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Prediction of Turbulence-Generated Noise in Unheated Jets

Profile image of Nicholas GeorgiadisNicholas Georgiadis

Abstract

The model-based approach, used by the JeNo code to predict jet noise spectral directivity, is described. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. A Reynolds-averaged Navier-Stokes (RANS) solution yields the required mean flow for the solution of the propagation Green s function in a locally parallel flow. The RANS solution also produces time- and length-scales needed to model the non-compact source, the turbulent velocity correlation tensor, with exponential temporal and spatial functions. It is shown that while an exact non-causal Green s function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at low to moderate Mach numbers, the polar directivity of radiated sound is not entirely captured by this Green s function at high subsonic and supersonic acoustic Mach numbers. Results pres...

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Subsonic and Supersonic Jet Noise Predictions from Statistical Source Models
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AIAA Journal, 1997

Subsonic and supersonic jet noise is determined numerically from statistical source models. The goal is to develop prediction methods for high-speed jet noise for application to aeronautical and space transportation systems. In this framework, a combination of a k-² turbulence closure with an acoustic analogy provides an interesting way to compute such radiated acoustic elds. Three acoustic analogies are investigated. First, the classical Lighthill theory in combination with Ribner's results is applied to calculate jet mixing noise. The second method relies on the Goldstein-Howes convected wave equation, which is used to improve the predicted supersonic jet mixing noise in the upstream direction. It is necessary to properly account for acoustic wave convection, and then, one nds that the Doppler factor features an exponent of ¡ 3 in the associated power law. A model based on the Ffowcs Williams-Maidanik analysis then is developed to estimate the Mach-wave noise component that dominates forward arc radiation when the convection Mach number is supersonic. Comparisons between aerodynamic and calculated acoustic results on the one hand, and available measurements on the other hand, are carried out. It is shown that the last two models yield improved supersonic jet mixing noise predictions.

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The Modified Complementary Technique applied to the Mach 0.85 axisymmetric jet for noise prediction
Mark Glauser

13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference), 2007

The Complementary Techniques 6 are modified to estimate the most energetic turbulent features of a Mach 0.85, axisymmetric jet in the prominent sound-source regions of the flow via Spectral Linear Stochastic Estimation. 11, 28 This model estimate is three-dimensional, comprises all three components of the velocity field and is time resolved. The technique employs the pressure field as the unconditional input, that which is measured within the hydrodynamic periphery of the jet flow where signatures (pressure) are known to comprise a reasonable footprint of the turbulent large-scale structure. Spectral estimation coefficients are derived from the joint second order statistics between coefficients that are representative of the low-order pressure field (Fourier-azimuthal) and of the low-order velocity field (POD). A bursting like event is manifest in the model estimate and is similar to what was found in the low-speed jet studies. 9 Lighthill's analogy is effected and a prediction of the far-field acoustics is performed. This work, thus constitutes a benchmark for developing dynamical system models from hydrodynamic pressure signatures for estimating and predicting the behavior of the deterministic energy containing events that govern many of the physical constituents in turbulent flows.

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Turbulent jet flow noise prediction
Bendiks Boersma

The text of the abstract follows. In this paper we describe a numerical approach to completely determine the structure of a low Reynolds number compressible jet o w and to compute the associated sound waves in the far eld. The method is applied to simulate a Reynolds number 4; 000, Mach number 0:8 jet, with the results validated by comparison with the jet reproduced experimentally. The mean o w and far eld sound results are shown to while matching conditions are created experimentally inside a low pressure tank. The mean o w results of the DNS are seen to correspond well with our experimental results, and to be compatible with those published in the literature. The semi-analytically obtained sound eld is shown to be identical to that obtained purely by the DNS in the near eld, while in the far eld matches those obtained by us experimentally, and compatible with experimental results previously published.

