Hydrodynamics of a rigid stationary flat plate in cross-flow near the free surface

In this work, the flow normal to a rectangular flat plate with sharp angles in the presence of the free surface and gravity has been studied numerically, using a three dimensional (3D) large Eddy simulation methodology. Most of the previous studies on this geometry consider either periodic assumptions or laminar regime Re ∼ O(10³). The numerical study described here, with a fully 3D simulation of the flat plate in turbulent regime Re ∼ O(10⁵), had not been reported earlier. Important differences have been found with respect to the laminar case or when periodic boundary conditions are assumed. The influence of the gravity force and the free surface interface on the hydrodynamics of the problem is extremely relevant for industrial applications. The simulations are initially validated using a reference case with a plate with sharp corners and a single phase laminar 3D-periodic configuration. The time averaged drag force, the velocity, and pressure fields are compared as well against the case of the plate with smooth corners. Finally, in the case of the two-phase 3D numerical simulations, the drag force and the vorticity fields in the near wake of the plate are compared to recent experimental work [S. Satheesh and F. J. Huera-Huarte, “Effect of the free surface on a flat plate translating normal to the flow,” Ocean Eng. 171, 458–468 (2019)]. These experiments were used as a guideline for the computational setup; consequently, the values of most of the dimensionless parameters are the same. A second scenario where the free surface is replaced by a solid wall is considered. Two important observations show up after this research: first, the characteristic unsteady frequencies that are found associated with two periodic regimes disappear when 3D cases are evaluated. In such a scenario, no dominant frequencies are found. Second, a critical submergence depth (distance) between the upper part of the plate and the free surface (or solid wall) has been found, where the drag force shows a maximum value. These observations are discussed in relation to the pressure distribution, the vortex structures formed at the wake, and the gap flow formed between the plate and the free surface.