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.