The generation of tones in a supersonic planar jet impinging on a flat plate normally has been investigated by performing compressible large-eddy simulations using low-dissipation and low-dispersion finite differences. At the exit of a straight nozzle of height $h$, the jet is ideally expanded, and has a Mach number of 1.28 and a Reynolds number of $5\times 10^{4}$. Four distances between the nozzle and the plate between $3.94h$ and $9.1h$ have been considered. Flow snapshots and mean velocity fields are first presented. The variations of turbulence intensities and of the convection velocity in the jet shear layers are then examined. The properties of the jet near fields are subsequently described, in particular by applying Fourier decomposition to the pressure fields. Several coexisting tones appear to be generated by aeroacoustic feedback loops establishing between the nozzle lip and the flat plate, which also lead to the presence of hydrodynamic–acoustic standing waves. The tone frequencies are consistent with those given by the aeroacoustic feedback model and with measurements for high-aspect-ratio rectangular jets. The jet oscillation modes at these frequencies are characterized, and found to agree with experimental data. Their symmetric or antisymmetric natures are shown to be well predicted by a wave analysis carried out using a vortex sheet model of the jet, providing the allowable frequency ranges for the upstream-propagating acoustic waves. Thus, it is possible, for an ideally expanded impinging planar jet to predict both the frequencies of the tones and the symmetric or antisymmetric nature of the corresponding oscillation modes by combining the aeroacoustic feedback model and the wave analysis.

The aeroacoustic feedback loop establishing in a supersonic round jet impinging on a flat plate normally has been investigated by combining compressible large-eddy simulations and modelling of that loop. At the exit of a straight pipe nozzle of radius $r_{0}$, the jet is ideally expanded, and has a Mach number of 1.5 and a Reynolds number of $6\times 10^{4}$. Four distances between the nozzle exit and the flat plate, equal to $6r_{0}$, $8r_{0}$, $10r_{0}$ and $12r_{0}$, have been considered. In this way, the variations of the convection velocity of the shear-layer turbulent structures according to the nozzle-to-plate distance are shown. In the spectra obtained inside and outside of the flow near the nozzle, several tones emerge at Strouhal numbers in agreement with measurements in the literature. At these frequencies, by applying Fourier decomposition to the pressure fields, hydrodynamic-acoustic standing waves containing a whole number of cells between the nozzle and the plate and axisymmetric or helical jet oscillations are found. The tone frequencies and the mode numbers inferred from the standing-wave patterns are in line with the classical feedback-loop model, in which the loop is closed by acoustic waves outside the jet. The axisymmetric or helical nature of the jet oscillations at the tone frequencies is also consistent with a wave analysis using a jet vortex-sheet model, providing the allowable frequency ranges for the upstream-propagating acoustic wave modes of the jet. In particular, the tones are located on the part of the dispersion relations of the modes where these waves have phase and group velocities close to the ambient speed of sound. Based on the observation of the pressure fields and on frequency–wavenumber spectra on the jet axis and in the shear layers, such waves are identified inside the present jets, for the first time to the best of our knowledge, for a supersonic jet flow. This study thus suggests that the feedback loop in ideally expanded impinging jets is completed by these waves.

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Flow structure oscillations and tone generation mechanisms in an underexpanded round jet impinging on a flat plate normally have been investigated using compressible large-eddy simulations. At the exit of a pipe nozzle of diameter D, the jet is characterized by a nozzle pressure ratio of 4.03, an exit Mach number of 1, a fully expanded Mach number of 1.56, and a Reynolds number of 6 × 10 4. Four distances between the nozzle and the plate of 2.08D, 2.80D, 3.65D, and 4.66D are considered. Snapshots of vorticity, density, pressure, and mean velocity flowfields are first presented. The latter results compare well with data of the literature. In three cases, in particular, a Mach disk appears to form just upstream from the plate. The convection velocity of flow structures between the nozzle and the plate, and its dependence on the nozzle-to-plate distance, are then examined. The properties of the jet near pressure fields are subsequently described using Fourier analysis. Tones emerge in the spectra at frequencies consistent with those expected for an aeroacoustic feedback loop between the nozzle and the plate as well as with measurements. Their amplitudes are particularly high in the presence of a near-wall Mach disk. The axisymmetric or helical natures of the jet oscillations at the tone frequencies are determined. The motions of the Mach disk found just upstream from the plate for certain nozzle-to-plate distances are then explored. As noted for the jet oscillations, axially pulsing and helical motions are observed, in agreement with experiments. Finally, the intermittency of the tone intensities is studied. They significantly vary in time, except for the two cases where the near-wall Mach disk has a nearly periodic motion at the dominant tone frequency.

In the first part of the paper, a modified artificial dissipation mechanism permitting to perform Large-Eddy Simulations of highly compressible flows is proposed. This dissipation mechanism is evaluated using one linear 2-D test case and two non-linear 2-D test cases. In the second part, the flow and acoustic near-field of rectangular supersonic jets are explored using compressible LES based on this modified artificial dissipation mechanism. At the exit of a converging diverging rectangular nozzle of aspect ratio 2 and of design Mach number 1.5, the jets are overexpanded. Four simulations with four different temperature ratios ranging from 1 to 3 are performed in order to characterize the effect of the temperature on the aerodynamic and aeroacoustic fields of the jets. The geometry of the nozzle and the exit conditions are chosen in order to match those in the experimental study conducted at the University of Cincinnati. It is shown that the total number of cells in the shock cell structure decreases with the increase of the temperature ratio. However, the temperature does not influence the size of the first shock cell and the linear decrease of the shock cell size in the downstream direction. The Overall Sound Pressure Levels are then plotted along the minor and major axis. It is seen that the intensity of the screech feedback mechanism increases with the Temperature Ratio. Moreover, for JetTR25 and JetTR3, the strong flapping motion of the jet along the minor axis due to the screech feedback mechanism seems to yield to an asymmetric organization of the Mach wave radiation. The convection velocity of the turbulent structures in the jet shear layers along the minor axis is then studied. Once normalized by the jet exit velocity, the convection velocity is shown to decrease with the jet temperature ratio. In the last part of the paper, the near-and farfield acoustic are studied. In the near-field, screech tones which frequencies are consistent with both experimental data and a theoretical model are observed. In the far-field, four acoustic components typical of non-ideally supersonic jets are observed, namely the screech noise, the broadband shock-associated noise, the mixing noise and the Mach wave noise. Their directivities and frequencies are in agreement with experimental results and models.

