Campus Units

Chemical and Biological Engineering

Document Type

Article

Research Focus Area

Computational Fluid Dynamics

Publication Version

Published Version

Publication Date

11-25-2020

Journal or Book Title

Journal of Fluid Mechanics

Volume

903

First Page

A5

DOI

10.1017/jfm.2020.615

Abstract

A hyperbolic two-fluid model for gas–particle flow derived using the Boltzmann–Enskog kinetic theory is generalized to include added mass. In place of the virtual-mass force, to guarantee indifference to an accelerating frame of reference, the added mass is included in the mass, momentum and energy balances for the particle phase, augmented to include the portion of the particle wake moving with the particle velocity. The resulting compressible two-fluid model contains seven balance equations (mass, momentum and energy for each phase, plus added mass) and employs a stiffened-gas model for the equation of state for the fluid. Using Sturm's theorem, the model is shown to be globally hyperbolic for arbitrary ratios of the material densities Z=ρf/ρp (where ρf and ρp are the fluid and particle material densities, respectively). An eight-equation extension to include the pseudo-turbulent kinetic energy (PTKE) in the fluid phase is also proposed; however, PTKE has no effect on hyperbolicity. In addition to the added mass, the key physics needed to ensure hyperbolicity for arbitrary Z is a fluid-mediated contribution to the particle-phase pressure tensor that is taken to be proportional to the volume fraction of the added mass. A numerical solver for hyperbolic equations is developed for the one-dimensional model, and numerical examples are employed to illustrate the behaviour of solutions to Riemann problems for different material-density ratios. The relation between the proposed two-fluid model and prior work on effective-field models is discussed, as well as possible extensions to include viscous stresses and the formulation of the model in the limit of an incompressible continuous phase.

Comments

This article is published as Fox, Rodney, Frédérique Laurent, and Aymeric Vié. "A Hyperbolic Two-Fluid Model for Compressible Flows with Arbitrary Material-Density Ratios." Journal of Fluid Mechanics 903 (2020): A5. DOI: 10.1017/jfm.2020.615. Posted with permission.

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

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