Converged Velocity Field for Rotors by a Blended Potential Flow Method

Abstract

Potential-flow solutions for rotor induced flow by the He method give good convergence on the disk but can provide only a crude approximation off of the disk. The Morillo-Duffy formulation can give all three components off the disk, but the results converge poorly on the disk. Furthermore, Morillo-Duffy solutions converge very slowly for the velocity downstream in the limit as wake skew angle approaches 90o edgewise flow). In this work, new variables––called the Nowak-He variables––are introduced that provide both the He velocity and the Morillo-Duffy velocity from a single set of states. In addition, an approximate downstream velocity field is obtained from the adjoint theorem that gives the exact downstream velocity as skew angle approaches 90o. The blending of these three velocity fields is shown to give robust and accurate convergence to the potential-flow equations at all flight conditions.