The Transom-Stern Modeled as a Backward Facing Step

In this paper the hydrodynamics of a transom stern vessel are studied numerically by examining the canonical problem of a backward-facing step with a free surface (BFSFS). Numerically, two Navier-Stokes solvers are used to simulate the backward facing step with a free surface; a two-dimensional unsteady code that utilizes the level set method for interface capturing is compared with the commercial software FLUENT. To address turbulence closure the level set code uses the Spalart-Allmaras turbulence model, while the FLUENT results utilize the Detached-Eddy Simulation formulation with the Spalart-Allmaras turbulence model near the body, and the LargeEddy Simulation in the wake region of the domain. Comparisons between the present work, inviscid theories, and experiments show that viscosity is important in the prediction of wave slope and length. It is shown that the wavelength behind the body is much shorter than that predicted by inviscid linear theory. A previous streamfunction bilinear shear current theory is used to account for the viscous wake effect on the wavelength. Additionally, analysis of the velocity fields indicates the presence of vortex shedding. A frequency analysis is performed that identifies a dominant shedding frequency occurring at a Strouhal number of 0.2