Oscillating wings in compressible subsonic flow

Abstract

The problem of estimating flutter and stability derivatives for wings of finite span describing simple harmonic oscillations in compressible flow is considered. It is shown that the problem can be reduced to a similar one for an equivalent wing in incompressible flow. The lateral dimensions of the equivalent wing are ~/(1 - M²) times those of the original wing and the frequency of oscillation is increased by the factor (1 - M²) -1 where M denotes the Mach number of the compressible flow. The mode of oscillation is different but related to that of the original wing and leads to a more complicated condition for tangential flow. It is suggested, however, that sufficient accuracy might be obtained by representing the boundary condition to first-order accuracy in the frequency and then solving quite generally the integral equation which determines the velocity potential at the surface of the wing. The comparisons made in Table 1 and Figs. 2a to 2d indicate that the above procedure is reasonably satisfactory in the two-dimensional case. For M = 0.7, the values of the derivatives given by the formulae derived in this report show fair agreement with the 'exact' results of Refs. 1 and 2 over a wide range of frequency parameter values. Since flutter derivatives for wings of finite span are not usually very sensitive to variations in frequency parameter, the scheme of calculation suggested should be sufficiently accurate for all practical purposes when the combined effects of thickness and viscosity are negligible. It does, however, require a reliable method for calculating derivatives for low aspect ratio wings in incompressible flow, since the aspect ratio of the equivalent wing is ~/(1 - M²) times that of the original wing and becomes small for the higher values of M.