Journal
INTERNATIONAL JOURNAL OF MULTIPHASE FLOW
Volume 122, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijmultiphaseflow.2019.103138
Keywords
Eulerian-Lagrangian; Multiphase flow; Shock-particle interaction; Pseudo-turbulence
Categories
Funding
- NASA Space Technology Research Fellowship
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In this work, we present a rigorous derivation of the volume-filtered viscous compressible Navier-Stokes equations for disperse two-phase flows. Compared to incompressible flows, many new unclosed terms appear. These terms are quantified via a posteriori filtering of two-dimensional direct simulations of shock-particle interactions. We demonstrate that the pseudo-turbulent kinetic energy (PIKE) systematically acts to reduce the local gas-phase pressure and consequently increase the local Mach number. Its magnitude varies with volume fraction and filter size, which can be characterized using a Knudsen number based on the filter size and inter-particle spacing. A transport equation for PTKE is derived and closure models are proposed to accurately capture its evolution. The resulting set of volume-filtered equations are implemented within a high-order Eulerian-Lagrangian framework. An interphase coupling strategy consistent with the volume filtered formulation is employed to ensure grid convergence. Finally PTKE obtained from the volume-filtered Eulerian-Lagrangian simulations are compared to a series of two- and three-dimensional direct simulations of shocks passing through stationary particles. (C) 2019 Elsevier Ltd. All rights reserved.
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