Unsteady Compressible Pairwaise Interaction Extended Point-Particle model

An efficient means to compute multiphase flow problems is to utilize the Euler-Lagrange simulation method. Various developments have been made for the case in the incompressible regime using the pairwise interaction extended point-particle (PIEP) model. The current work extends the PIEP model to cope with the unsteady nature of compressible multiphase flows. A framework is developed using acoustic wave solution and compressible Maxey-Riley-Gatignol equation to predict unsteady secondary forces on a sphere under the influence of a scattering sphere nearby. A case with two spheres while a weak shock passes through is studied. The model is capable of capturing the arrival timing of the scattered signal. Comparisons are made with the force prediction from a particle resolved 2-sphere unsteady simulation.