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Aeroacoustics of innovative aircraft cannot disregard the development of low-order models for the jet noise source, which are essential to assess the propulsion–airframe interactions from the conceptual design stage. The main scope of this work is to provide a noise source model that can be coupled with relatively low computational cost methods for aeroacoustic scattering. To this end, this paper presents for the first time a multiobjective optimization of the zeroth-mode wave-packet in the jet near field. The importance of calibrating the model with near-field pressure data stems from the fact that in new aircraft, the engine nacelles are typically positioned at a few diameters from the wing or fuselage. In this work, the near field of a high subsonic jet at a Mach number of 0.9 is represented as a cylindrical surface radiating the pressure disturbances of a wave-packet source, which is optimized using large-eddy simulation data from three lines at different radial distances. The optimized model has been tested at Strouhal numbers between 0.25 and one, and the optimized solutions have been chosen using a Pareto-ranking criterion considering the wave-packet prediction over an extra line. A good agreement is achieved between the reference data and model predictions for multiple near-field radial distances.

The interactions between upstream-propagating guided jet waves and shear-layer instability waves near the nozzle of subsonic and nearly ideally expanded supersonic, isothermal free jets are investigated for jets at Mach numbers between 0.50 and 2 with fully laminar exit boundary layers of different thicknesses. The velocity spectra in the shear layers downstream of the nozzle exhibit strong narrow peaks for the first azimuthal modes, associated with growing Kelvin–Helmholtz instability waves. The frequencies of the predominant peaks are close, but not necessarily equal, to those of the most amplified instability waves predicted from the mean flow fields using linear stability analysis. They also fall in most cases within or very near the allowable frequency bands of the free-stream upstream-propagating guided jet waves obtained using a vortex-sheet model and jump from one band to another as the Mach number increases. At these frequencies, moreover, high levels organized into elongated stripes are found in the jet potential core and standing-wave patterns are visible at the edges of the shear layers in the power spectral densities of pressure and velocity fluctuations. Therefore, the free-stream upstream-propagating guided jet waves appear to interact with and excite the instability waves near the nozzle of the present jets, as in screeching and impinging jets. This explains the disparities of the frequencies and azimuthal modes of the instability waves dominating early on in the shear layers of initially laminar jets and their discontinuous changes and staging behaviours as the jet velocity varies.

The generation of acoustic tones in four round jets at a Mach number of 0.9 impinging on a plate at a distance $L=6r_0$ from the nozzle exit, where $r_0$ is the nozzle radius, has been investigated by large-eddy simulation. Three plates are perforated by holes of diameters $h=2r_0$ , $3r_0$ and $4.4r_0$ , centred on the jet axis, whereas the fourth plate has no hole, in order to study the effects of the hole on the jet flow and acoustic fields. In all cases, acoustic tones emerge in the jet near field, upstream but also downstream of the plate for the perforated plates. Their frequencies are similar for all jets and close to those predicted for aeroacoustic feedback loops establishing between the nozzle and the plate, involving flow disturbances convected downstream and waves propagating upstream at the ambient speed of sound. Their levels, however, decrease with the hole diameter, by a few dB for $h\leqslant 3r_0$ but approximately by 40 dB for $h=4.4r_0$ . The features of the feedback loops are identified by computing two-dimensional space–time correlations and frequency–wavenumber spectra of the pressure fluctuations in the jet mixing layers. These loops are found to be closed by free-stream upstream-propagating guided jet waves, produced by the impingement of vortical structures on the plate for $h\leqslant 3r_0$ and by the scattering of the jet aerodynamic pressure fluctuations by the hole edges for $h=4.4r_0$ . Finally, an acoustic analogy is used to show that the contributions of the pressure fluctuations on the plate to the radiated noise are dominant.

