Selected Publications
Kent L. Gee and Alan T. Wall (et al.)
This paper summarizes a two-part special session, “Supersonic Jet and Rocket Noise,” which was held during the 174th Meeting of the Acoustical Society of America in New Orleans, Louisiana. The sessions were cosponsored by the Noise and Physical Acoustics Technical Committees and consisted of talks by government, academic, and industry researchers from institutions in the United States, Japan, France, and India. The sessions described analytical, computational, and experimental approaches to both fundamental and applied problems on model and full-scale jets and rocket exhaust plumes.
Brent O. Reichman, Blaine M. Harker, Trevor A. Stout, Eric B. Whiting, Kent L. Gee, and Tracianne B. Neilsen
Acoustical measurements were made in the very far field during a recent test firing of the five-segment QM-1 Space Launch System solid rocket motor at Orbital ATK. Data were taken using 6.35 mm and 12.7 mm type-1 microphones at three far-field locations to the sideline and aft of the nozzle at a range of 650-800 nozzle diameters. The experiment setup, including the appreciable terrain changes, is first discussed. Spectral and autocorrelation analyses highlight the variation of the noise with respect to observation angle. In addition, high-frequency spectral characteristics and waveform statistics are evidence of the significant nonlinear propagation over the propagation range. Terrain effects and data stationarity during the firing are discussed. This dataset is compared to measurements of other solid rocket motors at closer and farther ranges, including the GEM-60 and the four-segment Shuttle Reusable Solid Rocket Motor.
Sound intensity measurements using two microphones have traditionally been processed using a cross-spectral method with inherent error in the finite-sum and finite-difference formulas. The phase and amplitude gradient estimator method (PAGE) has been seen experimentally to extend the bandwidth of broadband active intensity estimates by an order of magnitude. To provide an analytical foundation for the method, bias errors in active intensity and specific acoustic impedance are presented and compared to those of the traditional method. Bias errors are reported for a plane-wave field and sound radiated from a monopole and a dipole. Additionally, bias errors are reported for reactive intensity, the estimation of which is unchanged by the PAGE method for the two-microphone case.
The phase and amplitude gradient estimator (PAGE) method can be used to increase the bandwidth of complex acoustic intensity estimates obtained with multi-microphone probes. Despite the increased bandwidth, errors arise when using this method, which is based on linear least-squares gradients, in non-planar fields. Examples of non-planar fields include the acoustic near field of a radiating source or near a null in a standing-wave field. The PAGE method can be improved by increasing the number of microphones and using a Taylor expansion to obtain higher-order estimates of center pressure, pressure amplitude gradient, and phase gradient. For one-dimensional active intensity in a simulated monopole field, a four-microphone probe is shown to converge to less than 0.2 dB error at a closer distance than a two-microphone probe with the same inter-microphone spacing. For reactive intensity in a standing wave field, increasing the number of microphones improves the bandwidth, and applying a higher-order method to traditional reactive intensity estimation outperforms higher-order PAGE.
A coherence-based method for unwrapping the relative phase between microphones is investigated. For
broadband signals, this method has the potential to lead to more accurate intensity vector estimations using
the Phase Amplitude and Gradient Estimator (PAGE) method [D. C. Thomas et al., J. Acoust. Soc. Am.
137, 3366-3376 (2015)] Simple unwrapping methods function by detecting phase jumps above a threshold
value, which works well for frequencies associated with high signal coherence. However, since unwrapping
for these methods is triggered by only one previous frequency data point, frequency ranges of low coherence
often contain unwrapping errors. By including coherence in a phase unwrapping algorithm, these errors can
be avoided. Ranges of relatively low coherence are given less weight in phase unwrapping and are checked
for unwrapping errors. For broadband signals with continuous relative phase, using both the coherence
and multiple data points to unwrap, frequencies associated with low coherence result in fewer unwrapping
errors. Phase values for jet noise data with low coherence (<0.1) have been successfully unwrapped using
this method, and have resulted in more reliable PAGE intensity estimates. This paper also investigates
unwrapping in interference nulls produced by coherent, radiating sources.
broadband signals, this method has the potential to lead to more accurate intensity vector estimations using
the Phase Amplitude and Gradient Estimator (PAGE) method [D. C. Thomas et al., J. Acoust. Soc. Am.
137, 3366-3376 (2015)] Simple unwrapping methods function by detecting phase jumps above a threshold
value, which works well for frequencies associated with high signal coherence. However, since unwrapping
for these methods is triggered by only one previous frequency data point, frequency ranges of low coherence
often contain unwrapping errors. By including coherence in a phase unwrapping algorithm, these errors can
be avoided. Ranges of relatively low coherence are given less weight in phase unwrapping and are checked
for unwrapping errors. For broadband signals with continuous relative phase, using both the coherence
and multiple data points to unwrap, frequencies associated with low coherence result in fewer unwrapping
errors. Phase values for jet noise data with low coherence (<0.1) have been successfully unwrapped using
this method, and have resulted in more reliable PAGE intensity estimates. This paper also investigates
unwrapping in interference nulls produced by coherent, radiating sources.
