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Journal ArticleDOI

Acoustic radiation from an airfoil in a turbulent stream

22 Aug 1975-Journal of Sound and Vibration (Academic Press)-Vol. 41, Iss: 4, pp 407-420
TL;DR: In this paper, a theoretical expression for the far-field acoustic power spectral density produced by an airfoil in a subsonic turbulent stream is given in terms of quantities characteristics of the turbulence.
About: This article is published in Journal of Sound and Vibration.The article was published on 1975-08-22. It has received 807 citations till now. The article focuses on the topics: Kutta–Joukowski theorem & K-epsilon turbulence model.
Citations
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Journal ArticleDOI
TL;DR: In this article, a theoretical method for calculating far field noise from an airfoil in an incident turbulent flow is extended to apply to the case of noise produced by turbulent flow past a trailing edge, and some minor points of the theory in reference are clarified.

800 citations

Journal ArticleDOI
TL;DR: In this article, the Kirchhoff formulation for moving surfaces is compared with the Ffowcs Williams Hawkings (FW-H) equation for the prediction of high-speed impulsive noise, in an effort to eliminate the need to compute the quadrupole contribution.

420 citations


Cites methods from "Acoustic radiation from an airfoil ..."

  • ...Blade response coherence functions were found and used in a noise radiation formula developed by Amiet [87]....

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Journal ArticleDOI
TL;DR: In this paper, a three-bladed wind turbine with a rotor diameter of 58m was used to characterize the noise sources and to verify whether trailing edge noise from the blades was dominant.

410 citations


Cites background from "Acoustic radiation from an airfoil ..."

  • ...wind turbines, airplanes, helicopters, fans), the characteristics of airfoil noise have been investigated extensively in both experimental and theoretical studies [3-13]....

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Journal ArticleDOI
TL;DR: In this paper, a leading-edge backscattering correction is derived, based on the solution of an equivalent Schwarzschild problem, and added to the original formula to account for all the effects due to a limited chord length, and to infer the far-field radiation off the mid-span plane.

385 citations


Cites background or methods from "Acoustic radiation from an airfoil ..."

  • ...In Amiet’s work [9], the scattering equivalent sources are defined as if the airfoil were infinite in the upstream direction, but the radiation integral is calculated over the effective finite chord length....

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  • ...The problem of broadband trailing-edge noise modelling, as stated by Amiet [9], has been revisited by adding a leading-edge back-scattering correction and a 3D extension to the original formulation....

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  • ...This back-scattering correction has been developed here because the induced loads do concentrate at the leading edge, in the same way as found in classical linearized theories of unsteady aerodynamics [21] (the derivative leading to P2 generates a factor of ðX þ 2Þ )....

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  • ...(4) This is the result derived by Amiet [9]....

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  • ...When addressing scattering problems in aeroacoustics, Amiet applies this result to determine the disturbance wall pressure generated when an incident vortical velocity field impinges on the leading edge of an airfoil [21] or when an incident (aerodynamic) wall pressure field is convected past the trailing edge [9]....

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Journal ArticleDOI
TL;DR: In this paper, the authors used a large horizontal microphone array, positioned at a distance of about one rotor diameter from the turbine, to locate and quantify the noise sources in the rotor plane and on individual blades.
Abstract: Acoustic field measurements were carried out on a 94-m-diam three-bladed wind turbine with one standard blade, one blade with trailing-edge serrations, and one blade with an optimized airfoil shape. A large horizontal microphone array, positioned at a distance of about one rotor diameter from the turbine, was used to locate and quantify the noise sources in the rotor plane and on the individual blades. The acoustic source maps show that for an observer at the array position, the dominant source for the baseline blade is trailing-edge noise from the blade outboard region. Because of convective amplification and directivity, practically all of this noise is produced during the downward movement of the blade, which causes the typical swishing noise during the passage of the blades. Both modified blades show a significant trailing-edge noise reduction at low frequencies, which is more prominent for the serrated blade. However, the modified blades also show tip noise at high frequencies, which is mainly radiated during the upward part of the revolution and is most important at low wind speeds due to high tip loading. Nevertheless, average overall noise reductions of 0.5 and 3.2 dB are obtained for the optimized blade and the serrated blade, respectively.

