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.

On least-order flow representations for aerodynamics and aeroacoustics

“…The aeroacoustic far-field data are computed from the LES data by a Ffowcs Williams-Hawkings solver for the Ma = 0.9 jet as described in Gröschel et al (2008). The physical validity of the OID assumption (2.12) is verified by known results: the fast pressure term (sometimes referred to as 'shear noise') has been shown to dominate in free jets in terms of the hydrodynamic, turbulent pressures, and to correlate better with the far-field pressure than the quadratic slow pressure ('self-noise') (see Lee & Ribner 1972;Scharton & White 1972;Seiner 1974;Seiner & Reetoff 1974;Schaffar 1979;Juvé et al 1980;Schaffar & Hancy 1982;Panda et al 2005). It has furthermore been demonstrated in Cavalieri et al (2011a,b,c) that coherent flow structures generate noise by means of a wavepacket mechanism, while Rodriguez Alvarez et al (2011) show how these wavepackets can be modelled in the framework of linear stability theory.…”

“…Yet an intuitive understanding of the noiseproducing structures is still in its infancy after more than five decades of jet noise research (see e.g. Panda, Seasholtz & Elam 2005). The complexity of this problem can be ascribed to the high dimensionality and the broadband spectrum of the flow state attractor.…”

Wavepackets in the velocity field of turbulent jets

“…These measurements allowed calculation of flow-acoustic correlations in two ways: the first was between a single point in the velocity field and a single microphone, as often done in the literature (Lee & Ribner 1972;Schaffar 1979;Juvé, Sunyach & Comte-Bellot 1980;Panda, Seasholtz & Elam 2005;Bogey & Bailly 2007); the second was between a given azimuthal mode in both the velocity and the acoustic field. The latter approach has a theoretical motivation, detailed in § 3.2, and allows the determination of correlations between wavepackets in the flow and the radiated sound field.…”

Experimental Investigation of Jet Noise Sources in a Hypersonic Nozzle at Takeoff

“…The coherence between these two data is indicated with isocontours, wherein the location of the sources is clearly illustrated. Panda et al [7] pointed out that the noise source measured by the Rayleigh scattering method exhibits strong directional characteristics, and they offered an explanation for the observed directional variation based on the two-noise source model [8][9][10]. These works provided essential information in terms of the behavior of the source, and these experimental evidences contribute to the important paper by Tam et al [11], wherein the behavior of the jet noise sources is clearly illustrated.…”

“…Panda et al [6,7] investigated the behavior of jet noise sources in a single round jet. They applied Rayleigh scattering method to measure the local density fluctuation in the jet, and by directly comparing the data with the pressure fluctuation obtained with far-field microphones, a cross-correlation analysis was carried out.…”