This study focuses on a water injection system, typical of those used to inject water in the motor jet plume of rocket engines to reduce noise, and particularly on the destabilization of the liquid jet that leads to a spray system. For that purpose, a large-eddy simulation is conducted for an experimental water jet of the literature. It is a sprinkler whose Reynolds number is [Formula: see text] and nozzle exit diameter is [Formula: see text], similar to injectors used for jet noise reduction studies at a reduced scale. A diffuse interface method is used to calculate the dense liquid phase, and the dispersed phase containing droplets is calculated with an Eulerian solver. Transfers between the dense and the dispersed phases are modeled in the coupling procedure, including the atomization and impingement processes. The jet mean radius and initial instability frequency are consistent with the experimental data, while the position of the jet transition varies with the fluctuation levels at the nozzle exit. The droplets are created in the shear layer and accumulate on the jet center when only the atomization process is considered. When also implemented, the impingement phenomenon, however, is shown to absorb the droplets before they reach the center.

In this paper, the acoustic pressure generated in the near field of a single stream cold jet is investigated. The analysis is focused on the effect of the initial conditions at the nozzle exit parametrized by considering two different turbulence levels and two different boundary layer thicknesses. The study has been performed by processing a numerical database obtained by large-eddy simulations (LES) of a jet flow at M = 0.9 and Re = 105. Pressure time series are obtained from pointwise virtual probes located in several radial and axial positions in the jet near-field. The acoustic pressure is extracted by the application of a consolidated wavelet-based procedure and the achieved acoustic signals are analyzed in terms of global quantities as well as by computing wavelet-reconstructed Fourier spectra. The results show that both the boundary-layer thickness and the turbulence level significantly affect the acoustic pressure in terms of its intensity and directivity whereas the distribution of energy in the frequency domain depends appreciably, only on the boundary-layer thickness.

Les effets du nombre de Mach sur les composantes tonales du bruit rayonné par des jets impactant une plaque, dues à l’établissement d’une boucle de rétroaction entre la buse et la plaque, sont étudiés en réalisant les simulations numériques de six jets impactant. La distance entre la plaque et la buse est de L=8r0, où r0 est le rayon de la buse, et les nombres de Mach d’éjection des jets varient entre 0.6 et 1.1. Au cours des simulations, les équations de Navier-Stokes compressibles et instationnaires en coordonnées cylindriques sont résolues à l’aide de schémas aux différences finies d’ordre élevé peu dissipatifs et peu dispersifs. Pour M=0.6, une composante tonale émerge de 2 à 3 dB au-dessus du bruit large-bande dans les spectres acoustiques, ce qui suggère une résonance peu marquée. Pour M≥0.75, un rayonnement acoustique tonal de forte intensité est observé vers l’amont de l’écoulement. Ce rayonnement est créé par une boucle de rétroaction s’établissant entre la buse et la plaque. Pour M≤1, les composantes tonales rayonnées sont associées à un mode d’oscillation axisymétrique du jet, tandis que pour M=1.1, elles sont liées à un mode axisymétrique et à un mode hélicoïdal, ce qui montre que le nombre de Mach affecte la structure azimutale des jets. Leurs fréquences diminuent avec le nombre de Mach. En ce qui concerne leurs amplitudes, elles augmentent d’environ 45 dB entre M=0.6 et 1, puis diminuent de 15 dB pour M=1.1.

Aeroacoustic analyses of new generation and highly innovative aircraft configurations such as Hybrid and Blended Wing Body cannot disregard the development of low-order models for the jet noise source, essential to assess the propulsion-airframe interactions since the conceptual/preliminary design stage. The use of wave-packets to model jet noise is based on the widely accepted hypothesis that the large-scale turbulent structures, responsible for noise peaks emitted by subsonic and supersonic jets, can be modelled as instability waves that grow and then decay with axial distance. In this study, a M=0.9 high-subsonic jet is represented as a cylindrical surface radiating the pressure disturbances of a wave-packet source, whose parameters are optimized using near-field information from LES simulations. The importance of calibrating the model with near-field pressure data stems from the fact that innovative aircraft configurations have engines nacelles typically positioned at a few diameters from the wing or fuselage. The main scope of this analysis is to provide a noise source model that can be coupled with Boundary Elements Method (BEM) codes for aeroacoustic scattering evaluations. A quite good agreement is achieved at multiple near-field radial distances between the simulation data and model prediction for the dominating 0th azimuthal mode at the selected Strouhal numbers up to 1.

