Separated flow past three-dimensional bodies as a singular perturbation problems

Abstract

This paper proposes a method for computing steady wake flows of an inviscid fluid over a threedimensional body with polygonal cross-section and arbitrary plan-form. The method is based on the technique of matched asymptotic expansions, assuming a large "aspect ratio". The far-field velocity potential is given essentially by a lifting line and a line source. The near-field, treated as two-dimensional, is solved by a suitable version of Tulin's double spiral vortex model which incorporates a downwash correction and an underpressure in the near-wake. The latter is related to the Reynolds number of the corresponding real flow using recent results by Tulin and Hsu and the authors. Numerical results for a few prototype problems (flat-plate airfoil with separation at both the leading edge and the upper surface, flat-plate wing with full or partial spoiler) are presented. The method can be efficiently implemented on a parallel computer.