Kyle G. Miller

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.

Model-scale jet noise analysis with a single-point, frequency-domain nonlinearity indicator

A single-point, frequency-domain nonlinearity indicator is calculated and analyzed for noise from a model-scale jet at Mach 0.85, Mach 1.8, and Mach 2.0. The nonlinearity indicator, νN, has been previously derived from an ensemble-averaged, frequency-domain version of the generalized Burgers equation (GBE) from Reichman, Gee, Neilsen, and Miller [J. Acoust. Soc. Am. 139, 2505-2513 (2016)]. The indicator gives the spatial rate of change due to nonlinear processes in sound pressure level (SPL) spectrum, and two other indicators from the GBE-νS and να-give the same quantity due to geometric spreading and absorption, respectively. Trends with frequency, angle, distance, and jet condition-supported both by spectral analysis and by calculation of the GBE-derived indicators-reveal a concentration of nonlinear effects along radials close to the plume with large overall SPLs. The calculated indicators for nonlinearity and absorption effects far from the source combine to give the same decay predicted by nonlinear theory for monofrequency sources. Trends in the νN indicator are compared with trends observed for other indicators such as pressure-derivative skewness and bicoherence, revealing both the qualitative and quantitative advantages of the νN indicator.

Quadspectral nonlinearity analysis of military jet aircraft noise waveforms

Understanding the impact of jet noise can be improved by quantifying the nonlinearity in a signal with a single-microphone measurement. Based on the quadspectral Morfey-Howell indicator, a nonlinearity gain factor called ν N has been derived from an ensemble-averaged, frequency-domain version of the generalized Burgers equation [Miller et al., AIP Conf. Proc. 1685, 090003 (2015)]. This gain factor gives a quantitative expression for the change in sound pressure level spectrum over distance. Past results show that ν N accurately characterizes nonlinear evolution of waves in simulation and model-scale jet data. Here, noise waveforms from a high-performance military jet aircraft are characterized using the ν N indicator; results are compared with those from other indicators that have been used previously (e.g., derivative skewness, time-waveform steepening factor, etc.). Far field results show that the nonlinear gains at high frequencies (>1 kHz) tend to balance the absorption losses, thus establishing the c...

Toward quantifying community response to crackle-containing jet waveforms

Although the phenomenon referred to as “crackle” has been previously described to be a dominant and annoying component of high-power military jet noise, its actual subjective impact is poorly understood. One of the challenges in quantifying jet crackle has been the identification of suitable metrics that are sensitive to the randomly occurring acoustic shocks responsible for the crackle percept [Gee et al., J. Acoust. Soc. Am. 121, EL1–EL7 (2007)]. This paper describes why understanding crackle could influence community perception of jet noise and recent waveform analyses of military jet noise that may provide insights how the phenomenon can be quantified perceptually. [Work supported by the USAFRL SBIR program.]

Asymptotic behavior of a frequency-domain nonlinearity indicator for solutions to the generalized Burgers equation

A frequency-domain nonlinearity indicator has previously been characterized for two analytical solutions to the generalized Burgers equation (GBE) [Reichman, Gee, Neilsen, and Miller, J. Acoust. Soc. Am. 139, 2505-2513 (2016)], including an analytical, asymptotic expression for the Blackstock Bridging Function. This letter gives similar old-age analytical expressions of the indicator for the Mendousse solution and a computational solution to the GBE with spherical spreading. The indicator can be used to characterize the cumulative nonlinearity of a waveform with a single-point measurement, with suggested application to noise waveforms as well.

Resonance of Complex Cylindrically Symmetric Cavities Using an Eigenfunction Expansion in Empty Cavity Modes

This paper presents a new method for calculating the cavity modes of cylindrically symmetric cavities and applies the method to stacked dielectric resonators (DRs) inside a conducting cylindrical shell. The modes of an arbitrary cavity are expressed using an eigenfunction expansion, the basis functions being the fields of an empty cavity. The wave equation for the electric displacement field, D, can be manipulated to eliminate derivatives of the discontinuous dielectric constant and provide an eigenvalue equation for the resonant frequencies of the cavity. The eigenvectors specify coefficients of the empty cavity modes that sum to compose the electric and magnetic fields. A test against theory is presented for an infinitely long dielectric cylinder inside an infinitely long cylindrical cavity, and the accuracy is better than 0.4% for nearly all modes. The calculated resonant frequencies of the quasi-TE011 (TE01δ) mode are also compared with the experimentally measured frequencies of resonant cavities containing DRs for ten different configurations; the results display an accuracy of better than 1.0% in all but one case. A link to a MATLAB implementation of the technique is provided.

Quantitative Nonlinearity Analysis of Model-Scale Jet Noise

The effects of nonlinearity on the power spectrum of jet noise can be directly compared with those of atmospheric absorption and geometric spreading through an ensemble-averaged, frequency-domain version of the generalized Burgers equation (GBE) [B. O. Reichman et al., J. Acoust. Soc. Am. 136, 2102 (2014)]. The rate of change in the sound pressure level due to the nonlinearity, in decibels per jet nozzle diameter, is calculated using a dimensionless form of the quadspectrum of the pressure and the squared-pressure waveforms. In this paper, this formulation is applied to atmospheric propagation of a spherically spreading, initial sinusoid and unheated model-scale supersonic (Mach 2.0) jet data. The rate of change in level due to nonlinearity is calculated and compared with estimated effects due to absorption and geometric spreading. Comparing these losses with the change predicted due to nonlinearity shows that absorption and nonlinearity are of similar magnitude in the geometric far field, where shocks ar...

Quantitative nonlinearity in subsonic and supersonic model-scale jet noise

Understanding the impact of jet noise, including annoyance due to crackle, can be improved by quantifying the nonlinearity in a signal with a single-microphone measurement. An ensemble-averaged, frequency-domain version of the generalized Burgers equation has been used to find a quantitative expression for the change in sound pressure level spectrum, Lp, with distance, r, due to the separate effects of geometric spreading, absorption, and nonlinearity. The nonlinear term, based on the dimensionless nonlinearity indicator known as “Q/S,” has been used to characterize the frequency-dependent nonlinearity as a function of angle and distance in subsonic (Mach-0.85), overexpanded (Mach-1.8), and ideally expanded (Mach-2.0) model-scale jet data. Analyses show that nonlinear effects in the Mach-2.0 data are about twice as strong as those in the Mach-1.8 data, but such effects are completely absent in the Mach-0.85 data. [Work supported by the AFRL SBIR program.]