8 - Velocity distributions

Summary

Introduction

The prediction of the velocity profile in a discharging silo is an essential preliminary to several topics of industrial importance. A knowledge of the velocities is required for the determination of the residence time distribution, the mixing properties of the silo and the rate of wall wear. However, the most important aspect of velocity analysis lies in the determination of whether the silo discharges in mass or core flow. As explained in chapter 1, each of these flow modes has its own advantages and it is therefore important to be able to predict in advance which will occur and how wide the flowing core will be in the case of core flow.

It must, however, be admitted that these objectives have not yet been achieved. There has been some success at predicting the velocity distribution in mass flow but as yet there is no satisfactory determination of the core/mass flow transition.

The main problem lies in the formulation of the mechanisms controlling the flow. In the stress analysis of a Coulomb material, we are confident that we understand the governing equations, the remaining problems lie solely in the solution of these equations. In velocity prediction there is less general agreement about the form of the governing equations. In particular, there are two radically different starting points. In one, known as kinematic modelling, it is assumed that the particles flow by falling into the spaces vacated by the departing particles in the layer beneath. In this case the velocity profiles will depend on geometric factors alone and will be independent of the stress distribution.