Taylor length scale measurement by laser Doppler velocimetry

 A new method for making direct measurements of the spatial velocity correlation coefficient, based on two-point laser Doppler velocimetry (LDV), has been developed. In this paper, the effects of control parameters on the correlation coefficient are being investigated. The main sources of experimental error have been identified and analysed. It appears that the probe volume length has a key effect on the accuracy of Taylor micro-scale measurement. A data processing procedure has been established and validated for the determination of this scale. The procedure shows that the portion of the correlation curve used to determine Taylor scale is a function of the integral scale to Taylor micro-scale ratio. Received: 7 June 1995/Accepted: 8 December 1997     

Micropositioning of a measuring volume in laser Doppler anemometry

Conclusion The method described in this paper permits to locate with high accuracy a LDA measuring volume relatively to a wall by means of a microthermocouple. In addition, this method allows to balance the intensities of the two laser beams and to control the exact size of the ellipsoid. When the LDA system is employed for two components measurements, this procedure permits to verify the coincidence of the two measuring volumes. This technique can also be used in laser tomography to locate, with high accuracy, a light sheet parallel to a wall (visualization of boundary layers).     

Effect of measurement volume size on turbulent flow measurement using ultrasonic Doppler method

This paper presents the results of an investigation on the effects of measurement volume size on the mean velocity profile and the Reynolds stress for fully developed turbulent pipe flows. The study employs the ultrasonic velocity profile method, which is based on the ultrasonic Doppler method. The ultrasonic Doppler method offers many advantages over conventional methods for flow rate measurement in the nuclear power plant piping system. This method is capable of measuring the instantaneous velocity profile along the measuring line and is applicable for opaque liquids and opaque pipe wall materials. Furthermore, the method has the characteristic of being non-intrusive. Although it is applicable to various flow conditions, it requires a relatively large measurement volume. The measurement volume of the present method has a disk-shape determined by the effective diameter of the piezoelectric element and the number of the wave cycles of the ultrasonic pulse. Considering this disk-shaped measurement volume and expressing the time-averaged velocity in a truncated Taylor series expansion around the value at the center of the measuring control volume, the value of the velocity can be obtained. The results are then compared with the data obtained from DNS and LDA measurements. The result shows that the effect of the measurement volume size appears in the buffer region and viscous sublayer.     

Discriminator laser Doppler velocimetry for measurement of liquid and particle velocities in sediment-laden flows

An accurate non-intrusive method of measurement of liquid and sediment velocities, called Discriminator Laser Doppler Velocimetry (DLDV) is described. The DLDV arrangement consists of a LDV, and a discriminator system that utilizes near on-axis diffraction from sediment particles passing through or grazing the LDV measurement volume to result in strong voltage signals. For liquid velocity statistics, velocity measurements associated with a discriminator voltage above a threshold are discarded; the discriminator signal is used to validate that only particle velocities are recorded during particle velocity measurement. Possible error sources in the use of DLDV are discussed. Measurements using DLDV in an open-channel alluvial sand-laden flow indicate differences between liquid and particle velocities even for dilute sand concentrations.The initial financial support of the project was provided by NSF, under grant CTS-9021149. Financial support from the Iowa Institute of Hydraulic Research in gratefully acknowledged.     

Assessment of turbulent spectral bias in laser Doppler velocimetry

A critical evaluation is made of the spectral bias which occurs in the use of a laser Doppler velocimeter (LDV). In order to accommodate the randomly sampled LDV data, statistical treatments of particle arrival times are needed. This is modeled as a doubly stochastic Poisson process which includes the intensity function of the velocity field. Three processing algorithms are considered for spectral estimates: the sample and hold method (SH), the modified Shannon sampling technique (SR), and the direct transform (RG). Assessment is made of these for varying data densities (0.05 ≤ d.d ≤ 5) and turbulence levels (t.i.=30%, 100%). The effects of the values of the Reynolds stress coefficients and the transversal standard deviation on the spectral contents were examined. As an improved version of the spectral estimator, the utility of POCS (the projection onto convex sets) has been tested in the present study. This algorithm is found useful to be in the region when d.d. ? 3.     

