Abstract
We obtain boundary conditions for two-dimensional flows of identical, nearly elastic, circular disks that interact with a flat wall to which identical, evenly spaced half-disks have been attached. Expressions for the transfer of momentum and energy from the boundary to the flow are obtained by statistical averaging over all possible wall-flow disk collisions. We improve upon the expressions derived by Jenkins and Richman [1986] by employing in the averaging process a more elaborate velocity distribution function obtained through the method of moments. In addition we expand the distribution function about a point near the flat wall that guarantees positive slip velocities. With these boundary conditions, we analyze a two-dimensional shear flow driven by parallel bumpy boundaries. The constitutive theory employed includes both the effects of particle collisions and particle transport on the transfer of momentum and energy throughout the flow. We demonstrate how the resulting profiles of velocity, granular temperature, and solid fraction are affected by changes in the geometry of the boundary. We also predict how the induced stresses vary with the geometry of the boundary and the average solid fraction within the flow.
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