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Theoretical model of scattering from flow ducts with semi-infinite axial liner splices

Published online by Cambridge University Press:  30 November 2015

Xin Liu ,
Hanbo Jiang ,
Xun Huang  and
Shiyi Chen
Xin Liu
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China
Hanbo Jiang
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China
Xun Huang*
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China
Shiyi Chen
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China
*
†Email addresses for correspondence: huangxun@pku.edu.cn, huangxun@ust.hk
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Abstract

In this paper we present a theoretical model to study sound scattering from flow ducts with a semi-infinite lining surface covered by some equally spaced rigid splices, which is of practical importance in the development of silent aeroengines. The key contribution of our work is the analytical and rigorous description of axial liner splices by incorporating Fourier series expansion and the Wiener–Hopf method. In particular, we describe periodic variations of the semi-infinite lining surface by using Fourier series that accurately represent the layout of rigid splices in the circumferential direction. The associated matrix kernel involves a constant matrix and a diagonal matrix. The latter consists of a series of typical scalar kernels. A closed-form solution is then obtained by using standard routines of Wiener–Hopf factorisation for scalar kernels. A couple of appropriate approximations, such as numerical truncations of infinite Fourier series, have to be adopted in the implementation of this theoretical model, which is validated by comparing favorably with numerical solutions from a commercial acoustic solver. Finally, several numerical test cases are performed to demonstrate this theoretical model. It can be seen that the proposed theoretical model helps to illuminate the essential acoustic effect jointly imposed by axial and circumferential hard–soft interfaces.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , pp. 62 - 83
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Copyright
© 2015 Cambridge University Press 

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