Single-Point Nonlinearity Indicators for the Propagation of High-Amplitude Acoustic Signals
Open Access
- Author:
- Falco, Lauren Elizabeth
- Graduate Program:
- Acoustics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- March 07, 2007
- Committee Members:
- Anthony A Atchley, Committee Chair/Co-Chair
Thomas B Gabrielson, Committee Member
Philip John Morris, Committee Member
Victor Ward Sparrow, Committee Member - Keywords:
- jet noise
nonlinear acoustics
nonlinearity indicators - Abstract:
- In the study of jet noise, prediction schemes and impact assessment models based on linear acoustic theory are not always sufficient to describe the character of the radiated noise. Typically, a spectral comparison method is employed to determine whether nonlinear effects are important. A power spectral density recorded at one propagation distance is extrapolated to a different distance using linear theory and compared with a measurement at the second distance. Discrepancies between the measured and extrapolated spectra are often attributed to nonlinearity. There are many other factors that can influence the outcome of this operation, though, including meteorological factors such as wind and temperature gradients, ground reflections, and uncertainty in the source location. Therefore, an improved method for assessing the importance of nonlinearity that requires only a single measurement is desirable. This work examines four candidate single-point nonlinearity indicators derived from the quantity $Q_{p^2p}$ found in the work of Morfey and Howell. These include: $Q_{neg}/Q_{pos}$, a ratio designed to test for conservation of energy; $Q_{pos}/p_{rms}^3$, a band-limited quantity that describes energy lost from a certain part of the spectrum due to nonlinearity; the spectral Gol'dberg number $Gamma_s$, a dimensionless quantity whose sign indicates the direction of nonlinear energy transfer and whose magnitude can be used to compare the relative importance of linear and nonlinear effects; and the coherence indicator $gamma_Q$, which also denotes the direction of nonlinear energy transfer and which is bounded between -1 and 1. Two sets of experimental data are presented. The first was recorded in a plane wave tube built of 2" inner-diameter PVC pipe with four evenly-spaced microphones flush-mounted with the inside wall of the tube. One or two compression drivers were used as the sound source, and an anechoic termination made of fiberglass served to minimize reflections from the far end of the tube. Both single-frequency signals and band-limited noise were used as sources, and waveforms were recorded at all four propagation distances. The second set of data was obtained at the model-scale jet facility at the University of Mississippi's National Center for Physical Acoustics. A computer controlled microphone boom was constructed to hold an array of six microphones. The array was rotated about the presumed location of the acoustic source center (4 jet diameters downstream of the nozzle exit), and two stationary microphones were mounted on the walls. Measurements were made for several jet conditions; data presented here represent Mach~0.85 and Mach~2 conditions. Application of the four candidate nonlinearity indicators to the experimental data reveals that each indicator has advantages and disadvantages. $Q_{neg}/Q_{pos}$ does not detect the presence of shocks as postulated, but it does conform to expectations in the shock-free region and support the use of $Q_{pos}$ as an indicator. The main advantage of $Q_{pos}/p_{rms}^3$ is that it can be used for band-limited measurements. Increased indicator values are seen for signals with higher source frequencies and amplitudes that are expected to undergo stronger nonlinear evolution. However, no physical meaning can yet be derived from the numerical value of the indicator. The spectral Gol'dberg number $Gamma_s$ is the most promising of the candidate quantities. It has the ability to indicate the direction of nonlinear energy transfer as well as provide a comparison between the strengths of linear and nonlinear effects. These attributes allow it to be used to qualitatively predict the evolution of a spectrum. The coherence indicator $gamma_Q$ also specifies the direction of nonlinear energy transfer, but its numerical value holds less meaning. However, it is bounded between -1 and 1, so values near zero denote very weak or no nonlinearity, and values near -1 or 1 denote strong nonlinearity. Further, because it is bounded, it does not become unstable for spectral components beneath the system noise floor.