Small Disturbance Transonic Flows About Oscillating Airfoils and Planar Wings.

Abstract : A theory and numerical solution method are presented for the problem of two or three dimensional flow about thin wings undergoing harmonic oscillations. The theory is based on a treatment of the unsteady flow as a small perturbation on the nonlinear steady flow. The coupled governing equations for the steady and unsteady perturbation potentials are of mixed elliptic/hyperbolic type and are solved using the mixed differencing line relaxation techniques of Murman and Cole. The theory and solution method have been generalized to treat subsonic or supersonic freestream flows, solid or porous wall effects and three dimensional flow about planar wings. Calculations demonstrating each of these capabilities are presented. Accuracy of the method for realistic steady and unsteady flows is examined by comparison to more exact numerical results and experimental data. The comparison indicates that the present method provides a useful and efficient inviscid solution. Quantitative differences between the present results and experimental data are attributed primarily to viscous effects, pointing out the importance of such effects for transonic flows.