An analytical and numerical study of granular flows in hoppers.

摘要

This work investigates the characteristics of a steady state flow of granular material, under the influence of gravity, in two and three dimensional hoppers of simple geometry. Simulations of such flows are of particular interest to various industries, such as the food and mining industries, where the handling of large quantities of granular materials in hoppers and silos is routine. While understanding and simulation of time-dependent phenomena are the ultimate goals in this field, those phenomena are still poorly understood and thus their study is beyond the scope of this research. It has been observed that steady flows can provide reasonable approximations, and the corresponding steady state model has consequently been the focus of a great deal of research. Historically, these steady state models have been approached using only smooth radial fields, and even today most practical hopper design uses these fields as their basis. Our work represents the first time that quality numerical methods have been brought to bear on the model equations in their original form, without assuming smoothness of the resulting fields. Two different, yet related, models for stress/velocity consisting of systems of hyperbolic conservation laws and algebraic relations are considered and discussed. The radial stress and velocity fields, and the stability of those fields, are studied briefly with both analytical and numerical results presented. More importantly, a Runge-Kutta Discontinuous Galerkin method is implemented and applied to various boundary value problems involving perturbed stress and velocity fields arising from discontinuous changes in parameters such as hopper wall angle or hopper wall friction.