Progress on Green's Function Calculations for Non-Axisymmetric Jets

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Emission of Sound From Turbulence Convected by a Parallel Mean Flow in the Presence of a Confining Duct

An approximate method for calculating the noise generated by a turbulent flow within a semi-infinite duct of arbitrary cross section is developed. It is based on a previously derived high-frequency solution to Lilley's equation, which describes the sound propagation in transversely-sheared mean flow. The source term is simplified by assuming the turbulence to be axisymmetric about the mean flow direction. Numerical results are presented for the special case of a ring source in a circular duct with an axisymmetric mean flow. They show that the internally generated noise is suppressed at sufficiently large upstream angles in a hard walled duct, and that acoustic liners can significantly reduce the sound radiated in both the upstream and downstream regions, depending upon the source location and Mach number of the flow

Modeling and Prediction of the Noise from Non-Axisymmetric Jets

The new source model was combined with the original sound propagation model developed for rectangular jets to produce a new version of the rectangular jet noise prediction code. This code was validated using a set of rectangular nozzles whose geometries were specified by NASA. Nozzles of aspect ratios two, four and eight were studied at jet exit Mach numbers of 0.5, 0.7 and 0.9, for a total of nine cases. Reynolds-averaged Navier-Stokes solutions for these jets were provided to the contactor for use as input to the code. Quantitative comparisons of the predicted azimuthal and polar directivity of the acoustic spectrum were made with experimental data provided by NASA. The results of these comparisons, along with a documentation of the propagation and source models, were reported in a journal article publication (Ref. 4). The complete set of computer codes and computational modules that make up the prediction scheme, along with a user's guide describing their use and example test cases, was provided to NASA as a deliverable of this task. The use of conformal mapping, along with simplified modeling of the mean flow field, for noise propagation modeling was explored for other nozzle geometries, to support the task milestone of developing methods which are applicable to other geometries and flow conditions of interest to NASA. A model to represent twin round jets using this approach was formulated and implemented. A general approach to solving the equations governing sound propagation in a locally parallel nonaxisymmetric jet was developed and implemented, in aid of the tasks and milestones charged with selecting more exact numerical methods for modeling sound propagation, and developing methods that have application to other nozzle geometries. The method is based on expansion of both the mean-flowdependent coefficients in the governing equation and the Green's function in series of orthogonal functions. The method was coded and tested on two analytically prescribed mean flows which were meant to represent noise reduction concepts being considered by NASA. Testing (Ref. 5) showed that the method was feasible for the types of mean flows of interest in jet noise applications. Subsequently, this method was further developed to allow use of mean flow profiles obtained from a Reynolds-averaged Navier-Stokes (RANS) solution of the flow. Preliminary testing of the generalized code was among the last tasks completed under this contract. The stringent noise-reduction goals of NASA's Fundamental Aeronautics Program suggest that, in addition to potentially complex exhaust nozzle geometries, next generation aircraft will also involve tighter integration of the engine with the airframe. Therefore, noise generated and propagated by jet flows in the vicinity of solid surfaces is expected to be quite significant, and reduced-order noise prediction tools will be needed that can deal with such geometries. One important source of noise is that generated by the interaction of a turbulent jet with the edge of a solid surface (edge noise). Such noise is generated, for example, by the passing of the engine exhaust over a shielding surface, such as a wing. Work under this task supported an effort to develop a RANS-based prediction code for edge noise based on an extension of the classical Rapid Distortion Theory (RDT) to transversely sheared base flows (Refs. 6 and 7). The RDT-based theoretical analysis was applied to the generic problem of a turbulent jet interacting with the trailing edge of a flat plate. A code was written to evaluate the formula derived for the spectrum of the noise produced by this interaction and results were compared with data taken at NASA Glenn for a variety of jet/plate configurations and flow conditions (Ref. 8). A longer-term goal of this task was to work toward the development of a high-fidelity model of sound propagation in spatially developing non-axisymmetric jets using direct numerical methods for solving the relevant equations. Working with NASA Glenn Acoustics Branch personnel, numerical methods and boundary conditions appropriate for use in a high-resolution calculation of the full equations governing sound propagation in a steady base flow were identified. Computer codes were then written (by NASA) and tested (by OAI) for an increasingly complex set of flow conditions to validate the methods. The NASA-supplied codes were ported to the High-End Computing resources of the NASA Advanced Supercomputing facility for testing and validation against analytical (where possible) and independent numerical solutions. The cases which were completed during the course of this contract were solutions of the two-dimensional linearized Euler equations with no mean flow, a uniform mean flow and a nonuniform mean flow representative of a parallel flow jet