International audience; Large-eddy simulations (LES) of five overexpanded rocket jets impinging on a plate located at a distance of 30r 0 , where r 0 = D/2 is the nozzle radius, and of the corresponding free jet have been performed. The jets are at an exhaust Mach number of 3.1 and a Reynolds number of 2 × 10 5. Four plates are perforated with a hole of diameter h = 1.33D, 2D, 3D and 4D, whereas the last one is not, in order to investigate the effects of the hole on the jet flow and acoustic fields. The acoustic levels are highest for the non-perforated plate, and decrease as the hole diameter increases, due to weaker interactions between the jet and the plate. In comparison with the levels of the free jet, they are higher by about 5 dB for the full plate, 4 dB for h = 1.33D and 2D, 3 dB for h = 3D and 2 dB for h = 4D. In the upstream direction, for the free jet, the broadband shock associated noise (BBSAN) is dominant. For the impinging jets, spatial Fourier transforms and two-dimensional spatial correlations show that the main upstream noise component is produced by the impingement of the jet turbulent structures on the plate, and that the reflections of the Mach waves on the plate are negligible. In the downstream direction, for the free jet and down to the plate for the impinging jets, the acoustic field is dominated by Mach waves produced by the convection of the jet coherent structures at a supersonic velocity. Downstream of the plate, sound waves are generated by interactions between the jet flow and the plate.

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° .

International audience; The generation of noise by jets with highly disturbed laminar boundary-layer profiles at the nozzle exit, also referred to as initially nominally laminar jets in the literature, is investigated using large-eddy simulation and linear stability analysis. Four jets at a Mach number of 0.9 and a Reynolds number of 5 × 10 4 , one with a nonlaminar boundary-layer profile and three others with laminar profiles, are considered for exit peak turbulence intensities equal to 6% in the nonlaminar case and to 9% in the laminar ones. The jets with laminar boundary-layer profiles all radiate greater sound pressure levels than the jet with a nonlaminar profile but weaker initial disturbances. This particularly appears at high frequencies for the jets with a thinner boundary layer compared with the nonlaminar case. These results are shown to be related to the dependence on the shape of the boundary-layer profile of the most unstable frequencies downstream of the nozzle. For a laminar profile, these frequencies are similar to those obtained downstream in the mixing-layer profiles, whereas they are higher for a nonlaminar profile. Despite larger nozzle-exit flow disturbances, this leads to longer-term persistence of coherent large-scale structures in the shear layers, hence stronger velocity fluctuations and noise levels, for the present initially nominally laminar jets than for the other one.

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.

International audience; We investigate the distributions of length and velocity scales in a Mach 0.9 isothermal round jet for the purpose of developing a linear surface-based model for the noise source that can be informed by the time-averaged flow field. Large eddy simulation of the flow enables the computation of two-point space-time correlations throughout the jet and its near acoustic field. The resulting time, length, and convective-velocity scales are examined on the surface of peak Reynolds stress (SPS), representing the location of the most energetic eddies, and on a "radiator surface" at the boundary between the rotational and irrotational fields. The radiator surface is defined such that the convective velocity distribution on it matches that on the surface of peak Reynolds stress. The location of the radiator surface, and distributions of flow scales on it, are critical elements of the noise source model and are examined in detail. The nature of the space-time correlations, and resulting scales, differ significantly for axial velocity fluctuations and pressure fluctuations. Velocity-based correlations appear to capture localized turbulent events, while pressure-based correlations appear dominated by the interaction of large eddies with the surrounding potential flow. Consequently the axial and radial distributions of the corresponding length scales exhibit different trends. Correlation scales on the radiator surface are larger than on the SPS thus indicating that fine-scale vortical motions do not make a significant imprint on the radiator surface. Scales associated with the Reynolds-averaged flow field, relevant to low-cost modeling, are emulated from LES data and compared to the LES-based scales. Simple relationships are established that may aid the development of rapid predictive models.

