Using large eddy simulation to explore sound-source mechanisms in jets

This paper presents an analysis of data generated by means of large eddy simulation for a single-stream, isothermal Mach 0.9 jet. The acoustic field is decomposed into Fourier modes in the azimuthal direction, and filtered by means of a continuous wavelet transform in the temporal direction. This allows the identification of temporally localised, high-amplitude events in the radiated sound field for each of the azimuthal modes. Once these events have been localised, the flow field is analysed so as to determine their cause. Results show high-amplitude, intermittent sound radiation for azimuthal modes 0 and 1. The mode-0 radiation, which dominates low-angle emission, is found to result from the temporal modulation of a basic axisymmetric wave-packet structure within the flow. Similar intermittent activity, observed, again within the flow, for azimuthal mode 1 suggests a link between the modes 0 and 1 dynamics. Both the amplitude and spatial extent of the axisymmetric wave-packet are modulated, and the strongest axisymmetric propagative disturbances are found to radiate from the downstream end of the wave-packet at moments when the wave envelope becomes truncated. The observed behaviour is modelled using a line-source wave-packet ansatz which includes parameters that account for the said modulation. Inclusion of these parameters, which allow the wave-packet to “jitter” in a manner similar to that observed, leads to good quantitative agreement (accurate to within 1.5 dB), at low emission angles, with the acoustic field of the LES. This result is in contrast with results obtained using a time-averaged wave-packet (one which does not jitter), for which a 12 dB error is observed. This result shows that the said modulations are the salient source feature for the low-angle sound emission of the jet considered. Analysis of a longer time series shows the occurrence of several similar high-amplitude bursts in the axisymmetric mode of the acoustic pressure, and a calculation of the radiated sound for this longer time-series, again using the wave-packet ansatz, once again leads to good agreement with the LES (now accurate to within 1 dB).     

Source characterization of a subsonic jet by using near-field acoustical holography

In the present study, patch near-field acoustical holography was used in conjunction with a multireference, cross-spectral sound pressure measurement to visualize the sound field emitted by a subsonic jet and to predict its farfield radiation pattern. A strategy for microphone array design is described that accounts for the low spatial coherence of aeroacoustic sources and for microphone self-noise resulting from entrained flow near the jet. In the experiments, a 0.8-cm-diameter burner was used to produce a subsonic, turbulent jet with a Mach number of 0.26. Six fixed, linear arrays holding eight reference microphones apiece were disposed circumferentially around the jet, and a circular array holding sixteen, equally spaced field microphones was traversed along the jet axis to measure the sound field on a 30-cm-diameter cylindrical surface enclosing the jet. The results revealed that the jet could be modeled as a combination of eleven uncorrelated dipole-, quadrupole-, and octupole-like sources, and the contribution of each source type to the total radiated sound power could be identified. Both the total sound field reconstructed in a three-dimensional space and the farfield radiation directivity obtained by using the latter model were successfully validated by comparisons to directly measured results.     

Flow characteristics of the large scale wave-like structure of a supersonic round jet

A model is developed for the large scale coherent structure of subsonic and supersonic axisymmetric jets. A fluctuation in the jet flow is regarded as being separable into a time-averaged component, a periodic wave-like component and a random small scale component. The small scale fluctuation is viewed as both the driving and dissipative mechanism for the wave-like component. An energy balance model is developed which examines thinterchange of energy between the mean flow and the large scale motion. The effect of wave-like fluctuation amplitude on its own and the mean flow development is examined. Calculations of contours of equal pressure level in the jet near field are made. A model for the mechanism by which locally subsonic components of the wave-like structure may radiate noise to the far field is examined. The method for calculating the radiated noise is discussed.     

An experimental study of jet noise part II: Shock associated noise

The characteristics of the sound field of shock-containing under-expanded jet flows are studied by measuring the noise from a convergent nozzle operated over an extensive envelope of supercritical jet operating conditions. The measurements were conducted in an anechoic facility. They are complementary to the turbulent mixing noise experiments (described in Part I) for subsonic and fully-expanded (shock-free) supersonic jets. The overall results from shock-containing jets are compared directly with the corresponding results from shock-free jets, and the effects of nozzle pressure ratio and jet exhaust temperature on broadband shock-associated noise are assessed independently. For a supersonic jet, the regimes of jet operating conditions, observer angles, and frequencies over which the sound field is dominated by shock-associated noise are identified. Finally, the spectral results are compared in a preliminary manner with the spectra predicted by an existing theoretical model, and good agreement is obtained in most cases.     

