The aeroacoustics of jet pipes and cascades

This thesis is concerned with theoretical studies in two areas related to the noise of modern turbofan aeroengines. In the first case, we are concerned with the propagation of internally generated sound though the propulsion nozzle to the farfield, including the effects of diffraction by the jet pipe, refraction and Doppler amplification by the mean flow and the exchange of energy between acoustic and hydrodynamic modes at the nozzle lip. Both low and high frequencies are discussed. In the low frequency case, the essential aim is the derivation of simple analytical expressions and their interpretation in the context of various forms of acoustic analogy, and the analysis is continued to second order in a frequency parameter or Helmholtz number, giving predictions of the farfield directivity and of the magnitude of reflected waves in excellent agreement with experiments, and yet expressible in simple analytical fashion. An essential element of the solution of these problems is the satis¬faction of a Kutta condition at the nozzle lip. In the high frequency case, two approximate theories are formulated, and compared with each other and with exact solutions. The theories we handle are Kirchhoff's approximation and the geometric theory of diffraction. The aim is again to provide a theoretical framework in which as many effects as possible can be handled in a rational manner. The final two chapters are concerned with a particular aspect of compressor noise - the buzzsaw field generated by blading non--uniformities. This field is determined by the variation of shock strength of a non-uniform cascade. This is achieved by a combination of analysis of the detached shock waves ahead of a non-uniform cascade and a linear examination of the outflow from the cascade showing this to depend on area alone, at typical operating conditions, 'The upshot is a relation between the pressure rise across the shock wave ahead of the nth and (n - 1)th blades. This relation is in significantly better agreement with experiment than relations using attached shock waves, and provides a theoretical basis for blade shuffling procedures designed to alleviate buzzsaw noise. The aim throughout the thesis is to take the calculations as far as is possible and sensible by purely analytical means and to provide simple physical insight into the mechanisms involved.