Campus Units

Chemical and Biological Engineering, Ames Laboratory

Document Type


Research Focus Area

Computational Fluid Dynamics

Publication Version

Submitted Manuscript

Publication Date


Journal or Book Title

International Journal of Multiphase Flow

First Page





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 (PTKE) 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.


This is a manuscript of an article published as Shallcross, Gregory S., Rodney O. Fox, and Jesse Capecelatro. "A volume-filtered description of compressible particle-laden flows." International Journal of Multiphase Flow (2019): 103138. DOI: 10.1016/j.ijmultiphaseflow.2019.103138. Posted with permission.

Copyright Owner

Elsevier Ltd.



File Format


Published Version