Scattering of wavepackets by a flat plate in the vicinity of a turbulent jet

We present an investigation of the acoustic scattering due to the presence of a flat plate in the vicinity of a turbulent subsonic jet. Experiments have been performed to measure changes in the velocity and sound fields for Mach numbers ranging from 0.4 to 0.6, and for distances between the plate and the jet axis ranging from 1 to 2 jet diameters. Results show only very slight changes in the mean flow induced by the plate, and no differences in the velocity fluctuation amplitudes on the jet centreline, suggesting that wave-packet models derived for jets without installation effects may be representative of the installed case, at least for the jet–plate distances considered here. The acoustic results, on the other hand, include a significant increase in the low-frequency sound radiation, and phase opposition between the shielded and unshielded sides of the plate. There is an exponential decay of the scattered sound with increasing jet–plate distance, suggesting that low-frequency radiation is due to the scattering of evanescent hydrodynamic wavepackets in the jet near field. To model this phenomenon, we calculate sound generation from wave-packet sources in two ways: on one hand we use a tailored Green?s function that accounts for the presence of a semi-infinite, rigid flat plate; and, on the other, we solve numerically the Helmholtz equation, with boundary conditions representative of a finite flat plate, using a fast multipole boundary element method. In agreement with the experimental measurements, numerical calculations capture the phase opposition between shielded and unshielded sides, and the scattered sound depends exponentially on the position of the plate. This exponential dependence is related to non-compact effects associated with wavepackets, as compact sources would lead to an algebraic dependence. Acoustic pressure directivities computed for the finite and semi-infinite flat plates agree well where acoustic reflection and diffraction from the trailing edge of the plates are concerned. However, additional diffraction effects associated with the leading and lateral edges of the finite plate, and which take the form of multiple lobes in the directivity, are illustrated by the comparison. As the plate dimensions are increased, i.e. the Helmholtz number is increased, the solution approaches that obtained for the semi-infinite plate.     

Sound radiation from point sources in circular motion

The moving-source approach used by Morfey and Tanna for broad-band sound radiation from a point force in circular motion is adopted in this paper to evaluate the sound radiated in the far field due to point sources of random time variation rotating uniformly in a circle at subsonic speed. It is shown that the sound pressure results (overall and spectral density) for the volume velocity source can be easily extracted from the corresponding results for a rotating point force. An expression for the sound field of a point volume displacement source in arbitrary motion is derived and this is applied to the special case of uniform circular motion. The effects of acceleration of the sources due to circular motion on the radiated sound are established. Applications include noise from tip jet rotors, compressors and marine propellers.     

The distribution of headways in traffic noise simulation

In recent years researchers in jet turbulence and jet noise have become increasingly interested in what is termed “large scale coherent jet structures”. There is now considerable evidence that azimuthally coherent structures can be generated by acoustically forcing a jet from upstream. However, the evidence for such structures in unforced jets, except close to the nozzle at low Reynolds numbers, is, at best, circumstantial. The role of such structures in subsonic jet noise production is also completely unproven. In an attempt to establish a link between azimuthally coherent structures and the jet noise field a number of experimenters have recently made azimuthal cross-correlation measurements of either the near field pressure or far field noise, and used the observed coherence to infer the existence of an azimuthally coherent source field. The term azimuthally coherent is used here to infer that the source region is dominated by low order azimuthal components, with relatively little contribution coming from the higher azimuthal components. The purpose of this paper is to question the interpretation of that data. Specifically the sound field generated by a simple ring source with various types of azimuthal coherence is considered theoretically. It is shown that the azimuthal coherence of both the near and far field pressures is principally a function of the Helmholtz number and in many cases of practical interest is relatively insensitive to any coherent structure of the source.     

