Unsteady Compressible Pairwise Interaction Extended Point-Particle Model

An efficient pairwise interaction framework is developed using acoustic wave solution and compressible Maxey-Riley-Gatignol (MRG) equation to predict unsteady forces on a particle subjected to an incoming planar shock, in the presence of other neighboring particles. The time-dependent perturbing effect of each neighbor is evaluated with the acoustic approximation and the total perturbing influence of all the neighbors is calculated with a summation of all the neighbors. Comparing the force signal obtained with the model with that experienced by particle-resolved (PR) simulations, it is established that (i) the compressible MRG model is capable of capturing the unsteady nature of force as the primary shock and its reflections off the neighbors pass over the particle, and (ii) superposition of perturbations by each neighbor is a reasonable approximation. Furthermore, even though in computing the perturbation flow the acoustic equation was used, the framework is extendable to higher shock Mach number cases, and if needed PR simulations can be used.