Mach and Reynolds number dependency of the unsteady shock-induced drag force on a sphere

Abstract

Shock–particle interaction is an important phenomenon in a wide range of technological applications and natural phenomena, and the development of accurate models for this interaction is therefore of interest. This study investigates the transient forces during shock–particle interaction at particle Reynolds numbers between 100 and 1000, and incident shock wave Mach numbers between 1.22 and 2.51. This is achieved with the aid of particle-resolved large-eddy simulations. The simulation results show that shock–particle interaction differs qualitatively for subcritical and supercritical incident flow conditions. By decomposing the total force, the inviscid and viscous unsteady forces are estimated. The inviscid unsteady component is significantly larger than the viscous contribution, but the magnitude of the viscous component is comparable to steady-state drag. The predictions of current state of the art force models are compared to the computed particle forces. For subcritical flows, the models are quite successful in predicting the drag. For these conditions, the magnitudes of both the inviscid and viscous unsteady force models agree well with the simulation results, but the transient nature of the viscous unsteady force history is not well captured. For supercritical flows, the inviscid unsteady force model is not able to capture the force dynamics. This highlights the need for the development of unsteady force models for supercritical flow conditions.