Noise generation by instabilities in low Reynolds number supersonic jets

An experimental investigation of noise generation by instabilities in low Reynolds number supersonic air jets has been performed. Sound pressure levels, spectra and acoustic phase fronts were measured with a traversing condenser microphone in the acoustic field of axisymmetric, perfectly expanded, cold jets of Mach numbers 1·4, 2·1 and 2·5. Low Reynolds numbers in the range from Re = 3700 to Re = 8700 were obtained by exhausting the jets into an anechoic vacuum chamber test facility. This contrasts with Reynolds numbers of over 10⁶ for similar jets exhausting into atmospheric pressure. The flow fluctuations of the instability in all three jets have been measured with a hot-wire and the results are documented in a previous paper by Morrison and McLaughlin. Acoustic measurements show that the major portion of the sound radiated by all three jets is produced by the instability's rapid growth and decay that occurs near the end of the potential core. This takes place over a relatively short distance (less than two wavelengths of the instability) in the jet. In the lower two Mach number jets the instability has a phase velocity less than the ambient acoustic velocity. In the Mach number 2·5 jet the instability phase speed is 1·11 times the ambient acoustic velocity. In this case the acoustic phase fronts indicate the possibility of a Mach wave component. It was also determined that low level excitation at the dominant frequency of the instability actually decreased the radiated noise by suppressing the broad band component.     

Turbulence and heat excited noise sources in single and coaxial jets

The generation of noise in subsonic high Reynolds number single and coaxial turbulent jets is analyzed by a hybrid method. The computational approach is based on large-eddy simulations (LES) and solutions of the acoustic perturbation equations (APE). The method is used to investigate the acoustic fields of one isothermal single stream jet at a Mach number 0.9 and a Reynolds number 400,000 based on the nozzle diameter and two coaxial jets whose Mach number and Reynolds number based on the secondary jet match the values of the single jet. One coaxial jet configuration possesses a cold primary flow, whereas the other configuration has a hot primary jet. Thus, the configurations allow in a first step the analysis of the relationship of the flow and acoustic fields of a single and a cold coaxial jet and in a second step the investigation of the differences of the fluid mechanics and aeroacoustics of cold and hot coaxial jets. For the isothermal single jet the present hybrid acoustic computation shows convincing agreement with the direct acoustic simulation based on large-eddy simulations. The analysis of the acoustic field of the coaxial jets focuses on two noise sources, the Lamb vector fluctuations and the entropy sources of the APE equations. The power spectral density (PSD) distributions evidence the Lamb vector fluctuations to represent the major acoustic sources of the isothermal jet. Especially the typical downstream and sideline acoustic generations occur on a cone-like surface being wrapped around the end of the potential core. Furthermore, when the coaxial jet possesses a hot primary jet, the acoustic core being characterized by the entropy source terms increases the low frequency acoustics by up to 5 dB, i.e., the sideline acoustics is enhanced by the pronounced temperature gradient.     

On the Mach number and temperature dependence of jet noise: Results from a simplified numerical model

Numerical simulations of sound radiation from perturbed round jets are used, firstly to explore the structure of the sound sources and then to carry out a parametric study of the effect of jet Mach number and jet temperature. The simplified model problem includes a steady base jet flow, maintained in the absence of disturbances, superimposed with instability waves that are free to interact nonlinearly. Simulations over a range of subsonic jet Mach numbers show that a nonlinear mechanism dominates over a linear mechanism for low-frequency sound radiation, while for supersonic Mach numbers the linear mechanism is dominant. Additional insight is gained from a frequency-wavenumber analysis, including a transformation in the radial direction. With this decomposition, the acoustic field is located by the arc of a circle in plots of radial against streamwise wavenumber for discrete frequencies. The transformation is applied to both the pressure field, showing the sound directivity, and to selected source terms, showing characteristic directivity patterns for the streamwise and radial quadrupole terms. Decreasing the Mach number leads to a reduction in amplitude of the sources and of the sound radiation. Simulations with broadband forcing show that the qualitative effects of Mach number and jet heating are captured by this approach, which requires less resolution than a direct numerical simulation. A significant increase in the strength of the acoustic radiation for cold jets is observed, which is worthy of further investigation.     

