On the Evolution of Crackle in Jet Noise from High-Performance Engines

Abstract

Crackle, the impulsive quality sometimes present in supersonic jet noise, has traditionally been defined in terms of the pressure waveform skewness. However, recent work has shown that the pressure waveform time derivative is a better quantifier of the acoustic shocks believed to be responsible for its perception. This paper discusses two definitions of crackle, waveform asymmetry versus shock content, and crackle as a source or propagation-related phenomenon. Data from two static military jet aircraft tests are used to demonstrate that the skewed waveforms radiated from the jet undergo significant nonlinear steepening and shock formation, as evidenced by the skewness of the time derivative. Thus, although skewness is a source phenomenon, crackle's perceived quality is heavily influenced by propagation through the near field and into the far field to the extent that crackle is caused by the presence of shock-like features in the waveform. Nomenclature = frequency of maximum radiation = sampling frequency OASPL = overall sound pressure level, dB re 20 µPa = pressure waveform, in pascals = time derivative of pressure, in Pa/s PDF = Probability density function = skewness of pressure, "pressure skewness" = skewness of pressure time derivative, "derivative skewness"

Skewness and shock formation in laboratory-scale supersonic jet data

“…The authors concluded that skewed waveforms radiate from the shear layer but that the shock content forms during the course of propagation, which could have important implications regarding the perception of jet crackle. 17,18 The ideally and over-expanded laboratory data discussed in this Letter both strengthen and extend these prior conclusions.…”

Supersonic Jet Noise Reduction by Nozzle Fluidic Inserts with Simulated Forward Flight

“…Additionally, the skewness of the pressure derivative has a strong lobe with a maximum that aligns with the peak noise direction, and rapidly decreases at higher angles. Both of these results agree with observations from laboratory measurements by Gee et al [29], Krothapalli et al [30], and Barrs and Tinney [31], in addition to agreeing with the trends observed from full scale measurements [32]. The previously documented significant reductions in OASPL are observed in Fig.…”

On the convection velocity of source events related to supersonic jet crackle

“…Either the pressure wave develops a sawtooth shape in the course of propagation, or it emerges from a local process with such a waveform. With regard to the former mechanism, Gee et al (2005Gee et al ( , 2008Gee et al ( , 2012Gee et al ( , 2013 conclude that nonlinear propagation is responsible for the discrepancies between observed and linearly predicted propagation pointing to an increase of pressure time-derivative skewness along the Mach wave emission angle in near-field full-scale measurements as evidence of cumulative steepening of the jet noise. With regard to the latter, Fiévet et al (2016) utilize a wave packet approach to show that nonlinear steepening alone is insufficient to produce steepened waveforms in the range-restricted laboratory environment and conclude that the waveforms must be generated by some local mechanism in or near the jet plume.…”

“…Their original test proposed that the pressure skewness should exceed 0.4 for crackle. More recent work has found the skewness of the pressure time derivative to be a more appropriate indicator (McInerny 1996;Krothapalli, Venkatakrishnan & Lourenco 2000;Gee et al 2007Gee et al , 2013. How the degree of crackle relates to the actual pressure waveform derivative is a perceptual question that remains elusive, but regardless of the test used, the basic criterion for perception of crackle is the presence of sawtooth-like pressure waveforms.…”