/1.4979632},
journal = {Physics of Fluids},
number = 4,
volume = 29,
place = {United States},
year = {Tue Apr 11 00:00:00 EDT 2017},
month = {Tue Apr 11 00:00:00 EDT 2017}
}
Web of Science
Works referenced in this record:
CFD modeling of particle–particle heat transfer in dense gas-solid fluidized beds of binary mixture
journal, February 2012
- Chang, Jian; Wang, Gang; Gao, Jinsen
- Powder Technology, Vol. 217
Velocity correlations in dense granular shear flows: Effects on energy dissipation and normal stress
journal, March 2007
- Mitarai, Namiko; Nakanishi, Hiizu
- Physical Review E, Vol. 75, Issue 3
Nonlinear elasto-plastic model for dense granular flow
journal, February 2010
- Kamrin, Ken
- International Journal of Plasticity, Vol. 26, Issue 2
Rheology of a granular gas under a plane shear
journal, February 2007
- Saitoh, Kuniyasu; Hayakawa, Hisao
- Physical Review E, Vol. 75, Issue 2
Extended kinetic theory applied to dense, granular, simple shear flows
journal, April 2014
- Berzi, Diego
- Acta Mechanica, Vol. 225, Issue 8
Dynamics of dense sheared granular flows. Part 1. Structure and diffusion
journal, July 2009
- Kumaran, V.
- Journal of Fluid Mechanics, Vol. 632
Collisional cooling with multi-particle interactions
journal, December 2003
- Luding, Stefan; Goldshtein, Alexander
- Granular Matter, Vol. 5, Issue 3
A modified kinetic theory for frictional granular flows in dense and dilute regimes
journal, July 2013
- Chialvo, Sebastian; Sundaresan, Sankaran
- Physics of Fluids, Vol. 25, Issue 7
How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model
journal, December 1998
- Luding, Stefan; McNamara, Sean
- Granular Matter, Vol. 1, Issue 3
Instability in the evolution equations describing incompressible granular flow
journal, January 1987
- Schaeffer, David G.
- Journal of Differential Equations, Vol. 66, Issue 1
The interface between fluid-like and solid-like behaviour in two-dimensional granular flows
journal, April 1992
- Zhang, Yi; Campbell, Charles S.
- Journal of Fluid Mechanics, Vol. 237
Kinetic theory for identical, frictional, nearly elastic spheres
journal, March 2002
- Jenkins, James T.; Zhang, Chao
- Physics of Fluids, Vol. 14, Issue 3
Nearest-neighbor statistics for packings of hard spheres and disks
journal, April 1995
- Torquato, S.
- Physical Review E, Vol. 51, Issue 4
Simple shear flows of dense gas-solid suspensions at finite Stokes numbers
journal, April 1996
- Sangani, Ashok S.; Mo, Guobiao; Tsao, Heng-Kwong
- Journal of Fluid Mechanics, Vol. 313
Dense inclined flows of inelastic spheres
journal, August 2007
- Jenkins, James T.
- Granular Matter, Vol. 10, Issue 1
Revisiting Johnson and Jackson boundary conditions for granular flows
journal, August 2011
- Li, Tingwen; Benyahia, Sofiane
- AIChE Journal, Vol. 58, Issue 7
Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks
journal, January 1985
- Jenkins, J. T.; Richman, M. W.
- Physics of Fluids, Vol. 28, Issue 12
Numerical Simulation of Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy
journal, January 2008
- van der Hoef, M. A.; van Sint Annaland, M.; Deen, N. G.
- Annual Review of Fluid Mechanics, Vol. 40, Issue 1
Multiple pathways for SOS-induced mutagenesis in Escherichia coli: An overexpression of dinB/dinP results in strongly enhancing mutagenesis in the absence of any exogenous treatment to damage DNA
journal, December 1997
- Kim, S. -R.; Maenhaut-Michel, G.; Yamada, M.
- Proceedings of the National Academy of Sciences, Vol. 94, Issue 25
A constitutive law for dense granular flows
journal, June 2006
- Jop, Pierre; Forterre, Yoël; Pouliquen, Olivier
- Nature, Vol. 441, Issue 7094
Mixing and segregation in a bidisperse gas–solid fluidised bed: a numerical and experimental study
journal, February 2004
- Bokkers, G. A.; van Sint Annaland, M.; Kuipers, J. A. M.
