Identification of Nonlinear and Near-Field Effects in Jet Noise Using Nonlinearity Indicators

Abstract

In the collection and analysis of high-amplitude jet noise data for nonlinear acoustic propagation, both model-scale and full-scale measurements have limitations. Model-scale measurements performed in anechoic facilities are usually limited by transducer and data acquisition system bandwidths and maximum propagation distance. The accuracy of fullscale measurements performed outdoors is reduced by ground reflections and atmospheric effects. This paper describes the use of two nonlinearity indicators as complementary to ordinary spectral analysis of jet noise propagation data. The first indicator is based on an ensemble-averaged version of the generalized Burgers equation. The second indicator is the bicoherence, which is a normalized version of the bispectral density. These indicators are applied to Mach-0.85 and Mach-2.0 unheated jet noise data collected at the National Center for Physical Acoustics. Specifically, the indicators are used to separate geometric near-field effects from nonlinear propagation effects for the Mach-2.0 data, which cannot be done conclusively using comparisons of power spectral densities alone.

Bicoherence analysis of model-scale jet noise

“…For each boom location, 2 20 samples of time waveform data were acquired with a 24-bit Motu 896 recorder at 192 ksamples/s, but the maximum analysis frequency was limited to 75 kHz because of the 6.35 mm microphones' frequency response. 12 The boom's axis was located 4 D j downstream of the nozzle exit plane. This location is within the visible Mach-wave radiation region of the jet [see the Schlieren visualization in Fig.…”

POD based spectral Higher-Order Stochastic Estimation

“…In earlier research performed by Blackstock (personal communication) it was shown that nonlinearities should be considered in studying jet noise propagation. A recent investigation on identifying nonlinear propagation was performed by Gee et al (2007), 34 that was mainly based on bispectral analysis. The investigation was limited to single sensor analysis and was therefore spatially isolated.…”

Toward Active Control of Noise from Hot Supersonic Jets

“…Applications can be found in the literature and include the work of Mclnerny & Ölcmen (2005), Petitjean et al (2006), Gee et al (2007a) and Kuo et al (2010). Originally derived by Morfey & Howell (1981), this indicator starts with the general from of the Burgers equation for spherically outgoing waves.…”

“…These bispectral methods identify nonlinearities by computing the quadratic bicoherence, which is essentially the second-order variant of the well-known linear coherence. By applying these techniques one can essentially identify the frequencies at which two signals are linearly and nonlinearly related (Gee et al , 2007a. Since the bispectral technique is an identification technique and does not provide the direct capability of estimation and prediction, another technique, developed in the field of system identification, was introduced which started with the work of Tick (1961).…”