Forces on Staggered Airfoil Cascades in Unsteady In-Phase Motion

We consider incompressible potential flow through a cascade of staggered thin airfoils in general, unsteady, in-phase motion. 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. The results are then specialized to harmonic motion, and applied to plunging, pitching, and sinusoidal gusts. All 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. They agree with the unstaggered results of Kemp and Ohashi when the stagger angle is zero. Typical numerical 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 stagger and solidity on unsteady cascade aerodynamics.