Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on fluid forces

A two-dimensional free surface flow past a circular cylinder forced to perform streamwise oscillations in the presence of an oncoming uniform flow is investigated at a Reynolds number of R=200 and fixed displacement amplitude, A  =0.13, for the forcing frequency-to-natural shedding frequency ratios, f/f0=1.5f/f0=1.5, 2.5, 3.5. The present two-fluid model is based on a velocity–pressure formulation of the two-dimensional continuity and unsteady Navier–Stokes equations. The continuity and Navier–Stokes equations are discretized using a finite volume approximation for two fluid regions. An improved volume-of-fluid method is employed to capture for the displacement of the free surface. The objective of this study is to examine the effects of the frequency ratios, f/f0=1.5f/f0=1.5, 2.5, 3.5, and the cylinder submergence depths, h=0.25, 0.5, 0.75, on the fluid forces at a fixed Froude number of Fr=0.2. The relationship between the changes in the wake dynamics of the cylinder described in Bozkaya et al. (2011) and in the properties of fluid forces is also discussed.