Unsteady lift of a flapped airfoil by indicial concepts

Abstract

A practical method is described for computing the unsteady lift on an airfoil due to arbitrary motion of a trailing-edge flap. The result for the incompressible case is obtained in state-space form by means of Duhamel superposition and employing an improved exponential approximation to Wagner's indicia! lift function. For subsonic compressible flow, the indicial lift at small values of time due to impulsive trailing-edge flap deflection is obtained from linear theory in conjunction with the aerodynamic reciprocal theorems. These results are used with experimental results for the oscillating case to obtain complete exponential approximations for the indicial response due to impulsive flap deflection. The final result for the unsteady lift due to an arbitrary flap motion in subsonic flow is obtained in state-space form. Numerical results and comparisons with experimental data are shown.