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Research Papers: Design and Analysis

A Numerical Study on the Sensitivity of the Discrete Element Method for Hopper Discharge

[+] Author and Article Information
H. Kruggel-Emden, S. Rickelt, S. Wirtz, V. Scherer

Department of Energy Plant Technology, Ruhr-Universitaet Bochum, Universitaetsstrasse 150, D-44780 Bochum, Germany

J. Pressure Vessel Technol 131(3), 031211 (Apr 29, 2009) (10 pages) doi:10.1115/1.3122022 History: Received December 07, 2007; Revised July 15, 2008; Published April 29, 2009

Based on the time-driven discrete element method, granular flow within a hopper is investigated. The main focus is thereby set on hopper vessel design variables such as discharge rates and applied wall pressures. Within the used model contacts are assumed as linear viscoelastic in normal and frictional-elastic in tangential direction. The hopper geometry is chosen according to Yang and Hsiau (2001, “The Simulation and Experimental Study of Granular Materials Discharged From a Silo With the Placement of Inserts,” Powder Technol., 120(3), pp. 244–255), who performed both experimental and numerical investigations. The considered setup is attractive because it involves only a small number of particles enabling fast modeling. However, the results on the experimental flow rates reported are contradictory and are afflicted with errors. By an analysis of the hopper fill levels at different points of time, the correct average discharge times and flow rates are obtained. Own simulation results are in good agreement with the experimental flow rates and discharge times determined. Based on the thereby defined set of simulation parameters, a sensitivity analysis of parameters such as friction coefficients, stiffnesses, and time steps is performed. As flow properties, besides the overall discharge times, the discharge time averaged axial and radial velocity distributions within the hopper and the normal stresses on the side walls during the first seconds of discharge are considered. The results show a strong connection of the friction coefficients with the discharge times, the velocity distributions, and the stresses on the side walls. Other parameters only reveal a weak often indifferent influence on the studied flow properties.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 2

Experimentally obtained particle positions at (a) t=2.4 s and (b) t=4.2 s by Yang and Hsiau (1) and (c) t=2.4 s and (d) t=4.2 s by own simulations

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Figure 3

Results for the discharge time, the probability density of the horizontal and vertical velocities, and the time averaged normal stresses on the side walls for a variation of the particle/particle friction coefficient μPP

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Figure 4

Results for the discharge time, the probability density of the horizontal and vertical velocities and the time averaged normal stresses on the side walls for a variation of the particle/side wall friction coefficient μPSW

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Figure 5

Results for the discharge time, the probability density of the horizontal and vertical velocities, and the time averaged normal stresses on the side walls for a variation of the particle/front wall friction coefficient μPFW

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Figure 6

Results for the discharge time, the probability density of the horizontal and vertical velocities and the time averaged normal stresses on the side walls for a variation of the normal coefficients of restitution ePPn, ePFWn, ePSWn

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Figure 7

Results for the discharge time, the probability density of the horizontal and vertical velocities and the time averaged normal stresses on the side walls for a variation of the normal and tangential stiffnesses kPPn, kPFWn, kPSWn, kPPt, kPFWt, and kPSWt with kn=kt and en=const

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Figure 8

Results for the discharge time, the probability density of the horizontal and vertical velocities and the time averaged normal stresses on the side walls for a variation of the tangential stiffnesses kPPt, kPFWt, and kPSWt

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Figure 9

Results for the discharge time, the probability density of the horizontal and vertical velocities, and the time averaged normal stresses on the side walls for a variation of the number of steps n a collision is resolved with

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