Coalescence of nonlinear acoustic waves, with application to supersonic jet noise
The focus of this dissertation is the phenomenon of coalescence that occurs when neighboring acoustic waveforms propagate in nearly the same direction and intersect to form a larger-amplitude waveform with increased nonlinear distortion. Coalescence is proposed as an explanation for the observation of steepened Mach waveforms and crackle close to a lab-scale, Mach 3 jet flow in prior studies, which contradicted theoretical predictions for that jet. A numerical model based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) nonlinear wave equation is developed to demonstrate that coalescence leads to increased waveform steepening. Simulations also demonstrate that the resulting change in waveform steepening is sensitive to the intersection angle, waveform duration, and geometrical spreading. Experiments are discussed that employ a spark source to generate controlled, coalescing waves in order to examine the phenomenon. The interacting waves are tracked using schlieren imaging to compare waveform steepening in coalescing and non-coalescing waves. High frame-rate schlieren images of sound waves propagating from the post potential core region of a laboratory-scale Mach 3 jet are captured in a narrow field of view along the Mach wave propagation path to study the development and evolution of coalescence. Numerous examples of coalescence events are identified in the near field of the jet, demonstrating that coalescence plays a significant role in waveform steepening in that region. The proper orthogonal decomposition (POD) is applied with translating coordinates to compare the reduced-order behavior of coalescing waves from both simulations and experiments. To supplement the schlieren database, a large-eddy simulation (LES) of a Mach 3 jet is analyzed to identify coalescing waves. Coalescence events detected in the LES are correlated with metrics that indicate increased waveform steepening. Image classification techniques based on convolutional neural networks are developed for the identification of coalescing waves in the LES pressure database and in wide field-of-view schlieren images of the jet flow. The impact of different training methods is explored for transfer learning applied to a pre-trained network. The machine learning approach successfully and efficiently identifies coalescence events in both large databases.
Acoustics, Coalescence, Jet noise, Mach waves, Machine learning, Crackle, Proper orthogonal decomposition, Convolutional neural networks
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