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Sources of high-speed jet noise: Analysis of LES data and modeling
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Procedia Engineering, 2010

Results from recent LES studies of high-speed jet flows and its near and far-field noise (Mendez et al. AIAA-2010-271) are reviewed with an emphasis on validation of the LES results. Far-field noise is predicted using data collected on a conical FW-H surface. Very good agreement with the measurement reported by Bridges & Wernet (AIAA-2008-2834) is observed. Data analysis of the flow disturbances within the jet and in the near-field is used to better characterize the sound source processes. We analyze LES data of Bodony and Lele (Phys. Fluids, vol. 46, 2005) using a filter in the wavenumber-frequency domain. The supersonic components of pressure and radial velocity fluctuation show peaks within the jet and show the U 8 j scaling behavior consistent with the far-field radiated noise levels. The observed scaling is also consistent with a perturbation expansion of nearly incompressible turbulent fluctuations within the jet flow. Linear global mode analysis of the non-parallel jet mean flow is performed. Features of Mach wave radiation are evident in the global modes for supersonic convection. Large transient growth is found due to convective non-normality. Some implications of this analysis for jet noise modeling are discussed.

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Noise prediction for increasingly complex jets. Part II: Applications
Michael Shur

2005

This Part I presents a detailed description of a numerical system built and tested with the final goal of reaching an accuracy of 2-3 dB over a meaningful range of frequencies for airliner engine noise, while having low empiricism and a general-geometry capability. The turbulence is treated by Large-Eddy Simulation with grids of around 1 million points, slightly upwind-biased high-order differencing, and implicit time integration. The code can incorporate boundaries and multi-block grids (thus avoiding the centerline singularity), and capture shocks. The sub-grid scale model is de-activated, because on present grids it strongly interferes with transition in the mixing layer. Without unsteady inflow forcing, the shear-layer roll-up and three-dimensionalization are realistic and reasonably insensitive to the grid. The far-field noise is computed using the permeable Ffowcs-Williams/Hawkings (FWH) formulation without external quadrupoles. The treatment of the disk that closes the FWH surface near the outflow must be approximate, since the turbulent region is unbounded, and is crucial; it benefits from a change of variable from density to pressure, and other mitigating steps. Tests are presented in support of the key elements of the strategy. In a simple isothermal jet, the system is close to the 2-3 dB target both in terms of directivity and of spectrum, up to a Strouhal number of about 1.5. In Part II, the following effects are explored with overall success: jet Mach numbers from 0.3 to slightly supersonic with under-expansion (generating shock cells), jet heating, co-flow, and "synthetic chevrons."

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Investigation of high supersonic jet noise: non-linear propagation effects and flow-acoustics correlations
Christophe Bogey

17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference), 2011

In this paper, the data obtained by LES for an initially laminar and overexpanded jet at Mach number 3.3 and Reynolds number 10 5 are reexamined in order to investigate the nonlinear effects on the propagation of the acoustic waves, and the normalized flow/acoustics cross-correlations. To study the non-linear propagation effects at the direction φ = 60 • and up to 240 radii from the nozzle exit, the LES near field is propagated in far-field by solving either the isentropic linearized Euler equations or the full Euler equations. The comparisons of the acoustic data obtained from the two methods clearly show that the non-linear effects are strong up to about 240 radii from the nozzle exit. Using the far-field acoustic results from the non-linear propagation, the normalized cross-correlations between the turbulent flow quantities and the acoustic pressure signals at the direction φ = 60 • are then evaluated to give some information on sound generation. A sound source which may be similar to that one observed in subsonic jets is first found on the jet axis in the vicinity of the end of the potential core. Other sound sources attributed to the supersonic convection of turbulent vortices are noticed. Finally, the normalized cross-correlations between the fluctuating density along the jet axis and the acoustic pressure display correlation bands between the 3rd and the 5th shock cells. These bands might be linked with the screech generation mechanism.

