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

摘要

Kinetic theory (KT) has been successfully used to model rapid granular flows in which particle interactions arefrictionless 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 ofinelastic frictional particles under microgravity. The main reason that the classical KT fails to model these flowsis due to its inability to account for the particle surface friction and its inelastic behavior, which are the two mostimportant factors that need be considered in modeling collisional granular flows. In this study, we have modifiedtheKT model that is able to incorporate these two factors. The inelasticity of a particle is considered by establishinga velocity-dependent expression for the restitution coefficient based on many experimental studies found in theliterature, and the particle friction effect is included by using a tangential restitution coefficient that is related tothe particle friction coefficient. Theoretical predictions of the free cooling process by the classical KT and the improvedKTare comparedwith the experimental results from a study conducted on an airplane undergoing parabolicflights 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 frictionare important in predicting the free cooling process of granular flows; the modified KT model that integrates thesetwo factors is able to improve the simulation results and leads to better agreement with the experimental results.