Modeling of Unsteady Forces on Particles in Compressible Flow

The unsteady force on particles in viscous compressible flows is studied. Based on earlier work by Parmar et al. (Phil. Trans. Roy. Soc. A, 366, 2161-2175, 2008) on the behavior of the unsteady force on particles in inviscid compressible flows, a simple model for the unsteady force at finite Mach and Reynolds numbers is proposed. This model involves a composite kernel that consists of the addition of the inviscid finite-Mach-number kernel of Parmar et al. and the incompressible finite-Reynolds-number kernel of Mei and Adrian (J. Fluid Mech., 270, 133-174, 1992). The model is compared to a kernel derived from a numerical simulations and found to agree well. The results imply that the effect of compressibility at subcritical Mach numbers is restricted to intermediate acoustic time scales. For short and long acoustic time scales, the unsteady drag force is dominated by viscous effects.