Acoustic characteristics of interacting supersonic jets

This study was intended primarily to reveal more information about the noise producing mechanisms of supersonic jets. Two identical, small, cold air, supersonic, overexpanded jets were tested at selected angles, varying from parallel to 90 degrees intersecting, and at various distances apart. Schlieren photographs of the jet structure and far field sound data were obtained. Close spacing of the parallel jets caused acoustic attenuation, which reached a maximum at one diameter centerline spacing, where the sound of two jets nearly equals that of a single jet. In every case the intersecting jets merged into a single supersonic jet.The overall sound power level of intersecting jets is generally higher than that of two independent jets, because of the turbulent mixing of the two jet flows. A maximum level is reached when the jets intersect at a point near the middle of the flow region containing repetitive shocks. For the parallel jets and intersecting jets at large separation, the sound levels are lower in the plane containing the jet centerlines. For intersecting jets at small separation, however, this shielding effect is reversed.     

Analysis of the radiated information in spinning sound fields

The information content of a spinning sound field is analyzed using a combination of exact and asymptotic results, in order to set limits on how accurately source identification can be carried out. Using a transformation of the circular source to an exactly equivalent set of line source modes, given by Chebyshev polynomials, it is found that the line source modes of order greater than the source wavenumber generate exponentially small fields. Asymptotic analysis shows that the remaining, lower order, modes radiate efficiently only into a region around the source plane, with this region shrinking as the mode order is increased. The results explain the ill-conditioning of source identification methods; the successful use of low order models in active noise control; and the low radiation efficiency of subsonic jets.     

Developments in jet noise modelling—theoretical predictions and comparisons with measured data

Spectral information on the sound radiated from turbulent shock-free jets is now available over a wide range of Strouhal numbers, for jet densities ranging from 0·3 to 2 times the ambient density and jet velocities ranging from 0·3 to 2 times the ambient sound speed. In order to account for some of the trends observed, a jet noise model is developed which takes account of acoustic-mean flow interaction. The model is based on a shear flow analogy, for which the governing equation is Lilley's equation, and numerical solutions are obtained for sources representative of turbulent mixing noise. Analytic solutions developed for low- and high-frequency excitation show good agreement with the numerical results. Finally, the model predictions are compared with measurements on hot and isothermal jets.     

Broadband sound generation by confined turbulent jets

Sound generation by confined stationary jets is of interest to the study of voice and speech production, among other applications. The generation of sound by low Mach number, confined, stationary circular jets was investigated. Experiments were performed using a quiet flow supply, muffler-terminated rigid uniform tubes, and acrylic orifice plates. A spectral decomposition method based on a linear source-filter model was used to decompose radiated nondimensional sound pressure spectra measured for various gas mixtures and mean flow velocities into the product of (1) a source spectral distribution function; (2) a function accounting for near field effects and radiation efficiency; and (3) an acoustic frequency response function. The acoustic frequency response function agreed, as expected, with the transfer function between the radiated acoustic pressure at one fixed location and the strength of an equivalent velocity source located at the orifice. The radiation efficiency function indicated a radiation efficiency of the order (kD)2 over the planar wave frequency range and (kD)4 at higher frequencies, where k is the wavenumber and D is the tube cross sectional dimension. This is consistent with theoretical predictions for the planar wave radiation efficiency of quadrupole sources in uniform rigid anechoic tubes. The effects of the Reynolds number, Re, on the source spectral distribution function were found to be insignificant over the range 20002.5. The influence of a reflective open tube termination on the source function spectral distribution was found to be insignificant, confirming the absence of a feedback mechanism.     

Noise Prediction in Subsonic Flow Using Seventh-Order Dissipative Compact Scheme on Curvilinear Mesh