Wave steepening and shock coalescence due to nonlinear propagation effects are investigated for a cold Mach 3 jet. The jet flow and near pressure fields are computed using large-eddy simulation. The near acoustic field is propagated to the far field by solving the linearized or the weakly nonlinear Euler equations. Near the angle of peak levels, the skewness factors of the pressure fluctuations for linear and nonlinear propagations display positive values that are almost identical. Thus, the positive asymmetry of the fluctuations originates during the wave generation process and is not due to nonlinear propagation effects. Compressions in the signals are much steeper for a nonlinear than for a linear propagation, highlighting the crucial role of nonlinear distortions in the formation of steepened waves. The power transfers due to nonlinear propagation are examined for specific frequencies by considering the spatial distribution of the Morfey-Howell indicator in the near and far acoustic fields. They are in good agreement with the direct measurements performed by comparing the spectra for nonlinear and linear propagations. This shows the suitability of the Morfey-Howell indicator to characterize nonlinear distortions for supersonic jets.

The links between coherent structures in the shear layer of an isothermal Mach 2 jet and steepened Mach waves just outside the jet are investigated using large-eddy simulation. Conditional averages...

International audience; Four initially highly disturbed round jets at a Mach number of 0.9 impinging on a plate located at a distance L = 6r 0 , where r 0 is the nozzle radius, have been computed by Large-Eddy Simulation (LES). Three of the plates have a hole of diameter d = 2r 0 , 3r 0 and 4.4r 0 , centered on the jet axis, whereas the fourth one has no hole, in order to study the effects of the hole diameter on the jet flow and acoustic fields. For the cases with no hole and the holes of diameter d = 2r 0 and 3r 0 , a feedback loop establishes between the jet nozzle and the plate, which generates intense tones in the acoustic spectra. For d = 4.4r 0 , a similar feedback loop is observed, but it generates tones of weaker amplitude. For all cases, the feedback frequency is in agreement with the classical model of an aeroacoustic feedback between the nozzle and the plate. The acoustic levels are however reduced when the hole diameter increases. The same standing wave pattern between the nozzle and the plate is highlighted by a study of the aerodynamic field at the main tonal frequency. Moreover, for d = 2r 0 and 3r 0 , flow rate fluctuations are caused by turbulent structures passing through the hole at the feedback frequency, which creates a tonal radiation downstream of the plate. A model of this radiation by a monopole source of equivalent flow rate is proposed.

The presence and properties of acoustic peaks near the nozzle of impinging rocket jets have been investigated. Four jets at a Mach number of 3.1 impinging on a plate at a distance L = 15r0, 20r0, 25r0 and 30r0 from the nozzle, where r0 is the nozzle radius, have been computed using large-eddy simulations. In all cases, upstream-travelling pressure waves are generated by the jet impingement on the plate, with amplitudes decreasing with the nozzle-to-plate distance. The near-nozzle pressure spectra contain peaks, at frequencies not varying much with this distance. For L ≥ 20r0, the spectra are dominated by a low-frequency peak, whereas two additional high-frequency peaks emerge for L = 15r0. The low-frequency peak is associated with the azimuthal mode nθ = 0, whereas the two other ones are due to strong components for modes nθ ≥ 1. As for near-nozzle tones for free and impinging jets at lower Mach numbers, the peak frequencies fall close to the frequency bands of the upstream-propagating guided jet waves, showing a link between the peaks and the latter waves. Regarding the peak levels, they do not change significantly with the nozzle-to-plate distance for the low-frequency peak, but they decrease by 1.5 to 18 dB as the distance increases for the other peaks. Finally, for L ≥ 20r0, the near-nozzle peak frequency is close to that of the strongest shear-layer structures, indicating a connexion between the upstream noise and these structures. For L = 15r0, a shock-leakage mechanism of a near-plate shock is found to generate the upstream noise.

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.

International audience; A flux reconstruction technique is presented to perform aeroacoustic computations using implicit high-order spatial schemes on multiblock structured grids with nonconforming interfaces. The use of such grids, with mesh spacing discontinuities across the block interfaces, eases local mesh refinements, simplifies the mesh generation process, and thus facilitates the computation of turbulent flows. In this work, the spatial discretization consists of sixth-order finite-volume implicit schemes with low-dispersion and low-dissipation properties. The flux reconstruction is based on the combination of noncentered schemes with local interpolations to define ghost cells and compute flux values at the grid interfaces. The flow variables in the ghost cells are calculated from the flow field in the grid cells using a meshless interpolation with radial basis functions. In this study, the flux reconstruction is applied to both plane and curved nonconforming interfaces. The performance of the method is first evaluated by performing two-dimensional simulations of the propagation of an acoustic pulse and of the convection of a vortex on Cartesian and wavy grids. No significant spurious noise is produced at the grid interfaces. The applicability of the flux reconstruction to a three-dimensional computation is then demonstrated by simulating a jet at a Mach number of 0.9 and a diameter-based Reynolds number of 4 × 10 5 on a Cartesian grid. The nonconforming grid interface located downstream of the jet potential core does not appreciably affect the flow development and the jet sound field, while reducing the number of mesh points by a factor of approximately two.

