A cascade-cataract charge flow model for power draft of tumbling mills

Abstract

The existing models of mill power draft are in general not flexible and versatile enough to incorporate the effects of high mill speed and charge loading, liner design and slurry rheology etc., in a phenomenologically consistent manner. A multi-torque model is derived in which the complex and varied patterns of tumbling charge movement are represented by coupled cascading-cataracting flows, with or without the superimposition of centrifuging and layering of the charge components. The torque equations are cast in a dimensionless form in order to demonstrate a parameter estimation scheme and to present simulation results in a generalized format. The model has been tested extensively with published torque data over a wide range of mill speeds, charge fillings and under conditions of layering of mill liners by thick slurries. Examples are given where by simple adjustment of a charge split parameter the model is able to track accurately the highly time-dependent torque profiles encountered in the ball mill grinding of concentrated slurries. The model could be useful for design, operation and control of tumbling mills, including rod and autogenous mills.