A. McAlpine

Boundary-layer instability noise on aerofoils

An experimental and theoretical investigation has been carried out to understand the tonal noise generation mechanism on aerofoils at moderate Reynolds number. Experiments were conducted on a NACA0012 aerofoil section in a low-turbulence closed working section wind tunnel. Narrow band acoustic tones were observed up to 40 dB above background noise. The ladder structure of these tones was eliminated by modifying the tunnel to approximate to anechoic conditions. High-resolution flow velocity measurements have been made with a three-component laser-Doppler anemometer (LDA) which have revealed the presence of strongly amplified boundary-layer instabilities in a region of separated shear flow just upstream of the pressure surface trailing edge, which match the frequency of the acoustic tones. Flow visualization experiments have shown these instabilities to roll up to form a regular Karman-type vortex street. A new mechanism for tonal noise generation has been proposed, based on the growth of Tollmien–Schlichting (T–S) instability waves strongly amplified by inflectional profiles in the separating laminar shear layer on the pressure surface of the aerofoil. The growth of fixed frequency, spatially growing boundary-layer instability waves propagating over the aerofoil pressure surface has been calculated using experimentally obtained boundary-layer characteristics. The effect of boundary-layer separation has been incorporated into the model. Frequency selection and prediction of T–S waves are in remarkably good agreement with experimental data.

On the spatio-temporal development of small perturbations of Jeffery-Hamel flows☆

This paper presents a new linear theory of small two-dimensional perturbations of a Jeffery-Hamel flow of a viscous incompressible fluid, in order to understand better the stability of the steady flow driven between inclined plane walls by a line source at the intersection of the walls. Because the variables of space and time are not all separable, a modified form of normal modes is used in solving the linearized equations of motion. The modes only satisfy the equations asymptotically far downstream. They are proportional to an exponential function of the ratio of time to the square of the radial distance, rather than of time alone. An eigenvalue problem to determine the modes is derived, a problem which reduces to the Orr-Sommerfeld problem in the special case when the walls are parallel, that is when the primary Jeffery-Hamel flow is plane Poiseuille flow. The results indicate that a small divergence of the walls is an astonishingly strong destabilizing influence on plane Poiseuille flow, and a small convergence a strong stabilizing influence. The relationship of the modes to the stability of the flow is discussed critically.

On the prediction of “buzz-saw” noise in acoustically lined aero-engine inlet ducts

Abstract Aero-engines operating with supersonic fan tip speeds generate an acoustic signature containing energy spread over a range of harmonics of the engine shaft rotation frequency. These harmonics are commonly known as the “buzz-saw” tones. The pressure signature attached to a supersonic ducted fan will be a sawtooth waveform. The non-linear propagation of a high-amplitude irregular sawtooth upstream inside the inlet duct redistributes the energy amongst the buzz-saw tones. In most modern aero-engines the inlet duct contains an acoustic lining, whose properties will be dependent on the mode number and frequency of the sound, and the speed of the oncoming flow. Such effects may not easily be incorporated into a time-domain approach; hence the non-linear propagation of an irregular sawtooth is calculated in the frequency domain, which enables liner damping to be included in the numerical model. Results are presented comparing noise predictions in hard-walled and acoustically lined inlet ducts. These show the effect of an acoustic liner on the buzz-saw tones. These predictions compare favourably with previous experimental measurements of liner insertion loss (at blade passing frequency), and provide a plausible explanation for the observed reduction in this insertion loss at high fan operating speeds.

A weak-scattering model for turbine-tone haystacking outside the cone of silence

We consider the scattering of sound by turbulence in a jet shear layer. The turbulent, time-varying inhomogeneities in the flow scatter tonal sound fields in such a way as to give spectral broadening, which decreases the level of the incident tone, but increases the broadband level around the frequency of the tone. The scattering process is modelled for observers outside the cone of silence of the jet, using high-frequency asymptotic methods and a weak-scattering assumption. An analytical model for the far-field power spectral density of the scattered field is derived, and the result is compared to experimental data. The model correctly predicts the behaviour of the scattered field as a function of jet velocity and tone frequency.