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Improved jet noise predictions in subsonic flows using an approximate composite asymptotic expansion of the adjoint Green's function in Goldstein's analogy
Adrian Sescu

AIAA AVIATION 2020 FORUM, 2020

Our recent work on jet noise modeling (Afsar et al. 2019, PhilTrans. A., vol. 377) has confirmed that non-parallel flow effects are needed to determine the wave propagation aspect of the jet noise problem. The acoustic spectrum calculated using an asymptotic representation of non-parallel flow effects produces the correct spectral shape of the small angle radiation beyond that which can be predicted using a parallel (i.e. non-spreading) mean flow approximation to determine the wave propagation tensor in Goldstein's generalized acoustic analogy formulation. While the peak noise predicted using this approach works remarkably well at low frequencies (up to and slightly beyond the peak Strouhal number), the high frequency prediction in Afsar et al. (2019) relied upon an ad-hoc composite asymptotic formula for the propagator that was also restricted to the small angle spectra. In this paper we therefore attempt to remedy this defect by using the O(1) frequency locally parallel flow Green's function as a kind-of outer solution to the propagator tensor in which the non-parallel flow theory used in the latter reference acts as the 'inner' solution that is valid at low frequencies and is transcendentally small beyond the peak frequency. The hope is that this approach will allow more robust high frequency predictions with a single set of turbulence parameters for the acoustic spectrum at any given acoustic Mach number. In other words, both non-parallel and locally parallel regions of the propagator tensor solution are multiplied by the same turbulence source structure in the acoustic spectrum integral. The paper highlights the basic formalism of the low frequency jet noise theory and summarises the technical problems and strategy we use to extend this approach to higher frequencies.

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Progress in Computational Aeroacoustics in Predicting the Noise Radiated from Turbulent Flows
Aldo Rona

The International Journal of Acoustics and Vibration, 1997

In recent years a number of simple unsteady flows involving the interaction between vortices have been studied using computational fluid dynamics. These have been extended to include the sound radiated to the far field either by Direct Numerical Simulation, by the use of acoustic analogies, or by the use of Kirchoff methods. For more complex flows results have been obtained using methods based on solving the time dependent large scale flow structures using the unsteady Reynolds Averaged Navier-Stokes equations and then using acoustic analogies to derive the noise in the radiation field. Some success has been made with the latter methods in the predictions of the noise radiated from the flow over cavities at supersonic speeds, where the noise characteristics are dominated by large scale events associated with self-excited flow oscillations. Similar methods are being applied to other self-excited flows, and ultimately to turbulent flows such as jets. The paper describes these methods and results together with some limited preliminary comparisons with experimental data. In an Appendix an extension of Lighthill's equation for aerodynamic noise is presented covering the effects of flow-acoustic interaction.

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Reprint of: Sources of high-speed jet noise: analysis of LES data and modeling
Parviz Moin

Procedia IUTAM, 2010

Results from recent LES studies of high-speed jet flows and its near and far-field noise (Mendez et al. AIAA-2010-271) are reviewed with an emphasis on validation of the LES results. Far-field noise is predicted using data collected on a conical FW-H surface. Very good agreement with the measurement reported by Bridges & Wernet (AIAA-2008-2834) is observed. Data analysis of the flow disturbances within the jet and in the near-field is used to better characterize the sound source processes. We analyze LES data of Bodony and Lele (Phys. Fluids, vol. 46, 2005) using a filter in the wavenumber-frequency domain. The supersonic components of pressure and radial velocity fluctuation show peaks within the jet and show the U 8 j scaling behavior consistent with the far-field radiated noise levels. The observed scaling is also consistent with a perturbation expansion of nearly incompressible turbulent fluctuations within the jet flow. Linear global mode analysis of the non-parallel jet mean flow is performed. Features of Mach wave radiation are evident in the global modes for supersonic convection. Large transient growth is found due to convective non-normality. Some implications of this analysis for jet noise modeling are discussed.