375 citations


Additional excerpts

  • ...retical studies [3–13]....

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References
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Journal ArticleDOI
TL;DR: In this paper, a theory for estimating the sound radiated from a fluid flow, with rigid boundaries, which as a result of instability contains regular fluctuations or turbulence is initiated, based on the equations of motion of a gas.
Abstract: A theory is initiated, based on the equations of motion of a gas, for the purpose of estimating the sound radiated from a fluid flow, with rigid boundaries, which as a result of instability contains regular fluctuations or turbulence. The sound field is that which would be produced by a static distribution of acoustic quadrupoles whose instantaneous strength per unit volume is ρv i v j + p ij - a 2 0 ρ δ ij , where ρ is the density, v i the velocity vector, p ij the compressive stress tensor, and a 0 the velocity of sound outside the flow. This quadrupole strength density may be approximated in many cases as ρ 0 v i v j . The radiation field is deduced by means of retarded potential solutions. In it, the intensity depends crucially on the frequency as well as on the strength of the quadrupoles, and as a result increases in proportion to a high power, near the eighth, of a typical velocity U in the flow. Physically, the mechanism of conversion of energy from kinetic to acoustic is based on fluctuations in the flow of momentum across fixed surfaces, and it is explained in § 2 how this accounts both for the relative inefficiency of the process and for the increase of efficiency with U . It is shown in § 7 how the efficiency is also increased, particularly for the sound emitted forwards, in the case of fluctuations convected at a not negligible Mach number.

4,697 citations

Journal ArticleDOI
TL;DR: In this paper, an extension to Lighthill's general theory of aerodynamic sound was made to incorporate the influence of solid boundaries upon the sound field, and it was shown that these effects are exactly equivalent to a distribution of dipoles, each representing the force with which unit area of solid boundary acts upon the fluid.
Abstract: An extension is made to Lighthill's general theory of aerodynamic sound, so as to incorporate the influence of solid boundaries upon the sound field. This influence is twofold, namely (i) reflexion and diffraction of the sound waves at the solid boundaries, and (ii) a resultant dipole field at the solid boundaries which are the limits of Lighthill's quadrupole distribution. It is shown that these effects are exactly equivalent to a distribution of dipoles, each representing the force with which unit area of solid boundary acts upon the fluid. A dimensional analysis shows that the intensity of the sound generated by the dipoles should at large distances x be of the general form I$\propto $ $\rho \_{0}$ U$\_{0}^{6}$a$\_{0}^{-3}$ L$^{2}$x$^{-2}$, where U$\_{0}$ is a typical velocity of the flow, L is a typical length of the body, a$\_{0}$ is the velocity of sound in fluid at rest and $\rho \_{0}$ is the density of the fluid at rest. Accordingly, these dipoles should be more efficient generators of sound than the quadrupoles of Lighthill's theory if the Mach number is small enough. It is shown that the fundamental frequency of the dipole sound is one half of the frequency of the quadrupole sound.

1,760 citations

Proceedings ArticleDOI
24 Mar 1975

187 citations

Journal ArticleDOI
TL;DR: Similarity rules for the load distributions induced on a thin two-dimensional wing at subsonic speeds by sinusoidal gusts whose wave fronts are at an angle to the leading edge of the wing were constructed in this paper.
Abstract: Similarity rules are constructed for the load distributions induced on a thin two-dimensional wing at subsonic speeds by sinusoidal gusts whose wave fronts are at an angle to the leading edge of the wing. It is shown that these rules divide into two groups according to the value of a parameter dependent on the Mach number and the angle between the gust front and the wing. The similarity rules for each group relate all the members of the group to a simpler problem whose solution can be found by existing methods. The similarity between the two groups is also discussed in terms of the two methods of solution available and it is shown that each method of solution is applicable in all cases.

140 citations