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.
In this paper, we present the results of the explosive dispersal of particles in high-speed environments. We carry out Euler–Lagrange numerical simulations of a source at quiescent ambient conditions as well as moving at Mach numbers of 3 and 6. Particle volume fractions of 0%, 1%, and 4.5% are presented. The detonation profile is computed with the Jones–Wilkins–Lee equation of state using a reactive burn model. Non-static cases provide a framework to consider the effect of a bow shock and pre-existing high-speed flow conditions on the dispersal process. We also compute averages of both static and dynamic pressures, as well as impulse density histories on virtual probe planes to characterize the momentum of the flow and particles that would deposit on a target. Results suggest that the presence of the particles can have a substantial effect on the pressure average of the virtual target planes.
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