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Turbulent jet flows at the Mach number equal to 0.25 from an industrial nozzle are studied using the large eddy simulation (LES). The feasibility of controlling the jet flow and noise by using chevrons is explored. A comparative study is carried out between the baseline and chevrons nozzles with the focus paid to the influences of the chevrons on the flow mixing and noise. The results show that the chevrons can significantly change the flow field. Especially the jet potential core length is reduced. In addition, the contours of velocity in the cross sections of the jet change from circular into daisy shaped structures by the chevrons. Flow visualization using the vorticity and the Q criterion shows that large vortical structures in the shear layer are fragmented into small-scale eddies. Meanwhile, the sound pressure level of the jet noises is weakened by chevrons.

Broadband shock-associated noise (BBSAN) is an important component of supersonic jet noise for jets at off-design conditions when the pressure at the nozzle exit is different from the ambient. Two high-area-ratio under-expanded supersonic jets at nozzle pressure ratios (NPRs) 3.4 and 4.2 are considered. The jets correspond to conditions of the experiment in the Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC) in the Supersonic Jet Facility of Monash University. Flow solutions are obtained by the large eddy simulation (LES) and Reynolds averaged Navier–Stokes (RANS) methods. The solutions are validated against the particle image velocimetry (PIV) data. For noise spectra predictions, the LES solution is combined with the time-domain Ffowcs Williams–Hawkings method. To probe the accuracy of the reduced-order method based on acoustic analogy, the RANS solutions are substituted in the Morris and Miller BBSAN method, where different options for modelling of the acoustic correlation scales are investigated. The noise spectra predictions are compared with the experimental data from the non-anechoic LTRAC facility and the NASA empirical sJet model. Apart from the low frequencies influenced by the jet mixing noise, the RANS-based acoustic predictions align with those from LES for most frequencies in the range of Strouhal numbers (St) 0.4 < St < 2 within 1–2 dB.

This paper aims to study the microjet’s efficacy as a management tool for the duct’s flow field. The nozzle was correctly expanded for a diameter ratio of 1.6 (i.e., area ratio = 2.56). The Mach numbers considered were from 1.25 to 2. The investigation shows that the development and recovery of the duct flow are smooth at lower Mach numbers. At Mach 1.48, jet noise was reduced considerably when the control is initiated. For higher Mach numbers of the study, namely Mach 1.6, 1.8, and 2.0, the flow’s oscillatory nature was noticed. This phenomenon reiterates that the nozzles flow is wave-dominated. For most of the flow, the flowing nature remains unaltered due to control. The flow remained connected with the duct for duct length twice the nozzle exit diameter.

The directivity of noise from three large-eddy simulations of turbulent jets at Mach 0.7, 0.9, and 1.5 is investigated using spectral proper orthogonal decomposition (SPOD). The most energetic patt...

International audience; Acoustic measurements of unheated supersonic underexpanded jets with ideally-expanded Mach numbers of 1.14, 1.38 and 1.50 are presented. Of the three components of supersonic jet noise, the focus is on the broadband shock-associated noise (BBSAN) component. Motivated by the modelling of BBSAN using the wavepacket framework, a traversable microphone ring is used to decompose the acoustic pressure into azimuthal Fourier modes. Unlike noise radiated downstream, BBSAN is dominated by azimuthal modes 1 through 3 which are approximately 3-4dB/St stronger than the axisymmetric component. Crucially, the relative contribution of successive modes to BBSAN is sensitive to observer angle and jet operating condition. Four azimuthal modes are necessary to reconstruct the total BBSAN signal to within 1dB/St accuracy for the conditions presented here. The analysis suggests, however, that the number of modes required to maintain this accuracy increases as the peak frequency shifts upward. The results demonstrate the need to carefully consider the azimuthal content of BBSAN when comparing acoustic measurements to predictions made by jet noise models built on instability theory.

Measurements of full-scale high-performance military aircraft reveal phenomena that are not widely seen at laboratory scales. However, recent modifications to large eddy-simulation (LES) methods al...

Aeroacoustic analyses of jet flows have benefited greatly from a decomposition of turbulent pressure fluctuations into hydrodynamic and acoustic components. This is typically accomplished using signal processing techniques based on phase speeds, coherence properties or spectral analyses. We present an approach, building on the Momentum Potential Theory (MPT) approach of (Doak, 1989), to split pressure fluctuations into their hydrodynamic, acoustic and entropic, collectively designated fluid-thermodynamic (FT), components. Key advantages are that the approach is applicable everywhere in the jet i.e, not restricted to the near-acoustic field, and does not need user-defined thresholds. The effectiveness of the technique is demonstrated by analyzing the flowfields of three simulated jets, to encompass moderate-compressible to supersonic conditions. The statistical properties and wavepacket dynamics of each pressure component, and their relationships with the unsplit pressure are elaborated. The acoustic pressure field has the form of a wavepacket that attenuates downstream and whose modal analysis reveals low-rank behavior. At each Mach number examined, the acoustic pressure also identifies the relative prominence of each of three components: i) waves with upstream propagating energy content (negative group velocity), ii) supersonically traveling radiating downstream waves, and iii) subsonically convected evanescent waves, which follow the convection pattern of hydrodynamic eddies in the turbulent region. With increasing Mach number, the radiating and convected bands of energy move closer to each other. The hydrodynamic pressure also displays a wavepacket structure, but its features are different: it displays large-scale subsonically convected structures even past the core collapse region. Thus, in the turbulent region of the jet, the acoustic pressure displays smaller integral time scales of fluctuations than the hydrodynamic component. The acoustic pressure field, which includes a zero-crossing in its radial profiles, displays larger wavelengths than the hydrodynamic pressure field, correlates better with the near-field pressure signal and captures the radiated component of noise, especially at shallow angles. These properties make it a suitable field for informing pressure-based wavepacket models for jet noise.

The current state of the use of large-eddy simulations (LESs) in jet aeroacoustics is reviewed. Various computational techniques are discussed, as well as methods to extend the LES results to the a...

