Rapid noise prediction models for serrated leading and trailing edges

Leading- and trailing-edge serrations have been widely used to reduce the leading- and trailing-edge noise in applications such as contra-rotating fans and large wind turbines. Recent studies show that these two noise problems can be modelled analytically using the Wiener-Hopf method. However, the resulting models involve infinite-interval integrals that cannot be evaluated analytically, and consequently implementing them poses practical difficulty. This paper develops easily-implementable noise prediction models for flat plates with serrated leading and trailing edges, respectively. By exploiting the fact that high-order modes are cut-off and adjacent modes do not interfere in the far field except at sufficiently high frequencies, an infinite-interval integral involving two infinite sums is approximated by a single straightforward sum. Numerical comparison shows that the resulting models serve as excellent approximations to the original models. Good agreement is also achieved when the leading-edge model predictions are compared with experimental results for sawtooth serrations of various root-to-tip amplitudes, whereas a qualitative evaluation of TE noise model shows that an accurate characterisation of the wall pressure statistics beneath the boundary layers is crucial for accurate TE noise prediction. Importantly, the models developed in this paper can be evaluated robustly in a very efficient manner. For example, a typical far-field noise spectrum can be calculated within milliseconds for both the trailing- and leading-edge noise models on a standard desktop computer. Due to their efficiency and ease of numerical implementation, these models are expected to be of particular importance in applications where a numerical optimization is likely to be needed

Acoustic emission due to the interaction between shock and instability waves in 2D supersonic jet flows

An analytical model is developed to study the sound produced by the interaction between shock and instability waves in two-dimensional supersonic jet flows. The jet is considered to be of vortex-sheet type and 2D Euler equations are linearised to determine the governing equations for shock, instability waves, and their interaction. Pack's model is used to describe shock waves, while instability waves are calculated using spatial stability analysis. The interaction between shock and instability waves can be solved analytically by performing Fourier transform and subsequently using the method of steepest descent. Sound produced by the interaction between the instability wave and a single shock cell is studied first, after which that due to a number of cells follows. We find that the model developed in this study can correctly predict the frequencies of the fundamental screech tone and its first and second harmonics. We show that the predicted sound directivity, even from a single shock cell, is in good agreement with experimental data. In particular, this model shows the strongest noise emission close to the upstream direction but the emitted noise starts to rapidly decay as the observer angle approaches 180 degrees, which is in accordance with experimental results; this suggests that the effective noise from a single shock cell is far from of the monopole type as assumed in the classical Powell's model. We find that the noise directivity is very sensitive to the local growth rate of the instability waves and the noise is generated primarily through the Mach wave mechanism.Comment: submitted to the Journal of Fluid Mechanic

An experimental study of the effects of lobed nozzles on installed jet noise

Abstract: Jet noise remains a significant aircraft noise contributor, and for modern high-bypass-ratio aero-engines the strong interaction between the jet and aircraft wing leads to intensified installed jet noise. An experiment is carried out in this paper to study the effects of lobed nozzles on installed jet noise. It is found that the lobed nozzles, compared to round nozzles, have similar effects on installed jet noise for all the plate positions and Mach numbers tested. On the shielded side of the plate, the use of lobed nozzles leads to a noise reduction in the intermediate- and high-frequency regimes, which is thought to be due to a combination of enhanced jet mixing and more effective shielding effects by the flat plate. On the reflected side of the plate, noise reduction is only achieved in the intermediate frequency range; the little noise reduction or a slight noise increase observed in the high-frequency regime is likely due to enhanced jet mixing. On both sides of the plates, little noise reduction is achieved for the low-frequency noise due to the scattering of jet instability waves. This is likely to be caused by the fact that lobed nozzles cause negligible change to the dominant mode 0 (axisymmetric) jet instability waves. That the jet mean flow quickly becomes axisymmetric downstream of the jet exit could also play a role. Graphic abstract

Installed jet noise

This thesis studies the prediction and reduction of installed jet noise, combining both analytical and experimental techniques. In the prediction part, it starts with formulating a low-order but robust isolated jet noise prediction model, based on which a remarkably fast code with pre-informed data is developed. A semi-empirical low-order model is then developed to predict installed jet noise. The model consists of two parts, the first of which is based on the Lighthill's acoustic analogy theory. The second part embraces Amiet's approach to model the sound due to the scattering of jet instability waves. It is shown that the significant low-frequency noise enhancement observed in installed jet experiments is due to the scattering of near-field instability waves. The trailing edge scattering model can successfully predict noise spectra at all distinct angles. The quadrupole-induced high-frequency sound is either efficiently shielded at $90^\circ$ to the jet axis on the shielded side or enhanced by around $3$ dB at $90^\circ$ on the reflected side. But these effects gradually diminish as the observer angle decreases. The high-frequency spectra can be robustly predicted at large observer angles while deviation occurs at low observer angles due to jet refraction effects. An experimental study on installed jet noise is then conducted. The effects of plate positions and Mach numbers are studied. Excellent agreement between the experimental results and model predictions is achieved at low frequencies for all plate positions and Mach numbers tested. At high frequencies, the noise spectra at $90^\circ$ on the reflected side can also be correctly predicted. At lower observer angles, deviations occur due to jet refraction effects. In the noise reduction part, an experimental study is firstly carried out to study the effects of lobed nozzles on installed jet noise at constant flow rates. It is found that lobed nozzles do not noticeably change the installed jet noise spectra at low frequencies. However, they do result in a slight noise reduction at high frequencies. To understand why lobed nozzles hardly change low-frequency installed jet noise, an analytical stability analysis for lobed vortex sheets is performed. The results show that lobed jets change both the convection velocity and the temporal growth rate of instability waves. The changes become more pronounced as the number of lobes $N$ and the penetration ratio $\epsilon$ increase. A second set of experiments is carried out to explore the possibility of reducing installed jet noise by using two pylons. The results show that even in the most conservative case installed jet noise is reduced by around $2\sim3$ dB at low frequencies. It is concluded that using two pylons to reduce installed jet noise has significant practical potential.Cambridge Trust China Scholarship Counci

