(25d) Interpretation of Specularity Coefficient Used In Boundary Conditions for Rapid Granular Flows

Tingwen Li^1,2, Sofiane Benyahia¹

1. National Energy Technology Laboratory, Morgantown, WV 26505, U.S.A.

2. URS Corporation, Morgantown, WV 26505, U.S.A. Abstract

In this presentation, we revisit Johnson and Jackson boundary conditions for rapid granular flows (Johnson PC, Jackson R. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics. 1987; 176: 67-93). The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semi-analytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measureable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.