Analysis of carrier phase fluctuations during the passage of a shock wave through a particle cloud

Shock wave interaction with particle clouds of moderate volume fractions generates fluctuations in the carrier phase that are of the order of the mean flow. The majority of effective field models used for such flows neglect these fluctuations, resulting in erroneous bulk flow fields and subsequently erroneous particle distributions. We investigate the nature of these fluctuations using three-dimensional particle resolved LES simulations of shock waves passing through particle clouds, varying incident shock Mach numbers, particle number densities, and volume fractions. The simulations are performed using an entropy stable numerical scheme on a Voronoi background mesh with body fitted structured meshes around each particle. The particles are assumed to be stationary during the simulated time interval. Analysis of the results shows that the dominant fluctuation production term is the product of the forces on the particles and the mean carrier phase velocity. We also observe that the pressure-dilatation correlation is highly correlated with this production term.