An experimental study is conducted on unsteady pressure fluctuations occurring near the nozzle exit and just outside the shear layer of compressible jets. These fluctuations are related to ‘trapped waves’ within the jet's potential core, as investigated and reported recently by other researchers. Round nozzles of three different diameters and rectangular nozzles of various aspect ratios are studied. The fluctuations manifest as a series of peaks in the spectra of the fluctuating pressure. Usually the first peak at the lowest frequency (fundamental) has the highest amplitude and the amplitude decreases progressively for successive peaks at higher frequencies. These ‘trapped wave spectral peaks’ are found to occur with all jets at high subsonic conditions and persist into the supersonic regime. Their characteristics and variations with axial and radial distances, jet Mach number and aspect ratio of the nozzle are documented. For round nozzles, the frequency of the fundamental is found to be independent of the jet's exit boundary layer characteristics and scales with the nozzle diameter. On a Strouhal number (based on diameter) versus jet Mach number plot it is represented by a unique curve. Relative to the fundamental the frequencies of the successive peaks are found to bear the ratios of 5/3, 7/3, 9/3 and so on, at a given Mach number. For rectangular nozzles, the number of peaks observed on the major axis is found to be greater than that observed on the minor axis by a factor approximately equal to the nozzle's aspect ratio; the fundamental is the same on either edge. For all nozzles the onset of screech tones appears as a continuation of the evolution of these peaks; it is as if one of these peaks abruptly increases in amplitude and turns into a screech tone as the jet Mach number is increased.

A quantitative assessment of the acoustic source field produced by a laboratory-scale heated jet with a gas dynamic Mach number of 1.55 and an acoustic Mach number of 2.41 is performed using arrays of microphones that are traversed across the axial and radial plane of the jet's acoustic field. The nozzle contour comprises a method of characteristics shape so that shock-related noise is minimal and the dominant sound production mechanism is from Mach waves. The spatial topography of the overall sound pressure level is shown to be dominated by a distinct lobe residing on the principal acoustic emission path, which is expected from flows of this kind with supersonic convective acoustic Mach numbers. The sound field is then analysed on a per-frequency basis in order to identify the location, strength, convection velocity and propagation angle of the various axially distributed noise sources. The analysis reveals a collection of unique data-informed polar patterns of the sound intensity for each frequency. It is shown how these polar patterns can be propagated to any point in the far field with extreme accuracy using the inverse square law. Doing so allows one to gauge the kinds of errors that are encountered using a nozzle-centred source to calculate sound pressure spectrum levels and acoustic power. It is proposed that the measurement strategy described here be used for situations where measurements are being used to compare different facilities, for extrapolating measurements to different geometric scales, for model validation or for developing noise control strategies.

A model-scale experimental investigation of an installed jet–pylon–wing configuration was conducted at the University of Southampton, with the scope to study the effect a pylon has on noise generation and to clarify its impact on the fluctuating wall-pressure load. The set-up consisted of two single-stream nozzles, a baseline axisymmetric annular nozzle and a partially blocked annular pylon nozzle. The nozzles were tested first isolated and then installed next to a NACA4415 aerofoil ‘wing’ at a single nozzle–wing position. The jet Mach number was varied between $0.5 \leq M_{{j}} \leq 0.8$ and measurements were performed both under static and in-flight ambient flow conditions up to ${M_{{f}} = 0.2}$ . The jet flow-field qualification was carried out using a single-velocity-component hot-wire anemometer probe. The pressure field on the wing surface was investigated using two miniature wall-pressure transducers that were flush-mounted in the streamwise and spanwise directions within the pressure side of the wing. A linear ‘flyover’ microphone array was used to record the noise radiated to the far field. The unsteady pressure data were analysed in both time and frequency domains using multi-variate statistics, highlighting a far-field noise reduction provided by the presence of the pylon only in the installed case. Furthermore, the wake field generated behind the pylon is seen to significantly modify the wall-pressure fluctuations, particularly at streamwise locations close to the pylon trailing edge.

We study a turbulent jet issuing from a cylindrical nozzle to characterise coherent structures evolving in the turbulent boundary layer. The analysis is performed using data from a large-eddy simulation of a Mach 0.4 jet. Azimuthal decomposition of the velocity field in the nozzle shows that turbulent kinetic energy predominantly resides in high azimuthal wavenumbers; the first three azimuthal wavenumbers, that are important for sound generation, contain much lower, but non-zero amplitudes. Using two-point statistics, low azimuthal modes in the nozzle boundary layer are shown to exhibit significant correlations with modes of same order in the free-jet region. Spectral Proper Orthogonal Decomposition (SPOD) is used to distill a low-rank approximation of the flow dynamics. This reveals the existence of tilted coherent structures within the nozzle boundary layer and shows that these are coupled with wavepackets in the jet. The educed nozzle boundary-layer structures are modelled using a local linear stability analysis of the nozzle mean flow. Projection of the leading SPOD modes on the stability eigenmodes shows that the organised boundary-layer structures can be modelled using a small number of stable eigenmodes of the boundary-layer branch of the eigenspectrum, indicating the prevalence of non-modal effects. Finally local and global resolvent analysis of the mean-flow are performed. It is shown that the most-energetic nozzle structures can be successfully described with optimal resolvent response modes, whose associated forcing modes are observed to tilt against the nozzle boundary-layer, suggesting that the Orr mechanism underpins these organised, turbulent, boundary-layer structures., 38 pages, 31 figures. Submitted to Journal of Fluid Mechanics

We present a two-point model to investigate the underlying source mechanisms for broadband shock-associated noise (BBSAN) in shock-containing supersonic jets. In the model presented, the generation of BBSAN is assumed to arise from the non-linear interaction between downstream-propagating coherent structures with the quasi-periodic shock cells in the jet plume. The turbulent perturbations are represented as axially-extended wavepackets and the shock cells are modelled as a set of stationary waveguide modes. Unlike previous BBSAN models, the physical parameters describing the hydrodynamic components are not scaled using the acoustic field. Instead, the characteristics of both the turbulent and shock components are educed from large-eddy simulation and particle image velocimetry datasets. Apart from using extracted data, a reduced-order description of the wavepacket structure is obtained using parabolised stability equations (PSE). The validity of the model is tested by comparing far-field sound pressure level predictions to azimuthally-decomposed experimental acoustic data from a cold Mach 1.5 underexpanded jet. At polar angles and frequencies where BBSAN dominates, good agreement in spectral shape and sound amplitude is observed for the first three azimuthal modes. Encouraging comparisons of the radiated noise spectra, in both frequency and amplitude, reinforce the suitability of using reduced-order linear wavepacket sources for predicting BBSAN peaks. On the other hand, the mismatch in sound amplitude at interpeak frequencies reveals the role of wavepacket jitter in the underlying sound generating mechanism., Comment: 37 pages, 16 figures. Submitted to JFM

