Estimation of turbulence power spectra from randomly sampled data by curve-fit to the autocorrelation function applied to laser-Doppler anemometry

Abstract

The development of a novel slotting technique for the estimation of the autocorrelation function (ACF) of randomly sampled data has eliminated the major disadvantages of the Mayo algorithm. The reduced variance of the estimators in the vicinity of τ = 0 and the elimination of estimators greater than 1 has opened the possibility to approximate the ACF with a curve-fit, leading to a noise-free estimator of the power spectrum. In this paper we describe an analytical function, based on known properties of turbulence power spectra, which is suited to the approximation of the ACF from randomly sampled laser-Doppler anemometry (LDA) data with noise. Using simulated LDA data, based on both simulated and hot-wire measured turbulence signals, it is shown that the method estimates the power spectrum with an error of less than 25% over six decades of power. Application to various LDA data sets shows that the analytical function, derived from the spectral properties, is sufficiently flexible to describe ACFs from data sets of pipe flow, mixing layer flow, flow in stirred tanks and flows around airfoils. An extension of the technique could be in automatic incorporation of periodic components and compensation for data sets with a high velocity bias (turbulence intensities > 40%).

Spectral Analysis of Uneven Data in a Bipolar Charging Agglomeration System

“…Although, the presence of the slope in an energy spectrum does not prove the existence of an inertial subrange, it is, nevertheless, a useful indicator and facilitates further analysis using local isotropy assumptions [11]. The decay of the spectrum should increase monotonically with increasing frequency above a second start frequency [12], so that the slope after the second start frequency should be steeper than ±5/3. While resampling methods can be used to obtain an estimated spectrum that is guaranteed to be positive, results at higher frequencies can be severely biased.…”

Estimation of turbulence power spectra for bubbly flows from Laser Doppler Anemometry signals

“…Another class of techniques employs a slot correlation (Benedict et al, 2000) followed by a cosine transform. The approach taken by Van Maanen and Oldenziel (1998) is to fit a general model to the slot correlation coefficients; the estimated power spectrum is the Fourier transform of the fitted model. The final class of techniques comprises the Lomb-Scargle method (Lomb, 1974;Scargle, 1989) which originates from astrophysics.…”

On the choice of the number of samples in laser Doppler anemometry signal processing

“…In recent years research on the improvement of LDA systems has been directed, among other aspects, towards its application to turbulent flows. [6][7][8][9][10] The spatial resolution takes on major importance in this context, because high velocity gradients, widening the spectrum of the received signals, may take place in the flow. Moreover, this application emphasizes the trade-off between two important features of the system, namely, the precision and the measurement rate.…”