Measurement of acoustic velocity components in a turbulent flow using LDV and high-repetition rate PIV

The present study provides theoretical details and experimental validation results to the approach proposed by Minotti et al. (Aerosp Sci Technol 12(5):398–407, 2008) for measuring amplitudes and phases of acoustic velocity components (AVC) that are waveform parameters of each component of velocity induced by an acoustic wave, in fully turbulent duct flows carrying multi-tone acoustic waves. Theoretical results support that the turbulence rejection method proposed, based on the estimation of cross power spectra between velocity measurements and a reference signal such as a wall pressure measurement, provides asymptotically efficient estimators with respect to the number of samples. Furthermore, it is shown that the estimator uncertainties can be simply estimated, accounting for the characteristics of the measured flow turbulence spectra. Two laser-based measurement campaigns were conducted in order to validate the acoustic velocity estimation approach and the uncertainty estimates derived. While in previous studies estimates were obtained using laser Doppler velocimetry (LDV), it is demonstrated that high-repetition rate particle image velocimetry (PIV) can also be successfully employed. The two measurement techniques provide very similar acoustic velocity amplitude and phase estimates for the cases investigated, that are of practical interest for acoustic liner studies. In a broader sense, this approach may be beneficial for non-intrusive sound emission studies in wind tunnel testings.