Models for acoustic propagation through turbofan exhaust flows

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of previous solutions is that they do not allow for the jet nozzle to protrude a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). In this paper we use the matrix Wiener-Hopf technique, which will allow precisely the finite nacelle-jet nozzle separation to be included. The crucial step in our work is to factorise a certain matrix as a product of terms analytic and invertible in the upper/lower halves of the complex plane. The way we do this matrix factorisation is quite different in the buried and protruding nozzle cases. In the buried case our solution method is the so-called pole-removal technique. In the technically more demanding protruding case, however, we must first use Pade approximants to generate a uniformly-valid, meromorphic representation of a certain function, before the same pole-removal method can be applied. Sample results are presented, investigating in particular the effects of exit plane stagger. © 2007 by B Veitch and N Peake.