ANALYTICAL STUDIES OF SOME ACOUSTIC PROBLEMS OF JET ENGINES

This thesis presents analytical studies of internal noise generation and transmission in jet engines and its radiation from the duct ends. The propagation and generation of acoustic waves in a choked nozzle is considered first. Pressure and entropy fluctuations caused by gas stream non-uniformities like "hot spots," are incident on the nozzle entrance. A novel noise-generation mechanism is uncovered where acoustic waves are produced by a distribution of sources of strength proportional to the entrance entropy fluctuation and local gradient of the mean flow velocity. The propagation of acoustic waves in a moving medium in the presence of semi-infinite or finite boundaries is then considered. A transformation is introduced which relates the solutions of such problems to the solutions of associated problems in a stationary medium. The method is described by discussing the Sommerfeld problem of diffraction of a plane wave by a half plane immersed in a subsonically moving medium. When the plane has a trailing edge, it is shown that both reflection and shadow regions expand; while the opposite occurs for a leading edge,in which circumstance an additional diffracted wave also appears. In the supersonic case, all the diffraction problems are related to a single reference problem, solved by Fourier transform methods. A decomposition of the pressure field in a "geometrical optics" field and a diffracted field is given, showing some remarkable similarities with the subsonic case solution. The radiation of acoustic modes from a duct immersed in a subsonically moving medium is treated by a similar transform method. The presence of the uniform flow has roughly the same effect as an increase in frequency of the incident wave, at constant mode number. The effect of acoustical lining on the radiation pattern is examined, and side radiation is shown to be greatly reduced for the lower order modes. The transmission and reflection of acoustic waves incident on a blade row is analyzed by the transform method,and the transmission and reflection coefficients for the blade row immersed in a moving medium are expressed in terms of the basic acoustic characteristics of the blade row in a stationary medium.