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

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.

Deep neural networks for waves assisted by the Wiener–Hopf method

“…This relation is the classical solution of a cylindrical duct acoustic equation and can be obtained by separation of variables [13]. The radial wavenumber α mn satisfies the solid wall boundary condition, dJ m (α mn r)/dr = 0 when r = 1.…”

“…The current work is primarily focused on the using of the Wiener-Hopf method, from which, the former works [6,11] already give the analytical solution for the idealized duct set-up as follows: More details, such as analyticity half-planes and algebraic properties at infinity, can be found in the references [6,11]. Some more advanced topics, such as matrix kernel and approximated kernel factorization, can be found in the references [13,21,24,41]. Readers of interest can refer to the literature and details are omitted here for brevity.…”

“…In addition, Rienstra [23] has studied the fan noise control problem with semi-infinite lined duct walls by using the Wiener-Hopf technique. Liu et al [13] and Jiang et al [14] have further studied semi-infinite, azimuthally non-uniform liners by incorporating Fourier expansions into the Wiener-Hopf technique, respectively.…”

A theoretical study of serrated leading edges in aerofoil and vortical gust interaction noise

“…The current paper would endeavour to simplify our previous model by incorporating Fourier transform into the Wiener-Hopf method. The Wiener-Hopf method is a powerful mathematical tool and has been heavily used for two types of classical wave problems in fluid mechanics: duct radiations [22][23][24][25][26] and flat plate diffractions [10,18,21,27]. The current problem falls into the second type, which usually has a much simpler Wiener-Hopf kernel than duct radiation problems.…”

Acoustic performance of a resonating perforated liner with incident axial and circumferential acoustic modes

“…The splices can make the damper face smaller relative to the wavelength and may thus cause a significant reduction in acoustic performance at some conditions. The redistribution of this energy from these rigid splices can be shown computationally to be a function of the number and widths of the splices; although, the precise mechanics are poorly understood with the three-dimensional analysis being computationally demanding [18,20,21,22,23,24].…”