Response surface method optimization of uniform and axially segmented duct acoustics liners

An extensive duct acoustics propagation study is presented that has been conducted to assess the design of a liner for an aeroengine inlet duct. The aim is to predict how different liner configuarations, at various flight conditions affect the attenuation of sound in an inlet. Two different noise source models are used: single mode and multimode. These represent the two principal fan noise sources: tonal and broadband noise. The two noise source models are then combined to predict the overall attenuation. An optimization procedure based on a response surface model is presented, to investigate a uniform and an axially segmented acoustic liner. The objective function used in the optimization is based on an approximate calculation of the perceived noise level. The aim is to utilize and axially segmented liner to increase, compared to a unifrom liner, the overall sound attenuation that is predicted. The main feature that emerges is that it is possible to increase the attenuation with an axially segmented liner only when a limited number of propagating modes are present.

Multimode radiation from an unflanged, semi-infinite circular duct with uniform flow.

Multimode sound radiation from an unflanged, semi-infinite, rigid-walled circular duct with uniform subsonic mean flow everywhere is investigated theoretically. The multimode directivity depends on the amplitude and directivity function of each individual cut-on mode. The amplitude of each mode is expressed as a function of cut-on ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles, and for equal power per mode. The directivity function of each mode is obtained by applying a Lorentz transformation to the zero-flow directivity function, which is given by a Wiener-Hopf solution. This exact numerical result is compared to an analytic solution, valid in the high-frequency limit, for multimode directivity with uniform flow. The high-frequency asymptotic solution is derived assuming total transmission of power at the open end of the duct, and gives the multimode directivity function with flow in the forward arc for a general family of mode amplitude distribution functions. At high frequencies the agreement between the exact and asymptotic solutions is shown to be excellent.

Far-field sound radiation due to an installed open rotor

Future single rotation propeller and contra-rotating advanced open rotor concepts promise a significant fuel efficiency advantage over current generation turbofan engines. The development of rotors which produce a minimum level of noise is a critical technical issue which needs to be resolved in order for these concepts to become viable aircraft propulsors. Noise and emissions are subject to stringent legislative requirements, thus accurate models are required in order to predict the noise radiated from aircraft engines. In this article, the development of a theoretical model to predict noise levels of an installed open rotor is reported. First a canonical problem is examined: how to predict the pressure field produced by a rotating ring of point sources adjacent to a rigid cylinder. Analytic expressions for the far-field pressure from a rotating ring of single-frequency monopole and dipole point sources, located near an infinitely long rigid cylinder, immersed in a constant axial mean flow, are explicitly formulated. Illustrative results show how the far-field pressure is affected by varying the source rotational direction, source location and source radius. Next the solution of the canonical problem is utilized to formulate a more advanced model to predict the noise due to an installed open rotor. In this model, the rotor noise sources are represented by a distribution of rotating sources. The adjacent aircraft fuselage is modeled by the rigid cylinder, and the effect of the fuselage boundary layer and other steady distortions are neglected. Also neglected is the scattering from other surfaces such as the pylon, wing and centerbody. This distributed source model can be used to calculate the effect of scattering of open rotor noise by an adjacent cylindrical fuselage. The model can be used to calculate both rotor-alone tones and tones produced by periodic unsteady loading on the rotor blades. Practical examples are provided which show how the effect of blade rotational direction and propeller location relative to the fuselage affect the sound produced by the interaction of a pylon wake with a rotor in a pusher configuration.

