Unsteady Naval Hydrodynamic Computations Using Lagrangian Vorticity Methods

A novel method to compute the 3-D unsteady hydrodynamics with application to undersea vehicles is presented. This approach solves the vorticity equation, which is derived from the momentum equation of the Navier-Stokes equations. Most problems of Navy interest involve incompressible flow, that may be described in terms of the vorticity alone. Specific geometries are represented using surface source and vortex panels whose strength is prescribed to satisfy the no-slip and no-flux boundary conditions. Vorticity is diffused from the vortex sheets onto the body surface to maintain a vorticity balance. Vorticity in the flow is specified at points and the vorticity at any other point in the field is obtained via linear interpolation. Interpolation is performed by constructing tetrahedra using Delaunay triangularization. Tetrahedra provide the control volume to integrate over to obtain the velocity and the connectivity of the control points provides a basis to construct derivatives. A sub-grid scale eddy viscosity model was implemented into the solution algorithm to model turbulent flow effects. This method was then validated for a sphere at Reynolds numbers of 1.14 million and unsteady flow development past a cone. Quality of the computed flows was compared with data obtained with experimental data. Lastly, unsteady propeller turbulent inflow computations were performed for the purpose of establishing boundary conditions for unsteady blade force computations