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Gravity-driven granular free-surface flow around a circular cylinder

Published online by Cambridge University Press:  27 February 2013

X. Cui  and
J. M. N. T. Gray
X. Cui*
Affiliation:
Aerospace Engineering, Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield S1 1WB, UK
J. M. N. T. Gray
Affiliation:
School of Mathematics and Manchester Centre for Nonlinear Dynamics, University of Manchester, Manchester M13 9PL, UK
*
†Email address for correspondence: x.cui@shu.ac.uk
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Abstract

Snow avalanches and other hazardous geophysical granular flows, such as debris flows, lahars and pyroclastic flows, often impact on obstacles as they flow down a slope, generating rapid changes in the flow height and velocity in their vicinity. It is important to understand how a granular material flows around such obstacles to improve the design of deflecting and catching dams, and to correctly interpret field observations. In this paper small-scale experiments and numerical simulations are used to investigate the supercritical gravity-driven free-surface flow of a granular avalanche around a circular cylinder. Our experiments show that a very sharp bow shock wave and a stagnation point are generated in front of the cylinder. The shock standoff distance is accurately reproduced by shock-capturing numerical simulations and is approximately equal to the reciprocal of the Froude number, consistent with previous approximate results for shallow-water flows. As the grains move around the cylinder the flow expands and the pressure gradients rapidly accelerate the particles up to supercritical speeds again. The internal pressure is not strong enough to immediately push the grains into the space behind the cylinder and instead a grain-free region, or granular vacuum, forms on the lee side. For moderate upstream Froude numbers and slope inclinations, the granular vacuum closes up rapidly to form a triangular region, but on steeper slopes both experiments and numerical simulations show that the pinch-off distance moves far downstream.

JFM classification

Compressible Flows: Compressible Flows Granular media: Granular media Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 720 , 10 April 2013 , pp. 314 - 337
Copyright
©2013 Cambridge University Press

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Cui and Gray supplementary movie

Movie showing the flow of a sand avalanche past a circular cylinder as in figures 7 and 8.

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Cui and Gray supplementary movie

Movie showing the development of the steady state non-pareille avalanche

Download Cui and Gray supplementary movie(Video)
Video 2.8 MB