FLUTTER OF LOW-ASPECT-RATIO WINGS PART I CALCULATION OF PRESSURE DISTRIBUTIONS FOR OSCILLATING WINGS OF ARBITRARY PLANFORM IN SUBSONIC FLOW BY THE KERNEL-FUNCTION METHOD

摘要

Based on a numerical solution of the pressure-downwash integral equation, an improved method of calculating the pressure distribution on an oscillating wing of arbitrary plan form in subsonic flow was developed. Over the platform a continuous pressure distribution which satisfied the boundary conditions at the edges was first assumed. The coefficients of each terms in the pressure series were to be evaluated by a downwash colloca¬tion method at a set of preferred stations on the platform. Using these collocation stations, maximum possible accuracies in the lift, moment, etc. were obtainable for a given number of stations. The numerical integration was accomplished by taking a summation of the point values of the integrand at a set of special integration stations. The feature of this method was that by using these integration stations the singularities in the kernel function were properly taken care of, and with the availability of the kernel function tabulation the numerical work was considerably reduced. The locations of both the collocation stations and the integration stations were formally derived and the validities of the claims were formally proved. Several numerical examples were worked out in both two and three- dimensional cases. The two-dimensional results compared with the exact results with very good accuracies. Results on the total lift and total moment on a 45 constant chord swept wing of aspect ratio two at M = 0, k = 0.4 and M = 0.8, k = 0.4 were also obtained. The result for M = 0, k = 0.4 case was compared with incompressible experimental result with reasonable agreement.