PANEL METHOD FORMULATION FOR OSCILLATING AIRFOILS IN SUPERSONIC-FLOW

In the present work, the mathematical model for two-dimensional unstea dy supersonic flow based on the reduced potential equation, also known as the hyperbolic Helmholtz equation, is presented and discussed. The purpose is to develop a rigorous formulation, in order to bring into light the correspondence between the supersonic and subsonic panel met hod theory. Source and doublet integrals are obtained, and Laplace tra nsformation demonstrates that these are both solutions to the complete problem. It is shown that the doublet-only formulation reduces to a V olterra integrodifferential equation of the second kind, and a numeric al method is proposed in order to solve it. To the authors' knowledge, this is the first reported solution to the unsteady supersonic thin a irfoil problem through the use of doublet singularities. Comparisons w ith the source-only method are shown for the problem of a flat plate i n harmonic heave. Results for the problems of a flat plate in harmonic pitch and under a sinusoidal gust are also presented. The doublet pan el method was used to assess the importance of considering unsteady te rms in the solution, as opposed to applying quasisteady formulations.