Modeling of the unsteady force for shock-particle interaction

The interaction between a particle and a shock wave leads to unsteady forces that can be an order of magnitude larger than the quasi-steady force in the flow field behind the shock wave. Simple models for the unsteady force have so far not been proposed because of the complicated flow field during the interaction. Here, a simple model is presented based on the work of Parmar et al. (Phil Trans R Soc A 366:2161-2175, 2008). Comparisons with experimental and computational data for both stationary spheres and spheres set in motion by shock waves show good agreement in terms of the magnitude of the peak and the duration of the unsteady force.