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International audience; Numerical simulations of temporally-developing round jets at a diameter-based Reynolds number of 12,500 are carried out with the aim of investigating temperature effects on the formation of the steepened acoustic waves usually associated with crackle noise. One isothermal and four hot jets at a static temperature equal to 2 or 4 times that of the ambient medium are considered. The isothermal jet has a Mach number of 2 while the hot jets have either the same Mach number or the same jet speed as the isothermal jet. At a constant Mach number, the pressure levels and skewness factors are higher at a higher temperature, indicating a more pronounced steepened aspect of the acoustic waves. This increase is due to the rise of the jet speed from 2 to 4 times the ambient sound speed in that case. When the jet velocity is constant, lower pressure levels are obtained at a higher temperature, and a slight reduction of the skewness factor is observed. This reduction is explained by the decrease of the ratio between the convection speed and the jet velocity with temperature. The present study thus allows us to isolate the effects of temperature on the generation of steepened waves near high-speed free shear flows.

International audience; In the present study, two-dimensional spatial correlations are calculated in the flow and the near pressure fields of two isothermal round jets at a Mach number of 0.9, computed by highly-resolved simulations using cylindrical coordinates (r , θ, z). The two jets have diameter-based Reynolds numbers of 3, 125 and 100, 000, and they are initially weakly and strongly disturbed, respectively. For both jets, correlations are evaluated between signals at a given point, namely flow fluctuations on the jet axis at the end of the potential core and pressure fluctuations in the jet near field, and 2-D fields acquired in sections (z, r). The full signals but also the axisymmetric and first azimuthal modes are considered. Overall, despite the significant differences in Reynolds number and nozzle-exit conditions, the results for the two jets are very similar. Strong levels of correlations are obtained over large spatial regions and long time periods, providing information on noise generation mechanisms. In particular, the 2-D correlation fields reveal the presence of a wavepacket-like structure growing in the jet mixing layers, centered on a correlation spot in the potential core, and peaking in amplitude around the end of the jet core, which leads to the emission of sound waves in the downstream direction.

Three planar impinging supersonic jets of infinite extent are simulated using compressible large eddy simulations in order to study the effects of the angle of impact on the flow and acoustic fields of the jet. At the exit of a nozzle of height h, they are ideally expanded and have an exit velocity uj, yielding a Mach number of 1.28 and a Reynolds number of 5 × 104. They impinge on a flat plate at a distance 5.5 h from the nozzle lips with angles of 60°, 75°, and 90° between the jet direction and the plate. Mean velocity flows and snapshots of density, pressure, and vorticity are first shown. The mean convection velocity of the turbulent structures in the jet shear layers is then determined. The sound pressure levels are computed, and several tones due to the presence of a feedback mechanism are found to establish between the nozzle lips and the flat plate. They agree well with the corresponding measurements and with the classical model of the feedback mechanism. Moreover, when the angle of impact deviates from 90° to 75°, a jump from the third to the fourth mode of the feedback mechanism and a reduction in intensity are noted. By applying a Fourier decomposition to the near pressure fields, hydrodynamic–acoustic standing waves are found for each dominant tone frequency. Moreover, as suggested by amplitude fields and velocity spectra in the jet shear layers, the feedback mechanism seems to establish mainly along the lip that is farther away from the plate when the impact angle is not normal. This jump from the third to the fourth mode is similar to the jump observed experimentally for an angle of impact of 90° when the nozzle-to-plate distance increases from 5.5 h to 5.85 h. Finally, for an angle of impact of 60°, it is seen that none of the modes of the feedback persists in time, but that several modes randomly establish during short periods of time. These rapid switches between different modes lead to several tones that are less energetic on average and centered on St = 0.25.

