Near-field flow of submarines and ships advancing in a stable stratified fluid

A methodology is presented to predict density stratified flows in the near-field of naval vessels. The approach uses a single-phase level set method for the free surface, a dynamic overset technique to handle motions and controllers for self-propulsion and maneuvering. The density is solved with a higher-order transport equation coupled with momentum and mass conservation. Turbulence is implemented with a k−ε/k−ω based Delayed Detached Eddy Simulation (DDES) approach modified to add density gradients. Evaluation tests were performed for a two-dimensional square cavity, including grid and time step studies, and the stratified flow past a sphere, showing good agreement with available data. The stratified flow was studied for a self-propelled ship and a submarine. Density, velocity, pressure and turbulent quantities at the exit plane of the near-field contain a description of the relevant scales of the flow and can be used to compute the far-field stratified flow. It is shown that, as is the case of surface waves, the generation of internal waves requires energy that results in an increase in resistance. Moreover, the presence of a density interface against the hull results in a thickening of the boundary layer, just as in a solid/free surface juncture flow.