Reduced-Order Comparison of Simulated and Measured Coalescing Mach Waves near Supersonic Jets

Prior measurements of the sound field produced by a laboratory-scale, Mach 3 jet flow (Baars and Tinney, Journal of Sound and Vibration, Vol. 333, No. 12, 2014, pp. 2539–2553; Fiévet et al., AIAA Journal, Vol. 54, No. 1, 2016, pp. 254–265) suggest that acoustic waveforms steepen early on in their development. This explained the discrepancy between theoretical predictions, based on effective Gol’dberg numbers, that shocks should not form, and observations of steepened Mach waves close to laboratory-scale jets. The present work continues studying this phenomenon by exploring coalescence processes that occur when neighboring waveforms intersect, forming larger-amplitude waveforms with increased cumulative nonlinear distortion. A numerical model based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation is developed to show that coalescence-induced steepening is sensitive to the intersection angle between adjacent waveforms, waveform duration, and cylindrical spreading effects. High frame-rate schlieren images of sound waves propagating from the post-potential core region of a laboratory-scale Mach 3 jet are then captured along an angle following the ridge of most intense noise to study the development and evolution of coalescence. A shock detection algorithm isolates shock-like events, which are tracked using a translating coordinate system and decomposed using proper orthogonal decomposition. Reduced-order reconstructions of both schlieren images and the KZK model identify common patterns that characterize the shock coalescence process.