Feedback Loop Mechanism in Underexpanded Impinging Jets Using Entropy Based Instability Model

Aeroacoustic feedback loop mechanism of underexpanded supersonic jets impinging on a flat plate have been analyzed. The feedback loop mechanism studied, corresponds to the one that can occur between the standoff shock cell (last shock cell upstream of the flat plate) and the flat plate. It is expected that the particular feedback loop in considerations is responsible for some of the large acoustic tones radiated that can be observed in such kind of configurations. An analytical model based on entropy fluctuations and linear stability theory has been considered following the derivations by Kuo and Dowling. Frequency of tones produced are assumed to be influenced by frequency of the standoff shock oscillations sustained by the feedback loop mechanism. A Python routine has been developed to implement the model. The routine is validated against data from experimental and numerical studies available in literature by comparing the frequency of the tones. The predicted frequencies have been found to be in satisfactory agreement to those observed in experimental and numerical studies, showing that the feedback between shock and flat plate plays a key role in the acoustic tones produced.