Fluid–structure interaction in rectilinear flows: Four analytical solutions

Abstract

A simple idea to include fluid–structure interaction (FSI) in classic rectilinear flow problems is presented. By allowing a solid boundary to behave as a rigid body, instead of holding it at constant motions, dynamic FSI problems amenable to analytical methods are obtained. Four examples (Stokes's first problem, Couette flow, rotating disk, and rotating sphere) are extended and solved by Laplace transform. Closed-form expressions of the solid velocity are obtained either for the general case or in the large-time limit, and the effects of solid inertia are discussed. In all cases, the total displacement of the solid before the coupled system reaches steady-state is obtained exactly. These solutions have general theoretical interest and can also be used to validate numerical methods.