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

Abstract

The present study provides theoretical details and experimental validation results to the approach proposed by Minotti et al. (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 multitone 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 windtunnel testings.

Liner Impedance Eduction Under Shear Grazing Flow at a High Sound Pressure Level

“…Especially, the acoustic velocity field can be obtained with a specific post-processing technique. 20 The acoustic velocity is defined here as the component of the signal that is correlated with the loudspeaker signal. It can be educed from the extraneous noise (mainly due to the turbulent flow) by a technique similar to the three-microphone signal enhancement technique.…”

Statistical Inference Method for Liner Impedance Eduction with a Shear Grazing Flow

“…in which σ 2 i denotes the noise variance, and is either determined experimentally or set up a priori. In the present study, σ 2 i has been estimated for the pressure measurements by assuming a 0.5 dB uncertainty in measured amplitude and a 1 deg uncertainty in measured phase, whereas for the LDV measurements, a bootstrap approach has been followed, as in Léon et al [17], to provide an approximation of experimental variance for the velocity-field measurements (see Sec. IV.B).…”

“…v GṼ p expjΦv∕ls (16) in which the phase of the acoustic velocities, referenced by the loudspeaker, is defined as Φu∕ls arctan ImGŨ ;ls ReGŨ ;ls (17) Φv∕ls arctan ImGṼ ;ls ReGṼ ;ls (18) The approach retained in the present work to evaluate an estimator d GŨ ;ls (respectively, d GṼ ;ls ) of the cross-power spectral function GŨ ;ls (respectively, GṼ ;ls ) relies on a Welch's overlapped segmented average (WOSA) method. For the acoustic-velocity amplitude estimator d GŨ ;ls (respectively, d GṼ ;ls ), spectral leakage and amplitude errors yielded by the choice of a windowing function have to be taken into account for an accurate, unbiased estimation.…”

“…Regarding the acoustic phasedifference estimator Φu∕ls (respectively, Φv∕ls) the simplest method is to evaluate the phase of d GŨ ;ls (respectively, d GṼ ;ls ) at the closest desired frequency, on a single frequency bin. An exhaustive analysis of estimators is available in Léon et al [17].…”

“…The data used as input for the eduction method can be either acoustic-pressure or acoustic-velocity measurements. The acousticvelocity fields were measured by LDV and an advanced postprocessing technique [17] was applied, which also provided the measurement uncertainties. An evolutionary Markov chain Monte Carlo (MCMC) technique was selected to explore the target posterior probability density functions (PDF) of interest.…”