Investigation of noise sources in high-speed jets via correlation measurements

Abstract

To locate noise sources in high-speed jets, the far-field sound pressure fluctuations $p^\prime $ were correlated with each of density $\rho $, axial velocity $u$, radial velocity $v$, $\rho uu$ and $\rho vv$ fluctuations measured from various points in jet plumes. Detailed surveys were conducted in fully expanded, unheated plumes of Mach 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. The technique uses a continuous-wave narrow line-width laser, Fabry–Perot interferometer and photon counting electronics. Laser light scattered by air molecules from a 1.06 mm long region on the narrow beam was collected and spectrally resolved by the interferometer. It was observed that the fluctuation spectra for air density inside the plume were in general similar to those of axial velocity spectra, while the radial velocity spectra were somewhat different. For the correlation study, microphone polar angles were varied from 30$^\circ$ to 90$^\circ$ to the jet axis. The sound pressure fluctuations $p^\prime $ at the shallowest 30$^\circ$ angle provided the highest correlation with turbulent fluctuations. The correlations sharply decreased as the polar angle was increased to 60$^\circ$, beyond which all data mostly fell below the experimental noise floor. Among all turbulent fluctuations $\langle\rho uu; p^\prime\rangle$ correlations showed the highest values. Correlation with the first-order terms $\langle\rho ^\prime \bar{u} \bar{u}; p^\prime \rangle$, $\langle\skew3\bar\rho \bar{u}u^\prime; p^\prime\rangle$ and third-order terms $\langle\rho ^\prime u^\prime u^\prime ;p^\prime\rangle$ was higher than that from the second-order terms $\langle\skew3\bar\rho u^\prime u^\prime ;p^\prime \rangle$ and $\langle\bar u\rho ^\prime u^\prime ; p^\prime \rangle$. Both $\langle v^\prime ; p^\prime \rangle$ and $\langle\rho vv; p^\prime \rangle$ correlations with the 90$^\circ$ microphone signal fell below the experimental noise floor, while that from the shallow 30$^\circ$ microphone showed weaker values. By moving the laser probe to various locations in the jet, it was found that the strongest noise source lay downstream of the end of the potential core and extended many diameters beyond. Correlation measurements from turbulent fluctuations along the lip shear layer showed a Mach-number dependency: significant values were measured in supersonic jets, while correlations fell below the noise floor for subsonic jets. Various additional analyses showed that fluctuations from large coherent structures mostly contributed to the measured correlation, while that from small-scale structures fell below the noise floor.