A novel Markov chain method for predicting granular mixing process in rotary drums under different rotation speeds

Abstract

The granular mixing in rotary drums has been intensively studied using discrete element method (DEM). However, DEM is computationally intensive. When the operating condition (such as rotation speed) of the drum is changed, a new round of time-consuming DEM simulation must be performed, whereas the data generated in previous rounds are not utilized. In order to solve this problem, we propose a Hermite interpolation-based Markov chain method (HI-MCM) to replace DEM simulation, so that granular mixing process under new drum speeds can be quickly predicted. HI-MCM utilizes the data generated by only several DEM simulations to establish Markov chain models, with which the granular mixing process at new rotation speeds can be then quickly predicted by Hermite interpolated Markov chain models. Tests demonstrate that the particle spatial distribution and mixing degree predicted by HI-MCM agrees well with DEM simulation results, while the computing time is less than 1% of that needed by DEM and current Markov chain methods. Moreover, the proposed HI-MCM shows good robustness to the change of Markov chain parameter (learning time step). The proposed method has potential usages in online prediction of granular mixing in rotary drums.