Unsteady flow past a square cylinder placed close to a free surface

Two-dimensional flow past a square cylinder close to a free surface is studied numerically to investigate the effect of Froude numbers (0.0–0.6) and gap ratios (0.2–1.2) on the wake behavior and integral parameters. The multiphase approach with the modified volume of fluid method is employed to study the flow. InterFoam, a two-phase incompressible flow solver in OpenFOAM, has been used to simulate the flow field. The surface deformation is found to increase with the increasing Froude number, which, in turn, produces substantial surface vorticity to cross-cancel the vorticity of the separated shear layer generated near the top surface of the cylinder. At high Froude numbers, merging of shed vortices in the cylinder downstream was encountered that possessed a period twice that in the formation region. For a fixed Froude number, with a decrease in the gap ratio, the amount of cross-cancellation between the top shear layer and the free surface increases. This enhanced interaction leads to diffusion of the vortices from the top shear layer to smaller downstream distances as the cylinder moves close to the free surface. Under such effects, the integral parameters (drag and lift coefficients and Strouhal number) are found to be a strong function of the Froude number and gap ratio. A comparison study of the wake structures with that of a circular cylinder shows the close resemblance in the large scale structures of the two flow fields. In terms of integral parameters, both the bluff bodies possess a similar behavior with the variations of the Froude number and gap ratio, but the magnitudes are quite different due to the differences in the separation points.