Prediction of installed jet noise

A semianalytical model for installed jet noise is proposed in this paper. We argue and conclude that there exist two distinct sound source mechanisms for installed jet noise, and the model is therefore composed of two parts to account for these different sound source mechanisms. Lighthill’s acoustic analogy and a fourth-order space–time correlation model for the Lighthill stress tensor are used to model the sound induced by the equivalent turbulent quadrupole sources, while the trailing-edge scattering of near-field evanescent instability waves is modelled using Amiet’s approach. A non-zero ambient mean flow is taken into account. It is found that, when the rigid surface is not so close to the jet as to affect the turbulent flow field, the trailing-edge scattering of near-field evanescent waves dominates the low-frequency amplification of installed jet noise in the far-field. The high-frequency noise enhancement on the reflected side is due to the surface reflection effect. The model agrees well with experimental results at different observer angles, apart from deviations caused by the mean-flow refraction effect at high frequencies at low observer angles.The first author (B.L.) wishes to gratefully acknowledge the financial support co-funded by the Cambridge Commonwealth European and International Trust and the China Scholarship Council. The third author (I.N.) wishes to acknowledge the UK Turbulence Consortium (UKTC) for the high-performance computing time to carry out the LES simulation on ARCHER under EPSRC grant no. EP/L000261/1 and under a PRACE award on HERMIT

Experimental validation of the hybrid scattering model of installed jet noise

Jet installation causes jet noise to be amplified significantly at low frequencies and its physical mechanism must be understood to develop effective aircraft noise reduction strategies. A hybrid semi-empirical prediction model has recently been developed based on the instability-wave-scattering mechanism. However, its validity and accuracy remain to be tested. To do so, in this paper we carry out a systematic installed jet-noise experiment in the laboratory using a flat plate instead of an aircraft wing. We show that reducing H (the separation distance between the flat plate and jet centreline) causes stronger low-frequency noise enhancement while resulting in little change to the noise shielding and enhancement at high frequencies. Decreasing L (the axial distance between the jet exit plane and the trailing edge of the plate) results in reduced noise amplification at low frequencies and also weakens both the shielding and enhancement at high frequencies. Increasing the jet Mach number abates the installation effects. It is shown that the hybrid model developed in the earlier work agrees with experimental measurements and can capture the effects of varying H, L and jet Mach number extremely well. It is concluded that the model captures the correct physics and can serve as an accurate and robust prediction tool. This new physical understanding provides insights into innovative strategies for suppressing installed jet noise.Cambridge Commonweath European and Internatinoal Trust and the China Scholarship Counci

On the acoustic optimality of leading-edge serration profiles

Leading-edge serrations are studied extensively as a way of reducing leading-edge noise and have been shown to be able to reduce leading-edge noise significantly. Previous experiments showed that different serration geometries have different noise reduction capabilities. However, the optimal serration geometry has not been known. Consequently, there are no guides that can be used at the design stage of serrations. In this paper, by performing an asymptotic analysis, we show that in order to achieve greater noise reduction in the high frequency regime (k1h >> 1, where k1 denotes the streamwise hydrodynamic wavenumber and h half of the root-to-tip amplitude of serrations), the serration profile cannot have stationary points. Therefore, piecewise smooth profiles free of stationary points are more desirable. Moreover, we show that greater noise can be achieved in the high frequency regime by using serrations that are sharper around the non-smooth points. The underlying physical mechanisms of these findings are discussed. Based on these findings, a new type of serration profile is proposed, and analytical model evaluations confirm its improved acoustic performance in the frequency range of interest. At low frequencies, a slight deterioration may be expected, but this is often negligible. To verify the conclusion drawn from the analysis, we perform an experimental study to investigate the acoustic performance of this new serration design. The results show that it is indeed superior than conventional sawtooth serrations. For example, a remarkable 7 dB additional noise reduction is observed in the intermediate frequency range with no perceivable noise increase elsewhere. The trends predicted by the analysis are well validated by the experiment. It is expected that these findings can serve as an essential guide for designing serrations, and lead to more acoustically optimized serration geometries