In this paper, the origin and the properties of the oscillation modes in screeching nonideally expanded rectangular jets are investigated using compressible implicit LES of rectangular supersonic jets. At the exit of a converging diverging rectangular nozzle of aspect ratio 2 and of design Mach number 1.5, the jets are under-and over-expanded. Seven simulations with four different temperature ratios ranging from 1 to 3 and two different nozzle pressure ratios are performed. The geometry of the nozzle and the exit conditions are chosen such that to match the experimental study conducted at the University of Cincinnati. First, the over-expanded jets are studied. It is shown that the total number of shock cells decreases with increased temperature ratio. However, the temperature does not influence the size of the first shock cell and the linear decrease of the shock cell size in the downstream direction. The spreading of the jet is observed to be higher along the minor axis plane than along the major axis plane. The intensity of the screech noise increases with the temperature ratio in the present study although the opposite is observed in the experiments. Moreover, for jet temperature ratios of 2.5 and 3, the strong flapping motion of the jet along the minor axis plane due to the screech feedback mechanism yields to an antisymmetric organization of the Mach wave radiation. Thereafter, the near-and far-field acoustic are studied. In the near-field, screech tones are captured, whose frequencies are consistent with both experimental data and theoretical models. In the far-field, four acoustic components typical of non-ideally expanded supersonic jets are observed, namely the screech noise, the broadband shock-associated noise, the mixing noise and the Mach wave noise. Their directivities and frequencies are in agreement with experimental results and models. The mechanism of the screech noise generation is studied by using a Fourier decomposition of the pressure field. For the four over-expanded jets, a flapping motion along the diagonal or along the minor axis plane of the jet is noted. Finally, the hypothesis that the acoustic waves completing the feedback loop in these jets are linked to the upstreampropagating acoustic wave modes of the equivalent ideally expanded jets is tested. Using a jet vortex sheet model to describe the dispersion relations of these modes, it is found that this hypothesis allows us to explain the antisymmetric jet oscillation observed at the screech frequencies. Based on frequency-wavenumber decomposition of the pressure fluctuations in the jets, it is shown that at the screech frequencies, acoustic waves propagating in the upstream direction at the ambient speed of sound exist also in the jet flow, additionally

Supersonic round jets have been computed by compressible Large Eddy Simulation (LES) using low-dispersion and low-dissipation schemes. The jets are underexpanded, and are characterized by a Nozzle Pressure Ratio of N P R = Pr/Pamb = 4.03, where Pr is the stagnation pressure and Pamb is the ambient pressure. They have a fully expanded Mach number of Mj = 1.56, an exit Mach number of Me = 1, and a Reynolds number of Rej = ujD/ν = 5 × 10 4 , where ue and D are the jet exit velocity and the nozzle diameter, respectively. A free jet is first considered. Four jets impinging on a flat plate normally are then examined. The distance L between the nozzle lip and the flat plate varies from L = 4.16r0 up to L = 9.32r0 where r0 = D/2, for the impinging jets. The effects of the plate on the aerodynamic and acoustic properties of the jets are thus studied. For the free jet, snapshots of density, pressure and vorticity are presented. Mean velocity fields are displayed, they are in good agreement with experimental data. The near pressure field of the jet is investigated using Fourier decomposition. A screech tone component is found, at a frequency comparing well with experimental data and theoretical models. For the four impinging jets, similarly, flow snapshots and mean flow fields are shown. The results obtained are similar to the corresponding measurements. The convection velocity of large-scale structures in the jet shear layers is then evaluated and an expression giving the average convection velocity between the nozzle lips and the flat plate is proposed. The near pressure fields are then explored, and the main properties of the aeroacoustic feedback mechanism occurring between the nozzle lip and the flat plate are presented. The results are consistent with theoretical models and experimental data.

In this paper, an experimental characterisation of low Reynolds number rotors is performed in an anechoic room. Two commercially available two-bladed rotors as well as four three-dimensional (3D)-printed rotors with different numbers of blades (from two to five) are tested. The latter have canonical geometry, with an NACA0012 blade section profile, extruded in the radial direction with constant chord and constant 10° pitch. The experimental setup and the 3D printing strategy are first validated using results from the literature for the commercially available rotors. For all the tested rotors, four noise characteristics are analysed: the overall sound pressure level (OASPL), the amplitude of the blade passing frequency (BPF), and the amplitude of its first harmonic and the high-frequency broadband noise. For all the rotors, an increase in all noise characteristics is observed with the rotational speed (rpm) for all directivity angles. Moreover, an interesting change of pattern is observed for the amplitudes of the BPF and of its first harmonic, with, in the vicinity of the rotor plane, a minimum value for low rpm and/or high number of blades, and a maximum value for high rpm and/or low number of blades. This change in directivity leads to a similar change of directivity of the OASPL. For the broadband noise, a dipole-like pattern is obtained with a minimum value at θ=−10°, i.e., aligned with the trailing edge and thus indicating the generation of trailing edge noise. Finally, scaling laws that characterise the amplitude of the different noise components with respect to the rpm are proposed.