The feedback loops of discrete tones in under-expanded impinging jets

The upstream-propagating waves of feedback loops in under-expanded impinging jets are investigated through several typical flow conditions. Schlieren image capturing and far-field acoustic measurement are applied to the jet. The flow structures related to the discrete tones are extracted through dynamic mode decomposition (DMD), and the standing waves formed by the resonance are identified from the normalized amplitude fields of the chosen DMD modes. Spatial Fourier transforms are applied along the axial direction on the chosen DMD modes to obtain the spatial wavenumber spectra, from which the two wave disturbances caused by the interaction between Kelvin–Helmholtz (K–H) waves and shock cells can be identified. The upstream and downstream-propagating components of the feedback loop are rebuilt, respectively, via bandpass filtering. The wavenumbers of the upstream-propagating components in the feedback loop and the wavenumbers of disturbance waves are compared along the jet shear layer; the results suggest more than one closure mechanism of the feedback loop. For the impinging tones which have the same frequencies as the A1 and B modes in free jet, the closure mechanism of the feedback loop is the Mach radiation generated by the interaction between K–H waves and shock cells. For the other tones, their frequencies are consistent well with the allowable frequency ranges of the neutral wave mode. The combination of the neutral wave mode with the classical feedback loop model also gives strong evidence that the upstream-propagating waves for these tones may be the jets' inherent neutral wave.