Analytical solution for the rolling-mode granular motion in rotary kilns

An analytical expression is derived to calculate the profile of the active layer thickness of a rolling granular bed in rotary kilns. It is based on the previous numerical model described in AIChE Journal [J. Mellmann, E. Specht, X.Y. Liu, Prediction of rolling bed motion in rotating cylinders, AIChE J. 50 (11) (2004) 2783–2793]. With the analytical expression, the maximal thickness and the mass flow in the active layer can be calculated conveniently in dependence on the rotation speed, the filling degree, the kiln diameter and the material properties. The influence of the material can be described only by the particle diameter and the dynamic angle of repose. No fitting parameter is necessary. It is shown that the deviation of the analytical from the numerical results is negligibly small under practical operating conditions. With the analytical model, measured results from own experiments can be predicted well, and measurements given in the literature can be now compared with one another. Results of this work are of direct utility for engineering design of large-scale technical rotary kilns.