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Eulerian-Eulerian Description of the Interaction of a Shock With Particles Through Godunov’s Scheme

[+] Author Affiliations
Quang Truong, Gustaaf B. Jacobs

San Diego State University, San Diego, CA

Babak Shotorban

University of Alabama in Huntsville, Huntsville, AL

Paper No. FEDSM2013-16567, pp. V01CT25A006; 8 pages
  • ASME 2013 Fluids Engineering Division Summer Meeting
  • Volume 1C, Symposia: Gas-Liquid Two-Phase Flows; Industrial and Environmental Applications of Fluid Mechanics; Issues and Perspectives in Automotive Flows; Liquid-Solids Flows; Multiscale Methods for Multiphase Flow; Noninvasive Measurements in Single and Multiphase Flows; Numerical Methods for Multiphase Flow; Transport Phenomena in Energy Conversion From Clean and Sustainable Resources; Transport Phenomena in Materials Processing and Manufacturing Processes; Transport Phenomena in Mixing; Turbulent Flows: Issues and Perspectives
  • Incline Village, Nevada, USA, July 7–11, 2013
  • Conference Sponsors: Fluids Engineering Division
  • ISBN: 978-0-7918-5556-0
  • Copyright © 2013 by ASME


This paper is on an Eulerian-Eulerian (EE) approach that utilizes Godunov’s scheme to deal with a running shock that interacts with a cloud of particles. The EE approach treats both carrier phase (fluid phase) and dispersed phase (particle phase) in the Eulerian frame. In this work, the fluid equations are the Euler equations for the compressible gas while the particle equations are based on a recently developed model to solve for the number density, velocity, temperature, particle sub-grid scale stresses, and particle sub-grid scale heat fluxes. The carrier and dispersed phases exchange momentum and heat, which are modeled through incorporating source terms in their equations. Carrier and dispersed phase equation form a hyperbolic set of differential equations, which are numerically solved with Godunov’s scheme. The numerical solutions are obtained in this work for a two-dimensional normal running shock interacting with a rectangular cloud of particles. The results generated by the EE approach were compared against the results that were generated by a well-stablished Eulerian-Lagragian (EL) approach that treats the carrier phase in an Eulerian frame, while does the dispersed phase in a Lagrangian framework where individuals particles are traced and solved. For the considered configuration, the EE approach reproduced the EL results with a very good accuracy.

Copyright © 2013 by ASME



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