The aeroacoustics of slowly diverging supersonic jets

Goldstein, M. E.; Leib, S. J.

doi:10.1017/s0022112008000311

Cited by 105 publications

(101 citation statements)

References 30 publications

(55 reference statements)

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“…The equation is singular at the radial positionr c whereŪ (r c ) = −ω/k; herer c may be referred to as the 'envelope critical layer' in order to distinguish it from the usual (phase) critical layer r c . A critical layer of the former type appears in certain generalized formulation of acoustic analogy (Goldstein & Leib 2008), where the singularity has to be removed by reintroducing the weak non-parallel effect of the base flow since all other terms are predesignated as sources. In our study, the signature p m is of hydrodynamic nature for r = O(1), and thus viscous effects are at our disposal and can be used to smoothed out the singularity.…”

Section: The Nonlinearly Generated Slowly Breathing 'Mean Field'mentioning

confidence: 99%

Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet

Huerre

2009

J. Fluid Mech.

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A possible fundamental physical mechanism by which instability modes generate sound waves in subsonic jets is presented in the present paper. It involves a wavepacket of a pair of helical instability modes with nearly the same frequencies but opposite azimuthal wavenumbers. As the wavepacket undergoes simultaneous spatial-temporal development in a circular jet, the mutual interaction between the helical modes generates a strong three-dimensional, slowly modulating, 'mean-flow distortion'. It is demonstrated that this 'mean field' radiates sound waves to the far field. The emitted sound is of very low frequency, with characteristic time and length scales being comparable with those of the envelope of the wavepacket, which acts as a noncompact source. A matched-asymptotic-expansion approach is used to determine, in a self-consistent manner, the acoustic field in terms of the envelope of the wavepacket and a transfer factor characterising the refraction effect of the background base flow. For realistic jet spreading rates, the nonlinear development of the wavepacket is found to be influenced simultaneously by non-parallelism and non-equilibrium effects, and so a composite modulation equation including both effects is constructed in order to describe the entire growth-attenuation-decay cycle. Parametric studies pertaining to relevant experimental conditions indicate that the acoustic field is characterised by a single-lobed directivity pattern beamed at an angle about 45 o − 60 o to the jet axis, and a broadband spectrum centred at a Strouhal number St ≈ 0.07 − 0.2. As the nonlinear effect increases, the radiation becomes more efficient and the noise spectrum broadens, but the gross features of the acoustic field remain robust, and are broadly in agreement with experimental observations.

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Section: The Nonlinearly Generated Slowly Breathing 'Mean Field'mentioning

confidence: 99%

Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet

Huerre

2009

J. Fluid Mech.

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“…Over the course of decades of theoretical development some acoustic analogies have been found to be more useful than others in constructing predictive tools. Goldstein & Leib [1] and Khavaran [2], have shown that fluctuations of velocity are the leading terms in cold jets that need to be modeled to predict far-field sound autocorrelation, arguably the final statistic of interest in this context. When the jet is heated, velocity fluctuations begin to lose dominance and turbulent enthalpy fluctuations and their correlations with the velocity become more important.…”

Section: What To Measure?mentioning

confidence: 99%

Validating LES for Jet Aeroacoustics

Bridges

2011

49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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I. AbstractEngineers charged with making jet aircraft quieter have long dreamed of being able to see exactly how turbulent eddies produce sound-and this dream is now coming true with the advent of large eddy simulation (LES). Two obvious challenges remain: validating the LES codes at the resolution required to see the fluid-acoustic coupling, and the interpretation of the massive datasets that result in having dreams come true. This paper primarily addresses the former, the use of advanced experimental techniques such as particle image velocimetry (PIV) and Raman and Rayleigh scattering, to validate the computer codes and procedures used to create LES solutions. It also addresses the latter problem in discussing what are relevant measures critical for aeroacoustics that should be used in validating LES codes. These new diagnostic techniques deliver measurements and flow statistics of increasing sophistication and capability, but what of their accuracy? And what are the measures to be used in validation? This paper argues that the issue of accuracy be addressed by cross-facility and cross-disciplinary examination of modern datasets along with increased reporting of internal quality checks in PIV analysis. Further, it is argued that the appropriate validation metrics for aeroacoustic applications are increasingly complicated statistics that have been shown in aeroacoustic theory to be critical to flowgenerated sound. II. IntroductionA. The Problem Typical aeroacoustic problems are bedeviled at several levels. First, the fluid flow generating the acoustic field is turbulent, and the description of this flow has a high degree of freedom. That is to say in classical engineering terms that the flow and its associated sound is described by a large number of modes over many scales. A subset of aeroacoustic problems, typically involving resonance, can be described more simply, but from an engineering perspective if the flow is simple then the method of manipulating the flow to enhance or remove the sound is also simple. Second, the sound is the result of slight phase imperfections from the compressibility of the flow. Indeed, if the flow were truly incompressible there would be no noise as all dilatations would cancel out. Third, and most significant for engineers attempting to predict the acoustic field, the sound is such a small part of the solution that it is easily lost to approximations used in analysis. Thus, the field of aeroacoustics is still a research topic instead of being an engineering science.Of the approaches used on aeroacoustics all run into the problems mentioned above. Empirical approaches are largely successful for cases where the turbulence has simple scaling with the geometry such as simple jets and turbulent boundary layer noise. However, make a change to the geometry that changes the turbulence beyond the simple description underlying the noise model and the empirical noise model falls apart. Think modifications to nozzle geometries or fuselage-wing interfaces. Most theoretical approaches have pro...

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“…The Generalized Acoustic Analogy (GAA) 24,26 is an exact rearrangement of compressible Navier-Stokes equations, governing the fluctuations about an arbitrary base flow. Goldstein (2003) 24 discusses various choices for the base flow.…”

Section: Iiib Acoustic Analogy Computationmentioning

confidence: 99%

Effects of heating on noise radiation from a two-dimensional mixing layer: direct computation and acoustic analogy predictions

Sharma

Lele

2011

17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)

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Sound radiation from mixing layers is studied by numerical solution of two-dimensional unsteady compressible Navier-Stokes equations and acoustic analogy predictions. The splitter plate is included inside the computational domain using high-order overset mesh method. No inflow forcing is provided. Three different cases are considered where the free stream density ratio (or the inverse of temperature ratio) of slower to faster stream is varied from 1 to 2.7, keeping the velocity ratio and Reynolds numbers fixed. It is observed that as the highspeed stream is heated, the initial instability is accelerated but the saturation amplitude of streamwise velocity fluctuations do not vary. The saturation amplitudes of density fluctuations were found to increase proportionally to difference in free stream densities whereas the nearfield pressure fluctuations were found to decrease with heating. A simple scaling is suggested for the near field pressure fluctuation amplitude. In the far-field away from the shear layer on the slower stream side, a reduction in peak pressure fluctuations with increased heating is observed. The sound radiation is observed to become less directional as the high-speed stream is heated. The cause of the reduced noise radiation with heating is analyzed using Goldstein's generalized acoustic analogy (GAA). Two base flows are treated: the time averaged flow and a uniform flow. In both the cases the GAA source terms display the expected scaling behavior with the enthalpy flux source term increasing with heating. It is suggested that cancellation amongst the source terms is partly responsible for the observed reduction in radiated sound.

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The aeroacoustics of slowly diverging supersonic jets

Cited by 105 publications

References 30 publications

Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet

Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet

Validating LES for Jet Aeroacoustics

Effects of heating on noise radiation from a two-dimensional mixing layer: direct computation and acoustic analogy predictions

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