PERSPECTIVE - NUMERICAL SIMULATIONS OF WAKES AND BLADE-VORTEX INTERACTION

A method for simulating incompressible flows past airfoils and their w akes is described. Vorticity panels are used to represent the body, an d vortex blobs (vortex points with their singularities removed) are us ed to represent the wake. The procedure can be applied to the simulati on of completely attached flow past an oscillating airfoil. The rate a t which vorticity is shed from the trailing edge of the airfoil into t he wake is determined by simultaneously requiring the pressure along t he upper and lower surface streamlines to approach the same value at t he trailing edge and the circulation around both the airfoil and its w ake to remain constant. The motion of the airfoil is diiscretized, and a vortex is shed from the trailing edge at each time step. The vortic es are convected at the local velocity of fluid particles, a procedure that renders the pressure continuous in an inviscid fluid. When the v ortices in the wake begin to separate they are split into more vortice s, and when they begin to collect they are combined. The numerical sim ulation reveals that the wake, which is originally smooth, eventually coils, or wraps, around itself, primarily under the influence of the v elocity it induces on itself, and forms regions of relatively concentr ated vorticity. Although discrete vortices are used to represent the w ake, the spatial density of the vortices is so high that the computed velocity profiles acorss a typical region of concentrated vorticity ar e quite smooth. Although the computed wake evolves in an entirely invi scid model of the flowfield, these profiles appear to have a viscous c ore. The computed spacing between the regions of concentrated vorticit y in the wake and the circulations around them are in good agreement w ith the experimental results. As an application, a simulation of the i nteraction between vorticity in the oncoming stream and a stationary a irfoil is also discussed.