Hybrid Source Model for Predicting High-Speed Jet Noise

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

doi:10.2514/1.j050707

Cited by 78 publications

(81 citation statements)

References 14 publications

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“…non-heat related) components of R λ jκ l ( y,η,τ ) only. The resulting acoustic spectrum formula simplifies to that given by G&L and Leib and Goldstein [10]. The propagator solution Γ λ j ( x | y;ω ) !…”

Section: Summary Of Goldsteinõs Generalized Acoustic Analogy Approachmentioning

confidence: 93%

Supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green’s function and LES data

Afsar¹,

Sescu

Sassanis

et al. 2017

23rd AIAA/CEAS Aeroacoustics Conference

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This version is available at https://strathprints.strath.ac.uk/61100/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge. In this paper we continue efforts aimed at modeling jet noise using self-consistent analytical approaches within the generalized acoustic analogy (GAA) formulation. The GAA equations show that the far-field pressure fluctuation is given by a convolution product between a propagator tensor that depends on the (true) non-parallel jet mean flow and a generalized fluctuating stress tensor that is a stationary random function of time and includes the usual fluctuating ReynoldsÕ stress tensor as well as enthalpy fluctuation components. Here, we focus on approximating the propagator tensor by determining an appropriate asymptotic solution to the adjoint vector GreenÕs function that it depends on by using an asymptotic approach at all frequencies of interest for jet noise prediction. The GreenÕs function is then rationally approximated by a composite formula in which the GSA (Goldstein-Sescu-Afsar, J. Fluid Mech., vol. 695, pp. 199-234, 2012) non-parallel flow GreenÕs function asymptotic solution is used at low frequencies and the O(1) frequency parallel flow GreenÕs function is used for all frequencies thereafter. The former solution uses the fact that non-parallelism will have a leading order effect on the GreenÕs function everywhere in the jet under a distinguished scaling in which the jet spread rate is of the same order as the Strouhal number for a slowly-diverging mean flow expansion. Since this solution, however, is expected to apply up to the peak frequency, the latter O(1) frequency GreenÕs function in a parallel flow must be used at frequencies thereafter.We investigate the predictive capability of the composite GreenÕs function for the prediction of supersonic axi-symmetric round jets at fixed jet Mach number of 1.5 and two different temperature ratios (isothermal & heated) using Large-eddy simulation data. Our results show that, in the first instance, excellent jet noise predictions are obtained using the non-parallel flow asymptotic approach, remarkably, up to a Strouhal number of 0.5. This is true for both heated and un-heated jets. Furthermore, we develop the analytical approach required to extend this solution by appropriate asymptotic approximation to O(1) frequencies. Nomenclature

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Section: Summary Of Goldsteinõs Generalized Acoustic Analogy Approachmentioning

confidence: 93%

Supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green’s function and LES data

Afsar¹,

Sescu

Sassanis

et al. 2017

23rd AIAA/CEAS Aeroacoustics Conference

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“…With the source being modelled empirically by using the data from Reynoldsaveraged Navier-Stokes calculations and large-eddy simulations, the acoustic analogy approach, especially its recent development, has been successful in predicting statistically properties of the noise generated by turbulence in jets; see Karabasov et al (2010), Leib & Goldstein (2011) and references therein for the latest results and interpretation of the theory. This approach cannot, however, be expected to explain all aspects of the sound generation process.…”

mentioning

confidence: 99%

On generation of sound in wall-bounded shear flows: back action of sound and global acoustic coupling

2011

J. Fluid Mech.

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formal asymptotic procedure was developed to calculate the sound radiated by unsteady boundary-layer flows that are described by the triple-deck theory. That approach requires lengthy calculations, and so is now improved to construct a simpler composite theory, which retains the capacity of systematically identifying and approximating the relevant sources, but also naturally includes the effect of mean-flow refraction and more importantly the back action of the emitted sound on the source itself. The combined effect of refraction and back action is represented by an 'impedance coefficient', and the present analysis yields an analytical expression for this parameter, which was usually introduced on a semi-empirical basis. The expression indicates that for Mach number M = O(1), the mean-flow refraction and back action of the sound have a leading-order effect on the acoustic field within the shallow angles to the streamwise directions. A parametric study suggests that the back effect of sound is actually appreciable in a sizeable portion of the acoustic field for M > 0.5, becomes more pronounced, and eventually influences the entire acoustic field in the transonic limit. In the supersonic regime, the acoustic field is characterized by distinctive Machwave beams, which exert a leading-order influence on the source. The analysis also indicates that acoustic radiation in the subsonic and supersonic regimes is fundamentally different. In the subsonic regime, the sound is produced by smallwavenumber components of the hydrodynamic motion, and can be characterized by acoustic multipoles, whereas in the supersonic regime, broadband finite-wavenumber components of the hydrodynamic motion contribute and the concept of a multipolar source becomes untenable. The global acoustic feedback loop is investigated using a model consisting of two well-separated roughness elements, in which the sound wave emitted due to the scattering of a Tollmien-Schlichting (T-S) wave by the downstream roughness propagates upstream and impinges on the upstream roughness to regenerate the T-S wave. Numerical calculations suggest that at high Reynolds numbers and for moderate roughness heights, the long-range acoustic coupling may lead to global instability, which is characterized by self-sustained oscillations at discrete frequencies. † Email address for correspondence: x.wu@ic.ac.uk 280 X. Wu The dominant peak frequency may jump from one value to another as the Reynolds number or the distance between the roughness elements is varied gradually.

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“…To identify the sources of jet noise, Tam & Auriault (1999) and Tam et al (2005) developed a model that can match the envelopes of space-time correlations in a moving frame. During the development of a hybrid source model for predicting high-speed jet noise, Leib & Goldstein (2011) proposed a nonseparable space-time correlation model in the moving frame.…”

Section: Wwwannualreviewsorg • Space-time Correlations In Turbulentmentioning

confidence: 99%

Space-Time Correlations and Dynamic Coupling in Turbulent Flows

Jin

Yang

2017

Annu. Rev. Fluid Mech.

140

100

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Space-time correlation is a staple method for investigating the dynamic coupling of spatial and temporal scales of motion in turbulent flows. In this article, we review the space-time correlation models in both the Eulerian and Lagrangian frames of reference, which include the random sweeping and local straining models for isotropic and homogeneous turbulence, Taylor's frozen-flow model and the elliptic approximation model for turbulent shear flows, and the linear-wave propagation model and swept-wave model for compressible turbulence. We then focus on how space-time correlations are used to develop time-accurate turbulence models for the large-eddy simulation of turbulence-generated noise and particle-laden turbulence. We briefly discuss their applications to two-point closures for Kolmogorov's universal scaling of energy spectra and to the reconstruction of space-time energy spectra from a subset of spatial and temporal signals in experimental measurements. Finally, we summarize the current understanding of space-time correlations and conclude with future issues for the field.

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Hybrid Source Model for Predicting High-Speed Jet Noise

Cited by 78 publications

References 14 publications

Supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green’s function and LES data

Supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green’s function and LES data

On generation of sound in wall-bounded shear flows: back action of sound and global acoustic coupling

Space-Time Correlations and Dynamic Coupling in Turbulent Flows

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