Using particle-resolved LES to improve Eulerian-Lagrangian modeling of shock-wave/particle-cloud interactions

We perform particle resolved large-eddy simulations of a shock wave passing through a random array of stationary particles, varying incident shock Mach number, particle number density and volume fraction. The variation of the mean flow is quantified by fitting the reflected and transmitted shock wave Mach numbers as power laws of these parameters. We analyze the fluctuations from locally volume averaged quantities, and find that the fluctuating kinetic energy is generated primarily by the forces on the particles, and reaches values as high as two thirds of the mean kinetic energy. We use the data from the particle-resolved simulations to close the volume averaged equations, in which the present problem can be formulated in one dimension, and demonstrate that correct drag laws and sub-grid closures are necessary for reliable predictions.