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

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References (10)

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parviz moin

1998

Data from the direct numerical simulation (DNS) of a turbulent, compressible (Mach=1.92) jet has been analyzed to investigate the process of sound generation. The overall goals are to understand how the di erent scales of turbulence contribute to the acoustic eld and to understand the role that linear instability waves play in the noise produced by supersonic turbulent jets. Lighthill's acoustic analogy was used to predict the radiate sound from turbulent source terms computed from the DNS data. Preliminary computations (for the axisymmetric mode of the acoustic eld) show good agreement between the acoustic eld determined from DNS and acoustic analogy. Further work is needed to re ne the calculations and investigate the source terms. Work was also begun to test the validity of linear stability wave models of sound generation in supersonic jets. An adjoint-based method was developed to project the DNS data onto the most unstable linear stability mode at di erent streamwise positions. This will allow the evolution of the wave and its radiated acoustic eld, determined by solving the linear equations, to be compared directly with the evolution of the near-and far-eld uctuations in the DNS.

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Prediction of Supersonic Jet Noise from a Statistical Acoustic Model and a Compressible Turbulence Closure
C Baily

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Modeling supersonic heated jet noise at fixedjetMach number using an asymptotic approach for the acoustic analogy Green’s function and an optimized turbulence model
Adrian Sescu

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In this study we show how accurate jet noise predictions can be achieved within Goldstein's generalized acoustic analogy formulation for heated and un-heated supersonic jets using a previously developed asymptotic theory for the adjoint vector Green's function and a turbulence model whose independent parameters are determined using an optimization algorithm. In this approach, mean flow non-parallelism enters the lowest order dominant balance producing enhanced amplification at low frequencies, which we believe corresponds to the peak sound at small polar observation angles. The novel aspect of this paper is that we exploit both mean flow and turbulence structure from existent Large Eddy Simulations database of two axi-symmetric round jets at fixed jet Mach number and different nozzle temperature ratios to show (broadly speaking) the efficacy of the asymptotic approach. The empirical parameters that enter via local turbulence length scales within the algebraic-exponential turbulence model are determined by optimizing against near field turbulence data post-processed from the LES calculation. Our results indicate that accurate jet noise predictions are obtained with this approach up to a Strouhal number of 0.5 for both jets without introducing significant empiricism.

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Prediction of supersonic jet noise using non-parallel flow asymptotics and LES data within Goldstein’s acoustic analogy
Adrian Sescu

2016

In this study we show how accurate jet noise predictions can be achieved within Gold-stein’s generalized acoustic analogy formulation for heated and un-heated supersonic jets using a previously developed asymptotic theory for the adjoint vector Green’s function. In this approach, mean flow non-parallelism enters the leading order dominant balance producing enhanced amplification at low frequencies, which we believe corresponds to the peak sound at small polar observation angles. We determine all relevant mean flow and turbulence quantities using Large Eddy Simulations of two axi-symmetric round jets at fixed jet Mach number and different nozzle temperature ratios. Certain empirical co-efficients that enter the turbulence length scales formula are tuned for good agreement with the far-field noise data. Our results indicate that excellent jet noise predictions are obtained using the asymptotic approach, remarkably, up to a Strouhal number of 0.5.

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Investigation of sound sources in subsonic jets using causality methods on LES data
Christophe Bogey

11th AIAA/CEAS Aeroacoustics Conference, 2005

Noise sources are investigated in subsonic jets at Mach numbers M = 0.6 and M = 0.9, with Reynolds numbers ReD = 1700 and ReD ≥ 10 5 , using data provided by Large Eddy Simulations (LES). The cross-correlations between signals of the radiated sound pressure and turbulence signals along jet axis and shear layer are in particular calculated. The normalized correlations are found to be significant, around 0.10, between the pressure radiated in the downstream direction and the centerline flow quantities. In the cases involving the sideline pressure or flow quantities along the shear layer, the correlations are much smaller. The maximum correlations are observed on the jet axis just at the end of the potential core, and fall at large emission angles. Furthermore the correlations appear to be lower as the Mach number is reduced, and to be enhanced as the Reynolds number is decreased. These correlations can be expected to be mostly due to the noise source radiating downstream, which may thus be located on the jet centerline at the end of the potential core. This flow region is moreover characterized by a dominant frequency over a large axial distance and by a high level of intermittency.

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