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Acoustic theory of the many-bladed contra-rotating propeller: analysis of the effects of blade sweep on wake interaction noise

Published online by Cambridge University Press:  11 April 2019

M. J. Kingan Open the ORCID record for M. J. Kingan [Opens in a new window]  and
A. B. Parry Open the ORCID record for A. B. Parry [Opens in a new window]
M. J. Kingan
Affiliation:
Department of Mechanical Engineering, University of Auckland, Auckland 1010, New Zealand
A. B. Parry*
Affiliation:
30 Ypres Road, Allestree, Derby DE22 2LZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

An analytical model is presented for the wake interaction tones produced by a contra-rotating propeller. We re-cast the usual far-field radiation formulae as a double integral over a nominal propeller source annulus. Assuming that the number of blades on both propellers is large, we evaluate the integral asymptotically in terms of its leading-order contributions from interior stationary or boundary critical points which represent the specific locations on the propeller annulus that dominate the sound radiation. The asymptotic approach is powerful producing results in the form of one-line algebraic formulae that contain no integrals or special functions yet remain accurate. The asymptotics show that sweep is not necessarily beneficial and can cause the blade design to become critical for particular tones and directions in terms of a continuum of interior points distributed along a line on the propeller source annulus producing a higher-order result and thus an enhanced radiated sound field. The paper also shows how the interior points are completely consistent with the sub- or super-critical gust response of a swept blade. Tones with low and zero azimuthal mode order are treated as special cases and the asymptotics show that, as the mode order reduces, the radiated sound becomes concentrated around the flight axis where even higher-order solutions are possible, including rings and annuli of stationary points around the propeller annulus. Full numerical calculations confirm the accuracy of the asymptotic approach.

JFM classification

Acoustics: Aeroacoustics Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 385 - 427
Copyright
© 2019 Cambridge University Press 

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