CUED Publications database

The acoustic Green's function for swirling flow with variable entropy in a lined duct

Mathews, JR and Peake, N (2018) The acoustic Green's function for swirling flow with variable entropy in a lined duct. Journal of Sound and Vibration, 419. pp. 630-653. ISSN 0022-460X

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© 2017 Elsevier Ltd This paper extends previous work by the authors (Journal of Sound and Vibration, 395:294-316,2017) on the acoustic field inside an annular duct with acoustic lining carrying mean axial and swirling flow so as to allow for non-uniform mean entropy, as would be found for instance in the turbine stage of an aeroengine. The main aim of this paper is to understand the effect of a non-uniform entropy on both the eigenmodes of the flow and the Green's function, which will allow noise prediction once we have identified acoustic sources. We first derive a new acoustic analogy in isentropic swirling flow, which allows us to derive the equation the tailored Green's function satisfies. The eigenmodes are split into two distinct families, acoustic and hydrodynamic modes, and are computed using different analytical methods; in the limit of high reduced frequency using the WKB method for the acoustic modes; and by considering a Frobenius expansion for the hydrodynamic modes. These are then compared with numerical results, with excellent agreement for all eigenmodes. The Green's function is also calculating analytically using the realistic limit of high reduced frequency, again with excellent agreement compared to numerical calculations. We see that for both the eigenmodes and Green's function the effect of non-uniform mean entropy is significant.

Item Type: Article
Divisions: Div A > Energy
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:12
Last Modified: 18 Oct 2018 02:46