Nigel Peake

Nigel Peake
University of Cambridge | Cam · Department of Applied Mathematics and Theoretical Physics

PhD

About

168
Publications
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3,622
Citations
Additional affiliations
October 1994 - present
University of Cambridge
Position
  • Professor of Applied Mathematics

Publications

Publications (168)
Article
We study the efficient approximation of highly oscillatory integrals using Filon methods. A crucial step in the implementation of these methods is the accurate and fast computation of the Filon quadrature moments. In this work we demonstrate how recurrences can be constructed for a wide class of oscillatory kernel functions, based on the observatio...
Article
We study the balance of outgoing and incoming power for acoustic wave scattering by a cascade of flat blades in uniform subsonic mean flow. In nonzero mean flow the Kutta condition at the trailing edge of the cascade plates leads to the production of vorticity in the form of unsteady vortex sheets attached at the trailing edges, which results in a...
Preprint
We study the efficient approximation of integrals involving Hankel functions of the first kind which arise in wave scattering problems on straight or convex polygonal boundaries. Filon methods have proved to be an effective way to approximate many types of highly oscillatory integrals, however finding such methods for integrals that involve non-lin...
Article
We consider the scattering of waves by an infinite three-dimensional cascade of finite-length flat blades in subsonic flow at zero angle of attack. This geometry is of specific relevance as it provides a model for the components in turbofan engines. We study the scattering problem analytically, considering both acoustical and vortical incident fiel...
Article
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,...
Article
The ability of some species of owl to fly in effective silence is unique among birds and provides a distinct hunting advantage, but it remains a mystery as to exactly what aspects of the owl and its flight are responsible for this dramatic noise reduction. Crucially, this mystery extends to how the flow physics may be leveraged to generate noise-re...
Article
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 analytica...
Article
Full-text available
The static reconfiguration of flexible beams exposed to transverse flows is classically known to reduce the drag these structures have to withstand. But the more a structure bends, the more parallel to the flow it becomes, and flexible beams in axial flows are prone to a flutter instability that is responsible for large inertial forces that drastic...
Article
Full-text available
A computational framework is proposed for the linear modal and nonmodal analysis of fluid systems consisting of a periodic array of n identical units. A formulation in either time or frequency domain is sought and the resulting block-circulant global system matrix is analyzed using roots-of-unity techniques, which reduce the computational effort to...
Presentation
Full-text available
This presentation will focus on calculating the modes and Green’s function for swirling flow in an finite duct. We will consider solutions to the linearised Euler equations for a compressible, perfect gas which will be either homentropic or isentropic. The base flow velocity will be have both varying shear and swirl. The duct will have hard walls o...
Article
This paper extends previous work by the authors (Journal of Sound and Vibration, 395:294-316,2017) on the acoustic field inside an annular duct with acoustic lining carrying mean axial and swirling flow so as to allow for non-uniform mean entropy, as would be found for instance in the turbine stage of an aeroengine. The main aim of this paper is to...
Article
An efficient approach is proposed to predict acoustic scattering with nonuniform potential flow effects for structures with rotational and translational symmetries. The convected wave equation is transformed to Helmholtz and Laplace equations using a time transformation. The boundary-element method is used to formulate scattering by rotationally sy...
Article
This paper considers the acoustic field inside an annular duct carrying mean axial and swirling flow and with either acoustically hard or lined walls. The particular aim is to compute the Green's function, which is required for predicting the noise generated by known acoustic sources, both approximately and numerically. Asymptotic approximations fo...
Article
Strategies for trailing edge noise control have been inspired by the downy canopy that covers the surface of exposed flight feathers of many owl species. Previous wind tunnel measurements demonstrate that canopies of similar characteristics can reduce pressure fluctuations on the underlying surface by as much as 30dB, and significantly attenuate ro...
Article
Full-text available
This work takes inspiration from the structure of the down covering the flight feathers of larger species of owls, which contributes to their ability to fly almost silently at frequencies above 1.6 kHz. Microscope photographs of the down show that it consists of hairs that form a structure similar to that of a forest. The hairs initially rise almos...
Article
Strategies for trailing-edge noise control have been inspired by the downy canopy that covers the surface of exposed flight feathers of many owl species. Previous wind-tunnel measurements demonstrate that canopies of similar characteristics can reduce pressure fluctuations on the underlying surface by as much as 30 dB and significantly attenuate ro...
