To better understand the interaction of a free surface wave motion with moving bluff bodies, a two-dimensional numerical study of the forced streamwise oscillation of a circular cylinder beneath a free surface is conducted based on a two-fluid model. Computations are carried out at a Reynolds number of R = 200, a fixed displacement amplitude, A = 0.13 and the forcing frequency-to-natural shedding frequency ratios, f/f (0) = 1.5,2.5,3.5. Finite volume discretization of the special integral form of two-dimensional continuity and unsteady Navier-Stokes equations (when a solid body is present) are performed on a fixed Cartesian grid. Improved volume-of-fluid method is used to discretize the free surface. The laminar asymmetric flow regimes in the near wake region and the fluid forces are analyzed at a fixed Froude number of Fr = 0.4 and for submergence depths at h = 0.25,0.5,0.75. A comparison of the present results with the case in the absence of a free surface is also included to illustrate the effects of inclusion of a free surface. The code validation in special cases shows good comparisons with previous numerical and experimental results. Flow regime analyses include free surface physics-based analysis, and results confirm findings of a recent work of Brons et al. [25].
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