A Second-Order Solution for an Oscillating Two-Dimensional Supersonic Airfoil

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In this paper a second-order solution, for the forces and moments produced by an oscillating two-dimensional airfoil of arbitrary cross section, has been determined. This solution was obtained by means of an iteration procedure. In the iteration procedure it was necessary to have a linearized solution of simple, closed form which was valid throughout the whole x, y plane. Existing solutions did not satisfy these requirements, thus, it was first necessary to develop a new linearized or first-order velocity potential. This potential was developed as a power series approximation, in frequency, to the exact linearized solution. Six terms of this series were developed and this sixth-order solution shown to be within a few percent of the exact linearized solution for reduced frequencies [...] less than 1.3. The first two terms of the series approximation were then used in the iteration process to produce the second-order solution in thickness. This solution which is valid to second-order in thickness and frequency has been determined for an oscillating airfoil of general cross section. The second-order terms were found to have a relatively strong influence on the final solution, particularly for the pitching moment. It will be seen in Section V that in many cases the second-order terms are larger in magnitude than the corresponding first order-terms and thus reverse the tendencies indicated by first-order theory. In particular, it was shown that the theoretical instability predicted by linearized theory for an airfoil of zero thickness is completely eliminated for an airfoil having a thickness ratio as small as three percent.