Off-axis alignment of an LDA-probe and the effect of astigmatism on measurements

A theoretical analysis of the positional accuracy of an LDA measurement volume using an off-axis alignment of a probe relative to an internal flow has been carried out. General performance parameters of measurements with a 1D-probe with an off-axis alignment are derived. In particular, the change in the fringe spacing, the relationship between the shift of the measurement volume and the probe movement, and the general 2-dimensional traversing properties of the measurement volume are considered. The displacement between the two LDA measurement volumes of a 2D-probe caused by astigmatism has been determined from exact calculations of the laser beam transmission. The benefits of a water-filled prism to ensure the coincidence of the measurement volumes and to reduce the effect of astigmatism on the data rate and the distortion of the measurement volume has been shown. A calculation procedure for the use of such a prism is given.The authors would like to thank Sulzer Innotec for support of this work and for permission to publish this paper. The work was also sponsored by Sulzer Pumps, Sulzer Turbo and Sulzer Hydro in a research project entitled Unsteady flow in turbomachinery. The support of Dr. Mick Casey is especially acknowledged, particularly for his help with the English text.     

Further considerations of the astigmatism error associated with off-axis alignment of an LDA-probe

 Off-axis alignment of an LDA-probe in internal flow measurement is always associated with the appearance of astigmatism and this may have a large effect on the measurement accuracy. In addition to the earlier investigations reported by Zhang and Eisele (1995a, 1996) it is shown that the improper off-axis alignment of the probe leads to separation of laser beams in the formation of the measurement volume. Quantitative calculations made in this paper give a sound basis for estimating this separation and the results imply that the error arising from beam separation is very serious both for LDA- and for PDA-measurements. In addition, the analysis in Sect. 3 reveals that the reduction of the data rate from astigmatism due to off-axis alignment of the probe depends on the focal length of the receiving optics. This relationship has been validated by experiment. Received: 23 December 1996/Accepted: 24 July 1997     

On the overestimation of the flow turbulence due to fringe distortion in LDA measurement volumes

 Fringe distortion with linear longitudinal variation in fringe spacing over the length of LDA measurement volume has been considered to influence the accuracy of flow measurement. The overestimation of the mean velocity and especially of the flow turbulence due to fringe distortion has been derived to be a function both of the fringe distortion number (which is a purely geometrical parameter of the measurement volume) and the flow turbulence to be measured. Against the usual expectation, it has been shown that the overestimation of the flow turbulence due to fringe distortion in the measurement volume could be neglected. Only for very low turbulence intensity dose the error become significant. As a reference this result could be used to estimate measurement errors which occur in the presence of other types of fringe distortion. Received: 2 December 1997/Accepted: 2 May 1998     

Distortion of LDA fringe pattern by tracer particles

For precise flow velocity measurements laser Doppler anemometry (LDA) is wide-spread in use in the laboratories of industry and universitarian research institutions. The LDA method has the advantage of being not intrusive and able to discriminate between forward and reverse velocities. So far, laser Doppler anemometry is believed to be one of the most accurate flow measuring techniques. However, recent investigations have shown that the period lengths of LDA signal bursts are not constant within an individual burst. This can induce an additional scatter in the signal frequency and in the determination of the flow velocity. Until now, the reason for the period variations has not been investigated in detail although the problem was observed before. This paper describes experimental investigations which show that the particle passage through the laser beams shortly before the point of superposition, i.e. the LDA measuring volume, yields a distorted LDA fringe pattern. Thus, the signal period length from an individual particle, passing the center of the measuring volume at the same time, varies according to the distortion of the fringe spacing.     

Error estimation of laser-Doppler anemometry measurements in fluids with spatial inhomogeneities of the refractive index

We report a combined experimental and theoretical investigation of the influence of spatial non-uniformities of the refractive index on the accuracy of laser Doppler anemometry (LDA) measurements in transparent fluids. One LDA beam is guided through heated air of a thermal boundary layer near a heated vertical flat plate. It is found that the hot air is deflecting the beam because of a modification of the refractive index n in the fluid. This deflection causes three effects: (1) spatial displacement of beam intersection, (2) waist mismatch in the measurement volume and (3) variation in interference fringe distance. With the help of a rotating disk calibration system the resulting displacement of the LDA measurement volume and the Doppler frequency variation is systematically studied at different temperatures. Using a simple model of beam propagation under the influence of well-defined temperature inhomogeneities, the displacement of measurement volume and change in Doppler frequency are calculated and are found to be in agreement with the experimental observations. The results provide a rational framework for an assessment of the accuracy of LDA data in arbitrary transparent fluids with non-uniform refractive index.     

