Laminar incompressible flow past parabolic bodies at angles of attack

Abstract

Numerical solutions of a two-dimensional steady laminar incompressible flow over semi-infinite parabolic bodies at angles of attack are obtained. All solutions are found by using a modified numerical approach to solve the time-dependent Navier-Stokes equations. The governing equations are written for the stream function and vorticity variables and are solved on a nonuniform body-fitted parabolic grid. A check of our solutions to those that exist in the literature at zero angle of attack showed excellent agreement. In addition, at zero angle of attack far from the leading edge, an expected correspondence to Blasius flow was found. At positive angles of attack, the body became aerodynamically loaded with lower pressures on its upper surface. At large enough angles of attack, the flow separated on the upper surface. In all of the cases examined, the flow separation was followed by a reattachment that defined a separation zone. An almost linear increase in the streamwise extent of the separation zone occurred with increasing angle of attack. The separation location and extent of the separation zone was a function of the nose Reynolds number. The results indicated that the shape factor could be used to provide a criterion for separation and reattachment in these cases. The characteristics of the separation zone for this geometry should prove to be an excellent basic flow to document the effect of leading-edge How separation on acoustic receptivity of boundary-layer instabilities.