Rectangular propulsion nozzles have advantages over circular nozzles, including easier thrust-vectoring and air-frame-integration. Jet noise is easier to study with circular jets (CJ), however, due to azimuthal homogeneity, which, together with low-rank acoustic dynamics enables simpler acoustic models. Using Large Eddy Simulations of rectangular jets (RJ) of various aspect ratios we show that acoustic fluctuation components exhibit comparably rapid convergence in azimuthal Fourier space even for high aspect ratios. A reduced-order model for RJ that retains near-field acoustic asymmetry can be constructed using only three leading azimuthal modes, but with two additional terms relative to CJ.

By injecting a mixture of gas and pyroclasts into the atmosphere, explosive volcanic eruptions frequently generate vortex rings, which are toroidal vortices formed by the jet's initial momentum. Here, we report high‐speed imaging and acoustic measurements of vortex rings sourcing from gas‐rich eruptive jets at Stromboli volcano (Italy). Volcanic vortex rings (VVRs) form at the vent together with an initial compression acoustic wave, VVRs maximum rise velocity being directly proportional to the amplitude and inversely proportional to the duration of the compression wave. The axial rise and acoustic signature of VVRs match well those predicted by recent fluid‐dynamic experiments. This good match allows using the high‐frequency (80–1,000 Hz) component of the jet sound and the time‐dependent rise of VVRs to retrieve two key eruption parameters: the Mach number of the eruptive jets (, Key Points Volcanic vortex rings are formed by gas‐rich, jet‐forming Strombolian‐style explosionsThe explosion acoustic signals bear the signature of the vortex rings and reveal supersonic eruptive jets with Mach number up to 1.5Vent diameter can be estimated from the time‐dependent rise of vortex rings at 0.7 m, in agreement with direct observation from Uncrewed Aerial Vehicle

The relation between different time scales of the finite-time Lyapunov exponent (FTLE) and the acoustic wave is studied. Gonzalez et al.’s proposition (“Finite-Time Lyapunov Exponent-Based Analysis...

The noise characteristics of a dual-stream jet of bypass ratios greater than 10 were investigated in response to area ratio, nozzle-operating conditions, installation effect, and chevron effect. The key conclusions were as follows. (1) The area ratio impacted the noise by up to 3 dB at aft angles and at mid-frequency for heated conditions. (2) The spectral variation due to the change of primary stream parameters was constant at low Strouhal numbers and diminished at high Strouhal numbers. (3) The impact of the secondary stream pressure was described by the scaling law of single-stream jets for unheated conditions. The flow parameters of other jets were required to describe the spectra of Strouhal numbers between 0.2 and 2.0, based on the secondary jet for heated conditions. (4) The installed jet noise was quantified for various wing configurations and was more pronounced at forward angles. (5) The chevron nozzle reduced overall noise by up to 4 dB, though it became less attractive when installed. The quantified information is expected to improve the estimation of noise from a dual-stream jet of high bypass ratios.

An experimental study of the azimuthal modes of the sound field generated by a single-stream round jet installed near a flat plate is presented. The investigation is conducted at subsonic Mach numb...

International audience; The characteristics of acoustic tones near the nozzle of jets are investigated for Mach numbers between M = 0.50 and 2 using large-eddy simulations. Peaks are observed in all cases. They are tonal for M ≥ 0.75 and broaden for lower Mach numbers. They are associated with the azimuthal modes nθ = 0 to nθmax, with nθmax = 8 for M = 0.75 and 1 for M = 2, for example. Their frequencies do not appreciably vary with the nozzle-exit boundary-layer thickness and turbulence and fall in the frequency bands predicted for the upstream-propagating guided jet waves using a vortex-sheet model. For all azimuthal modes, the peak intensities are highest for the first radial guided jet mode. They increase approximately as M^8 for M ≤ 1 and as M^3 for M ≥ 1, following the scaling laws of jet noise, suggesting that they mainly result from a band-pass filtering of the upstream-travelling sound waves by the guided jet modes. In support of this, the Mach number variations of the peak width and sharpness are explained by the eigenfunctions of the guided waves. Moreover, it appears that, for high subsonic Mach numbers, among the waves possibly resonating in the potential core, only those close to the cutoff frequencies of the guided jet modes can contribute to the near-nozzle peaks. Finally, the peaks are detectable in the far field for large radiation angles. For M = 0.90, for instance, they emerge for angles higher than 135° .

Motivated by design challenges related to aerospace propulsive jets, an experimental investigation has been conducted of the high Mach number jet plume flow field from a round convergent nozzle at under-expanded shock-containing conditions. Hot jets up to a total temperature ratio of 3 were considered. Laser doppler anemometry (LDA) measurements in the jet near field (first 15 nozzle exit diameters) captured the turbulent mixing process in detail, enabling the separate effects of compressibility and static temperature ratio (t) on the development of the velocity and turbulence profiles to be identified. Compressibility dominated in the initial shear layer region, whereas temperature effects controlled the downstream jet merging zone. Analysis of shear layer development demonstrated that, at all temperature ratios, a similar, but significantly stronger, damping effect was observed as in planar shear layers (correlated well by convective Mach number Mc). Consideration of the interaction of compressibility and temperature ratio – which reduce/enhance turbulent mixing respectively – provided for the first time a rational explanation of the observation that increasing jet temperature influenced flow development only up to a static temperature ratio t ~ 1.5, after which further increase has little effect. Measurements of the potential core length (Lp) were analysed to produce an empirical correlation that also illustrated the diminishing effects of heat addition at all jet Mach numbers. The data provide the improved understanding and empirical design techniques essential for developing technologies for jet noise and infra red (IR) signature reduction and represent an important validation test case for computational fluid dynamics (CFD) modelling.

