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An analytical correction to Amiet’s solution of airfoil leading-edge noise in non-uniform mean flows

Published online by Cambridge University Press:  12 November 2019

Siyang Zhong Open the ORCID record for Siyang Zhong [Opens in a new window] ,
Xin Zhang ,
Bo Peng  and
Xun Huang
Siyang Zhong*
Affiliation:
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong, PR China Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong, PR China
Xin Zhang*
Affiliation:
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong, PR China HKUST–Shenzhen Research Institute, Shenzhen, PR China
Bo Peng
Affiliation:
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong, PR China
Xun Huang
Affiliation:
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong, PR China State Key Laboratory of Turbulence and Complex Systems, Department of Aeronautics and Astronautics, College of Engineering, Peking University, Beijing, PR China
*
†Email addresses for correspondence: zhongsy@ust.hk, aexzhang@ust.hk
†Email addresses for correspondence: zhongsy@ust.hk, aexzhang@ust.hk
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Abstract

Gust/turbulence–leading edge interaction is a significant source of airfoil broadband noise. An approach often used to predict the sound is based on Amiet’s flat-plate solution. Analytical studies have been conducted to investigate the influences of airfoil geometries, non-uniform mean flows and turbulence statistics, which, however, were often too convoluted. In this work, the problem is revisited by proposing simple corrections to the standard flat-plate solution to account for the effect of non-uniform mean flows of real airfoils. A key step in the method is to use a new space–time transformation that is analogous to the Prandtl–Glauert transformation to simplify the sound governing equation with spatially varying coefficients to a classical wave equation, which is then solved using the Schwarzschild technique as in Amiet’s solution. The impacts of Mach number, wavenumber and airfoil geometry on the prediction accuracy are investigated for both single-frequency and broadband cases, and the results are compared against high-fidelity simulations. It predicts the sound reduction by the airfoil thickness, and reveals that the reduction is caused by the non-uniform streamwise velocity. The limitations of the model are discussed and the approximation errors are estimated. In general, the prediction error increases with the airfoil thickness, the sound frequency and the flow Mach number. Nevertheless, in all cases studied in this work, the proposed correction can effectively improve the prediction accuracy of the flat-plate solution much more efficiently compared to numerical solutions of the Euler equations using computational aeroacoustics.

JFM classification

Acoustics: Aeroacoustics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 882 , 10 January 2020 , A29
Copyright
© 2019 Cambridge University Press 

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