A finite wake theory for two-dimensional rotary wing unsteady aerodynamics

Abstract

The unsteady aerodynamic forces and moments of an oscillating airfoil for the fixed wing case were determined by Theodorsen along with the development of a lift deficiency function. Loewy subsequently developed an analogous lift deficiency function for the rotary wing case in which there are an infinite number of layers of shed vorticity, or wakes, below the reference airfoil. With the advent of computer panel codes that calculate the time histories of the wakes generated by oscillating airfoils, a theory is developed for the rotary wing case in which there are a finite number of layers of shed vorticity below the reference airfoil. This theory includes a lift deficiency function that is completely analogous to Loewy and Theodorsen. It has long been recognized that an airfoil oscillating in pure plunge produces a propulsive force ( Katzmayr effect ). Garrick used Theodorsen's work to develop equations for the propulsive force that include the lift deficiency function as a parameter. When either Loewy's lift deficiency function or the finite wake lift deficiency function is used, the effect of the propulsive force is greatly enhanced with the proper phase relationship of the wakes. The finite wake theory along with Garrick's work is used to describe the performance characteristics of Higher Harmonic Control. Specifically for the OH-6A, coupled pitch-plunge motion results in a propulsive force that significantly reduces the rotor drag force. Helicopter, Rotary wing, Unsteady aerodynamics, Wake, Propulsive force, Higher harmonic control, Hummingbird