Upstream-radiated rotor–stator interaction noise in mean swirling flow

A major component of the noise in modern aeroengines is rotor–stator interaction noise generated when the wake from the rotating fan impinges on a stator row downstream. An analytically based model for the prediction of upstream-radiated rotor–stator interaction noise is described, and includes the important effect of mean swirling flow on both the rotor wake evolution and the acoustic response. The analytic nature of the model allows for the inclusion of all wake harmonics and enables the response at all blade passing frequencies to be determined. An asymptotic analysis based on large rotor blade number is used to model the evolution of the rotor wake downstream in a cylindrical duct carrying mean swirling flow. The equations governing the axial evolution of the wake simplify to three coupled first-order differential equations in the interior, while close to the duct walls, a boundary-layer correction is required in order to satisfy the impermeability conditions at the boundaries. At the stator location, the wake is used as input into a local linear cascade model at each radius. The interaction of each wake harmonic gives rise to acoustic waves of multiple azimuthal order which contribute to the pressure field radiated back upstream. This enables the total acoustic response to be determined in terms of cylindrical duct modes in mean swirling flow. The effect of stator blade geometry (thickness, camber, angle of attack) and rotor–stator separation on the total upstream-radiated noise is determined. Blade geometry is shown to have a significant effect on the noise generated, and increasing the rotor–stator gap can lead to large reductions in noise levels. Asymptotic treatment of the acoustic field, based on large azimuthal order, is also considered and used to identify the dominant contributions to the total pressure field resulting from the rotor–stator interaction. The ray structure of the acoustic modes in swirl is shown to be very different in some cases from that in uniform flow

Noise generation by turbulence-propeller interaction in asymmetric flow

AbstractThis paper is concerned with a particular source of both broadband and tonal aeroengine noise, termed unsteady distortion noise. This noise arises from the interaction between turbulent eddies, which occur naturally in the atmosphere or are shed from the fuselage, and the rotor. This interaction produces broadband noise across a broad frequency spectrum. In cases in which there is strong streamtube contraction, which is especially true for open rotors at low-speed conditions (such as at take-off or for static testing), tonal noise at frequencies equal to multiples of the blade passing frequency are also produced, owing to the enhanced axial coherence caused by eddy stretching. In a previous paper (Majumdar & Peake, J. Fluid Mech., vol. 359, 1998, pp. 181–216), a model for unsteady distortion noise was developed in axisymmetric flow. However, asymmetric situations are also of much interest, and in this paper we consider two cases of asymmetric distortion: firstly that induced by the proximity of a second rotor, and secondly that caused by non-zero inclination to the flight direction, as found at take-off. This requires significant extension of the previous axisymmetric analysis. We find that the introduction of asymmetric flow features can have a significant decibel effect on the radiated sound power. For instance, in low-speed conditions we find that the tonal level is reduced significantly by the proximity of a second rotor, compared to the axisymmetric case, while the effect on the broadband levels is rather modest.RAVR acknowledges funding from an EPSRC Rolls Royce CASE award which made this work possible.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2014.48

On high-frequency sound generated by gust-aerofoil interaction in shear flow

AbstractA theoretical model is constructed to predict the far-field sound generated by high-frequency gust–aerofoil interaction in steady parallel shear flow, including the effects of aerofoil thickness. Our approach is to use asymptotic analysis of the Euler equations linearised about steady parallel shear flow, in the limits of high frequency and small, but non-zero, aerofoil thickness and Mach number. The analysis splits the flow into various regions around the aerofoil; local inner regions around the leading and the trailing edges where sound is generated and scattered; a surface transition region accounting for the curvature of the aerofoil; a wake transition region downstream of the aerofoil; and an outer region through which the sound propagates to the observer. Solutions are constructed in all regions, and matched using the principle of matched asymptotic expansions to yield the first two terms in the expansion of both the amplitude and the phase of the far-field pressure. Result are computed for the particular case of scattering of a gust by a symmetric Joukowski aerofoil placed in symmetric Gaussian parallel shear flow. The introduction of mean shear is shown to have a significant effect on the far-field directivity and on the total radiated power.This is the accepted manuscript for a paper published in the Journal of Fluid Mechanics, Volume 766, March 2015, pp 297- 325, doi: 10.1017/jfm.2015.2

Interaction of turbulence with the leading-edge stagnation point of a thin aerofoil

An asymptotic model is constructed to analyse the interaction of turbulence generated far upstream with a thin elliptic-nosed solid body in uniform flow. The leading-edge stagnation point causes significant deformation of incident vorticity, and hence our analysis focuses on the region of size scaling with the nose radius close to the stagnation point. Rapid distortion theory is used to separate the flow field generated by a single unsteady gust perturbation into a convective non-acoustic part, containing the evolution of the upstream vortical disturbance, and an acoustic part generated by the interaction of the vorticity with the solid surface, as is typical in gust–aerofoil interaction theory. Using single-frequency gust response solutions, along with a von Kármán energy spectrum, we find the turbulent pressure spectrum generated by homogeneous isotropic turbulence incident from far upstream. Both high- and low-frequency gusts are considered to allow approximations to be found for the turbulent pressure spectra close to the leading edge, and far from the body close to the incident stagnation streamline. Good agreement is shown between the asymptotic results for the near- and far-field leading-edge turbulent pressure spectra and recent experimental findings.The work in this paper was funded by EPSRC under grant EP/I010440/1.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Cambridge University Press

