Perspective: Numerical Simulations of Wakes and Blade-Vortex Interaction

A method for simulating incompressible flows past airfoils and their wakes is described. Vorticity panels are used to represent the body, and vortex blobs (vortex points with their singularities removed) are used to represent the wake. The procedure can be applied to the simulation of completely attached flow past an oscillating airfoil. The rate at which vorticity is shed from the trailing edge of the airfoil into the wake is determined by simultaneously requiring the pressure along the upper and lower surface streamlines to approach the same value at the trailing edge and the circulation around both the airfoil and its wake to remain constant. The motion of the airfoil is discretized, and a vortex is shed from the trailing edge at each time step. The vortices are convected at the local velocity of fluid particles, a procedure that renders the pressure continuous in an inviscid fluid. When the vortices in the wake begin to separate they are split into more vortices, and when they begin to collect they are combined. The numerical simulation reveals that the wake, which is originally smooth, eventually coils, or wraps, around itself, primarily under the influence of the velocity it induces on itself, and forms regions of relatively concentrated vorticity. Although discrete vortices are used to represent the wake, the spatial density of the vortices is so high that the computed velocity profiles across a typical region of concentrated vorticity are quite smooth. Although the computed wake evolves in an entirely inviscid model of the flowfield, these profiles appear to have a viscous core. The computed spacing between the regions of concentrated vorticity in the wake and the circulations around them are in good agreement with the experimental results. As an application, a simulation of the interaction between vorticity in the oncoming stream and a stationary airfoil is also discussed.