International audience; The present paper reports an investigation of the statistical properties of pressure fluctuations in the near field of subsonic compressible jets. The database analyzed has been obtained numerically by DNS and LES of two single-stream circular jets, having diameter-based Reynolds numbers of 3125 and 100,000 and Mach number 0.9, respectively, initially laminar and highly disturbed. Pressure fluctuations are extracted from several virtual probes positioned in the near field of the jets and covering a region from 0 to 20 diameters in the axial direction and from 0.5 to 3 diameters in the radial. An azimuthal decomposition of the pressure fluctuations is performed, and the statistical analysis is applied to the axisymmetric 0-mode component and compared to the results obtained from the full original signals. The intermittent behavior is investigated by the estimation of standard statistical indicators, such as probability distribution functions and flatness factor, as well as through conditional statistics based on the application of the wavelet transform. It is shown that downstream of the potential core, intermittency estimated through the traditional indicators is relevant even at the lowest Re for the full signals, whereas it is apparently not significant for the 0-mode component. The wavelet analysis provides an estimation of intermittency scale-by-scale and allows for the calculation of a frequencydependent FF. This approach reveals that the 0-mode component has a relevant degree of intermittency around the frequencies associated with the Kelvin-Helmholtz instability. The statistics of the intermittent events, in terms of their temporal appearance and energy content, are shown to be weakly sensitive to the jet Reynolds number and the universal behavior can be reproduced by simple stochastic models.

Resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-educed counterparts from high-fidelity large-eddy simulations (LES). We formulate resolvent analysis as an acoustic analogy that relates the near-field resolvent forcing to the near- and far-field pressure. We use an LES database of round, isothermal, Mach 0.9 and 1.5 jets to produce an ensemble of realizations for the acoustic field that we project onto a limited set of resolvent modes. In the near-field, we perform projections on a restricted acoustic output domain, $r/D = [5,6]$, while the far-field projections are performed on a Kirchhoff surface comprising a 100-diameter arc centered at the nozzle. This allows the LES realizations to be expressed in the resolvent basis via a data-deduced, low-rank, cross-spectral density matrix. We find that a single resolvent mode reconstructs the most energetic regions of the acoustic field across Strouhal numbers, $St = [0-1]$, and azimuthal wavenumbers, $m=[0,2]$. Finally, we present a simple function that results in a rank-1 resolvent model agreeing within 2dB of the peak noise for both jets., Comment: 14 pages, 11 figures, Accepted to the Journal of the Acoustical Society of America

Present experimental investigation reports effect of change in nozzle exit geometry on acoustic characteristics of compressible jet in the near and far field at jet exit Mach number 0.8. Three different nozzle configurations used in this investigation are circular, elliptical, and rectangular. Aspect ratio of elliptical and rectangular nozzle is 3. Equivalent nozzle exit diameter of all nozzle configurations is maintained constant as 40 mm. Results are presented by obtaining cross-correlation between near field and far field simultaneously measured pressure fluctuations. Acoustic characteristic along major and minor axis is different for elliptical and rectangular nozzle. Cross-correlation obtained indicates that noise source shifts closer to nozzle exit for elliptical as well as rectangular nozzle.

Passive control for suppressing mixing noise from Co-Flowing Jets (CFJ) is presented in this study. The idea behind this is to reduce the convective Mach number of turbulent eddies that produce intense sound radiation. The present study analyses co-flowing jets with a bypass ratio of 6.3 and the primary nozzle lip thickness of 10 mm. The aim of the study is to find the jet noise level in finite lip thickness in co-flowing jets. CFJ with finite lip thickness forms a recirculation zone (in the near field). The secondary core and recirculation zone are shielding the primary core by reducing the jet noise. A single free jet with a diameter equal to that of a primary nozzle of co-flowing jet is also studied for comparison. The results show that co-flow jet with finite lip thickness of 10mm for various emission angles and the Overall Sound Pressure Level (OASPL) level gets reduced when compared with the single free jet.

Abstract Jet noise remains a significant aircraft noise contributor, and for modern high-bypass-ratio aero-engines the strong interaction between the jet and aircraft wing leads to intensified installed jet noise. An experiment is carried out in this paper to study the effects of lobed nozzles on installed jet noise. It is found that the lobed nozzles, compared to round nozzles, have similar effects on installed jet noise for all the plate positions and Mach numbers tested. On the shielded side of the plate, the use of lobed nozzles leads to a noise reduction in the intermediate- and high-frequency regimes, which is thought to be due to a combination of enhanced jet mixing and more effective shielding effects by the flat plate. On the reflected side of the plate, noise reduction is only achieved in the intermediate frequency range; the little noise reduction or a slight noise increase observed in the high-frequency regime is likely due to enhanced jet mixing. On both sides of the plates, little noise reduction is achieved for the low-frequency noise due to the scattering of jet instability waves. This is likely to be caused by the fact that lobed nozzles cause negligible change to the dominant mode 0 (axisymmetric) jet instability waves. That the jet mean flow quickly becomes axisymmetric downstream of the jet exit could also play a role. Graphic abstract

The flow structures and the acoustic feedback loops of underexpanded round jets are investigated by numerical simulations. The jets have a Mach number of 1 at the nozzle exit and a diameter-based Reynolds number of . Three nozzle pressure ratios (NPRs) of 2.2, 2.4 and 2.6 are considered. The wavelengths of the screech tones are in good agreement with the experimental measurements on high-Reynolds-number jets in the literature. The screech tones are respectively at the A1 and B modes for the jets at NPRs of 2.2 and 2.6. Two screech tones at the A2 and B modes are identified in the jet at the NPR of 2.4 and the wavelet analyses conducted on the pressure fluctuations confirm that these two modes are contemporaneous. The amplitude and phase fields of fluctuating pressure at the screech frequencies are presented in the nozzle exit plane and azimuthal planes. The effective source locations of the screech tones are determined based on the distributions of the phase. The number of periods contained in the screech feedback loop is equal to the number of cells in the standing wave between the nozzle exit and the effective source. The screech frequencies estimated by the classical feedback model agree well with the numerical results at different modes. A modified model, in which the classical feedback model and the upstream-propagating acoustic wave mode of the jet are combined, shows that the screech feedback loops at the A1 and A2 modes are associated with the same acoustic wave mode. The modified model fails to estimate the screech frequencies at the B mode. Different feedback mechanisms lead to the coexistence of the A2 and B modes. The coherent structures corresponding to different screech modes are extracted by dynamic mode decomposition.

