Analysis of Resonance in Jet Screech with Large-Eddy Simulations

Screech resonance is studied with experimentally validated large-eddy simulation data for a 4:1 rectangular under-expanded jet at three nozzle pressure ratios. The analysis uses spectral proper orthogonal decomposition (SPOD) and spatial cross correlation to characterize the oppositely-traveling waves in the jet at the screech fundamental frequency. The results support recent theoretical framing of screech as absolute instability, and further reveal the spatial separation of individual processes for screech generation. From the leading-order SPOD mode, direct evidence of the guided jet mode being the screech closure mechanism, not the external acoustic feedback, is observed. A match in the spatial wavenumber suggests the guided jet mode is generated via interactions between the Kelvin-Helmholtz wave and the shock cells. The energy of the oppositely-moving waves shows spatially global and non-periodic behavior of the coherent structures in the streamwise direction. The ratio of wave energy identifies regions where distinct processes in screech generation take place by comparing the rate of energy propagation in the downstream direction to that of the upstream direction. The distinct regions correspond to initial shear layer receptivity, sound emission, guided jet mode excitation and decay of coherence. The leading-order SPOD mode also enables the approximation of Lighthill's stress tensor and allows for accurate calculation of the far-field screech tone amplitude with the acoustic analogy formulation. The current findings provide insights on building a physics-based reduced order model for screech amplitude prediction in the future.