Investigation of tone generation in ideally expanded supersonic planar impinging jets using large-eddy simulation

Abstract

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.

Flow Features near Plate Impinged by Ideally Expanded and Underexpanded Round Jets

“…Overall, for the ideally expanded jets, about 10 tones are noticed, as observed for ideally expanded planar supersonic jets experimentally [32] and numerically [33]. On the contrary, only two or three dominant tones are found for the nonideally expanded jets, as already noted in various experimental studies [6,7,34,35].…”

“…This structure is due to the generation of a hydrodynamic-acoustic standing wave by the aeroacoustic feedback mechanism. The number of cells in the standing wave is equal to the mode number of the feedback mechanism in the model of Ho and Nosseir [3], as shown by Gojon et al [33] using a model of an hydrodynamic-acoustic standing wave proposed by Panda et al [36]. The phase field at θ 0, in Fig.…”

“…17b reveals a cell structure between the nozzle and the plate, containing four cells. This structure is due to the generation of a hydrodynamic-acoustic standing wave by the aeroacoustic feedback mechanism, and the number of cells is equal to the mode number of the feedback mechanism [33]. Moreover, a symmetric organization with respect to the jet axis appears in the phase field of Fig.…”

Feedback loop and upwind-propagating waves in ideally expanded supersonic impinging round jets

“…More precisely, the lower and upper tone frequencies, respectively associated with varicose (symmetric) jet oscillation modes and with sinuous (antisymmetric) oscillation modes, are located in or very near the frequency ranges of the first symmetric and the first antisymmetric upstream-propagating acoustic modes. More recently, similar results were obtained by Gojon, Bogey & Marsden (2016) for ideally expanded supersonic impinging planar jets at a Mach number of 1.28 computed using large-eddy simulations (LES). In that work, in addition, the analysis of the upstream-propagating acoustic wave modes of the jet was combined with the classical feedback-loop model.…”

“…The latter authors investigated the staging behaviour of the oscillation frequency with the nozzle-to-plate distance and jet pressure ratio. Several 3-D LES have also been run for perfectly, over-and underexpanded impinging jets by Dauptain, Cuenot & Gicquel (2010), Brès et al (2011), Dauptain, Gicquel & Moreau (2012, Uzun et al (2013), Hildebrand & Nichols (2015), Gojon et al (2016) and Gojon & Bogey (2017), with the two last references being mentioned above. Based on their numerical results, Dauptain et al (2012) proposed an improved feedback-loop model in order to predict the tone frequencies generated by underexpanded jets.…”