Computational analysis of shock-induced flow through stationary particle clouds

Abstract

We investigate the shock-induced flow through random particle arrays using particle-resolved Large Eddy Simulations for different incident shock wave Mach numbers, particle volume fractions and particle sizes. We analyze trends in mean flow quantities and the unresolved terms in the volume averaged momentum equation, as we vary the three parameters. We find that the shock wave attenuation and certain mean flow trends can be predicted by the opacity of the particle cloud, which is a function of particle size and particle volume fraction. We show that the Reynolds stress field plays an important role in the momentum balance at the particle cloud edges, and therefore strongly affects the reflected shock wave strength. The Reynolds stress was found to be insensitive to particle size, but strongly dependent on particle volume fraction. It is in better agreement with results from simulations of flow through particle clouds at fixed mean slip Reynolds numbers in the incompressible regime, than with results from other shock wave particle cloud studies, which have utilized either inviscid or twodimensional approaches. We propose an algebraic model for the streamwise Reynolds stress based on the observation that the separated flow regions are the primary contributions to the Reynolds stress.

Particle-resolved simulations of shock-induced flow through particle clouds at different Reynolds numbers

“…The Mach number plots reveal that the flow becomes sonic just upstream of the downstream particle cloud edge. Similar observations have been made in other studies 29,41,43 , and this behaviour is very similar to that found in decreasing pressure. If the duct is sufficiently long, the flow chokes at the downstream exit, just like we observe here.…”

“…Additionally, the flow Mach number increases with downstream distance within the particle cloud 29,31,43 in a manner similar to that observed in Fanno flows 14 . The presence of nearby particles also affects the flow around each particle by changing the direction of the incoming flow, exposing it to particle wakes, etc.…”

“…Additionally, the peak location shifts towards higher fluctuation magnitudes. At Re p = 5000, the trend is similar up to x/L = 0.5, Osnes et al 29 found that the streamwise fluctuations in the interior of the particle cloud could be represented by…”

“…Osnes et al 29 showed that at the upstream particle cloud edge, the streamwise Reynolds stress gradient is of equal importance as the particle forces after the initial shock-related transient. As can be seen in fig.…”

“…The total number of control volumes is roughly 10 8 . The control volume sizes are similar to those used in Osnes et al 29,30 . Those studies investigated grid sensitivity based on the grid-convergence of the particle forces, resolution of viscous shear length scales, and convergence of spanwise velocity fluctuation correlations.…”