Wave scattering by an infinite cascade of non-overlapping blades

We consider the scattering of waves by an in finite three-dimensional cascade of fi nite-length at blades in subsonic fow at zero angle of attack. This geometry is of speci fic relevance as it provides a model for the components in turbofan engines. We study the scattering problem analytically, considering both acoustical and vortical incident fields, spanwise wavenumbers and transverse mean flow. Most importantly we extend previous work by lifting the restriction that adjacent blades overlap, a condition that had thus far been crucial for the analytical study of this problem. Our method of solution relies on the solution of three coupled boundary value problems using the Wiener-Hopf technique, corresponding to an uncoupled leading-edge approximation, and a subsequent trailing-edge and leading-edge correction. We provide exact expressions for observables in the system, depending only on the solution of a linear matrix equation. Specifi cally we find closed-form expressions for the far- field behaviour of the scattered potential upstream and downstream of the cascade, the upstream and downstream sound power, as well as the total unsteady lift on each blade in the cascade. A wide range of results are presented, and we see that the non-overlapping cascade is, as might be expected, typically more transparent to incident disturbances than the previously studied overlapping case.EPSRC grant EP/L016516/

Tunnelling effects for acoustic waves in slowly varying axisymmetric flow ducts

The multiple-scales Wentzel–Kramers–Brillouin (WKB) approximation is used to model the propagation of acoustic waves in an axisymmetric duct with a constriction in the presence of mean flow. An analysis of the reflection/transmission process of modes tunnelling through the constriction is conducted, and the key mathematical feature is the presence of two turning points, located at either real axial locations or in the complex plane. The resulting asymptotic solution consists of WKB solutions in regions away from the constriction and an inner solution valid in the near vicinity of the constriction. A solution which is uniformly valid throughout the duct is also derived. A range of test cases are considered, and the importance of accounting for the inner region, even in cases in which the turning points lie away from the real axis, is demonstrated.The Danish Council for Independent Research, Technology and Production Sciences (Grant ID: UK 95 OS63822 PO83004)This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jsv.2016.06.00

An analytically-based method for predicting the noise generated by the interaction between turbulence and a serrated leading edge

This paper considers the interaction of turbulence with a serrated leading edge. We investigate the noise produced by an aerofoil moving through a turbulent perturbation to uniform flow by considering the scattered pressure from the leading edge. We model the aerofoil as an infinite half plane with a leading edge serration, and develop an analytical model using a Green’s function based upon the work of Howe. This allows us to consider both deterministic eddies and synthetic turbulence interacting with the leading edge. We show that it is possible to reduce the noise by using a serrated leading edge compared with a straight edge, but the optimal noise-reducing choice of serration is hard to predict due to the complex interaction. We also consider the effect of angle of attack, and find that in general the serrations are less effective at higher angles of attack

Sound radiation from a semi-infinite lined duct

In this paper we consider the radiation properties of a pair of semi-infinite, parallel-plate ducts in which the inner duct is buried inside the outer duct. A Robin condition is applied to one of the inner walls (to represent an acoustic lining), while Neumann conditions are applied on all other surfaces. This leads to a matrix Wiener-Hopf problem, which requires the factorisation of a 3 × 3 matrix of a form which, to our knowledge, has not previously been considered in the literature and which is not directly amenable to standard pole-removal techniques. We derive the exact factorisation of this matrix here, and present results for the far-field scattered sound which show the effect of varying the properties of the wall lining

Natriuretic peptide receptors regulate cytoprotective effects in a human ex vivo 3D/bioreactor model

© 2013 Peake et al.; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Spectral study of the Laplace-Beltrami operator arising in the problem of acoustic wave scattering by a quarter-plane

The Laplace-Beltrami operator on a sphere with a cut arises when considering the problem of wave scattering by a quarter-plane. Recent methods developed for sound-soft (Dirichlet) and sound-hard (Neumann) quarter-planes rely on an a priori knowledge of the spectrum of the Laplace-Beltrami operator. In this paper we consider this spectral problem for more general boundary conditions, including Dirichlet, Neumann, real and complex impedance, where the value of the impedance varies like $\textit{α/=r, r}$ being the distance from the vertex of the quarter-plane and α being constant, and any combination of these. We analyse the corresponding eigenvalues of the Laplace-Beltrami operator, both theoretically and numerically. We show in particular that when the operator stops being self-adjoint, its eigenvalues are complex and are contained within a sector of the complex plane, for which we provide analytical bounds. Moreover, for impedance of small enough modulus |α|, the complex eigenvalues approach the real eigenvalues of the Neumann case.R.C. Assier would like to acknowledge the support by UK EPSRC (EP/N013719/1).This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Oxford University Press