The present paper treats the transient fluid forces experienced by a rigid circular cylinder moving along a radial line in a fluid initially at rest. The body is subjected to a rapid displacement of relatively small amplitude in relation to its radius. Both infinite and cylindrically confined fluid domains are considered. Furthermore, non-negligible amplitude motions of the inner cylinder, and viscous and compressible fluid effects are addressed, successively. Different analytical methods and models are used to tackle each of these issues. For motions of non-negligible amplitude of the inner cylinder, a potential flow is assumed and the model, formulated as a two-dimensional boundary perturbation problem, is solved using a regular expansion up to second order. Subsequently, viscous and compressible effects are handled by assuming infinitesimal amplitude motions. The viscous fluid forces are formulated by solving a singular perturbation problem of the first order. Compressible fluid forces are then determined from the wave equation. A nonlinear formulation is obtained for the non-negligible amplitude motion. The viscous and compressible fluid forces, formulated in terms of convolution products, are linked to fluid history effects induced by wave propagation phenomena in the fluid domain. These models are expressed with dimensionless parameters and illustrated for a specific motion imposed on the inner cylinder. The different analytical models permit coverage of a broad range of motions. Hence, for a given geometry and imposed displacement, the appropriate fluid model can be identified and the resulting fluid forces rapidly estimated. The limits of these formulations are also discussed.
Compressible Fluid Model of Korteweg Type with Free Boundary Condition: Model Problem