Chapter
The secret of certain owl species enabling them to fly stealthily is investigated and adapted to the suppression of aeroacoustic noise at the trailing edge of a wing or blade. Two features from the owl are mimicked: the poro-elastic trailing edge in the owl’s feather, and the fibrous canopy structure above the nominal wing surface. Initial modellin...
Article
This work takes inspiration from the structure of the down covering the flight feathers of larger species of owls, which contributes to their ability to fly almost silently at frequencies above 1.6 kHz. Microscope photographs of the down show that it consists of hairs that form a structure similar to that of a forest. The hairs initially rise almos...
Article
Full-text available
In this note we consider general formulation of Euler's equations for an inviscid incompressible homogeneous fluid with an oscillating body force. Our aim is to derive the averaged equations for these flows with the help of two-timing method. Our main result is the general and simple form of the equation describing the averaged flows, which are der...
Article
Full-text available
The Laplace-Beltrami operator (LBO) 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 LBO. In this article we consider this spectral problem for more general...
Article
Full-text available
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 po...
Article
Full-text available
The Kutta condition is applied to aerofoils with sharp trailing edges to allow for viscous effects to be considered within a simplified system of equations that are inviscid. This paper discusses in detail the inclusion of an unsteady Kutta condition at a sharp trailing edge during gust–aerofoil interaction and illustrates how the analytic solution...
Article
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...
Article
This paper is concerned with the elastic waveguide properties of an infinite pipe with circular cross section whose radius varies slowly along its length. The equations governing the elastodynamics of such shells are derived analytically, approximated asymptotically in the limit of slow axial variation, and solved by means of the WKB-method (Wentze...
Conference Paper
Full-text available
An analytical solution to high-frequency gust-aerofoil interaction in background steady flow that is uniform far upstream is compared to numerical results for realistic aerofoils with non-zero thickness. Currently, numerical codes struggle at high frequencies, and are typically only validated against flat-plate analytical solutions. Analytical solu...
Article
A non-modal stability analysis is presented for annular Poiseuille–Couette flow (APCF) which serves to complement existing linear and nonlinear stability studies. Modal linear stability analyses indicate a stabilizing trend for increasing inner cylinder velocity , though this is at odds with experimental studies of transition such as Shands et al....
Article
Full-text available
A 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,...
Article
Recent experimental studies have shown rich transition behaviour in rotating plane Couette flow (RPCF). In this paper we study the transition in supercritical RPCF theoretically by determination of equilibrium and periodic orbit tertiary states via Floquet analysis on secondary Taylor vortex solutions. Two new tertiary states are discovered which w...
Article
Full-text available
This 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 spe...
Conference Paper
Full-text available
An analytic model is created to explore the far-field high-frequency acoustic radiation generated by gust-aerofoil interactions in steady shear flows. The problem is analysed using standard analytic gust-aerofoil interaction techniques for solving the linearised Euler equations for a steady flow with an unsteady perturbation. The flow domain is sep...
Conference Paper
It is hypothesized that the structure of the down covering the flight feathers of larger species of owls contributes to their ability to fly almost silently at frequencies above 1.6kHz. Microscope photographs of the down show that it consists of hairs that form a structure similar to that of a forest. The hairs initially rise almost perpendicular t...
Article
Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute...
Article
We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°–65° from the pole (depending on the rotation rate). A neutral curve for gl...
Article
Full-text available
A theoretical model is developed for the sound scattered when a sound wave is incident on a cambered aerofoil at non-zero angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an adaptation of previous work which considered incident vortical disturbances. Only high-frequency sound waves...
Article
We consider the propagation of acoustic waves along a cylindrical duct carrying radially sheared axial mean flow, in which the duct radius is allowed to vary slowly along the axis. In previous work [A.J. Cooper & N. Peake, Journal of Fluid Mechanics 445 (2001) 207–234.] radially sheared axial mean flow with nonzero swirl in a slowly varying duct wa...
Article
Full-text available
This paper is concerned with modelling the effects of swirling flow on turbomachinery noise. We develop an acoustic analogy to predict sound generation in a swirling and sheared base flow in an annular duct, including the presence of moving solid surfaces to account for blade rows. In so doing we have extended a number of classical earlier results,...
Conference Paper
The interaction of a turbulent eddy with a semi-infinite, poroelastic edge is examined with respect to the effects of both elasticity and porosity on the efficiency of aerodynamic noise generation. The edge is modelled as a thin plate poroelastic plate, which is known to admit fifth-, sixth-, and seventh-power noise dependences on a characteristic...
