Modeling of shock-induced force on an isolated particle in water and air

The prediction of force on an isolated particle, while a shock is passing over it, is an important problem in many natural and industrial applications. Although the flow monotonically changes from the pre-shock to the post-shock state, the particle's force has been observed to behave nonmonotonically with a sharp peak when the shock is located halfway across the particle. This nonmonotonic behavior is due to the unsteady nature of the compression and rarefaction waves that radiate as the shock diffracts around the particle and, therefore, cannot be predicted by a quasi-steady model. An accurate force model must account for the unsteady nature of the flow and the sharp discontinues in the flow properties across the shock. In this work, we test four different inviscid models and observe that the compressible Maxey-Riley-Gatignol (C-MRG) model is the most accurate based on comparison with results from particle-resolved inviscid simulations at two different Mach numbers for both water and air as the medium. The C-MRG model is first demonstrated to predict the force on a stationary particle accurately and then extended to capture the force on a moving particle. Numerical complexities regarding the implementation of the C-MRG model are also discussed.