This paper considers how a complex axisymmetric jet modifies the structure of the propa- gator tensor in Goldstein’s generalized acoustic analogy. The jet flow we consider is in general a dual stream flow that operates either as a single jet or a complex co-axial jet flow. The latter of which is of interest to turbofan engine manufacturers. The form of the acoustic analogy that we use here is based on our recent work on jet noise modeling (Afsar et al. 2019, PhilTrans. A., vol. 377) that highlighted the importance of non-parallel flow effects in the correct calcu- lation of the propagator. The propagator calculation takes advantage of the fact that mean flow non-parallelism enters the lowest order asymptotic expansion of the former at sufficiently low frequencies of the same order as the jet spread rate. Whilst this might seem restrictive, our previously reported calculations at high subsonic and mildly supersonic jets indicate that the subsequent jet noise predictions remain accurate up to the peak frequency (typically at a Strouhal number based on jet velocity and diameter of ≈ 0.5 − 0.6) for the small angle acoustic radiation. One of critical assumptions of this approach is that the mean flow speed of sound squared is given by either the Crocco relation (in unheated jets) or the Crocco-Busemann relation for heated flows. Our analysis for the dual stream complex axisymmetric jet however shows that the latter assumption (in the form of Crocco-Busemann formula) is no longer an accurate representation of the speed of sound variation. We therefore present a more general form of the asymptotic analysis than that used in Afsar et al. (2019a & b). For the complex jet mean flow field, the mean flow speed of sound is otherwise arbitrary but must remain a single-valued function of the streamwise mean flow. The predictions based on this approach are shown to remain accurate up to the peak frequency. We discuss how to extend the range of validity by utilizing a suitable composite asymptotic solution for the Green’s function problem.

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 sum- marises the technical problems and strategy we use to extend this approach to higher frequen- cies.

International audience; An experimental investigation of the noise radiated by a ducted high pressure flow discharge through diaphragms and perforated plates is carried out for a large range of subsonic and supersonic operating conditions (Nozzle Pressure Ratio (NPR) from 1.2 to 3.6). A parametric study of the geometrical parameters is also conducted to characterize their influence on the acoustic radiation. This covers configurations from single diaphragms to multi-perforated plates with variable hole diameters and arrangements that are placed inside a cylindrical duct. Compared with the free discharge analysed in a first part of the study (perforated plates placed directly at the output of the duct), the discharge into a duct, which is closer to the practical applications, generates strong acoustic modifications. As expected, the broadband noise is disturbed by strong modulations due to acoustic resonances in the output duct (longitudinal resonances and transversal duct modes). However, as in the free configuration, a strong effect of the plate geometries on the mixing noise is observed, allowing to adapt or reduce this source. In particular, the increase of the ratio between the perforation spacing and the perforation diameter allows reducing the maximum amplitude of the mixing noise. Compared to the free-field discharge, the Sound Pressure Level (SPL) in the ducted configuration is on average proportional to the 6-th power of the velocity instead of the 8-th power. Moreover, there are two dominant frequency humps in the sound spectra. The low frequency one is characterized by a constant Helmholtz number, suggesting that the sound is shaped by the duct geometry, whereas the high frequency one is characterized by a constant Strouhal number suggesting that the sound is directly generated by the flow. Finally, for supersonic operating points, the screech radiation appearing with diaphragms in the free configuration is suppressed when the output duct is added but new high amplitude and low frequency tones appear for the largest diaphragms and perforated plates. These lines are due to a coupling between normal shock oscillations and longitudinal resonances.

We study the unsteady flow of a viscous fluid passing through a circular aperture in aplate characterized by a non-zero thickness. We investigate this problem by solving theincompressible Linearized Navier-Stokes Equations (LNSE) around a laminar base flow,in both the forced case (allowing to characterize the coupling of the flow with acousticresonators) and the autonomous regime (allowing to identify the possibility of purelyhydrodynamical instabilities). In the forced case, we calculate the impedances and discussthe stability properties in terms of a Nyquist diagram. We show that such diagramsallow us to predict two kinds of instabilities: (i) a conditional instability linked to theoverreflexion of an acoustic wave but requiring the existence of an conveniently tunedexternal acoustic resonator, and (ii) a purely hydrodynamic instability existing even in astrictly incompressible framework. A parametric study is conducted to predict the rangeof existence of both instabilities in terms of the Reynolds number and the aspect ratio ofthe aperture. Analysing the structure of the linearly forced flow allows to show that theinstability mechanism is closely linked to the existence of a recirculation region withinthe thickness of the plate. We then investigate the autonomous regime using the classicalnormal-mode ansatz. The analysis confirms the existence of the purely hydrodynamicalinstability in accordance with the impedance-based criterion. The spatial structure ofthe unstable eigenmodes are found to be similar to the structure of the correspondingunsteady flows computed using the forced problem. Analysis of the adjoint eigenmodesand of the adjoint-based structural sensitivity confirms that the origin of the unstabilitylies in the recirculation region existing within the thickness of the plate.

In this paper the wall pressure fluctuations induced by a compressible jet overflowing a flat plate were analysed with the scope of providing an analytical prediction of the two-points coherence. The reported approach follows the idea formulated by Efimtsov to model the coherence at relatively high Mach numbers and with a good accuracy in the low wave-numbers region. The database used for the model assessment refers to an experimental campaign carried out into the semi-anechoic chamber of the Roma Tre University using pressure transducers flush mounted at the wall of a rigid flat plate. The jet Mach number was varied within the compressible subsonic regime up to 0.9 and two different nozzle exhaust diameters were considered to analyse the effect of the Reynolds number. The tangential flat plate was installed at 0.75 diameters from the jet axis, a position that reproduces well a realistic jet-wing configuration. The ability of the model to predict the coherence function is verified for the whole range of conditions investigated and the achieved results are discussed with reference to the available literature.