Sound transmission in ducts with sheared mean flow

In this article the prediction of sound transmission in ducts with sheared mean ∞ow is examined. The application of this work is the acoustics of aircraft engine duct systems, speciflcally sound propagation in a turbofan bypass duct. The bypass is modelled as a circular-section annular duct with acoustic lining on the outer and inner duct walls, and contains a sheared mean ∞ow. Owing to the circular geometry, it is convenient to represent the acoustic fleld in terms of modes. Two difierent numerical methods are used to flnd the modes. Then, a mode-matching method is utilized, to determine the sound power transmission loss in a lined annular duct with sheared mean ∞ow. Several difierent mean ∞ow proflles are examined. In each case, the sound transmission is calculated for an annular duct with lining on both walls, and also lining on the outer or inner wall only. Results are presented for examples which make use of realistic duct dimensions, mass ∞owrate, sound frequency and acoustic liner impedance, although here only axisymmetric modes with azimuthal mode order m = 0 are examined. The objective is to examine how difierent sheared ∞ows afiect sound transmission in a lined annular duct, compared with a uniform mean ∞ow.

Computer-aided liner optimization for broadband noise

In this article the attenuation of broadband noise in an acoustically-lined circular-section duct is investigated. The aim is to predict how an axially segmented liner in∞uences the attenuation of broadband noise in an aero-engine intake. The sound fleld is modelled using a multi-modal representation, assuming an ensemble of uncorrelated modes over a wide range of frequencies. An optimization procedure based on a Response Surface Model is used to investigate the optimum uniform and axially-segmented acoustic liner that maximizes the attenuation of broadband noise. An approximate calculation of the Perceived Noise Level (PNL) is used for the objective function. In this article the beneflt of using an axiallysegmented liner instead of a uniform liner to attenuate broadband noise is demonstrated.

A weak scattering model for tone haystacking

The scattering of sound by turbulence in a jet shear layer is considered. Spectral broadening or ‘haystacking’ is the process whereby the turbulent, timevarying inhomogeneities in the ∞ow scatter tonal sound flelds, which decreases the level of the incident tone, but increases the broadband level around the frequency of the tone. The scattering process is modelled analytically, using high-frequency asymptotic methods and a weak-scattering assumption. Analytical models for the far-fleld spectral density of the scattered fleld are derived for two cases: (1) any polar angle including inside the cone of silence; (2) polar angles outside the cone of silence. At polar angles outside the cone of silence, the predictions from the two models are very similar, but using the second model it is considerably simpler to evaluate the far-fleld spectral density. Simulation results are compared to experimental data, albeit only at a polar angle of 90 ‐ . The model correctly predicts the behaviour of the scattered fleld as a function of jet velocity and tone frequency. Also simulations at other polar angles and a parametric study are presented. These simulations indicate how the ‘haystacking’ is predicted to vary as a function of the polar angle, and also as a function of the characteristic length, time and convection velocity scales of the turbulence contained in the jet shear layer. Spectral broadening is a phenomenon whereby a tonal sound fleld interacts with a random time-varying scattering medium, with the result that power is lost from the tone and distributed into a broadband fleld around the tone frequency. Spectral broadening has been observed in far-fleld measurements of turbine tones, and to a lesser extent, fan tones radiated from the rear of a turbofan engine. The efiect is caused by the interaction of the tones radiated from the engine exhaust duct with the turbulence in the jet shear layers. Turbulent jet shear layers are formed between the hot core jet and cold bypass streams, and also between the bypass and ∞ight streams. Sound radiated from the exhaust propagates through these turbulent shear layers, and owing to the unsteady nature of turbulent ∞ow, this can scatter sound over a range of frequencies. The resulting scattered broadband fleld, known colloquially as a ‘haystack’, can be measured well above the jet-noise broadband at some engine conditions. In the context of this work, when the proportion of scattered energy is small relative to the energy that remains in the tone, this is termed ‘weak scattering’. An example of the spectrum from a tonal fleld which has undergone ‘weak’ spectral broadening is shown in flgure 1, which is taken from the experimental work of Candel, Guedel, & Julienne. 1 The level of the tone is around 20dB above that of the haystacks. However, spectral broadening can lead to the disappearance of the tone itself, replaced by a broadband hump. In the context of this work, this would be termed ‘strong scattering’.