Computation of incipient separation via solution of the vorticity equation on a lagrangian mesh

Naval Undersea Warfare Center Hydrodynamics Branch Newport, RI 02841, USA

Abstract

A novel vorticity based solution methodology has been developed to compute unsteady flow, particularly separation. The vorticity of the flow is determined on a set of points and the vorticity in the field is computed by linear interpolation. This is accomplished by the construction of a connected set of triangular elements formed by Delaunay triangularization of the points in the field. Triangulation of the vorticity field enables computation of first and second order spatial derivatives of the vorticity field using a least squares formulation. An effective diffusion transport velocity was developed to account for spatial movement of the vorticity due to viscosity. Diffusion velocity and direct calculation of the Laplacian allows for a deterministic solution of viscous diffusion. The points are then advected at both the induced velocity (computed from the Biot-Savart integral) and the diffusion velocity. This solution scheme was found to be stable as it was applied to the problem of impulsively started flow about a NACA 0012 airfoil. The phenomena of incipient separation as well as initial development of the unsteady wake was examined.