Steady-State Computations of Granular Flow in an Axisymmetric Hopper

Abstract

Axisymmetric steady-state computations of plastic incompressible granular flow in a converging hopper are presented. The granular flow equations are solved as a first-order system of conservation laws plus a set of constitutive relations, using a conservative finite difference method. Newton’s method is used to solve the nonlinear partial differential equations (PDEs).The steady-state granular flow equations may change type from elliptic to hyperbolic. In this investigation, flow parameters and boundary conditions are chosen to ensure that the PDE system is elliptic. The transition from a “radial solution” similarity flow at the top of the hopper to a more general flow involving a boundary layer near the exit of the hopper is analyzed.