Force model for a freely moving spherical particle interacting with a planar shock

This is the authors' abstract. We don't add key points for this paper.

This study evaluates different forms of the inviscid-unsteady and viscous-unsteady forces in the Annamalai–Balachandar model for predicting the force on a freely moving spherical particle interacting with a planar shock wave under viscous conditions, based on particle-resolved simulations with a ghost-point immersed boundary method. Three particle dimensionless densities 1, 10, and 1000, representing low, moderate, and high particle densities, respectively, and three incident shock Mach numbers 1.22, 1.75, and 2.51 (corresponding to post-shock Mach numbers 0.31, 0.8, and 1.2 and representing low, moderate, and high Mach numbers) are considered. We examine two forms for both inviscid-unsteady and viscous-unsteady forces: Form I averages the relative momentum before computing its material derivative, while Form II reverses the order. The startup motion of a particle in compressible flows is numerically simulated. Key particle behaviors observed include sustained acceleration for moderate-to-high density particles, velocity overshoot (initial increase followed by decrease) for low-density particles at low-to-moderate Mach numbers, and moving with the shock wave for the low-density particle at high Mach numbers studied. Our results show that, for the viscous-unsteady force, Forms I and II yield nearly identical results for all cases. For the inviscid-unsteady force, the prediction accuracy for the total force using Form I is better for the low-density particle, comparable for the moderate density particle, and worse for the high-density particle, compared to Form II. Form I of the inviscid-unsteady force is overall better for the prediction of the impulse and the peak force on the particle.