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

Abstract

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.

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

“…For the other jets, the sound pressure levels obtained in the vicinity of the nozzle also reveal several tone frequencies [16,17]. The first four Strouhal numbers of the tones for which the levels are 5 dB higher than the broadband noise are reported in Table 2.…”

“…More information can be found in previous papers [16,17]. The jets have a temperature ratio (TR) TR T r ∕T amb 1, where T r and T amb are the stagnation and the ambient temperatures.…”

“…direction. A complete description of the meshes can be found in the previous papers [16,17]. The discretization of the wall jet forming after the jet impact is analyzed at r 4r 0 .…”

“…In previous studies by the authors [16,17], the feedback loop and the associated oscillations of the jets have been studied. In this paper, the azimuthal organization of turbulent structures in the jet shear layers and on the flat plate, in the wall jets created after the impact, are characterized from data provided by large-eddy simulations.…”

“…In this paper, the azimuthal organization of turbulent structures in the jet shear layers and on the flat plate, in the wall jets created after the impact, are characterized from data provided by large-eddy simulations. The aerodynamic and acoustic properties of the eight jets have been detailed previously in Gojon and Bogey [16] for the nonideally expanded jets and in Bogey and Gojon [17] for the ideally expanded jets. The spatial organization and the convection velocity of the turbulent structures in the wall jet are examined from the pressure and density fields on the plate.…”