Abstract

We (Ben Veitch & Nigel Peake) consider  the  noise  radiated  by two semi-infinite  coaxial circular  cylinders carrying (different) uniform axial  mean flows. The exit planes  are staggered axially by a  finite distance, and the inner cylinder is either buried upstream or protrudes downstream.  In earlier work (B. Veitch & N. Peake 2008, Journal of Fluid Mechanics, 613, 275—307) we solved the problem with rigid walls,  and we  now  extend this  work to allow for the presence of sound-attenuating   acoustic liners (specifically by lining the outer wall of the inner cylinder). The  key step in the solution is the factorisation of a 3×3 Wiener-Hopf matrix, and different methods for completing this   factorisation are required in the  buried and protruding cases, and specificlly in the protruding case  Pade approximants are required . We present  results  for the  far-field scattered  sound which demonstrate the effects of  wall lining in a  range of cases.