The GPU CABARET method for solving the Navier–Stokes equations coupled with the Ffowcs Williams–Hawkings scheme for far-field noise predictions is applied for conditions of the NASA SHJAR experiment corresponding to Set Point 3 and 7 in accordance with Tanna's classification. The questions addressed include the sensitivity of the flow and noise spectra solutions to the grid resolution and the inflow condition at the nozzle exit. To study the grid sensitivity, several “hand-made” multi-block curvilinear grids are considered along with a simple hanging-nodes-type grid that was automatically generated with OpenFOAM, whose solutions are cross-verified. To study the effect of the inflow jet condition, the flow and noise solutions based on the laminar inflow condition for Set Point 7 case are compared with the same based on modifying the interior nozzle geometry with a turbulence grid to generate the initial unsteadiness inside the nozzle so that both the centerline velocity fluctuations and the jet Mach number at the nozzle exit are preserved in accordance with the experiment. The numerical solutions obtained are compared with the experimental data and reference LES solutions available in the literature.

Jet noise remains the major contributor to airplane noise at take-off. In the past half-century of research, sound generation mechanisms in supersonic jets have been extensively characterized, while the sound sources in subsonic jets are still to be clearly identified. For the last two decades, Large Eddy Simulations (LES) have become a major tool for investigating jet noise sources due to their ability to capture detailed information in turbulent flows and their moderate cost that allows industrial applications. However, many challenges still arise when dealing with complex nozzle geometries and heating effects in the jet core. In this paper, subsonic jets with or without nozzle geometry at Mach number of 0.9 and moderately high Reynolds numbers ranging from 2 × 105 to 1 × 106 are computed using LES, providing a base of validation for different nozzle configurations and operating conditions. In this work, the high-order unstructured LES solver AVBP is combined with Ffowcs Williams and Hawkings’ acoustic analogy on unstructured grids. The vortex pairing phenomenon is evidenced without properly triggering the turbulence in the jet at the nozzle exit. Hence, a non-geometrical tripping, where the firsts prism layers of the mesh at the nozzle wall are removed, is proposed and shown to be a successful method for triggering proper turbulence development in shear layers for the cases with nozzle. Moreover, it is more easily implemented because it does not require any geometrical modifications and it generates more natural turbulence than previous methods, leading the path to actual industrial dual-stream configurations. Both isothermal and heated jet flow cases are performed and validated with existing experimental data in terms of aerodynamics and acoustics, which demonstrates the capacity of an unstructured LES solver to correctly simulate both cold and heated jet noise phenomena.

A single-point, frequency-domain nonlinearity indicator is calculated and analyzed for noise from a model-scale jet at Mach 0.85, Mach 1.8, and Mach 2.0. The nonlinearity indicator, νN, has been previously derived from an ensemble-averaged, frequency-domain version of the generalized Burgers equation (GBE) from Reichman, Gee, Neilsen, and Miller [J. Acoust. Soc. Am. 139, 2505-2513 (2016)]. The indicator gives the spatial rate of change due to nonlinear processes in sound pressure level (SPL) spectrum, and two other indicators from the GBE-νS and να-give the same quantity due to geometric spreading and absorption, respectively. Trends with frequency, angle, distance, and jet condition-supported both by spectral analysis and by calculation of the GBE-derived indicators-reveal a concentration of nonlinear effects along radials close to the plume with large overall SPLs. The calculated indicators for nonlinearity and absorption effects far from the source combine to give the same decay predicted by nonlinear theory for monofrequency sources. Trends in the νN indicator are compared with trends observed for other indicators such as pressure-derivative skewness and bicoherence, revealing both the qualitative and quantitative advantages of the νN indicator.

In this work, jet noise reduction using a swirling flow surrounding a circular free jet has been demonstrated. The passive control scheme induces swirl from six flat vanes fixed in an annular passage with vane angles from 0 to 50°, with the corresponding swirl numbers ranging from 0 to 0.91. Noise measurements in terms of overall sound pressure levels, directivity patterns, acoustic spectra; and flow measurements in terms of centerline pitot survey and flow visualization have been carried out to evaluate the efficacy of the passive control scheme. The co-axial swirl jets always reduce the low frequency noise, irrespective of the nozzle pressure ratio. The screech tone is entirely eliminated and broadband shock associated noise mitigated by the co-axial swirl jets. The results of highly under expanded supersonic cases, show that, the weak swirl generates higher noise and high swirl generates lower noise for the same nozzle pressure ratio. The centerline pitot pressure measurements reveal that the co-axial swirl jets decrease the core lengths and the number of shock cells compared to the free jet. The flow visualization study shows that Mach disks are generated at lower pressure ratios for the co-axial swirl jets compared to free jet. The present work proposes swirl as an excellent passive tool for jet noise suppression.

The dynamics of a supersonic jet emanating from a high-aspect-ratio rectangular nozzle is investigated using dynamic mode decomposition. In the analysis, dynamic mode decomposition is applied to flowfield data obtained from a large-eddy simulation and the significance of each extracted mode to the snapshot data series is determined using a sparsity-promoting method. Furthermore, in order to assess the validity of the resulting modes, they are compared with the unprocessed large-eddy simulation data in terms of frequency content, sound pressure levels, and space–time correlations. It is found that the accuracy of the modes predicted by the dynamic mode decomposition is sufficient and that the modes deemed as most important give a good representation of the jet flow dynamics. Moreover, the jet flow, at the simulated conditions, is known (from experiments) to be dominated by a screech mechanism. The dynamic mode decomposition methodology, as set up in the present study, is able to isolate the jet screech mode, and the frequency of the extracted mode is in excellent agreement with previous observations.

Imperfectly expanded supersonic jets contain a shock-cell structure in the jet plume which plays a role in generating screech tones along with other jet noise sources. Depending on the Mach number of the jet, two types of jet motion or “jet modes”—a toroidal mode and flapping mode may occur, resulting in the generation of different screech tones that are not harmonics of each other. At a given jet condition, these jet modes (and the corresponding screech tones) can switch between each other based on environmental conditions in a seemingly non-deterministic manner. Understanding when mode-switching occurs at a fine time resolution can provide better understanding of the sensitivity of the jet structure dynamics. This work presents the preliminary results of a novel method that predicts when a particular screech tone is active using non-negative matrix factorization. Using this technique, spectrograms of jet noise are decomposed into a set of basis vectors corresponding to the screech tones present in the jet, and a set of activation functions that indicate when each screech basis is dominant. An activation function comparison technique is then used to identify activations corresponding to mode-switching.