Conference Paper
The present study aims at investigating the effect of a swirling mean flow and a lined annular duct on rotor trailing-edge noise. The objectives are to investigate these effects on the eigenvalues and a tailored Green's function on one hand and on the realistic case of the fan trailing-edge noise on the other hand. Indeed, the mean flow in between...
Article
Full-text available
The interaction of a turbulent eddy with a semi-infinite poroelastic edge is examined with respect to the effects of both elasticity and porosity on the efficiency of aerodynamic noise generation. The scattering problem is solved using the Wiener–Hopf technique to identify the scaling dependence of the resulting aerodynamic noise on plate and flow...
Article
Full-text available
This paper provides a review of important results concerning the Geometrical Theory of Diffraction and Geometrical Optics. It also reviews the properties of the existing solution for the problem of diffraction of a time harmonic plane wave by a half-plane. New mathematical expressions are derived for the wave fields involved in the problem of diffr...
Conference Paper
The present study aims at accounting for swirling mean flow effects on rotor trailing-edge noise. Indeed, the mean flow in between the rotor and the stator of the fan or of a compressor stage is highly swirling. The extension of Ffowcs-Williams & Hawkings' acoustic analogy in a medium at rest with moving surfaces and of Goldstein's acoustic analogy...
Conference Paper
The present study aims at developing an acoustic formulation for the sound generated by the interaction of solid surfaces (such as blades) with an unsteady flow in an annular duct with swirl. Indeed, the mean flow in between the rotor and the stator of the fan or of a compressor stage is highly swirling. As a result, in order to properly predict th...
Article
This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin’s theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green’s functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane i...
Article
Full-text available
This paper presents an analytic expression for the acoustic eigenmodes of a cylindrical lined duct with rigid axially running splices in the presence of flow. The cylindrical duct is considered to be uniformly lined except for two symmetrically positioned axially running rigid liner splices. An exact analytic expression for the acoustic pressure ei...
Article
In this review we describe current scientific and technological issues in the quest to reduce aeroengine noise, in the face of predicted rapid increases in the volume of air traffic, on the one hand, and increasingly strict environmental regulation, on the other. Alongside conventional ducted turbofan designs, new open-rotor contra-rotating power p...
Article
In a recent paper (J. Computational Acoustics10 (2002) 387–405) Tam has claimed that the famous Lighthill Acoustic Analogy predicts the wrong flow field for the simple problem of the propagation of a normal shock. However, we show that Tam has misinterpreted the results of his analysis, and that when this error is corrected the results of the Acous...
Chapter
Full-text available
In the present investigation of thin aerofoil wakes we compare the global nonlinear dynamics, obtained by direct numerical simulations, to the associated local instability features, derived from linear stability analyses. A given configuration depends on two control parameters: the Reynolds number Re and the adverse pressure gradient m (with m < 0)...
Conference Paper
Turbulence, as naturally occurs in the atmosphere, is known to become highly anisotropic in the presence of the flow induced by a propeller. This turbulent distortion, caused by the streamtube contraction, significantly affects the tonal content of the radiated noise due to turbulence ingestion. We present here an analytic framework in which turbul...
Conference Paper
It is known theoretically [1–3] that infinitely long fluid loaded plates in mean flow exhibit a range of unusual phenomena in the ‘long time’ limit. These include convective instability, absolute instability and negative energy waves which are destabilized by dissipation. However, structures are necessarily of finite length and may have discontinui...
Conference Paper
Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylind...
Conference Paper
This work forms part of a project on the use of large eddy simulation (LES) for broadband rotor-stator interaction noise prediction. In this paper, we focus on LES calculations of noise sources on and close to a blade trailing edge. We consider two test cases; one an isolated NACA0012 airfoil in flow, and the other an industry-standard rotating fan...
Article
In this paper we present an analytical solution to the problem of sound radiation from semi-infinite coaxial cylinders, as a model for rearward noise emission by aeroengines. The cylinders carry uniform subsonic flows, whose Mach numbers may differ from each other and from that of the external flow. The incident field takes the form of a downstream...
Article
Full-text available
We consider the stability of small perturbations to a uniform inviscid compressible flow within a cylindrical linear-elastic thin shell. The thin shell is modelled using Flügge's equations, and is forced from the inside by the fluid, and from the outside by damping and spring forces. In addition to acoustic waves within the fluid, the system suppor...
