Modeling And Analysis Of Mixing Process Of Granular System In Rotary Drums

Rotary drum is the most common equipment for processing granular materials and is widely used in many fields such as metallurgy,chemical industry,civil engineering,pharmacy,and agriculture.The mixing process of the granular material in the drum largely determines the product quality and the efficiency of the rotary drum equipment.However,due to its complex behavior combing solid and fluid,the modeling and analysis methods for granular mixing have been the research hot spot and challenge in the interdisciplinary field of particle engineering and control engineering.Discrete Element Method(DEM)is a common mechanism modeling method for particle dynamics.The dynamic equations for each particle are established in DEM based on Newton's second law,and then solved using numerical computation to obtain the trajectory and velocity of each particle.However,DEM has the shortcomings of numerous model parameters,time-consuming calibration of key parameters,and huge amount of calculation.At present,DEM is basically used in offline numerical simulation of granular mixing,and cannot meet the requirements of fast prediction and analysis in practical applications.The present work aims to solve the above problems in the framework of the National Natural Science Foundation project “Real-time measurement of the material flow process in rotary kilns in hostile environments: measuring mechanism and methodology”(Grant No.61374149).Firstly,the DEM model for granular mixing in rotary drum is established and a fast calibration method for DEM model is proposed;then,intelligent models driven by DEM simulation data are established for fast prediction and analysis of the dynamic mixing and the steady-state of the granular material,which have important theoretical value and broad application prospects.The main contributions and conclusions of the present work are as follows:(1)The DEM mechanism model for spherical granular material in a rotary drum is established;then,parameter sensitivity analysis is performed on PFC simulation platform for the established DEM model.The results show that the particle friction coefficient is found to be a model parameter that mostly affects the granular mixing.Simulation analysis of the granular mixing features(steady-state repose angle,feature repose angle)demonstrates that the feature repose angle increases monotonically with the increase of the particle friction coefficient.(2)The traditional calibration methods are rather cumbersome and time-consuming.Therefore,a fast automatic calibration method for the key parameters(particle friction coefficient)of the DEM model is thus proposed based on the feature repose angle,which outperforms traditional calibration methods.The proposed method iteratively adjusts the friction coefficient in DEM model,and automatically controls the start and stop of DEM simulation until the error between the simulated feature repose angle and the experimental value meets the required accuracy.The proposed calibration method is tested on an experimental rotary drum platform and compared with traditional calibration methods that are based on steady-state repose angle.Results show the proposed calibration method is obviously more advantageous because the time needed for calibration is reduced greatly and the adjusted DEM model has same prediction accuracy.(3)The image-based detecting method can only obtain the surface mixing process.In order to study whether the surface mixing process can accurately represent the whole mixing process,the surface mixing process and the whole mixing process of the granular system in the rotary drum are simulated by the calibrated DEM model,and the mixing process curve and steady-state features(steady-state repose angle,mixing time)with varying rotation speed and drum length are analyzed.Results show that the rotation speed has more influence on the steady-state features.As the drum length increases,the difference between the surface mixing and the whole mixing exceeds 30% in the aspects of steady-state features.This conclusion provides theoretical basis for evaluating the accuracy of the image-based detecting method for granular mixing process.(4)Due to its numerous model parameters and time-consuming calculation,DEM model is not suitable for fast prediction and analysis of the granular mixing.For this reason,two intelligent models driven by DEM simulation data are proposed in the present work for fast prediction of the dynamic mixing process and steady-state features,respectively.(i)Based on the particle trajectory data generated by DEM simulation at known speeds,a Markov chain model based on Hermite interpolation is established,which can quickly predict the dynamic mixing process curve at new rotation speeds.Experiments show that prediction results by the proposed model agree well with DEM simulation results,while the calculation time is only about 0.34% of that needed by DEM,which has obvious advantages;compared with other Markov chain based models,the proposed model is less sensitive to parameters such as number of Markov chain cells and learning time step.It is therefore more suitable for fast prediction and analysis of the dynamic process of granular mixing in the rotary drum at different rotation speeds.(ii)A support vector machine(SVM)intelligent model is trained using existing DEM simulation data,which is then used for predicting the steady-state features(mixing time and steady-state repose angle)of granular mixing.Tests show that the established SVM model can quickly predict the steady-state features at different rotation speeds,filling rates and drum sizes.The predicted results are similar to DEM simulation results,while the calculation time is only milliseconds,far less the time needed by DEM simulation(at least 1 hour).Therefore,the established SVM intelligent model can replace DEM model to solve the practical demands for fast prediction of the steady-state features of granular mixing in rotary drums.