Jets with Mach numbers $M\gtrsim 1.5$ are well known to emit an intense, fricative, so-called crackle sound, having steep compressions interspersed with weaker expansions that together yield a positive pressure skewness $S_{k}>0$. Its shock-like features are obvious hallmarks of nonlinearity, although a full explanation of the skewness is lacking, and wave steepening alone is understood to be insufficient to describe its genesis. Direct numerical simulations of high-speed free-shear flows for Mach numbers $M=0.9$, $1.5$, $2.5$ and $3.5$ in the Reynolds number range $60\leqslant Re_{\unicode[STIX]{x1D6FF}_{m}}\leqslant 4200$ are used to examine the mechanisms leading to such pressure signals, especially the pressure skewness. For $M=2.5$ and $3.5$, the pressure immediately adjacent the turbulence already has the large $S_{k}\gtrsim 0.4$ associated with jet crackle. It also has a surprisingly complex three-dimensional structure, with locally high pressures at compression-wave intersections. This structure is transient, and it simplifies as radiating waves subsequently merge through nonlinear mechanisms to form the relatively distinct and approximately two-dimensional Mach-like waves deduced from laboratory visualizations. A transport equation for $S_{k}$ is analysed to quantify factors affecting its development. The viscous dissipation that decreases $S_{k}$ is balanced by a particular nonlinear flux, which is (of course) absent in linear acoustic propagation and confirmed to be independent of the simulated Reynolds numbers. Together these effects maintain an approximately constant $S_{k}$ in the near acoustic field.

We used a reflected shock tube to investigate the acoustic signature of a hot jet at the far-field. Experiments were performed at Mach = 1.4 and a total temperature of T t = 950 Kelvin. Far-field acoustic signatures of the hot jet at six polar angles θ = 15˚ to θ = 90˚ from the jet axis) were measured and imaged by the means of continuous wavelet transform in scalograms. The results were compared with experiments from a steady test facility at similar test conditions. Further, the primary characteristics of noise events in jet far-field were compared with analytical models considering wavepacket as the main source of jet noise. The results indicate that higher frequency events at θ = 90˚ occur with a small time shift relative to the low azimuthal mode base event. This phenomenon might be the main reason why the acoustic signal at the side angles behaves more noisily than at low polar angles.

The gas-thrust region of a large volcanic eruption column is predominately a momentum-driven, fluid flow process that perturbs the atmosphere and produces sound akin to noise from jet and rocket engines, termed “jet noise”. We aim to enhance understanding of large-scale volcanic jets by studying an accessible, less hazardous fumarolic jet. We characterize the acoustic signature of ~ 2.5-meter wide vigorously jetting fumarole at Aso Volcano, Japan using a 5-element infrasound array located on the nearby crater. The fumarole opened on 13 July 2015 on the southwest flank of the partially collapsed pyroclastic cone within Aso Volcano's Naka-dake crater and had persistent gas jetting, which produced significant audible jet noise. The array was ~ 220 m from the fumarole and 57.6° from the vertical jet axis, a recording angle not typically feasible in volcanic environments. Array processing is performed to distinguish fumarolic jet noise from wind. Highly correlated periods are characterized by sustained, low-amplitude signal with a 7–10 Hz spectral peak. Finite difference time domain method numerical modeling suggests the influence of topography near the vent and along the propagation path significantly affects the spectral content, complicating comparisons with laboratory jet noise. The fumarolic jet has a low estimated Mach number (0.3 to 0.4) and measured temperature of ~ 260 °C. The Strouhal number for infrasound from volcanic jet flows and geysers is not known; thus we assume a peak Strouhal number of 0.19 based on pure-air laboratory jet experiments. This assumption leads to an estimated exit velocity of the fumarole of ~ 79 to 132 m/s. Using published gas composition data from 2003 to 2009, the fumarolic vent area estimated from thermal infrared images, and estimated jet velocity, we estimate total volatile flux at ~ 160–270 kg/s (14,000–23,000 t/d).

Supersonic jets that are subject to off-design operating conditions are marked by three distinct regions in their far-field spectra: mixing noise, screech and Broadband Shock Associated Noise (BBSAN). BBSAN is conspicuous by the prominent multiple peaks. The Morris and Miller BBSAN model that is based on an acoustic analogy, offering a straightforward implementation for RANS, forms the foundation of the present work. The analogy model robustly captures the peak frequency noise, that occurs near Strouhal number of about 1, based on the nozzle exit diameter but leads to major sound under prediction for higher frequencies. In the jet mixing noise literature, it has been shown that an inclusion of frequency dependence into the characteristic length and temporal scales of the effective noise sources improves the far-field noise predictions. In the present paper, several modifications of the original Morris and Miller model are considered that incorporate the frequency dependent scales as recommended in the jet mixing noise literature. In addition to these, a new mixed scale model is proposed that incorporates a correlation scale that depends both on the mean-flow velocity gradient and the standard mixing noise-type scaling based on the dissipation of turbulent kinetic energy. In comparison with the original Morris and Miller model, the mixed scale model shows considerable improvements in the noise predictions for the benchmark axisymmetric convergent-divergent and convergent jets. Further to this validation, the new model has been applied for improved predictions for elliptic jets of various eccentricity. It has been shown that, for the same thrust conditions, the elliptical nozzles lead to noise reduction at the source in comparison with the baseline axisymmetric jets.

Experience gained from previous jet noise studies with the unstructured large-eddy simulation flow solver “Charles” is summarized and put to practice for the predictions of supersonic jets issued f...

