Boundary layer modeling of granular flow in the transverse plane of a partially filled rotating cylinder

Abstract During the processing of particulate materials in rotary kilns and driers the transverse motion generated in the bed is the primary factor controlling renewal of material at the exposed bed surface. The rate of surface renewal, in turn, determines the degree of material mixing and the rate of heat transfer from the freeboard to the bed. An experimental campaign launched to investigate granular flow behavior in a transverse plane of a rotary cylinder suggests that a continuum model based on the constitutive equations developed for gravity flow in chutes may be adopted, in some particular cases, to describe flow in the shear (active) layer. A model is developed in which the dimensions of the shear layer, the region near the free surface, is assumed thin thereby permitting the governing equations to reduce to Prandtl's boundary layer equations which are solved to obtain the depth and velocity profiles within the layer. Because the density at the free surface is discontinuous for the flow regimes of practical interest, the continuum assumption breaks down at the free surface, hence, a stress-free boundary condition has been avoided. In place of this a surface velocity constraint from the experimental campaign has been applied which, therefore, makes the model deficient in exploring the full potential of the boundary layer analogy. Nevertheless, the appropriate velocity trends are predicted well into the bed with the results comparing favorably with experimental data.