The radiation of sound by the instability waves of a compressible plane turbulent shear layer
TL;DR: In this article, the problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved, and the solution provided is valid up to the acoustic far-field region.
Abstract: The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.
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TL;DR: Theoretical results concerning the instability of axisymmetric jets are reviewed in this paper for inviscid parallel jet flow and various parameters affecting jet instability such as shear layer thickness, Mach number, temperature ratio, and external flow velocity are discussed.
540 citations
TL;DR: A hierarchy of computational approaches that range from semi-empirical schemes that estimate the noise sources using mean-flow and turbulence statistics, to high-fidelity unsteady flow simulations that resolve the sound generation process by direct application of the fundamental conservation principles is discussed in this paper.
520 citations
Cites background from "The radiation of sound by the insta..."
...[318] Tam CKW, Morris PJ....
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...This modulation results in noise radiation from subsonically convected instability wave disturbances [300,318,32,319]....
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TL;DR: In this paper, the authors review evidence of the existence, energetics, dynamics, and acoustic efficiency of wave packets and highlight how extensive data available from simulations and modern measurement techniques can be used to distill acoustically relevant turbulent motions.
Abstract: Turbulent jet noise is a controversial fluid mechanical puzzle that has amused and bewildered researchers for more than half a century. Whereas numerical simulations are now capable of simultaneously predicting turbulence and its radiated sound, the theoretical framework that would guide noise-control efforts is incomplete. Wave packets are intermittent, advecting disturbances that are correlated over distances far exceeding the integral scales of turbulence. Their signatures are readily distinguished in the vortical, turbulent region; the irrotational, evanescent near field; and the propagating far field. We review evidence of the existence, energetics, dynamics, and acoustic efficiency of wave packets. We highlight how extensive data available from simulations and modern measurement techniques can be used to distill acoustically relevant turbulent motions. The evidence supports theories that seek to represent wave packets as instability waves, or more general modal solutions of the governing equations, and confirms the acoustic importance of these structures in the aft-angle radiation of high subsonic and supersonic jets. The resulting unified view of wave packets provides insights that can help guide control strategies.
517 citations
TL;DR: In this paper, a semi-empirical theory is developed for the prediction of the spectrum, intensity, and directivity of the fine-scale turhulence noise from high-speed jets.
Abstract: It is known that turhulent mixing noise from high-speed jets consists of two components. They are the noise from large turbulent structures in the form of Mach wave radiation and the less directional fine-scale turbulence noise. The Mach wave radiation dominates in the downstream direction. The fine-scale turbulence noise dominates in the sideline and upstream directions. A semiempirical theory is developed for the prediction of the spectrum, intensity, and directivity of the fine-scale turhulence noise. The prediction method is self-contained. The turbulence information is supplied by the k-e turhulence model. The theory contains three empirical constants beyond those of the k-e model. These constants are determined by best fit of the calculated noise spectra to experimental measurements. Extensive comparisons between calculated and measured noise spectra over a wide range of directions of radiation,jet velocities, and temperatures have heen carried out. Excellent agreements are found. It is believed that the present theory offers significant improvements over current empirical or semiempirical jet noise prediction methods in use. There is no first principle jet noise theory at the present time.
430 citations
TL;DR: In this article, the authors derived a scaling formula that the intensity of shock associated noise varies as (Mj2 − Md2)2 where Mj and Md are the fully expanded jet operating Mach number and nozzle design Mach number, respectively.
371 citations
References
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01 Jan 1974
TL;DR: A computer algorithm that computes the discrete Fourier transform much faster than other algorithms, is explained and examples and detailed procedures are provided to assist the reader in learning how to use the algorithm.
1,823 citations
TL;DR: In this article, large-scale structures in the form of instability waves are shown to be present in an acoustically and aerodynamically well behaved jet even at high Mach numbers.
Abstract: Large-scale structures in the form of instability waves are an inherent part of a shearlayer mixing process. Such structures are shown to be present in an acoustically and aerodynamically well behaved jet even at high Mach numbers. They do not directly radiate significant acoustic power in a subsonic jet, but do govern the production of the turbulent fluctuations which radiate broad-band jet noise. Over the whole subsonic Mach number range, a significant increase in jet noise can be produced by exciting the shear layer with a fluctuating pressure at the nozzle of only 0·08 % of the jet dynamic head but with the correct Strouhal number. Such excitation by internal acoustic, aerodynamic or thermal fluctuations could explain the variability of jet noise measurements between different rigs and could also be responsible for some components of ‘excess’ noise.
484 citations
TL;DR: In this paper, coherent axisymmetric structures in a turbulent jet are modelled as linear instability modes of the mean velocity profile, regarded as the profile of a fictitious laminar inviscid flow.
Abstract: Coherent axisymmetric structures in a turbulent jet are modelled as linear instability modes of the mean velocity profile, regarded as the profile of a, fictitious laminar inviscid flow. The usual multiple-scales expansion method is used in conjunction with a family of profiles consistent with similarity laws for the initial mixing region and approximating the profiles measured by Crow & Champagne (1971), Moore (1977) and other investigators, to deal with the effects of flow divergence. The downstream growth and approach to peak amplitude of axisymmetric wave modes with prescribed real frequency is calculated numerically, and comparisons are made with various sets of experimental data. Excellent agreement is found with the wavelength measurements of Crow & Champagne. Quantities such as the amplitude gain which depend on cumulative effects are less well predicted, though the agreement is still quite tolerable in view of the facts that this simple linear model of slowly diverging flow is being applied far outside its range of strict validity and that many of the published measurements are significantly contaminated by nonlinear effects. The predictions show that substantial variations are to be expected in such quantities as the phase speed and growth rate, according to the flow signal (velocity, pressure, etc.) measured, and that these variations depend not only on the axial measurement location but also on the cross-stream position. Trends of this kind help to explain differences in, for example, the preferred Strouhal number found by investigators using hot wires or pressure probes on the centre-line, in the mixing layer or in the near field.
430 citations