A Bhatnagar-Gross-Krook-like Model Kinetic Equation for a Granular Gas of Inelastic Rough Hard Spheres

Journal Article · Fri May 20 04:00:00 EDT 2011 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3562623· OSTI ID:21511587

Santos, Andres ^[1]

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1. Departamento de Fisica, Universidad de Extremadura, E-06071 Badajoz (Spain)

The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the translational velocity v of the center of mass but also on the angular velocity {omega} of the particle. Moreover, the collision rules couple v and {omega}, involving not only the coefficient of normal restitution {alpha} but also the coefficient of tangential restitution {beta}. The aim of this paper is to propose an extension to inelastic rough particles of a Bhatnagar-Gross-Krook-like kinetic model previously proposed for inelastic smooth particles. The Boltzmann collision operator is replaced by the sum of three terms representing: (i) the relaxation to a two-temperature local equilibrium distribution, (ii) the action of a nonconservative drag force F proportional to v-u(u being the flow velocity), and (iii) the action of a nonconservative torque M equal to a linear combination of {omega} and {Omega}({Omega} being the mean angular velocity). The three coefficients in F and M are fixed to reproduce the Boltzmann collisional rates of change of {Omega} and of the two granular temperatures (translational and rotational). A simpler version of the model is also constructed in the form of two coupled kinetic equations for the translational and rotational velocity distributions. The kinetic model is applied to the simple shear flow steady state and the combined influence of {alpha} and {beta} on the shear and normal stresses and on the translational velocity distribution function is analyzed.

• OSTI ID: 21511587
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1333; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR VELOCITY
CENTER-OF-MASS SYSTEM
COLLISIONS
DIFFUSION
DISTRIBUTION
DISTRIBUTION FUNCTIONS
DRAG
EQUATIONS
EQUILIBRIUM
FUNCTIONS
KINETIC EQUATIONS
PARTICLES
RELAXATION
SHEAR
SPHERES
STEADY-STATE CONDITIONS
STRESSES
TORQUE
VELOCITY