In this paper, we investigate the performance of the seventh-order hybrid cell-edge and cell-node dissipative compact scheme (HDCS-E8T7) on curvilinear mesh for noise prediction in subsonic flow. In order to eliminate the errors due to surface conservation law (SCL) is dissatisfied with curvilinear meshes, the symmetrical conservative metric method (SCMM) is adopted to calculate the grid metric derivatives for the HDCS-E8T7. For the simulation of turbulence flow which may have main responsibility for the noise radiation, the new high-order implicit large eddy simulation (HILES) based on the HDCS-E8T7 is employed. Three typical cases, i.e., scattering of acoustic waves by multiple cylinder, sound radiated from a rod-airfoil and subsonic jet noise from nozzle, are chosen to investigate the performance of the new scheme for predicting aeroacoustic problem. The results of scattering of acoustic waves by multiple cylinder indicate that the HDCS-E8T7 satisfying the SCL has high resolution for the aeroacoustic prediction. The potential of the HDCS-E8T7 for aeroacoustic problems on complex geometry is shown by the predicting sound radiated from a rod-airfoil configuration. Moreover, the subsonic jet noise from nozzle has been successfully predicted by the HDCS-E8T7.     

旋流燃烧室内同向和反向旋转射流湍流流动的数值模拟

针对发展高效低污染旋流燃烧技术的需要,对旋流燃烧室内两股同轴旋转射流相互作用的湍流旋流流动进行了数值模拟.计算中采用了一种新的代数Reynolds应力模型和QUICK离散格式.在两股射流同向旋转和反向旋转两种条件下,将模拟得到的燃烧室内湍流旋流流动的时均气体轴向速度场、切向速度场和静压场与实验数据进行了比较.     

Direct computation and aeroacoustic modelling of a subsonic axisymmetric jet

A numerical algorithm for acoustic noise predictions based on solving Lilley's third order wave equation in the time-space domain is developed for a subsonic axisymmetric jet. The sound field is simulated simultaneously with the source field calculation, which is based on a direct solution of the compressible Navier-Stokes equations. The computational domain includes both the nearfield and a portion of the acoustic farfield. In the simulation, the detailed sound source structure is provided by the nearfield direct numerical simulation (DNS), while the sound field is obtained from both the DNS and the numerical solution to the non-linear Lilley's equation. The source terms of Lilley's equation are used to identify the apparent sound source locations in the idealized axisymmetric low-Reynolds number jet. The sound field is mainly discussed in terms of instantaneous pressure fluctuations, frequency spectra, acoustic intensity and directivity. A good agreement is found between the predictions from the axisymmetric Lilley's equation and the DNS results for the sound field. Limitations and perspectives of the simulation are also discussed.     

Experimental investigation of an inversion technique for the determination of broadband duct mode amplitudes by the use of near-field sensor arrays

This paper is an experimental investigation of an inverse technique for deducing the amplitudes of the modes radiated from a turbofan engine, including schemes for stablizing the solution. The detection of broadband modes generated by a laboratory-scaled fan inlet is performed using a near-field array of microphones arranged in a geodesic geometry. This array geometry is shown to allow a robust and accurate modal inversion. The sound power radiated from the fan inlet and the coherence function between different modal amplitudes are also presented. The knowledge of such modal content is useful in helping to characterize the source mechanisms of fan broadband noise generation, for determining the most appropriate mode distribution model for duct liner predictions, and for making sound power measurements of the radiated sound field.     

Imaging of directional distributed noise sources

This study relates to the acoustic imaging of noise sources that are distributed and strongly directional, such as in turbulent jets. The goal is to generate high-resolution noise source maps with self-consistency, i.e., their integration over the extent of the noise source region gives the far-field pressure auto-spectrum for a particular emission direction. Self-consistency is possible by including a directivity factor in the formulation of the source cross-spectral density. The resulting source distribution is based on the complex coherence, rather than the cross-spectrum, of the measured acoustic field. For jet noise, whose spectral nature changes with emission angle, it is necessary to conduct the measurements with a narrow-aperture array. Three coherence-based imaging methods were applied to a Mach 0.9 turbulent jet: delay-and-sum beamforming; deconvolution of the beamformer output; and direct spectral estimation that relies on minimizing the difference between the measured and modeled coherences of the acoustic field. The delay-and-sum beamforming generates noise source maps with strong spatial distortions and sidelobes. Deconvolution leads to a five-fold improvement in spatial resolution and significantly reduces the intensity of the sidelobes. The direct spectral estimation produces maps very similar to those obtained by deconvolution. The coherence-based noise source maps, obtained by deconvolution or direct spectral estimation, are similar at small and large observation angles relative to the jet axis.