International audience; Local fluctuations in a Mach 1.3 cold jet are tracked to understand the genesis of nearfield directivity and intermittency. A newly developed approach leveraging two synchronized large-eddy simulations is employed to solve the forced Navier–Stokes equations, linearized about the evolving unsteady base flow. The results are summarized by exposing the effect of two acoustically significant turbulent regions: the lip-line and core collapse location. The near-acoustic field displays the clear signature of the two regions. However, for both regions, the nearfield evolution of the perturbation field is characterized by generation of intermittent wavepackets, which propagate into the near-acoustic field and gradually acquire their expected broadband and narrowband characteristics at sideline and downstream angles respectively. The simulations elucidate how higher frequencies are obtained in the sideline directions as lower frequencies are filtered out of the forcing fluctuations. Likewise, shallow-angle acoustic signals arise through filtering of high frequency content in that direction. The directivity and intermittency are connected to the filtering of scales by jet turbulence with empirical mode decomposition. The observations highlight the gradual evolution of seemingly random core turbulence into well-defined intermittent wavepackets in the nearfield of the jet. The manner in which centerline fluctuations are segregated into upstream, sideline, and downstream components is examined through narrowband correlations. A similar analysis for the lipline contribution shows primarily upstream and downstream patterns because of the larger structures in the shear layer.

Four models to predict jet mixing noise available in the literature are reviewed and compared. Two models are derived from the Lighthill Acoustic Analogy (LAA) and the other two use the Linearized Euler Equations (LEE) with added source terms. All models use input from a computational solution of the Reynolds-Averaged Navier–Stokes (RANS) equations and empirical functions to model turbulent correlations. The models are concerned with the sources of sound related to small turbulent structures. Results for an observer at 90 $$^{\circ }$$ to the jet axis are presented, where effects of sound-flow interaction are negligible and the small structures are considered to act as the dominant source. A range of subsonic jets issued from different nozzle geometries with different exit velocities and temperatures is considered. In addition, a ray tracing method to compute the effects of sound refraction is reviewed. The comparison of the numerical predictions with experimental data shows that using the LAA with an improved description of turbulence statistics results in a model as accurate as the ones based on the LEE that relies on less empirical coefficients and has a simpler mathematical derivation. The results corroborate the use of RANS along with LAA to model jet mixing noise.

The present experimental work highlights the acoustic far field and flow field characteristics of confined co-axial swirling pipe jets. Co-axial confinements with six vanes at angles of 0°, 20° and 40° are considered here. Two pipe lengths of L/D=0.5 and 2 are studied. The Mach numbers studied range from 0.85 to 1.83. An increase in the pipe length causes suppression of the transonic tones in non-swirl pipe jets. Swirl reduces the low frequency noise components and increases the high-frequency components compared to non-swirl jet. The broadband shock associated noise is mitigated by the swirl pipe jets. However, the screech tone is completely eliminated by the swirl pipe jets. Further, swirl pipe jets radiate low levels of noise at all the emission angles compared to non-swirl pipe jets, for both the pipe length cases at supersonic Mach numbers. Increase in the pipe length enhances the shock associated noise and OASPL for the non-swirl pipe jet. Centreline pitot survey and schlieren visualisation show a reduction in core length, reduction in the number of shock cells, weakening/destruction of the shock cells by the swirl pipe jets compared to the non-swirl pipe jets.

We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier–Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier–Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets Mach 0.9 and 2, and a three-dimensional jet Mach 1.5, impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near-and far-field regions.

International audience; The azimuthal structure and the generation process of steepened acoustic waves are investigated in the near field of temporal round jets at Mach numbers of 2 and 3. Initially, the shear layers of the jets are in a laminar state and display instability waves whose main properties are close to those predicted from linear temporal analysis. Then, they transition to a turbulent state and generate high-intensity Mach waves displaying sharp compressions typical of those recorded for jets producing crackle noise. These waves are first shown to be poorly reproduced when only the axisymmetric mode is considered, but to be well captured with the first five azimuthal modes. Their generation process is investigated by performing conditional averages of the flow and acoustic fields triggered by the detection of intense positive pressure peak close to the jets. No steepened waves are visible in the conditionally-averaged pressure profiles when the procedure involves only one azimuthal mode at a time. However, sharp compressions are obtained based on the first five modes taken together. In that case, the steep compressions are correlated over a limited portion of the jet circumference and are steeper as more azimuthal modes are considered. Moreover, a direct link is established between the steepened waves and the supersonic convection of large-scale coherent flow structures located in the supersonic core of the jets. This indicates that these waves constitute an extreme, nonlinear case of Mach wave radiation by these structures. In addition, the capacity of flow structures to generate sharp, steepened waves is related to their shapes. More particularly, flow structures with a large extent in the radial direction are shown to produce stronger and steeper Mach waves than those that are elongated in the flow direction.

A broadband equivalent acoustic source distribution can be used to model the sound field near a high-speed jet. Such models must account for the spatiospectral variation of the sound levels. This work presents a technique for obtaining such a model using a spectral decomposition method associated with large and fine-scale turbulent mixing noise to create broadband equivalent source distributions for each noise type. The large-scale turbulent mixing noise is represented by frequency-dependent wavepackets, while the fine-scale turbulent mixing noise is modeled as a frequency-dependent incoherent, extended source distribution. This technique is applied to acoustical measurements from an ideally expanded, unheated Mach 1.8 jet. The wavepackets model the sound field levels in the maximum radiation region, but the second incoherent source distribution is required to obtain the levels at the other locations. The combination of the incoherent source distribution and the wavepacket provides a broadband, equivalent acoustic source representation that adequately models the sound field for Strouhal numbers between 0.04 and 0.25. At higher Strouhal numbers, better agreement is obtained when accounting for a frequency-dependent shift in the apparent acoustic source region. This frequency-dependent source region is more important closer to the jet than in the far field.

This is a review of the two-source model of jet noise. The model was developed phenomenologically a number of years ago. One of the principal results associated with this model was the identification of two similarity jet noise spectra. This was accomplished through extensive comparisons with a large set of NASA spectrum data. It was found that these two noise spectra when combined appropriately would fit measured noise spectra of jets in any direction regardless of jet temperature and Mach number. Other experimental data in support of the two-source model have since been found. They are discussed in this paper. One of the purposes of this paper is to elaborate on the flow physics of turbulence, noise generation mechanisms and directivity that are the underpinnings of the model. More recent works show the similarity spectra are applicable, well beyond their original database, to noise of military jets, rockets and even volcanoes. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.