International audience; In a previous work [Bogey, J. Fluid Mech. 859, 1022 (2019)], the potential-core closing of temporally developing isothermal round jets at a Mach number M = 0.9 was shown to generate a strong axisymmetric noise component in the downstream direction. The persistence of this component is investigated in the present work for jets at M = 0.3, 0.6, 1.3, and 2 computed by direct numerical simulation, from a low subsonic to a high supersonic Mach number. The flow and sound fields are presented, and the Mach number scaling of their magnitudes and spectral content is examined. The centerline velocity and hydrodynamic pressure spectra are close to each other using k z r 0 in abscissa, where k z and r 0 are the axial wave number and the initial jet radius, respectively. The sound spectra for M 1.3 collapse well when they are plotted as a function of k z r 0 M −1 and adjusted in amplitude using a M 7.5 power law, whereas a k z r 0 scaling and a lower power-law exponent seem to apply to the spectra for M 1.3. The flow and sound fields are then correlated with each other, and conditionally averaged based on a synchronization of the fields with the minimum values of centerline velocity at potential-core closing. The noise component radiated in the downstream direction for M = 0.9 is clearly identified for M = 0.6, 1.3, 2, and is also detected, albeit with more difficulty, for M = 0.3, indicating the presence of the associated sound source over a wide range of Mach numbers. In all cases, its generation process extracted by the conditional averaging consists in the growth of a spot of low velocity and a high vorticity level in the inner side of the mixing layer, reaching a peak intensity at its arrival on the axis and weakening subsequently. The use of different trigger conditions for the averaging suggests that, for a given Mach number, the amplitude of the acoustic waves radiated during that stage depends linearly on the velocity deficit and the strength of the vortical structures on the jet centerline at the time of potential-core closing.

The influence of the nozzle-exit boundary-layer profile on high-subsonic jets is investigated by performing compressible large-eddy simulations (LES) for three isothermal jets at a Mach number of 0.9 and a diameter-based Reynolds number of $5\times 10^{4}$, and by conducting linear stability analyses from the mean-flow fields. At the exit section of a pipe nozzle, the jets exhibit boundary layers of momentum thickness of approximately 2.8 % of the nozzle radius and a peak value of turbulence intensity of 6 %. The boundary-layer shape factors, however, vary and are equal to 2.29, 1.96 and 1.71. The LES flow and sound fields differ significantly between the first jet with a laminar mean exit velocity profile and the two others with transitional profiles. They are close to each other in these two cases, suggesting that similar results would also be obtained for a jet with a turbulent profile. For the two jets with non-laminar profiles, the instability waves in the near-nozzle region emerge at higher frequencies, the mixing layers spread more slowly and contain weaker low-frequency velocity fluctuations and the noise levels in the acoustic field are lower by 2–3 dB compared to the laminar case. These trends can be explained by the linear stability analyses. For the laminar boundary-layer profile, the initial shear-layer instability waves are most strongly amplified at a momentum-thickness-based Strouhal number $St_{\unicode[STIX]{x1D703}}=0.018$, which is very similar to the value obtained downstream in the mixing-layer velocity profiles. For the transitional profiles, on the contrary, they predominantly grow at higher Strouhal numbers, around $St_{\unicode[STIX]{x1D703}}=0.026$ and 0.032, respectively. As a consequence, the instability waves rapidly vanish during the boundary-layer/shear-layer transition in the latter cases, but continue to grow over a large distance from the nozzle in the former case, leading to persistent large-scale coherent structures in the mixing layers for the jet with a laminar exit velocity profile.