Power spectra of fluid velocities measured by laser Doppler velocimetry

The power spectrum and the correlation of the laser Doppler velocimeter velocity signal obtained by sampling and holding the velocity at each new Doppler burst are studied. Theory valid for low fluctuation intensity flows shows that the measured spectrum is filtered at the mean sample rate and that it contains a filtered white noise spectrum caused by the steps in the sample and hold signal. In the limit of high data density, the step noise vanishes and the sample and hold signal is statistically unbiased for any turbulence intensity.List of symbols A cross-section of the LDV measurement volume, m² - A empirical constant - B bandwidth of velocity spectrum, Hz - C concentration of particles that produce valid signals, number/m³ - d _m diameter of LDV measurement volume, m - f(₁, ₂ | u) probability density of t _i; and t _j given (t) for all t, Hz² - probability density for t _j-t_i, Hz - n (t, t) number of valid bursts in (t, t) = N + n - N (t, t) mean number of valid bursts in (t, t) - N _e mean number of particles in LDV measurement volume - valid signal arrival rate, Hz - mean valid signal arrival rate, Hz - R _uu time delayed autocorrelation of velocity, m²/s² - S _u power spectrum of velocity, m²/s²/Hz - t ₁, t ₂ times at which velocity is correlated, s - t _i, t _j arrival times of the bursts that immediately precede t ₁ and t ₂, respectively, s - t _ij t _j–t _i s - T averaging time for spectral estimator, s - T _u integral time scale of u (t), s - T Taylor's microscale for u (t), s - u velocity vector = U + u, m/s - u fluctuating component of velocity, m/s - U mean velocity, m/s - u _m sampled and held signal, m/s Greek symbols (t) noise signal, m/s - _m (t) sampled and held noise signal, m/s - bandwidth of spectral estimator window, radians/s - time between arrivals in pdf, s - Taylor's microscale of length = UT m - kinematic viscosity - ₁, ₂ arrival times in pdf, s - root mean square of noise signal, m/s - _u root mean square of u, m/s - delay time = t ₂ - t ₁ s - B duration of a Doppler burst, s - circular frequency, radians/s - _c low pass frequency of signal spectrum radians/s Other symbols ensemble average - conditional average - ^ estimate     

Application of nonlinear spectral analysis and signal reconstruction to laser Doppler velocimetry

Spectral analysis is a useful tool in engineering applications but many practical problems are encountered in computing power spectral densities (PSD), particularly in laser Doppler velocimetry where data are irregularly sampled. Methods to compute PSD are usely based on discrete Fourier transforms such as FFT. A non linear spectral analysis approach is tested and found to give better results, particularly with short data records. Results are also quite promising when non linear spectral analysis is combined with signal reconstruction to process irregularly sampled data.A preliminary version of this paper has been presented at LDA specialist meeting on the use of computers, May 1987, Institut Saint Louis, France     

Measurement of velocities in gas-liquid two-phase flow using laser Doppler velocimetry

Measurements of bubble and liquid velocities in two-phase flow have been made using a new forward/backward scattering Laser Doppler Velocimetry (LDV) technique. A standard LDV fiber optic probe was used to measure the bubble velocity using direct backscattered light. A novel retro-reflector and lens assembly permitted the same probe to measure the liquid velocity with direct forward-scattered light. Preliminary results show the usefulness of the technique in a duct of narrow thickness dimension.     

Geometric bias and time coincidence in 3-dimensional laser Doppler velocimeter systems

The measurement by a 3-d laser Doppler velocimeter of a turbulent flow has been numerically simulated. Errors associated with the probe volume geometry and the coincidence time window concept are revealed. One type of error occurs for high system data rates when multiple particles lead to system realizations. Another error occurs associated with a geometric bias discovered in the present study. This 3-d Idv geometric bias exists even for single-particle realizations and regardless of the system data rate. A technique for the elimination of the geometric bias is presented.     

Wavelet series method for reconstruction and spectral estimation of laser Doppler velocimetry data

Many techniques have been developed in order to obtain spectral density function from randomly sampled data, such as the computation of a slotted autocovariance function. Nevertheless, one may be interested in obtaining more information from laser Doppler signals than a spectral content, using more or less complex computations that can be easily conducted with an evenly sampled signal. That is the reason why reconstructing an evenly sampled signal from the original LDV data is of interest. The ability of a wavelet-based technique to reconstruct the signal with respect to statistical properties of the original one is explored, and spectral content of the reconstructed signal is given and compared with estimated spectral density function obtained through classical slotting technique. Furthermore, LDV signals taken from a screeching jet are reconstructed in order to perform spectral and bispectral analysis, showing the ability of the technique in recovering accurate information’s with only few LDV samples.     

Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow

Using a three-dimensional (3-D) particle-tracking velocimeter, detailed turbulent flow measurements were made in a plane channel with a one-sided 50% abrupt expansion, which acted as a backward-facing step. The turbulent channel flow reached a fully developed state well upstream of the step. The Reynolds number based on the upstream centerline velocity and the step height H was 5540. With the mean reattachment point located at 6.51H downstream of the step, the measurement region ranged from −2H upstream to 12H downstream of the step. Various turbulent statistics and the energy budget were calculated from numerous instantaneous vector distributions. As in previous experimental investigations, the Reynolds normal and shear stresses had maximum values upstream of the reattachment. The stress anisotropy tensor revealed a peculiar phenomenon near the reattachment wall, wherein the spanwise normal stress was the largest among the three normal stresses. The triple velocity correlations indicated large values in the separating shear layer, and hence the turbulent diffusion was a major term in the energy budget. Comparison was made between the present results and those of the direct numerical simulation (DNS) of Le et al. (1993), and it was found that the mean and fluctuating velocities, the Reynolds shear stress, and the turbulent energy budget were in excellent agreement, although there was a considerable difference in the inflow conditions.     

The influence of phase-averaging window size on the determination of turbulence quantities in unsteady turbulent flows

 The phase-averaging window size is shown to affect the measurement of phase-averaged turbulence quantities in unsteady turbulent flows. The flow turbulence is usually estimated on the assumption of quasi-constant flow velocity during the duration of the phase-averaging window. The calculated turbulence level then consists of two parts: one due to the turbulent velocity fluctuations and the other due to the changes in the mean flow velocity. This second part is shown to be directly proportional to the averaging window size. In order to determine the true turbulence the averaging window size has to be made as small as possible, especially if the unsteady flow exhibits large temporal gradients and the flow turbulence itself is small. Received: 9 April 1996/Acceped: 17 August 1996     

Smoothing and statistical evaluation of laser Doppler velocimetry data of turbulent flows in rotating and reciprocating machinery

 Arbitrarily time-distributed velocity information acquired by laser Doppler velocimeter systems needs special care when evaluated wrt. the mean velocity and the components of the Reynolds stress tensor. In rotating machinery, the arrival time information can be uniquely mapped to the angular position ϕ of the runner blades by using encoder signals relating a fixed runner position to an arrival time. It is convenient to statistically evaluate the velocity information of the detected particles in an angular window [ϕ₀−Δϕ/2,ϕ₀+Δϕ/2] in order to obtain mean velocities and turbulence values for an angular position ϕ₀. This approach has the inconvenience that turbulence values calculated from standard deviations are influenced by a possible variation in the mean velocity in the evaluation window. Other problems that arise with this “evaluation window” method are the influence of unevenly angular-distributed velocity information on the mean velocity or the poor resolution of maxima and minima of the mean velocity, which is similar to the problem pointed out by Jakoby et al. but being of second-order nature. In this paper, different improvements in the “evaluation window” method wrt these problems based on ideas found in a paper by McDonald and Owen are presented. A confidence interval calculation, generalizing the methods of Boutier, for all calculated values is included, which allows an appropriate window size Δϕ to be chosen for each particular situation. The different methods are compared using examples from wake flows of axial hydraulic turbomachinery measured in air and water. Received: 7 July 1999/Accepted: 18 November 1999     

Measurements of velocity spectra using time-resolving Doppler global velocimetry with laser frequency modulation and a detector array

Measuring velocity spectra in turbulent flows requires methods providing a high temporal resolution and a low measurement uncertainty. Hot-wire anemometry is often used, but it is intrusive. Laser Doppler anemometry is non-intrusive, but due to the statistical arrival of individual tracers provides no constant measurement rate. We therefore propose the use of Doppler global velocimetry (DGV), which is a contactless method allowing temporally equidistant measurements of continuous signals. Additionally, 2d measurements are possible instead of single point measurements. The commonly applied slow cameras are substituted by a fibre coupled detector array consisting of 25 avalanche photo diodes, which increases temporal resolution up to 10 μs. Contrarily to conventional DGV, a sinusoidal laser frequency modulation enables omitting the reference detector array. A correction of beam splitting and image misalignment errors is thus not necessary, but disturbances due to temporal fluctuations of the scattered light can occur and have to be reduced by increasing the modulation frequency. We validate the proposed system capability of synchronously measuring velocity spectra at multiple points in turbulent flows by presenting experimental results. The acquired velocity spectra in a wind tunnel experiment show good agreement with hot-wire comparison measurements within 0.1 m/s. An uncertainty analysis is given, which allows the achievable measurement uncertainty to be estimated as a function of the desired temporal resolution. An uncertainty down to 0.2 m/s can, for example, be achieved assuming a desired temporal resolution of 1 ms. These promising results open new perspectives for turbulence and correlation studies in flows such as to investigate the turbulence characteristics behind a truncated cylinder attached to a plate or the inlet of an aircraft turbine for flow characterisation in industry.     

