GRAVITY-DRIVEN FLOWS OF SMOOTH, INELASTIC DISKS BETWEEN PARALLEL BUMPY BOUNDARIES

The problem of a steady gravity-driven granular flow of identical, smooth, slightly inelastic, circular disks between parallel bumpy boundaries is analyzed. The balance laws, constitutive equations and boundary conditions obtained by the kinetic theory (Richman and Chou, 1988) are utilized. Both collisional and transport contributions to the fluxes of momentum and fluctuation energy are considered. The problem is reduced to a system of coupled differential equations governing the transverse variations of granular temperature, shear stress, and solid fraction with the appropriate boundary conditions. The numerical procedure is developed using a variation of shooting method in order to simultaneously satisfy all of the boundary conditions. The particle flux (discharge) calculated using the present theory compares favorably with the data from numerical simulations and air table experiments reported by Sanders et al. (1988).