Brent O. Reichman

Evolution of the derivative skewness for nonlinearly propagating waves

The skewness of the first time derivative of a pressure waveform, or derivative skewness, has been used previously to describe the presence of shock-like content in jet and rocket noise. Despite its use, a quantitative understanding of derivative skewness values has been lacking. In this paper, the derivative skewness for nonlinearly propagating waves is investigated using analytical, numerical, and experimental methods. Analytical expressions for the derivative skewness of an initially sinusoidal plane wave are developed and, along with numerical data, are used to describe its behavior in the preshock, sawtooth, and old-age regions. Analyses of common measurement issues show that the derivative skewness is relatively sensitive to the effects of a smaller sampling rate, but less sensitive to the presence of additive noise. In addition, the derivative skewness of nonlinearly propagating noise is found to reach greater values over a shorter length scale relative to sinusoidal signals. A minimum sampling rate is recommended for sinusoidal signals to accurately estimate derivative skewness values up to five, which serves as an approximate threshold indicating significant shock formation.

Acoustic Emissions from F-35 Aircraft during Ground Run-Up

A multi-organizational effort led by the Air Force Research Laboratory conducted acoustic emissions measurements on the F-35A and F-35B aircraft at Edwards Air Force Base, California in September 2013. These measurements followed American National Standards Institute/Acoustical Society of America S12.75-2012 to collect noise data to support community noise modeling and ground personnel noise exposure assessments. This field study utilized the most spatially extensive measurements of a military jet aircraft to date. In total, the microphone array was composed of 235 unique locations. These locations ranged from radial distances of 3 m outside the shear layer to 1,220 m from the aircraft with angular positions ranging from 0° (aircraft nose) to 160° (edge of the exhaust flow field). The acoustic emissions of the F-35 are presented for engine powers from idle to full augmented power (maximum afterburner). The acoustic emissions are characterized with spatial maps and are discussed in terms of overall and spectral band levels as well as statistical skewness measures. The directivity of the F-35 is described in general and in terms of variations in radial distances and individual spectral bands. Additionally, nonlinear propagation effects are identified and described along the peak radiation region for the range of engine powers.

Quantitative analysis of a frequency-domain nonlinearity indicator

In this paper, quantitative understanding of a frequency-domain nonlinearity indicator is developed. The indicator is derived from an ensemble-averaged, frequency-domain version of the generalized Burgers equation, which can be rearranged in order to directly compare the effects of nonlinearity, absorption, and geometric spreading on the pressure spectrum level with frequency and distance. The nonlinear effect is calculated using pressure-squared-pressure quadspectrum. Further theoretical development has given an expression for the role of the normalized quadspectrum, referred to as Q/S by Morfey and Howell [AIAA J. 19, 986-992 (1981)], in the spatial rate of change of the pressure spectrum level. To explore this finding, an investigation of the change in level for initial sinusoids propagating as plane waves through inviscid and thermoviscous media has been conducted. The decibel change with distance, calculated through Q/S, captures the growth and decay of the harmonics and indicates that the most significant changes in level occur prior to sawtooth formation. At large distances, the inviscid case results in a spatial rate of change that is uniform across all harmonics. For thermoviscous media, large positive nonlinear gains are observed but offset by absorption, which leads to a greater overall negative spatial rate of change for higher harmonics.

Comparison of Two Time-domain Measures of Nonlinearity in Near-field Propagation of High-power Jet Noise

Time-domain metrics are used to investigate the nonlinearity of the sound in the vicinity of the F-35 AA-1. The first measure considered is the average steepening factor (ASF), which we define as the inverse of the wave steepening factor and is a ratio of the expectation value of the positive slopes in the waveform to the expectation value of the negative slopes. The second nonlinearity metric is the skewness of the time derivative of the pressure waveform (derivative skewness), which describes the asymmetry of the distribution of slopes in the waveform. Spatial maps of both metrics applied to the F-35 AA-1 data reveal that regions of increasing derivative skewness correspond more closely to the maximum sound radiation area, whereas the largest values for the ASF seem aligned with the regions where the waveform amplitude distributions are most asymmetric. It is proposed that these two metrics reveal different characteristics of the nonlinear propagation of jet noise. The ASF is more representative of the average slopes, which are dominated by high frequencies. Conversely, the derivative skewness identifies of large positive slopes and hence relates to the shock content in the noise.

Modeling Far-field Acoustical Nonlinearity from F-35 Aircraft during Ground Run-up

The high noise levels associated with full-scale military aircraft result in nonlinear propagation, which results in acoustic shock formation and can alter noise perception. This propagation has been modeled for other aircraft but previous studies have been limited in scope, showing results for only select engine conditions and angles. Recent data measured near an F-35B allow for a more complete analysis of nonlinear propagation. Visual inspection of waveforms shows shock formation and persistence out to distances of up to 1220 m. Using an algorithm based on the Burgers equation, modified to include weak shock theory and an empirical correction for meteorological and ground effects, nonlinear and linear predictions are compared to measurements over a broad range of angles at 305 m. These analyses show that nonlinear effects become important in the maximum radiation direction at 75% thrust and increase with engine condition. At high engine powers, evidence of nonlinear propagation is found in the forward direction.

