NUMERICAL-STUDIES OF SEPARATED FLOW FROM BODIES WITH SHARP CORNERS BY THE VORTEX IN CELL METHOD

The Navier-Stokes equations are solved around arbitrary cross-sections in the laminar flow regime. A mixed Eulerian-Lagrangian scheme (Vortex-In-Cell Method) is used in combination with the Operator Splitting Technique. The main feature of this numerical model is the generation of discrete vortices all around the body surface; this is achieved in the frame of potential theory in combination with a conformal transformation of the body contour. Problems occur at sharp corners, since infinite velocity is predicted from the ideal fluid calculations. The treatment of the singular behavior will consist of a truncation of the mapping derivative at the corners. It is shown by applications for a square and a diamond that this artificial cutting-off does not strongly affect the mass coefficient and the drag force due to pressure. The drag force due to skin friction is more affected. An additional treatment is necessary in the immediate vicinity of the corners of a flat plate in a cross flow. This will consist of “slowing down” the vortices to avoid unrealistic motions due to convection. © 1994 Academic Press Ltd.