EFFECT OF AIRFOIL MEAN LOADING ON HIGH-FREQUENCY GUST INTERACTION NOISE (AEROACOUSTICS, FAN, TURBOMACHINERY).

Abstract

This dissertation investigates the effect of airfoil steady loading on the sound generated by the interaction of an isolated, zero-thickness airfoil with a high-frequency convected disturbance. The analysis is based on a linearization of the inviscid equations of motion about a nonuniform mean flow. The mean flow is assumed to be two-dimensional and subsonic. Throughout most of the dissertation, we assume that the Mach number is 0(1), though in one section we concentrate on the leading-edge region and study the behavior of the sound field as the Mach number tends to zero. The small parameter representing the amount of airfoil camber and incidence angle, and the large parameter representing the ratio of airfoil chord to disturbance wavelength, are utilized in a singular perturbation analysis. The analysis shows that essentially all of the sound is generated at the leading and trailing edges, in regions the size of the disturbance wavelength. The solution in the local-leading-edge region reveals several sound-generating mechanisms which do not exist for an airfoil with no mean loading. These mechanisms are not present at the trailing edge; the trailing edge is important only as a scatterer of the sound produced at the leading edge. The propagation of sound away from the airfoil edges is described by geometric acoustics, with the amplitude varying on the scale of the airfoil chord and the phase varying on the much smaller scale of the disturbance wavelength. In addition, a diffraction-type transition region exists downstream of the airfoil. Calculations of radiated acoustic power show that the sound field depends strongly on Mach number, gust characteristics, and airfoil steady loading. Small changes in these properties can produce large changes in radiated power levels. Most importantly, we find that the amount of power radiated correlates very well with the strength of the mean flow around the leading edge.