A machine learning approach to identifying waveform coalescence in supersonic jet noise

Abstract

The intersection of Mach waves in the near field of a jet can lead to a phenomenon referred to as coalescence, which is believed to increase acoustic waveform steepening more than predicted by effective Gol'dberg numbers [Baars et al., J. Fluid Mechanics 749, 331 (2014); Fiévet et al., AIAA Journal 54, 254 (2016)]. Recent studies have constructed algorithms to identify coalescing waveforms in narrow field-of-view (FOV) schlieren images, then compared the detected coalescence events to simulations by using reduced-order models [Willis et al., AIAA Journal 61, 2022 (2023)]. Large-FOV images can capture a larger region of the sound field but require a decrease in the imaging frame rate that decreases the effectiveness of previous coalescence-detection algorithms. A new method for coalescence detection is thus desired. Convolutional neural networks are trained using transfer learning and then applied to large-FOV schlieren intensity data to identify waveforms of interest for further analysis of coalescence. Two approaches are compared for network training, one using pressure data and the other using pressure gradient data, both simulated using the Khokhlov-Zabolotskaya-Kuznetzov (KZK) equation. Interacting waves classified as coalescing are examined both in single image frames and in translating coordinates that follow the waves as they propagate.