Measurements and Predictions of the Noise from Three-Stream Jets

An experimental and numerical investigation of the noise produced by high-subsonic and supersonic three-stream jets was conducted. The exhaust system consisted of externally-mixed-convergent nozzles and an external plug. Bypass- and tertiary-to-core area ratios between 1.0 and 2.5, and 0.4 and 1.0, respectively, were studied. Axisymmetric and offset tertiary nozzles were investigated for heated and unheated conditions. For axisymmetric configurations, the addition of the third stream was found to reduce peak- and high-frequency acoustic levels in the peak-jet-noise direction, with greater reductions at the lower bypass-to-core area ratios. For the offset configurations, an offset duct was found to decrease acoustic levels on the thick side of the tertiary nozzle relative to those produced by the simulated two-stream jet with up to 8 dB mid-frequency noise reduction at large angles to the jet inlet axis. Noise reduction in the peak-jet-noise direction was greater for supersonic core speeds than for subsonic core speeds. The addition of a tertiary nozzle insert used to divert the third-stream jet to one side of the nozzle system provided no noise reduction. Noise predictions are presented for selected cases using a method based on an acoustic analogy with mean flow interaction effects accounted for using a Green's function, computed in terms of its coupled azimuthal modes for the offset cases, and a source model previously used for round and rectangular jets. Comparisons of the prediction results with data show that the noise model predicts the observed increase in low-frequency noise with the introduction of a third, axisymmetric stream, but not the high-frequency reduction. For an offset third stream, the model predicts the observed trend of decreased sound levels on the thick side of the jet compared with the thin side, but the predicted azimuthal variations are much less than those seen in the data. Also, the shift of the spectral peak to lower frequencies with increasing polar angle is over-predicted. For an offset third stream with a heated core, it is shown that including the enthalpy-flux source terms in the acoustic analogy model improves predictions compared with those obtained using only the momentum flux

Measurements and Predictions of the Noise from Three-Stream Jets

An experimental and numerical investigation of the noise produced by high-subsonic and supersonic three-stream jets was conducted. The exhaust system consisted of externally-mixed-convergent nozzles and an external plug. Bypass- and tertiary- to-core area ratios between 1.0 and 2.5, and 0.4 and 1.0, respectively, were studied. Axisymmetric and offset tertiary nozzles were investigated for heated and unheated conditions. For axisymmetric configurations, the addition of the third stream was found to reduce peak- and high-frequency acoustic levels in the peak-jet-noise direction, with greater reductions at the lower bypass-to-core area ratios. For the offset configurations, an offset duct was found to decrease acoustic levels on the thick side of the tertiary nozzle relative to those produced by the simulated two-stream jet with up to 8 dB mid-frequency noise reduction at large angles to the jet inlet axis. Noise reduction in the peak-jet-noise direction was greater for supersonic core speeds than for subsonic core speeds. The addition of a tertiary nozzle insert used to divert the third-stream jet to one side of the nozzle system provided no noise reduction. Noise predictions are presented for selected cases using a method based on an acoustic analogy with mean flow interaction effects accounted for using a Green's function, computed in terms of its coupled azimuthal modes for the offset cases, and a source model previously used for round and rectangular jets. Comparisons of the prediction results with data show that the noise model predicts the observed increase in low-frequency noise with the introduction of a third, axisymmetric stream, but not the high-frequency reduction. For an offset third stream, the model predicts the observed trend of decreased sound levels on the thick side of the jet compared with the thin side, but the predicted azimuthal variations are much less than those seen in the data. Also, the shift of the spectral peak to lower frequencies with increasing polar angle is over-predicted. For an offset third stream with a heated core, it is shown that including the enthalpy-flux source terms in the acoustic analogy model improves predictions compared with those obtained using only the momentum- flux

