Estimation of turbulent velocity spectra from laser Doppler data

Abstract

We review the problem of spectral estimation from velocity data sampled irregularly in time by a laser Doppler anemometer (LDA) from very early estimators based on slot correlation to more refined estimators, which build upon a signal reconstruction and an equidistant re-sampling in time. The discussion is restricted to single realization anemometry, i.e. excluding multiple particle signals. We classify the techniques and make an initial assessment before describing currently used methods in more detail. An intimately related subject, the simulation of LDA data, is then briefly reviewed, since this provides a means of evaluating various estimators. Using the expectation and variance as figures of merit, the advantages and disadvantages of several estimators for varying types of turbulent velocity spectral distributions are discussed. A set of recommendations is put forward as a conclusion.

LDA measurements and turbulence spectral analysis in an agitated vessel

“…It is in agreement with Benedict at al. investigation [1]. Two other methods were compared: Slot correlation (SC) see section 1.3 and Sample and hold reconstruction (S+H) see section 1.2.…”

“…The estimation of spectral analysis from LDA data was reviewed by Benedict at al. [1] and classified them to the following groups:…”

Power spectral density of velocity fluctuations estimated from phase Doppler data

“…Fourier transform of this symmetrical function yields the power spectral density (PSD). The SC remains even today one of the most viable means for PSD and ACF estimations (Benedict et al, 2000). A large group of estimators is based on the concept of signal reconstruction and re-sampling at equal time intervals.…”

“…Other spectral estimator for LDA data was introduced by Nobach et al (1996), based on one-point reconstruction techniques, but employing a refinement which accounts in a statistical manner for the velocity change between a particle arrival and the sample instant. Spectral estimation techniques currently considered the most reliable, are explained in detail by Benedict et al (2000). We have acquired large set of velocity data using P/DPA on a realistic human airway model using monodispersed micron-size particles suspended in air flow (Jedelsky et al, 2011).…”

Autoregressive spectral estimation by application of the burg algorithm to irregularly sampled data

“…Many variants of slotting algorithms currently exist, among which are slotting with local normalization and fuzzy slotting [1]. Local normalization reduces the variance of the estimated covariance function.…”