Unsteady Flow through a Cascade of Airfoils with Steady Loading

Abstract

Incompressible potential flow through a cascade of staggered thin airfoils with steady loading in general, unsteady, in-phase motion is considered. With the assumptions of the Kutta condition and linearized wakes, exact analytical expressions are derived for pressure distribution, lift and moment, using conformal mapping applied to the velocity field. Mean attack angle and parabolic camber are considerd to give steady loading, and then the results are expressed in closed-form as quadratures, and reduce to the well-known relations for thin airfoil theory, as the solidity decreases to zero. Typical results are given in the figures. They should serve as a measure of the accuracy of numerical or approximate solutions, as well as representing in a simple way the effects of steady loading, stagger and solidity on unsteady cascade aerodynamics.