International audience; Two temporally developing isothermal round jets at a Mach number of 0.9 and Reynolds numbers of 3125 and 12 500 are simulated in order to investigate noise generation in high-subsonic jet flows. Snapshots and statistical properties of the flow and sound fields, including mean, root-mean-square and skewness values, spectra and auto-and cross-correlations of velocity and pressure, are presented. The jet at a Reynolds number of 12 500 develops more rapidly, exhibits more fine turbulent scales and generates more high-frequency acoustic waves than the other. In both cases, however, when the jet potential core closes, mixing-layer turbulent structures intermittently intrude on the jet axis and strong low-frequency acoustic waves are emitted in the downstream direction. These waves are dominated by the axisymmetric mode and are significantly correlated with centreline flow fluctuations. These results are similar to those obtained at the end of the potential core of spatially developing jets. They suggest that the mechanism responsible for the downstream noise component of these jets also occurs in temporal jets, regardless of the Reynolds number. This mechanism is revealed by averaging the flow and pressure fields of the present jets using a sample synchronization with the minimum values of centreline velocity at potential-core closing. A spot characterized by a lower velocity and a higher level of vorticity relative to the background flow field is found to develop in the interfacial region between the mixing layer and the potential core, to strengthen rapidly and reach a peak intensity when arriving on the jet axis, and then to break down. This is accompanied by the growth and decay of a hydrodynamic pressure wave, propagating at a velocity which, initially, is close to 65 per cent of the jet velocity and slightly increases, but quickly decreases after the collapse of the high-vorticity spot in the flow. During that process, sound waves are radiated in the downstream direction.

In high-speed aircraft, supersonic jets used for propulsion can lead to very intense aerodynamically generated acoustic noise. Thus, there is a need to study the aerodynamic and aeroacoustic properties of highly compressible jets. In previous studies, several simulations of supersonic jets have been conducted. Unfortunately, the turbulence intensity at the nozzle exit was dependent on the internal geometry of the nozzle and could not be tuned. This is a pity given that, as shown experimentally and numerically for subsonic and supersonic jets, the boundary layer state of the jet affects the jet flow and noise. In this study, a boundary-layer tripping method permitting to obtain an initially turbulent supersonic jet is studied. The influence of the tripped jet boundary layers on the flow and acoustic fields of the jet is analyzed. The impact of nozzle-exit turbulence levels on the noise radiation and notably on the acoustic components specific to supersonic jets (screech noise, broadband shock-associated noise, mixing noise and Mach wave radiation) is discussed.

In this Note, the origin of the oscillation modes of screeching round jets is investigated by assuming that the feedback part of the aeroacoustic loop responsible for screech noise can be modeled by considering the neutral acoustic wave modes of the equivalent ideally expanded jets.

International audience; Five temporally-developing isothermal round jets at a diameter-based Reynolds number ReD of 3,125 and Mach numbers M of 0.3, 0.6, 0.9, 1.3 and 2 have been computed using direct numerical simulation. The flow and near acoustic fields of the jets are described in detail, and cross-correlations between the two fields are presented in order to identify noise generation mechanisms, and especially that associated with the jet potential-core closing. That closing is found to occur later at a higher Mach number. Apart from that, the jet flow properties, including velocity spectra, are similar, and even nearly identical for M ≤ 1.3. The jets appear to radiate acoustic waves mainly in the downstream direction, with amplitude increasing and wavelength decreasing with the Mach number. More quantitatively, the noise spectra nearly collapse when they are plotted as as a function of kzr0M −1 , where kz is the axial wavenumber and r0 is the initial jet radius, and scaled in amplitude using a M 8 power law. The angle of sound emission is noted to decrease monotonically as time passes, except for the jet at M = 2 for which it is close to the angle expected for Mach waves over a long time period. Finally, significant values of correlations are obtained between the pressure waves propagating downstream in the jet near field and the flow fluctuations on the jet axis near the time of potential-core closing for M ≥ 0.6, with levels strengthening with the Mach number. The correlations calculated from the flow fluctuations at r = r0 are much weaker. For the jet at M = 2, however, they suggest the generation of Mach waves in the mixing layers. These results are comparable to those reported for spatially-developing jets.

