Shock-Particle-Interaction Study with a Hyperbolic Two-Fluid Model

Abstract

A hyperbolic two-fluid model for high-speed, monodisperse, gas--particle flow is employed to study the interaction of a thin, moderately dense (volume fraction α_p < 0.2) particle curtain impacted by an incident shock with Mach number M_s. Mimicking the experimental setup, the numerical setup consists of a one-dimensional shock tube with a thin particle curtain in the driven section. This allows to validate the two-fluid model against recent experimental campaigns exploring a wide range of particle diameters, material densities, volume fractions, curtain widths and shock speeds. In general, the two-fluid model allows to reproduce the experimental data where the highest discrepancy is obtained in the configurations with the smallest M_s. However, the main goal of this study is to explore the closures used in the two-fluid model. Attention is drawn to the particle-Mach-number (M_p) dependence of the drag and added-mass coefficients, which have not yet been explored extensively in the literature. Also, the two-fluid model based on kinetic theory includes a particle pressure accounting for particle--fluid--particle (pfp) interactions. Thus, a parametric study is presented to evaluate the impact of several model parameters such as the drag coefficient, the added-mass coefficient, and the magnitude of the pfp pressure. The complete drag model accounting for particle Reynolds number Re_p,M_p and α_p is more accurate than previous drag models depending only on Re_p and α_p. Due the high particle-to-gas density ratio, the added-mass model has only a minor impact on the results. On the other hand, the magnitude of the pfp pressure has a real impact on the spread of the curtain due to the high slip velocity.

Keywords: gas-particle flow, kinetic theory of granular flow, added mass, pseudoturbulence, shock-particle interactions