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A multiphase model for compressible granular–gaseous flows: formulation and initial tests

Published online by Cambridge University Press:  18 January 2016

Ryan W. Houim  and
Elaine S. Oran
Ryan W. Houim*
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
Elaine S. Oran
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: [email protected]
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Abstract

A model for predicting the behaviour of a compressible flow laden with shocks interacting with granular material has been developed and tested. The model consists of two sets of coupled Euler equations, one for the gas phase and the other for the granular phase. Drag, convective, heat transfer and non-conservative terms couple the two sets of governing equations. Intergranular stress acting on the grains is modelled using granular kinetic theory in dilute regimes where particle collisions are dominant and frictional–collisional pressure in dense regions where layers of granular material slide over one another. The two-phase granular–gaseous model, as a result, is valid from dilute to densely packed granular regimes. The solution of these nonlinearly coupled Euler equations is challenging due to the presence of the non-conservative nozzling and work terms. A numerical technique, based on Godunov’s method, was designed for solving these equations. This method takes advantage of particle incompressibility to simplify the nozzling terms. It also uses the observation that a Riemann problem is valid in the region where gas can flow between particles and can be used to provide a physically accurate approximation of the non-conservative terms. The model and solution method are verified by comparisons to test problems involving granular shocks and two-phase shock-tube problems, and they are validated against experimental measurements of shock and dense particle-curtain interactions and transmitted oblique granular shocks.

JFM classification

Granular media: Granular media Multiphase and Particle-laden Flows: Multiphase flow Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 166 - 220
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© 2016 Cambridge University Press 

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