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The properties of the flow near the plate and in the wall jets have been investigated from large-eddy simulation data of round impinging jets. Four jets are underexpanded and four jets are ideally expanded, which allowed examination of the influence of the presence of shock-cell structures. The underexpanded jets are characterized by a fully expanded Mach number of 1.56 and an exit Mach number of 1. The ideally expanded jets have a Mach number of 1.5. The Reynolds number of the eight jets is equal to 6 × 104. The jets impinge normally on a flat plate located from 4.16r0 to 12r0 downstream of the nozzle and generate acoustic tones due to an aeroacoustic feedback mechanism. In this paper, the near pressure and density fields of the jets are characterized using Fourier transform on the nozzle exit plane, the plate, and an azimuthal plane. First, mean and rms radial velocities of the wall jets are examined. The impact of the shock-cell structure on the wall jet is discussed. The pressure spectra on the plate are then shown as a function of the radial coordinate. The tone frequencies are all visible where the jet shear layers impinge the plate, but only some of them emerge in the wall jet created after the impact. For the ideally expanded jets, the temporal organization of the wall jet along the frequencies of the feedback mechanism decreases with the nozzle-to-plate distance, but for the non-ideally expanded jets, this organization is linked to the oscillation of the Mach disk located just upstream of the plate. Consecutively, the amplitude and the phase fields at the tone frequencies are represented on the three planes mentioned earlier. Similar spatial organizations of the turbulent structures are found in the jet shear layers and in the wall jets. Thus, axisymmetric and helical arrangements of the structures in the jet shear layers lead to concentric and spiral distributions of the structures on the plate, respectively. In particular, for one of the underexpanded jets, a spiral shape and concentric rings, associated with two tone frequencies generated simultaneously, are observed on the flat plate in the pressure and density phase fields. Finally, the convection velocity of the turbulent structures at the tone frequencies in the wall jets are evaluated based on phase fields, and the mean convection velocity is computed using cross correlations of radial velocity. The results are in good agreement with those from a recent experimental study of ideally expanded impinging jets.

A computational method for the simulation of viscous and compressible gas–gas flows is presented. It consists in solving the Navier–Stokes equations associated with a convection equation governing the motion of the interface between two gases using high-order finite-difference schemes. A discontinuity-capturing methodology based on sensors and a spatial filter enables capturing shock waves and deformable interfaces. One-dimensional test cases are performed as validation and to justify choices in the numerical method. The results compare well with analytical solutions. Shock waves and interfaces are accurately propagated, and remain sharp. Subsequently, two-dimensional flows are considered including viscosity and thermal conductivity. In Richtmyer–Meshkov instability, generated on an air–SF6 interface, the influence of the mesh refinement on the instability shape is studied, and the temporal variations of the instability amplitude is compared with experimental data. Finally, for a plane shock wave propagating in air and impacting a cylindrical bubble filled with helium or R22, numerical Schlieren pictures obtained using different grid refinements are found to compare well with experimental shadow-photographs. The mass conservation is verified from the temporal variations of the mass of the bubble. The mean velocities of pressure waves and bubble interface are similar to those obtained experimentally.

Three isothermal round jets at a Mach number of 0.9 and a diameter-based Reynolds number of 105 are computed by large-eddy simulation using four different meshes in order to investigate the grid sensitivity of the jet flow field and noise. The jets correspond to two initially fully laminar jets and one initially strongly disturbed jet considered in previous numerical studies. At the exit of a pipe nozzle of radius r0, they exhibit laminar boundary-layer mean-velocity profiles of thickness [Formula: see text] and [Formula: see text], respectively. For the third jet, a peak turbulence intensity close to 9% is also imposed by forcing the boundary layer in the nozzle. The grids contain up to one billion points, and, compared to the grids used in previous simulations, they are finer in the axial direction downstream of the nozzle and in the radial direction on the jet axis and in the outer region of the mixing layers. The main flow field and noise characteristics given by the simulations, including the mixing-layer thickness, the centerline mean velocity, the turbulence intensities on the nozzle lip line and the jet axis, spectra of velocity and far-field pressure obtained from the jet near field by solving the isentropic linearized Euler equations, are presented. With respect to those from previous studies, the results are very similar for the initially laminar jet with thick boundary layers, but they differ significantly for the initially laminar jet with thin boundary layers and for the initially disturbed jet. For the latter two jets, using a finer grid leads to a faster flow development, to higher turbulence intensities in the shear layers and at the end of the potential core, to stronger large-scale structures, and to the generation of more low-frequency noise. Moreover, very small mesh spacings appear to be necessary all along the jet mixing layers, and in particular during their early stages of growth, to properly capture the formation and dynamics of the flow coherent structures and thus obtain results in good agreement with measurements available for high-Reynolds-number jets.

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International audience