Structure of the Small Amplitude Motion on Transversely Sheared Mean Flows

This paper considers the small amplitude unsteady motion of an inviscid non-heat conducting compressible fluid on a transversely sheared mean flow. It extends a previous result given in Goldstein (1978(b) and 1979(a)) which shows that the hydrodynamic component of the motion is determined by two arbitrary convected quantities in the absence of solid surfaces or other external sources. The result is important because it can be used to specify appropriate boundary conditions for unsteady surface interaction problems on transversely sheared mean flows in the same way that the vortical component of the Kovasznay (1953) decomposition is used to specify these conditions for surface interaction problems on uniform mean flows. But unlike the Kovasznay (1953) case the arbitrary convected quantities no longer bear a simple relation to the physical variables. One purpose of this paper is to derive a formula that relates these quantities to the (physically measurable) vorticity and pressure fluctuations in the flow

Assessment of Mixer-Ejector Nozzle with Thermal Acoustic Shield for Jet Noise Reduction

A tendency for excessive exhaust jet mixing noise from low bypass ratio turbofan engines is recognized as a key challenge in the design of commercial supersonic aircraft. In this work we investigate a unique combination of two noise mitigation methods as a novel strategy to reduce jet mixing noise. First, a thermal acoustic shield (TAS) is used to reflect high frequency acoustic waves at small angles to the jet axis; second, a mixer-ejector (ME) nozzle is used to mechanically shield noise propagating at large angles to the axis. The ME shroud also provides a convenient location for a TAS nozzle and improves TAS effectiveness by limiting the downstream extent of high frequency noise generation. In an additional benefit for a velocity-matched TAS stream, the ME allows a reduction in strength of the TAS outer shear layer which could serve as a secondary noise source. The present work provides a quantitative assessment of the ME-TAS concept, using a combination of RANS CFD simulations, acoustic analogy calculations for the farfield Green's function, and surrogate-based modeling and parameter space exploration. We first evaluate a subscale configuration, then use scaling arguments to apply subscale results to the systems-level analysis of a flight configuration; the latter configuration includes a generic low bypass ratio turbofan engine with an engine-driven electric generator for supplementary heating of the TAS stream. Additional RANS CFD calculations are performed for a notional ME-TAS geometry based on the full scale configuration, and various modeling assumptions and operational characteristics are evaluated. The ME-TAS concept is shown to provide effective shielding for high frequency jet noise, and should enable comparable noise suppression to a stand-alone ME of considerably greater length, weight and drag. In addition to investigating the integrated ME-TAS system, the present work differs from previous research into TAS and related fluidic shield concepts through the inclusion of modern numerical analysis tools and the systematic numerical examination of various design parameters

Modelling and prediction of the peak- radiated sound in subsonic axisymmetric air jets using acoustic analogy-based asymptotic analysis.

This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein 2003 JFM 488, 315–333. (doi:10.1017/S0022112003004890)) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (Ma). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low-frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation. We then address the predictive capability of the solution to this partial differential equation when used in the analogy through first-of-its-kind numerical calculations when an experimentally verified model of the turbulence source structure is used together with Reynolds-averaged Navier–Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at Ma = 0.9, for Strouhal numbers up to about 0.6, and at Ma = 0.5 using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 90° observation angle, the low-frequency noise could be as much as 10 dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green’s function. A low-frequency asymptotic approximation for the Green’s function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite decorrelation region. Numerical predictions of the sound field, based on three-dimensional RANS solutions to determine the mean flow, turbulent kinetic energy and turbulence length and time scales, for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region in the turbulence spectrum increases the low-frequency algebraic decay (the low frequency “roll-off”) of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspect-ratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties

Structure of the Small Amplitude Motion on Transversely Sheared Mean Flows.

This paper considers the small amplitude unsteady motion of an inviscid non-heat conducting compressible fluid on a transversely sheared mean flow. It extends a previous result given in Goldstein (1978(b) and 1979(a)) which shows that the hydrodynamic component of the motion is determined by two arbitrary convected quantities in the absence of solid surfaces or other external sources. The result is important because it can be used to specify appropriate boundary conditions for unsteady surface interaction problems on transversely sheared mean flows in the same way that the vortical component of the Kovasznay (1953) decomposition is used to specify these conditions for surface interaction problems on uniform mean flows. But unlike the Kovasznay (1953) case the arbitrary convected quantities no longer bear a simple relation to the physical variables. One purpose of this paper is to derive a formula that relates these quantities to the (physically measurable) vorticity and pressure fluctuations in the flow