Holger Nobach

Estimation of turbulent velocity spectra from laser Doppler data

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.

Laser Doppler anemometry data simulation: Application to investigate the accuracy of statistical estimators

Autoregressive models of order 1 are used to generate three-dimensional flowfields with specified probability distributions, spectra, and shear stress tensor. These known flowfields are then used to simulate the particle arrival statistics in laser Doppler anemometry for homogeneous particle densities. Further simulation steps allow modeling of the processor sampling and data acquisitions, providing all necessary data for investigating the bias and variance of statistical estimators. Results are presented for estimators of the first two moments of the velocity distribution function. Experimental data are obtained for verification purposes. The results demonstrate the technique`s potential for studying novel ot theoretically intractable estimators.

Analysis of dual-burst laser Doppler signals

The processing of signals from a laser Doppler anemometer (LDA) normally requires that the signals originate from single particles. Therefore, adequate validation procedures are implemented in available LDA processors, rejecting signals with more than one burst (multi-burst signals). In this article LDA signals are investigated with two overlapping bursts (dual-burst signals). The signal statistics and the necessity of burst separation are discussed. Furthermore, an algorithm is presented, which can be used to detect and to process dual-burst signals and, finally, the capability of the technique is demonstrated using simulated and experimentally obtained signals.

Model parameter estimation from non-equidistant sampled data sets at low data rates

A general method of model parameter estimation for irregularly sampled data is introduced, with special emphasis on estimation of the power spectral density. The main application is processing of data sets from a laser Doppler anemometer (LDA), for which often the mean data rate is low and the total data set duration is short. It is shown that the model parameter estimation can be quite effective under these conditions, resulting in consistent, bias-free estimates which exhibit very low variance. Simulations and experiments are used to examine the performance of the technique.

Correlation estimators for two-point laser Doppler anemometry

Using two-point LDA systems, estimates of the integral length scales of turbulent flowfields can be performed by forming the cross-correlation function of the two velocity records for various measurement volume separations. Several estimators for the cross-correlation function are reviewed and their bias and variance are examined as a function of particle density and of chosen processing parameters. The investigations were performed using numerical simulations.

Variable density turbulence tunnel facility

The Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany, produces very high turbulence levels at moderate flow velocities, low power consumption, and adjustable kinematic viscosity between 10(-4) m(2)/s and 10(-7) m(2)/s. The Reynolds number can be varied by changing the pressure or flow rate of the gas or by using different non-flammable gases including air. The highest kinematic viscosities, and hence lowest Reynolds numbers, are reached with air or nitrogen at 0.1 bar. To reach the highest Reynolds numbers the tunnel is pressurized to 15 bars with the dense gas sulfur hexafluoride (SF6). Turbulence is generated at the upstream ends of two measurement sections with grids, and the evolution of this turbulence is observed as it moves down the length of the sections. We describe the instrumentation presently in operation, which consists of the tunnel itself, classical grid turbulence generators, and state-of-the-art nano-fabricated hot-wire anemometers provided by Princeton University [M. Vallikivi, M. Hultmark, S. C. C. Bailey, and A. J. Smits, Exp. Fluids 51, 1521 (2011)]. We report measurements of the characteristic scales of the flow and of turbulent spectra up to Taylor Reynolds number R(λ) ≈ 1600, higher than any other grid-turbulence experiment. We also describe instrumentation under development, which includes an active grid and a Lagrangian particle tracking system that moves down the length of the tunnel with the mean flow. In this configuration, the properties of the turbulence are adjustable and its structure is resolvable up to R(λ) ≈ 8000.

A refined reconstruction-based correlation estimator for two-channel, non-coincidence laser Doppler anemometry

A new estimator is introduced for correlation functions between two or more channels of a laser Doppler anemometer. The estimator is based on a sample-and-hold reconstruction and resampling of each channel, thus eliminating the coincidence requirement between channels. The estimator is applicable to two-component or three-component laser Doppler anemometry (LDA), but is particularily interesting for two-point or multi-point LDA, where coincidence is practically non-existent. The estimator is fully derived in this paper and verified using simulated data sets. An appropriate transformation of coordinate systems is introduced for the case of a rotated or non-orthogonal measurement system.

Experimental Measurements of Lagrangian Statistics in Intense Turbulence

We report Lagrangian laboratory measurements of fluid turbulence at high Reynolds numbers. First, the experimental techniques that have made Lagrangian measurements possible, including both optical and acoustic particle tracking, are reviewed. Then some of the laboratory flows used in Lagrangian measurements are described and a selection of new experimental results are presented.

Measurement of Lagrangian acceleration in turbulent flows using the laser Doppler technique

The use of the laser Doppler technique for measuring Lagrangian acceleration with a high spatial resolution is introduced. The requirements in system alignment and accuracy of signal processing is estimated. Specifications of the optical design and the signal processing are given.

A fair review of non-parametric bias-free autocorrelation and spectral methods for randomly sampled data in laser Doppler velocimetry

Abstract This paper presents a comparison of currently available methods for non-parametric and bias-free estimation of the autocorrelation function and power spectral density from randomly sampled data. The primary motivation is the processing of velocity data obtained using laser Doppler techniques in turbulent flows. However, the methods are applicable to various other cases of random sampling, including those with small deviations from the ideal Poisson process. Whilst these methods have been compared in the literature before, a fair comparison of their relative performance requires that they be tested under identical conditions. This includes identical use of special processing options and identical processing parameters. This has not been achieved in the literature to date. An example application on publicly available laser Doppler data shows agreement between the results obtained with the different methods. Under this fair comparison, the methods converge in terms of their systematic and random errors, indicating that they are comparably efficient at using the available information content of the randomly sampled signal. The results also identify that the available methods are interchangeable and indicate a possible replacement for the current best-practice procedure in the laser Doppler community.