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The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c N t/RT10, where c N is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.

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Viscous compressible flow around a sphere is considered in the limit of zero Reynolds and Mach numbers. An exact expression for the force on the sphere undergoing arbitrary motion with compressibility effects is presented. Quasisteady, inviscid-unsteady, and viscous-unsteady force components are identified. Numerical results are in excellent agreement with the theory. The present formulation offers an explicit expression for the unsteady force in the time domain and can be considered as a generalization of the Basset-Boussinesq-Oseen equation to compressible flow.