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Technical Brief

# The homogeneous cooling state as a verification test for kinetic-theory-based continuum models of gas-solid flows

[+] Author and Article Information
William Fullmer

Department of Chemical and Biological Engineering, University of Colorado, 596 UCB, Boulder, CO 80309

Christine Hrenya

Department of Chemical and Biological Engineering, University of Colorado, 596 UCB, Boulder, CO 80309

1Corresponding author.

ASME doi:10.1115/1.4038916 History: Received August 17, 2016; Revised December 23, 2017

## Abstract

Granular and multiphase (gas-solids) kinetic-theory-based models have emerged a leading modeling strategy for the simulation of particle flows. Similar to the Navier-Stokes equations of single-phase flow, although substantially more complex, kinetic-theory-based continuum models are typically solved with computational fluid dynamics codes. Under the assumptions of the so-called homogeneous cooling state, the governing equations simplify to an analytical solution describing the cooling'' of fluctuating particle velocity, or granular temperature. The homogeneous cooling state is used here to verify the implementation of a recent multiphase kinetic-theory-based model in the open source MFiX code. Results from the verification test show that the available implicit (backward) Euler time integration scheme converges to the analytical solution with the expected first-order rate. A second-order accurate backward differentiation formula is also implemented and observed to converge at a rate consistent with its formal accuracy.

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