Abstract
Time-resolved particle image velocimetry (TR-PIV) has become a valuable tool for spatio-temporally resolved flow measurements. Current camera and laser technology has advanced such that time-domain events leading to sound generation can now be resolved over a reasonable spatial extent. This paper reports on the application of TR-PIV for the analysis of aeroacoustic sources in a free jet using the direct correlation between in-flow velocity fluctuations on the jet center-line and near-field pressure fluctuations. This correlation is considered both in the time domain and in the frequency domain (coherence), and the effect of TR-PIV errors on these estimates is considered by comparison to hot-wire anemometer measurements. In addition, a recently developed wavelet filtering technique is used to separate the acoustic and hydrodynamic components of recorded near-field pressure signals, enabling a gain in the signal-to-noise ratio. The results show that TR-PIV can recover the same time-domain correlation available from hot-wire and traditional PIV measurements, but that the frequency-domain estimates are corrupted by error, particularly at high frequencies. This result negates the principal benefit of using TR-PIV over PIV (the availability of coherence estimates). Despite this result, an analysis of the correlation signature gives evidence that large-scale, convecting, wave-like structures are associated with sound production, a result consistent with observations by many recent investigators. The analysis shows that in the presence of such large-scale structures, noise source localization based on the traditional correlation technique is ambiguous.
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Notes
The semi-colon indicates that u r u r is taken as a single quantity and correlated to p′.
q(x, t) = δ(y)δ(z)q(x, t) where \(\delta(\cdot)\) is the Dirac delta function.
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Acknowledgments
This work was supported by Science Foundation Ireland under contract number 09/RFP/ENM2469. The first author was also supported by a Natural Sciences and Engineering Research Council of Canada postgraduate scholarship.
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This work was first presented in condensed form at the 16th Int Symp on Applications of Laser Techniques to Fluid Mechanics in Lisbon, Portugal, 09–12 July, 2012.
This article is part of the Topical Collection on Application of Laser Techniques to Fluid Mechanics 2012.
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Appendix A: Baseline free jet flow
Appendix A: Baseline free jet flow
Figure 9 gives the mean and root-mean-square velocity development along the center-line of the free jet flow. There is close agreement between the historical LDA measurements for this jet (Kerhervé et al. 2010), the current TR-PIV measurements, and the current HWA measurements, which are only available from 2–4D Jet. For the TR-PIV measurements, there is a clear bias error in AOI1 (0–1.5D Jet). This error is not surprising when Fig. 5a shows that AOI1 is essentially random noise. Additionally, the edges of each AOI suffer from errors, which are likely the result of random noise. This is because the light sheet and camera focus were optimized for the center of each AOI, leaving less than ideal PIV conditions for the AOI edges. There is also a slight overestimation of the RMS fluctuations beyond the end of the potential core. The effect of these errors is a reduction in the magnitude of the correlation coefficient, but the general correlation features remain unaffected, allowing the interpretation of the results given in Sect. 5.3 to stand. Figure 10 shows that the axial turbulence intensity is significantly higher than the radial intensity. This helps justify the choice of u′ in the correlation instead of \(u'_r\) in the correlation.
More detail about the baseline jet flow, and its comparison to similar jets in the literature is available from Kerhervé et al. (2010). As a brief summary, the jet has a peak turbulence intensity of 16 % in the mixing region, the shear layer spreads at an angle of roughly 5°, and both the momentum and vorticity thicknesses increase roughly linearly with x at rates comparable to the relevant literature.
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Breakey, D.E.S., Fitzpatrick, J.A. & Meskell, C. Aeroacoustic source analysis using time-resolved PIV in a free jet. Exp Fluids 54, 1531 (2013). https://doi.org/10.1007/s00348-013-1531-5
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DOI: https://doi.org/10.1007/s00348-013-1531-5