Fluid Forces on a Moving Body at Low Amplitude in Fluid at Rest: Part 2 — Analytical and Numerical Study for an Accelerated Circular Cylinder

The present paper deals with the study of fluid forces in an incompressible viscous fluid at rest around an accelerated rigid circular cylinder. The movement subjected to the cylinder is an impulsive motion represented by a only one period of a sinusoidal acceleration. After this period, the cylinder is stopped. This study is performed for small displacement of the cylinder, i.e. for low KEULEGAN-CARPENTER numbers, and for various STOKES numbers. An analytical formulation of fluid forces exerted on a cylinder subjected to any motion is first proposed. The starting point of the analytical approach is the solution of fluid forces in steady state harmonic motion. A Fourier transform is applied on the harmonic solution to capture the wide frequency spectrum composing the transient motion. Then an inverse Fourier transform is applied on the expression to achieve the solution in the temporal space. A numerical simulation is then carried out with a CFD code using finite volume method with moving mesh technique in ALE formulation. The analytical and numerical solutions are exposed and discussed in the case of a cylinder subjected to a sine wave acceleration. The competition between the viscous diffusion time and the wave duration time is studied and highlights the history effect on pressure forces and shear forces.