Article
The work in this paper forms part of a project on the use of large eddy simulation (LES) for broadband rotor-stator interaction noise prediction. Here we focus on LES of the flow field near a fan blade trailing edge. The first part of the paper aims to evaluate LES suitability for predicting the near-field velocity field for a blunt NACA-0012 airfo...
Conference Paper
In this paper a semi analytic model for rotor - stator broadband noise is presented. The work can be split into two sections. The first examines the distortion of the rotor wake in mean swirling flow, downstream of the fan. Previous work by Cooper and Peake4 is extended to include dissipative effects. In the second section we consider the interacti...
Article
Full-text available
In this paper we consider the propagation of acoustic waves on top of an inviscid steady flow along a curved hollow or annular duct with hard or lined walls. The curvature of the duct centreline (which is not restricted to being small) and the wall radii vary slowly along the duct, allowing application of an asymptotic multiple-scales analysis. The...
Article
We investigate transient growth in high-Reynolds-number vortices with axial flow. Manycases of vortex instability are not fully explained by strong exponential instability modes, and transient growth could offer an alternative route to breakdown in such cases. Strong transient growth is found, in agreement with previous studies. We first discuss th...
Conference Paper
Full-text available
Military aircraft engine intakes are typically curved, the curvature and change in cross-section being significant but varying on a lengthscale far longer than a typical sound wave-length. This allows the use of the Method of Multiple Scales, as we presented at last year's conference. Here we further investigate this situation. After a briefly reca...
Article
This paper was published as European Journal of Mechanics Series B Fluids, 2007, 26 (3), pp. 344-353. It is available from http://www.sciencedirect.com/science/journal/09977546. Doi: 10.1016/j.euromechflu.2006.08.002 Metadata only entry This paper is concerned with the existence of local absolute instability in the boundary-layer flow over the oute...
Article
Full-text available
This paper was published as Advances in Turbulence XI: Proceedings of the 11th EUROMECH European Turbulence Conference, June 25-28, 2007, Porto, Portugal; Palma, J. M. L. M.; Silva Lopes, A. (Eds.), pp. 550-552. It is available from http://www.springer.com/materials/mechanics/book/978-3-540-72603-6 Metadata only entry By taking the local approach o...
Article
In this paper we consider the spectrum and stability properties of small-amplitude waves in three-dimensional inviscid compressible swirling flow with non-zero mean vorticity, contained in an infinitely long annular circular cylinder. The mean flow has swirl and sheared axial components which are general functions of radius. We describe the form of...
Article
Full-text available
In this paper, we derive weakly nonlinear equations for the dynamics of a thin elastic plate of large extent under conditions of heavy fluid loading. Two situations are then considered. First, we consider the case in which transverse motion of the plate generates a weaker in-plane motion, which is in turn coupled back to the evolution of the transv...
Article
The phenomenon of spatial transient growth in swirling duct flow with application to aeroengine duct acoustics is investigated. In a typical aeroengine a region of swirling flow exists between the rotor and the downstream stator. The possibility for optimal transient growth of disturbance energy, and of a norm related to the acoustic power radiated...
Article
This paper addresses analysis of wave motions in an unbounded sandwich plate with and without heavy fluid loading in the plane problem formulation. The effects of coupling of otherwise independent upon each other in-phase and anti-phase (with respect to the transverse motion of skins) modes, which could be produced by uneven pre-stress of the skins...
Conference Paper
Full-text available
We consider a straight cylindrical duct with a steady subsonic axial flow and a reacting boundary (e.g. an acoustic lining). The wave modes are separated into ordinary acoustic duct modes, and surface modes confined to a small neighbourhood of the boundary. Many researchers have used a mass–spring–damper boundary model, for which one surface mode h...
Conference Paper
Full-text available
In this paper we consider the propagation of acoustic waves along a curved hollow or annular duct with lined walls. The curvature of the duct centreline and the wall radii vary slowly along the duct, allowing application of an asymptotic multiple scales analysis. This generalises Rienstra's analysis of a straight duct of varying cross-sectional rad...
Conference Paper
We present results on the stability of compressible inviscid swirling flows in an annular duct. Such flows are present in aeroengines, for example in the by-pass duct, and there are also similar flows in many aeroacoustic or aeronautical applications. The linearised Euler equations have a ('critical layer') singularity associated with pure convecti...
Article
An asymptotic technique in the limit of large blade and vane number is employed to study the interaction in mean swirling flow of an unsteady rotor wake with a stator row downstream. The effect of various stator characteristics, including stator sweep,lean and number of vanes, on the tone noise radiated upstream is investigated. The important effec...
