Numerical Modeling and Analysis of Early Shock Wave Interactions with a Dense Particle Cloud

Abstract

Dense compressible multiphase flows exist in variable phase turbines, explosions, and fluidized beds, where the particle volume fraction is in the range 0.001 < α_d < 0.5. A simple model problem that can be used to study modeling issues related to these types of flows is a shock wave impacting a particle cloud. In order to characterize the initial shock-particle interactions when there is little particle movement, a two-dimensional (2-D) model problem is created where the particles are frozen in place. Qualitative comparison with experimental data indicates that the 2-D model captures the essential flow physics. Volume-averaging of the 2-D data is used to reduce the data to one dimension, and x-t diagrams are used to characterize the flow behavior. An equivalent one-dimensional (1-D) model problem is developed for direct comparison with the 2-D model. While the 1-D model characterizes the overall steady-state flow behavior well, it fails to capture aspects of the unsteady behavior. As might be expected, it is found that neglecting the unclosed fluctuation terms inherent in the volume-averaged equations is not appropriate for dense gas-particle flows.