Further Progress in Noise Source Identification in High Speed Jets via Causality Principle

To locate noise sources in high-speed jets, the sound pressure fluctuations p / , measured at far field locations, were correlated with each of density ρ, axial velocity u, radial velocity v, ρuu and ρvv fluctuations measured from various points in jet plumes. The experiments followed the cause-and-effect method of sound source identification, where the cross-correlation coefficients, , etc., could be related to various source terms of Lighthill’s equation. Detailed correlation surveys were conducted in three fully expanded, unheated plumes of Mach number 0.95, 1.4 and 1.8. The velocity and density fluctuations were measured simultaneously using a recently developed, non-intrusive, point measurement technique based on molecular Rayleigh scattering (Seasholtz, Panda & Elam, AIAA paper no 2002-0827). The technique uses a continuous wave, narrow line-width laser, Fabry-Perot interferometer and photon counting electronics. Light scattered by air molecules from a point on the laser beam was collected and spectrally resolved by a Fabry-Perot Interferometer. To determine Doppler shift caused by air flow, the image, formed after the interferometer, was split into two concentric parts and the intensity-ratio was measured by a pair of photomultiplier tubes. The change in the intensity ratio from that created by incident laser light provided a measure of a velocity component. Photo-electron counting over short-duration, contiguous bins provided a time history of velocity variation u(t), v(t). In addition, a part of the Rayleigh scattered light was measured directly, without passing through the interferometer, using a third photomultiplier tube to obtain a time history of density fluctuations ρ(t); and finally, multiplications of the time series data provided ρuu(t) and ρvv(t). Two separate collection arrangements were used to measure Doppler shifts from u and v velocity components. Fourier transforms of the time series data provided respective spectra. It was observed that the density spectra Sρ were in general similar to the axial velocity spectra while the radial velocity spectra Sv were somewhat different. The ρ-u cross-spectra show progressively decreasing correlation with increasing frequency. To determine sources of sound pressure fluctuations microphone signals from 50 nozzle diameters and at polar angles from 30° to 90° to the jet axis, were cross-correlated with individual flow variables. The sound pressure fluctuations at 30° to the jet axis provided the highest correlation coefficients with flow fluctuations. With an increase in microphone polar angle, the correlation coefficients decreased sharply, and beyond about 60° all correlation mostly fell below the experimental noise floor. Among all turbulent fluctuations correlations showed the highest values. Interestingly, , in all respects, were very similar to . Both