Form of Velocity Distribution Function for Rapid Granular Flows
Publication: Journal of Engineering Mechanics
Volume 116, Issue 6
Abstract
A simple delta function form of the velocity distribution function is proposed for smooth, uniform, slightly inelastic spheres in rapidly sheared granular flow. The collisional stresses are computed for simple‐shear flow and compared to existing theories. Good agreement is observed with more elaborate kinetic theories, numerical simulations, and shear cell data. The kinetic formulation is placed in the physically transparent form proposed by Bagnold. This formulation is used to show the sources of the discrepancy in results between existing data and the theory of Shen and Ackermann, which is based on Bagnold's formulation. It is shown that the discrepancies can be substantially alleviated by incorporating more detail into Shen and Ackermann's phenomenological picture of collisions, and by improving their estimate of the mean‐free path. Thus, it is shown that using the proper form for averaging has a much more significant effect on the magnitude of the predicted stresses than the form of the velocity distribution function. The delta function form can be employed to simplify calculations while retaining an acceptable level of accuracy.
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Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 116 • Issue 6 • June 1990
Pages: 1261 - 1275
Copyright
Copyright © 1990 ASCE.
History
Published online: Jun 1, 1990
Published in print: Jun 1990
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