Shear-layer perturbation responses from time-resolved schlieren data

A combination of physics-based and data-driven post-processing techniques is proposed to extract acoustic-related shear-layer perturbation responses directly from spatio-temporally resolved schlieren video. The physics-based component uses momentum potential theory to extract the irrotational (acoustic and thermal) component from density gradients embedded in schlieren pixel intensities. For the unheated shear layer, the method filters acoustic structures and tones not evident in the raw data. The filtered data are then subjected to an efficient data-driven dynamic mode decomposition reduced-order model, which provides the forced acoustic perturbation response for broad parameter ranges. A shear layer comprising Mach 2.461 and 0.175 streams, corresponding to a convective Mach number 0.88 and containing shocks, is adopted for illustration. The overall perturbation response is first obtained using an impulse forcing in the wall-normal direction of the splitter plate, extending into subsonic and supersonic streams. Subsequently, impulse and harmonic forcings are independently applied in a pixel-by-pixel manner for a precise receptivity study. The acoustic response shows a convective wavepacket and acoustic burst from the splitter plate. The interaction with the shock and associated wave dispersion emits a second, slower, acoustic wave. Harmonic forcing indicates higher frequency-dependent sensitivity in the supersonic stream, with the most sensitive location near the outer boundary-layer region, which elicits an order of magnitude larger acoustic response compared with disturbances in the subsonic stream. Some receptive forcing regions do not generate significant acoustic waves, which may guide excitation with low noise impact.