Stick-slip flow of high density polyethylene in a transparent slit die investigated by laser Doppler velocimetry

The oscillating flow instability of a molten linear high-density polyethylene is carefully studied using a single screw extruder equipped with a transparent slit die. Experiments are performed using laser Doppler velocimetry in order to obtain the local velocities field across the entire die width. At low flow rate, the extrusion is stable and steady state velocity profiles are obtained. During the instability, the velocity oscillates between two steady state limits, suggesting a periodic stick-slip transition mechanism. At high flow rate, the flow is mainly characterized by a pronounced wall slip. We show that wall slip occurs all along the die land. An investigation of the slip flow conditions shows that wall slip is not homogeneous in a cross section of the slit die, and that pure plug flow occurs only for very high flow rates. A numerical computation of the profile assuming wall slip boundary conditions is done to obtain the true local wall slip velocity. It confirms that slip velocities are of the same order of magnitude as those measured with a capillary rheometer.     

Laser and avalanche diodes for velocity measurement by laser Doppler anemometry

The paper describes the possibilities of using semiconductor components for laser Doppler anemometers. This includes laser diodes D at the transmitting optics and PIN and avalanche diodes at the receiver. The advantages and disadvantages of various laser diode types are described, reference is made to problems such as focussing and wavelength stabilization and practical hints are given for the use of LDA. Extensive measurements of the attainable signal-to-noise ratios (SNR) of photomultipliers and of a number of photodiodes of different make have shown that some photodiode models are now superior to photomultipliers. Laser diodes should be used together with photodiodes to construct miniaturized laser Doppler anemometers, as such semiconductor LDA are much more efficient than conventional anemometers with gas lasers and photo-multipliers. Moreover, miniaturized LDA designs can now also be used for battery operation and field application.     

Effect of particle polydispersity on particle concentration measurement by using laser Doppler anemometry

Measurement of particle concentration by laser Doppler anemometry (LDA) is studied on a vertical air jet seeded by a powder disperser with controlled particle and air flow rates. Particle arrival rate is utilized to retrieve particle number densities from conventional LDA operation. The effect of polydisperse nature of the particles is assessed. Comparisons between measured and estimated particle number densities suggest that only a certain portion of the particle population with a particle size to fringe spacing ratio around unity can be detected. Results indicate that reliable measurement of absolute particle concentration is possible for a particle population of narrow size distribution with an average diameter equivalent to fringe spacing. Present number density measurement technique which is useful for practical purposes with conventional LDA systems is found to yield physically reasonable profiles in both laminar and turbulent regimes.     

Simultaneous concentration and velocity measurements using combined laser-induced fluorescence and laser Doppler velocimetry: Application to turbulent transport

This paper describes the implementation of an optical technique, allowing to perform concentration and velocity measurements simultaneously and at the same point. This method is based on the coupling of laser-induced fluorescence of rhodamine B, applied to the determination of local concentration, and laser Doppler velocimetry. The method developed provides an accurate measurement of the concentration-velocity cross-correlation. The latter is a parameter linked to the eddy diffusivity tensor of a passive contaminant. This method was tested with a turbulent submerged free jet and it allowed the determination of the mean field of concentration and velocity, the concentration-velocity cross-correlation, and the local eddy diffusivity.List of symbols C molar concentration - c fluctuating part of the concentration - mean value of the concentration - concentration-velocity cross-correlation - D molecular diffusivity - (D _eddy) _ij eddy diffusivity tensor - I _abs absorbed intensity - I _e local incident intensity - K _opt optical constant - N number of samples - r _c half-width radius for the concentration profile - r _v half-width radius for the velocity profile - S _f fluorescence signal - Sc Schmidt number - V _c collection volume - U velocity - U _e flow velocity in the channel - U _i injection velocity Greek symbols kinetic energy dissipation rate - ₁ molar extinction coefficient for the laser radiation (in m²mol^–1l^–1) - ₂ molar extinction coefficient for the fluorescence signal (in m²mol^–1l^–1) - quantum yield - _c Batchelor scale - _k Kolmogorov scale - v kinematic viscosity - normalized values