- Powder Technology, Vol. 140, Issue 3
Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations
journal, May 2014
- Vescovi, D.; Berzi, D.; Richard, P.
- Physics of Fluids, Vol. 26, Issue 5
Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory
journal, April 2010
- Jenkins, James T.; Berzi, Diego
- Granular Matter, Vol. 12, Issue 2
The computer study of transport processes under extreme conditions
journal, August 1972
- Lees, A. W.; Edwards, S. F.
- Journal of Physics C: Solid State Physics, Vol. 5, Issue 15
Homogeneous cooling of rough, dissipative particles: Theory and simulations
journal, September 1998
- Luding, S.; Huthmann, M.; McNamara, S.
- Physical Review E, Vol. 58, Issue 3
Energy characteristics of simple shear granular flows
journal, November 2012
- Sun, Qicheng; Jin, Feng; Zhou, Gordon G. D.
- Granular Matter, Vol. 15, Issue 1
Dense fluid transport for inelastic hard spheres
journal, May 1999
- Garzó, V.; Dufty, J. W.
- Physical Review E, Vol. 59, Issue 5
Dense shearing flows of inelastic disks
journal, October 2006
- Jenkins, James T.
- Physics of Fluids, Vol. 18, Issue 10
Unsteady Couette granular flows
journal, September 1997
- Babic, Marijan
- Physics of Fluids, Vol. 9, Issue 9
Velocity distributions in homogeneous granular fluids: the free and the heated case
journal, September 1998
- van Noije, T. P. C.; Ernst, M. H.
- Granular Matter, Vol. 1, Issue 2
A modified cohesion model for CFD–DEM simulations of fluidization
journal, August 2016
- Gu, Yile; Ozel, Ali; Sundaresan, Sankaran
- Powder Technology, Vol. 296
Comparison of Kinetic Theory and Discrete Element Schemes for Modelling Granular Couette Flows
journal, October 1999
- Popken, Lars; Cleary, Paul W.
- Journal of Computational Physics, Vol. 155, Issue 1
Simple shear flows of dense gas-solid suspensions at finite Stokes numbers
journal, December 1997
- Balachandar, Sivaramakrishnan; Soldati, Alfredo
- International Journal of Multiphase Flow, Vol. 23, Issue 7, p. 106
Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations
text, January 2014
- Vescovi, Dalila; Berzi, Diego; Richard, Patrick
- arXiv
Velocity correlations in the dense granular shear flows: Effects on energy dissipation and normal stress
text, January 2006
- Mitarai, Namiko; Nakanishi, Hiizu
- arXiv
Homogeneous cooling of rough, dissipative particles: Theory and simulations
text, January 1998
- Luding, S.; Huthmann, M.; McNamara, S.
- arXiv
Works referencing / citing this record:
Continuum Modeling of Pressure‐Balanced and Fluidized Granular Flows in 2‐D: Comparison With Glass Bead Experiments and Implications for Concentrated Pyroclastic Density Currents
journal, June 2019
- Breard, E. C. P.; Dufek, J.; Roche, O.
- Journal of Geophysical Research: Solid Earth, Vol. 124, Issue 6
Granular flows in a rotating drum and on an inclined plane: Analytical and numerical solutions
journal, October 2018
- Meng, Xiannan; Wang, Yongqi; Feng, Feng
- Physics of Fluids, Vol. 30, Issue 10
A new kinetic theory model of granular flows that incorporates particle stiffness
journal, January 2019
- Duan, Yifei; Feng, Zhi-Gang
- Physics of Fluids, Vol. 31, Issue 1
Incorporation of velocity-dependent restitution coefficient and particle surface friction into kinetic theory for modeling granular flow cooling
journal, December 2017
- Duan, Yifei; Feng, Zhi-Gang
- Physical Review E, Vol. 96, Issue 6
Incorporation of Velocity-dependent Restitution Coefficient and Particle Surface Friction into Kinetic Theory for Modeling Granular Flow Cooling
text, January 2017
- Duan, Yifei; Feng, Zhi-Gang
- arXiv