Christopher Powles

Spectral broadening of jet engine turbine tones

The process of turbulent scattering is studied for the generic experiment conducted by Candel et al.1 applying an analytic weak scattering model and CAA computations. For the analytic weak scattering model an approximate form of the Lilley equation is used. The source terms of this equation are in terms of the turbulence and the incident acoustic field. In the CAA simulations the wave equation proposed by Pierce for sound in fluids with unsteady inhomogeneous flow is integrated. The unsteady turbulent base-flow is modeled using a stochastic method to generate turbulence with locally varying turbulence features as provided by time-averaged RANS. To study the spectral broadening effect analytically and computationally, the experimental set-up of Candel is considered, which involves an omnidirectional sound source, located on the axis of a round jet. The analytical predictions show very good agreement with the general trends as measured by Candel for an observer position normal to the jet axis. The computations reveal a spectral shape, which is in good agreement with those found in the experiments.

Comparison of sound power radiation from isolated airfoils and cascades in a turbulent flow

An analytical model of the sound power radiated from a flat plate airfoil of infinite span in a 2D turbulent flow is presented. The effects of stagger angle on the radiated sound power are included so that the sound power radiated upstream and downstream relative to the fan axis can be predicted. Closed-form asymptotic expressions, valid at low and high frequencies, are provided for the upstream, downstream, and total sound power. A study of the effects of chord length on the total sound power at all reduced frequencies is presented. Excellent agreement for frequencies above a critical frequency is shown between the fast analytical isolated airfoil model presented in this paper and an existing, computationally demanding, cascade model, in which the unsteady loading of the cascade is computed numerically. Reasonable agreement is also observed at low frequencies for low solidity cascade configurations.

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.

Effect of Centerbody Scattering on Advanced Open-Rotor Noise

Formulas for calculating the effect of centerbody scattering on the sound radiated from an advanced open rotor are presented. The effects of blade sweep and distributed blade loading are considered.Mach number effects are also implicitly included in the model. The work extends a previously published method and applies it to a practical situation in which scattering by the centerbody has a significant effect on the radiated sound field.

Scattering of Sound by Liner Splices: A Kirchhoff Model with Numerical Verification

Variations in the impedance of the acoustic liners in aeroengine intake ducts occur due to the presence of acoustically hard splices, which lead to scattering of the incident fan tone noise into a large number of azimuthal modes, and can significantly reduce the effectiveness of the liner. Currently available computational aeroacoustic packages are capable of modeling the scattering, but are generally impractical for direct application to liner optimization design studies, because they require a substantial quantity of CPU time. A Kirchhoff approximation is applied to a geometry of practical interest, and the predicted field is compared with that computed using a commercially available computational aeroacoustic package. The analytical and computational results are in good agreement for cases both with and without mean flow. A striking result is that the modal power in most of the forward-scattered modes is almost equal, except for a small number of modes close to the rotor-alone mode. The analytical model is found to be accurate for a physically useful combination of parameters, and provides both a method for rapid evaluation of the scattering, and a physical understanding of the process.

Green's functions in computational aeroacoustics*

The theory of Greens functions for the wave and Helmholtz equations is examined with particular attention to their use in aeroacoustics for the extrapolation of acoustic wavefields from numerical flow simulations. In a new synthesis that permits straightforward generalization of previously published results, spatial and temporal windowing functions are employed to provide equivalent-source expressions to account for both initial and boundary conditions. Detailed results describe the transformation of both source terms and Greens functions to take account of uniform subsonic mean flow, and expressions are given for free-field Greens functions, both with and without flow, in time, frequency and wavenumber domains. A worked example illustrates the non-uniqueness of the Greens function for a simple one-dimensional bounded problem.

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’.

Low and high frequency models for the prediction of noise due to cascade-turbulence interaction

Cascade theory is often used to predict the sound power radiation from a fan subject to incident turbulent flow, but in the high frequency regime it is slow due to the large number of Fourier modes required in the calculations. We demonstrate that the sound power spectrum due to a single isolated airfoil subject to the identical turbulent flow closely matches the equivalent cascade sound power spectrum at suciently high frequency. Several important dierences are apparent in the results and an understanding of these allows the identification of agreement frequencies above which the fast single airfoil theory may be substituted for the computationally expensive cascade theory with negligible dierence to the result.

Sound power due to an airfoil of arbitrary stagger angle in a turbulent flow

An analytical model of the sound power radiated from a at plate airfoil of in nite span in a 2D turbulent ow is presented. The e ects of stagger angle on the radiated sound power are included so that the sound power radiated upstream and downstream of the fan axis can be predicted, for application to the broadband noise due to turbomachinery. Closed-form asymptotic expressions, valid at low and high frequencies, are derived for the upstream, downstream and total sound power. A study of the e ects of chord length on the total sound power at all reduced frequencies is presented. The single-airfoil model presented in this paper is compared to an equivalent cascade model in a companion paper.

Numerical and Asymptotic Lilley-Equation Solutions for the Goldstein Jet-Noise Source Model

Far-field sound radiation from model sources in a jet shear layer has been calculated numerically using the stationary phase approximation. The jet column is modeled as an axisymmetric parallel shear flow, so jet spreading is neglected. For this simplified model, analytical predictions are provided in the low and high frequency limits, k0? >1 (k0 = acoustic wavenumber; ? = shear layer thickness). The low-frequency analytic result matches the numerical prediction quite closely up to k0? = 1; it accounts quantitatively for the observed strong scattering of quadrupole radiation by the mean velocity and density profiles in the jet. Further work is required to establish bounds of validity for the stationaryphase approximation, and to assess available high-frequency (k0?>1) approximations for the cone of silence region.