Article
Wave modes in a straight cylindrical duct with a locally reacting boundary and a steady subsonic axial flow are investigated. The duct modes are separated into ordinary duct modes and surface modes confined to a neighbourhood of the boundary. Previous asymptotic results of Rienstra for the surface modes assume that the dimensionless frequency ω is...
Article
In this paper we consider the diffraction of waves by a sharp edge in three-dimensional flow with non-zero mean vorticity. This is an extension of the famous Sommerfeld problem of the diffraction of waves by a sharp edge in quiescent conditions. The precise problem concerns an infinitely long annular circular cylinder, which contains a concentric s...
Article
Full-text available
An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1, −∞ < x < ∞ with mean flow Mach number M > 0 and a hard wall along x < 0 and a wall of impedance Z along x > 0. A minimum edge condition...
Article
Full-text available
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...
Conference Paper
This talk addresses wave propagation in an unbounded fluid-loaded elastic sandwich plate of symmetric composition. Several aspects are highlighted, including the interaction between shear and flexural waves and the coupling between the "in-phase" and "anti-phase" waves (with respect to transverse deflections of skins).
Article
Acoustic boundary element models are used to solve the Helmholtz equation in order to explore the nature of fluctuating hull pressures due to propeller sources when the wavelength of the underwater sound is comparable to the hull dimensions. Sources are represented by stationary monopoles and dipoles near a rigid hull. The results for submerged and...
Article
We consider the effects of blade mean loading on the noise generated by the interaction between convected vorticity and a blade row. The blades are treated as flat plates aligned at a non-zero incidence angle, $\delta$, to the oncoming stream, and we take harmonic components of the incident vorticity field with reduced frequency $k$, and use asympt...
Article
A theoretical model is used to investigate the effect of geometry, flow conditions and acoustic lining on the occurrence of acoustic resonance within aeroengine ducts. Semi-analytical methods are used to demonstrate that two types of acoustic resonance can be excited. The first is an intake resonance arising due to axial variation of the intake sha...
Article
Full-text available
In this paper we consider the dynamic behaviour of a fluid-loaded elastic plate of dimensionless length $2L$, set in a rigid baffle in the presence of uniform mean flow of dimensionless speed $U$, and including plate pre-tension (dimensionless tension $T$) and a spring foundation (dimensionless spring constant $\lambda$). Our aim is to extend previ...
Conference Paper
A method for modelling and predicting the noise generated by the interaction between the unsteady wake shed from the rotor and a downstream row of stators in a modern ultra-high bypass ducted turbofan engine is described. An analytically-based model is developed to account for three main features of the problem. First, the way in which a typical un...
Article
The aim of this paper is to survey a range of applications of high-frequency asymptotic methods in aeroacoustics. Specifically, we are concerned with problems associated with noise generation, propagation and scattering as found in large modern aeroengines. With regard to noise generation, we consider the interaction between high-frequency vortical...
Article
We consider the local convective and absolute instabilities of the boundary layer on a rotating sphere located in a uniform axial flow, extending our previous work, which considered still outer fluid. Axial flow is seen to stabilise the convective instabilities, and our predicted onset of the spiral vortices is in good agreement with existing exper...
Article
Measurements of boundary layer transition are presented for the case of cones of different apex angle and a large hemisphere spinning in still air. The apparatus for spinning the bodies has been specially designed to minimise vibrations. Measurements of the position and nature of the transition are made using flow visualisation and hot-wire measure...
Article
We review theoretical and computational investigations of wave excitation and evolution in fully-coupled flow-structure systems. A distinguishing feature of the body of work reviewed is its attempt to shed light on how and where waves come into being in response to some form of applied excitation. Identifying the properties of such waves and their...
Article
The radiation from an axisymmetric thin-walled cylinder is determined by using the Geometrical Theory of Di!raction. The non-uniformities associated with this theory are corrected by using uniform asymptotic techniques, and the far"eld velocity potential is calculated everywhere. The theory provides a paradigm for interpretation of geometrical feat...
Article
The analysis of the radiation from an axisymmetric duct using the Geometrical Theory of Diffraction and uniform asymptotics, presented in a companion paper, is extended to an asymmetric, scarfed cylinder. The generic theory from the application to axisymmetric cylinders is briefly recapitulated and the geometrical calculations necessary for the ana...

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