Noise of an overexpanded Mach 3.3 jet: non-linear propagation effects and correlations with flow

The noise emitted by an overexpanded round jet at a Mach number of 3.3 and a Reynolds number of 10(5), computed in a previous study using large-eddy simulation (LES), is investigated. In a first step, the non-linear sound propagation effects are quantified by performing two far-field wave extrapolations from the LES near-field data. The extrapolations are carried out by solving the linearized Euler equations in one case and the full Euler equations in the other, without atmospheric absorption, up to a distance of 240 radii from the jet nozzle exit. The non-linear effects are shown to be quite significant, resulting in a series of N-shaped waves in the pressure signals, and in weaker mid-frequency components and stronger high-frequency components in the spectra. Close to the peak directivity radiation angle, for instance, they lead to about a 8 dB loss and a 6 dB gain at the Strouhal numbers of 0.2 and 1, respectively. In a second step, noise generation mechanisms are discussed by calculating correlations between far-field pressure fluctuations and turbulent quantities in the jet. High levels of correlation are found with the centerline flow fluctuations at the end of the potential core, with the shear-layer flow fluctuations over a large axial distance, and with the centerline density fluctuations between the 3rd and the 5th shock cells. They are attributed to the intermittent intrusion of low-speed vortical structures in the potential core, to the supersonic convection of turbulent structures, and to the shock motions at the screech tone frequency.