Acoustic Shock Formation in Noise Propagation During Ground Run-Up Operations of Military Aircraft

A distinctive feature of many propagating, high-amplitude jet noise waveforms is the presence of acoustic shocks. Metrics indicative of shock presence, specifically the skewness of the time derivative of the waveform, the average steepening factor, and a new wavelet-based metric called the shock energy fraction (SEF), are used to quantify the strength and prevalence of acoustic shocks within waveforms recorded 10-305 m from a tethered military aircraft. The derivative skewness is more sensitive to the presence of the largest and steepest shocks, while the ASF and SEF tend to emphasize aggregate behavior of the entire waveform. These metrics are applied at engine conditions ranging from 50% to 150% engine thrust request, over a wide range of angles and distances, to assess the growth and decay of shock waves. The responses of these metrics point to significant shock formation occurring through nonlinear propagation out to 76 m from the microphone array reference position. Although these strongest shocks decay, the metrics point to continued nonlinear propagation in the far-field, out to 305 m. Many of these features are accurately characterized using a nonlinear propagation scheme based on the Burgers equation, but this scheme fails to account for multipath interference and significant atmospheric effects over the long propagation distances, resulting in an overestimation of nonlinearity metrics.

Characterizing acoustic shocks in high-performance jet aircraft flyover noise

Acoustic shocks have been previously documented in high-amplitude jet noise, including both the near and far fields of military jet aircraft. However, previous investigations into the nature and formation of shocks have historically concentrated on stationary, ground run-up measurements, and previous attempts to connect full-scale ground run-up and flyover measurements have omitted the effect of nonlinear propagation. This paper shows evidence for nonlinear propagation and the presence of acoustic shocks in acoustical measurements of F-35 flyover operations. Pressure waveforms, derivatives, and statistics indicate nonlinear propagation, and the resulting shock formation is significant at high engine powers. Variations due to microphone size, microphone height, and sampling rate are considered, and recommendations for future measurements are made. Metrics indicating nonlinear propagation are shown to be influenced by changes in sampling rate and microphone size, and exhibit less variation due to microphone height.

Comparison of nonlinear, geometric, and absorptive effects in high-amplitude jet noise propagation

In recent years, understanding of nonlinearity in noise from high-performance jet aircraft has increased, with successful modeling of nonlinear propagation in the far field. However, the importance and characteristics of nonlinearity in the near field are still debated. An ensemble-averaged, frequency-domain version of the Burgers equation can be inspected to directly compare the effects of nonlinearity on the sound pressure level with the effects of atmospheric absorption and geometric spreading on a decibel scale. This nonlinear effect is calculated using the quadspectrum of the pressure and the squared pressure waveforms. Results from applying this analysis to F-22A data at various positions in the near field reveal that in the near field the nonlinear effects are of the same order of magnitude as geometric spreading and that both of these effects are significantly greater than absorption in the area of maximum radiation. [Work supported by ONR and an ORISE fellowship through AFRL.]

Comparison of Noise from High-Performance Military Aircraft for Ground Run-up and Flyover Operations

While the majority of jet noise analysis takes place with a static jet or aircraft, airbase and community military jet noise exposure happens for the most part when the aircraft is in flight. Comparisons between flyover and ground run-up measurements for high-performance military aircraft have not been previously published. This paper presents comparisons between static ground run-up and flyover measurements for the F-35 operating at 150% Engine Thrust Request. The overall sound pressure levels and spectra are shown for the two scenarios, as well as indicators of nonlinear propagation and shock content, specifically the derivative skewness and average steepening factor. The overall sound pressure level is reduced in the peak radiation direction aft of the aircraft but increased in the forward direction. The peak frequency of the noise is relatively unaffected by flight effects, though the amplitude of each frequency may vary. The increase in level in the forward direction results in shock formation that is absent during ground run-up measurements.

Single-point characterization of spectral amplitude and phase changes due to nonlinear propagation

A frequency-domain representation of the Burgers equation reveals that the cross-spectrum between the pressure and pressure-squared waveforms can be used to calculate nonlinear frequency-domain effects of finite-amplitude sound propagation. The normalized version of the quadspectrum, Q/S, was introduced by Morfey and Howell and has since been used to point to the nonlinear transfer of energy between frequencies, in particular gaining use in the domain of high-amplitude jet noise propagation. However, one question that remained was that of the interpretation: The physical meaning of the amplitude of Q/S was unclear. Recent analytical work has recast Q/S and the normalized version of the cospectrum, C/S, as a way to estimate sound pressure level and phase changes due to nonlinearity with a single-point measurement. This paper uses various measurements within a plane-wave tube to verify the physical significance of the amplitude and phase changes predicted by Q/S and C/S. Experiments involving sinusoids and band-passed Gaussian noise at various amplitudes show the validity of the single-point measurement to measure the strength of nonlinear effects in both amplitude and phase.A frequency-domain representation of the Burgers equation reveals that the cross-spectrum between the pressure and pressure-squared waveforms can be used to calculate nonlinear frequency-domain effects of finite-amplitude sound propagation. The normalized version of the quadspectrum, Q/S, was introduced by Morfey and Howell and has since been used to point to the nonlinear transfer of energy between frequencies, in particular gaining use in the domain of high-amplitude jet noise propagation. However, one question that remained was that of the interpretation: The physical meaning of the amplitude of Q/S was unclear. Recent analytical work has recast Q/S and the normalized version of the cospectrum, C/S, as a way to estimate sound pressure level and phase changes due to nonlinearity with a single-point measurement. This paper uses various measurements within a plane-wave tube to verify the physical significance of the amplitude and phase changes predicted by Q/S and C/S. Experiments involving sinusoids and ...