Acoustic Scattering of Point Sources by a Moving Prolate Spheroid

Abstract

THIS paper contains a numerical prediction of bodyscattering effects on aircraft flyover noise. A simple model consisting of a moving prolate spheroid with trailing acoustic point sources is used to represent the complicated physical system of a subsonic jet aircraft flyover. Classical theories of scattering and diffraction are used to predict sound pressure levels on an imaginary plane below the body. This technique was developed for application in the study of installation effects for static and moving jets. Several approaches for calculating the scattered field of an acoustic point source near a stationary prolate spheroid are available, for example, Refs. 1 and 2. The method of geometric optics was selected because it provides solutions in a minimum amount of computer time and allows for sources off the axis of symmetry. Using the Lorentz transform described in Ref. 3, the scattered field of a moving body and source can be determined from an equivalent stationary problem. Contents Consider an acoustic point source near the end of a slender prolate spheroid where source and body are moving at a constant forward speed, Fig. 1. The rectangular coordinate axes* andy fall on the major and minor axes of the body. An imaginary observer plane is below and parallel to the x-y plane. The intersection of the z axis with this observer plane is defined as a reference point; all sound pressure levels (SPL) presented herein are normalized with respect to the SPL at the reference point. Figure 1 also indicates the position of the geometric shadow region. Only diffracted rays contribute to the solution in this region, whereas incident and scattered rays dominate the solution elsewhere. Geometric optics solutions are appropriate for high frequencies, that is, for frequencies whose wavelengths are considerably smaller than the dimensions of the body. The usual measure of normalized frequency is the product of the wave number (k=2irf/c) and the semimajor axis length a. A ka value of 50 is considered high. A comparison of geometric optics solution with other experimental and numerical results in Ref. 2 shows that geometric optics is very reliable except in the shadow region. Fortunately, in the present study, SPL values in the shadow region are not as important as those values near the reference point. Contouring of computed results demonstrate the significance of scattering and motion effects on flyover data. Normalized SPL are calculated for a grid of points on an observer plane, which is a distance of 20a below the body. A standard computer software routine is used to draw equal level contours for the data. Contours for a stationary point