Sound Radiation from a Lined Exhaust Duct with Lined Afterbody

AFT fan noise radiating from the bypass exhaust duct is usually attenuated by acoustic lining along the inside of the duct only. The unconventional treatment of the afterbody, recently proposed by Tester et al. [1–3] has been shown to provide an additional potential of damping of the order of 1 to 4 dB. This is remarkable, given the fact that most of the sound is supposed to radiate away from, rather than towards, the duct axis. In order to understand the underlying mechanisms, no-flow experiments and flow and no-flow CAA simulations have been performed, as well as comparison with a relatively simple analytical model [4] where only the afterbody is lined. In the present paper we derive an analytical Wiener-Hopf solution of a more complete version, where both the afterbody and the main duct outer wall is lined. This should enable a comparison between a lined duct with hard walled afterbody, and a lined duct with lined afterbody (with and without mean flow). The complexity of the problem leads to quite involved analysis and laborious formulas, but eventually a numerical evaluation provides first results that seem to confirm the earlier findings of Tester et al.