The phase and amplitude gradient estimator (PAGE) method for active acoustic intensity uses pairwise microphone transfer functions to obtain the phase gradient, which improves the calculation bandwidth over the traditional weighted quadspectral method. Additionally, for broadband sources, the PAGE theory indicates that the transfer function phase can be unwrapped to further extend the usable frequency range to beyond the spatial Nyquist frequency. Here, two experiments demonstrate intensity bandwidth extension by more than an order of magnitude using phase unwrapping. First, plane-wave tube results show accurate one-dimensional intensity calculations with the microphones separated by five wavelengths, 30 times the traditional limit. Second, two-dimensional measurements of a laboratory-scale jet with a four-microphone probe yield physically reasonable calculations at frequencies 15 times the traditional limit.
A new method for the calculation of vector acoustic intensity from pressure microphone measurements has been applied to the aeroacoustic source characterization of an unheated, Mach 1.8 laboratory-scale jet. Because of the ability to unwrap the phase of the transfer functions between microphone pairs in the measurement of a radiating, broadband source, physically meaningful near-field intensity vectors are calculated up to the maximum analysis frequency of 32 kHz. The new intensity method is used to obtain a detailed description of the sound energy flow near the jet. The resulting intensity vectors have been used with a raytracing technique to identify the dominant source region over a broad range of frequencies. Additional aeroacoustics analyses provide insight into the frequency-dependent characteristics of jet noise radiation, including the nature of the hydrodynamic field and the transition between the principal lobe and sideline radiation. Nomenclature d = spacing between two microphones = nozzle exit diameter , = transfer function between microphones a and b I = time-averaged vector intensity p = acoustic pressure = acoustic pressure magnitude = acoustic pressure phase , ( ) = quadspectrum between microphones a and b 1 Associate Professor, Dept. of Physics and Astronomy, N283 ESC, AIAA Senior Member.
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