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

Mathews, James R.; Peake, N.

doi:10.1016/j.jsv.2018.02.024

Cited by 18 publications

(18 citation statements)

References 23 publications

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“…Here, the reduction of the noise is measured relative to the straight leading edge (SLE) case. The noise reduction effect of WLEs has been demonstrated through mathematical (Lyu & Azarpeyvand 2017;Mathews & Peake 2018;Ayton & Kim 2018), experimental (Hansen et al 2012;Narayanan et al 2015;Chong et al 2015;Roger & Moreau 2016;Chaitanya et al 2017;Biedermann et al 2017;Juknevicius & Chong 2018) and computational studies (Lau et al 2013;Clair et al 2013;Kim et al 2016;Agrawal & Sharma 2016;Tong et al 2018). The previous studies reported that significant noise reduction (typically more than 3dB) was available for Strouhal numbers St LE 0.5 (normalised by the peak-to-root distance of the WLE and the free-stream velocity).…”

Section: Introductionmentioning

confidence: 99%

On the universal trends in the noise reduction due to wavy leading edges in aerofoil–vortex interaction

Turner

Kim

2019

J. Fluid Mech.

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Existing studies suggest that wavy leading edges (WLEs) offer substantial reduction of broadband noise generated by an aerofoil undergoing upstream vortical disturbances. In this context, there are two universal trends in the frequency spectra of the noise reduction which have been observed and reported to date: (i) no significant reduction at low frequencies followed by (ii) a rapid growth of the noise reduction that persists in the medium-to-high frequency range. These trends are known to be insensitive to the aerofoil type and flow condition used. This paper aims to provide comprehensive understandings as to how these universal trends are formed and what the major drivers are. The current work is based on very-high-resolution numerical simulations of a semi-infinite flat-plate aerofoil impinged by a prescribed divergence-free vortex in an inviscid base flow at zero incidence angle, continued from recent work by the authors (Turner & Kim, J. Fluid Mech., vol. 811, 2017, pp. 582–611). One of the most significant findings in the current work is that the noise source distribution on the aerofoil surface becomes entirely two-dimensional (highly non-uniform in the spanwise direction as well as streamwise) at high frequencies when the WLE is involved. Also, the sources downstream of the LE make crucial contributions to creating the universal trends across all frequencies. These findings contradict the conventional LE-focused one-dimensional source analysis that has widely been accepted for all frequencies. The current study suggests that the universal trends in the noise-reduction spectra can be properly understood by taking the downstream source contributions into account, in terms of both magnitude and phase variations. After including the downstream sources, it is shown in this paper that the first universal trend is due to the conservation of total (surface integrated) source energy at low frequencies. The surface-integrated source magnitude that decreases faster with the WLE correlates very well with the noise-reduction spectrum at medium frequencies. In the meantime, the high-frequency noise reduction is driven almost entirely by destructive phase interference that increases rapidly and consistently with frequency, explaining the second universal trend.

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Section: Introductionmentioning

confidence: 99%

On the universal trends in the noise reduction due to wavy leading edges in aerofoil–vortex interaction

Turner

Kim

2019

J. Fluid Mech.

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“…However if the far field were to experience a region of destructive interference it would be natural to assume there could be a corresponding region of constructive interference. The analytic solution obtained via Green's functions for the sound generated by individual vortices interacting with a wavy leading edge by Mathews & Peake (2018) indicates certain leading-edge profiles do increase noise as opposed to reducing it. Key to an increase or decrease in noise is the relative angle between the vortex path and the leading edge, which is also an important factor for swept leading edges (Adamczyk 1974).…”

Section: Introductionmentioning

confidence: 99%

An analytic solution for the noise generated by gust–aerofoil interaction for plates with serrated leading edges

Ayton

Kim

2018

J. Fluid Mech.

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This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a serrated leading edge in a background steady uniform flow. Viscous and nonlinear effects are neglected. The Wiener–Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to permit analytical progress. The solution is obtained in terms of a modal expansion in the spanwise coordinate; however, for low- and mid-range incident frequencies only the zeroth-order mode is seen to contribute to the far-field acoustics, therefore the far-field noise can be quickly evaluated. The solution gives insight into the potential mechanisms behind the reduction of noise for plates with serrated leading edges compared to those with straight edges, and predicts a logarithmic dependence between the tip-to-root serration height and the decrease of far-field noise. The two mechanisms behind the noise reduction are proposed to be an increased destructive interference in the far field, and a redistribution of acoustic energy from low cut-on modes to higher cut-off modes as the tip-to-root serration height is increased. The analytic results show good agreement in comparison with experimental measurements. The results are also compared against nonlinear numerical predictions where good agreement is also seen between the two results as frequency and tip-to-root ratio are varied.

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“…Currently, most studies of trailing-edge noise control have mainly focused on sawtoothshaped serrations [9][10][11][12], while studies of leading-edge serrations have considered potential aerodynamic drag penalties and primarily focused on wavy (sinusoidal) profiles of protuberances and tubercles [1,4,13]. More specifically, [5] has conducted experimental studies of a leading edge with curved sawtooth-shaped serrations and reached the conclusion that a serration with the largest amplitude (tip-to-root length) and the largest wavelength (period) is optimal.…”

Section: Introductionmentioning

confidence: 99%

“…To enable theoretical developments, an aerofoil is usually modeled as an infinite half plane with leading-edge serrations in the presence of uniform flows, and the incident turbulent flow is approximated by synthetic turbulence or simply a couple of eddies. By adopting such simplifications, the work [13] has developed an analytical model based on the modified Green's function from [16] and found that it is still difficult to predict the optimal serration design due to nonlinear interactions between eddies. Other than extending Howe's approach, [17] has adopted their previous approach [11] that combines coordinate transformation, Fourier series expansion and Schwarzschild techniques to propose an analytical model for leading-edge serrations.…”

Section: Introductionmentioning

confidence: 99%

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A theoretical study of serrated leading edges in aerofoil and vortical gust interaction noise

Huang

2019

Adv. Aerodyn.

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Serrated leading edges are one of the most promising passive aerodynamic control methods for the reduction of aerofoil-turbulence interaction noise. To elucidate the possible physical mechanisms, the current paper studies the simplified setup with aerofoil-vortical gust interaction and proposes an analytical model by incorporating Fourier transform into the Wiener-Hopf method. The proposed model suggests that the serrations operate on the incident vortical gusts as convolution, which leads to the innovative concept that models serrations as transfer functions in the wavenumber domain. Overall, the current theoretical study could provide a unique insight of the inherent aerodynamic noise control mechanisms of leading-edge serrations.

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

Cited by 18 publications

References 23 publications

On the universal trends in the noise reduction due to wavy leading edges in aerofoil–vortex interaction

On the universal trends in the noise reduction due to wavy leading edges in aerofoil–vortex interaction

An analytic solution for the noise generated by gust–aerofoil interaction for plates with serrated leading edges

A theoretical study of serrated leading edges in aerofoil and vortical gust interaction noise

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