Optical guidelines and signal quality for LDA applications in circular pipes

The optical performance of laser Doppler anemometer (LDA) technology in applications to circular pipes with an external plane wall has been clarified and quantified. It is shown that optical aberration is a persistent feature in such LDA measurements and measurements from each direction along a full pipe diameter are needed to obtain the flow distribution. For measurements of axial velocities in a circular pipe no special care has to be taken, even if the optical plane deviates from the pipe axis. For measurements of tangential and radial velocities detailed operating guidelines have been presented with respect to the shift of the measurement volume, its optical properties and the beam waist dislocations. The analysis reveals the possible influences on both the signal quality and the measurement accuracy.     

Precise flow rate measurements of natural gas under high pressure with a laser Doppler velocity profile sensor

This paper reports about the first application of a laser Doppler velocity profile sensor for precise flow rate measurements of natural gas under high pressure. The profile sensor overcomes the limitations of conventional laser Doppler anemometry (LDA) namely the effect of spatial averaging and the effect of fringe spacing variation (virtual turbulence). It uses two superposed, fan-like interference fringe systems to determine the axial position of a tracer particle inside the LDA’s measurement volume. Consequently, a spatial resolution of about 1 μm can be achieved and the effect of virtual turbulence is nearly eliminated. These features predestine the profile sensor for flow rate measurements with high precision. Velocity profile measurements were performed at the German national standard for natural gas, one of the world′s leading test facilities for precision flow rate measurements. As a result, the velocity profile of the nozzle flow could be resolved more precisely than with a conventional LDA. Moreover, the measured turbulence intensity of the core flow was of 0.14% mean value and 0.07% minimum value, which is significantly lower than reference measurements with a conventional LDA. The paper describes the performed measurements, gives a discussion and shows possibilities for improvements. As the main result, the goal of 0.1% flow rate uncertainty seems possible by an application of the profile sensor.     

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).     

How to get spatial resolution inside probe volumes of commercial 3D LDA systems

In laser Doppler anemometry (LDA) it is often the aim to determine the velocity profile for a given fluid flow. The spatial resolution of such velocity profiles is limited in principal by the size of the probe volume. The method of using time of flight data from two probe volumes allows improvements of the spatial resolution by at least one order of magnitude and measurements of small-scale velocity profiles inside the measuring volume along the optical axis of commercial available 3D anemometers without moving the probe. No change of the optical set-up is necessary. An increased spatial resolution helps to acquire more precise data in areas where the flow velocity changes rapidly as shown in the vicinity of the stagnation point of a cuboid. In the overlapping region of three measuring volumes a spatially resolved 3D velocity vector profile is obtained in the direction of the optical axis in near plane flow conditions. In plane laminar flows the probe volume is extended by a few millimetres. The limitation of the method to a plane flow is that it would require a two-component LDA in a very special off-axis arrangement, but this arrangement is available in most commercial 3D systems.     

Measurement accuracy of semiconductor LDA systems

A laser Doppler anemometer with a laser diode as the light source, has several advantages: i.e., low power consumption, compactness, and low cost. In order to be fully benefitted by these favorable characteristics, the measurement uncertainty, associated with wavefront distortion in the measuring volume, should be minimized. Furthermore, proper attention should be given to system misalignment caused by external perturbations, such as thermal expansion of the diode-collimator assembly. These considerations lead to a computational procedure for optimizing the layout of the semiconductor LDA system. Calculations are based on a generalized relation for fringe non-uniformity combined with a simulation model for the anemometry system. For this purpose, the optical field of a laser diode is described satisfactorily as a product of a Gaussian and a truncated Lorentzian distribution. The influence of various design parameters is examined by means of an extensive computational study as well as experimental evaluation involving precise scanning of the measuring volume. The performance is improved by employing a small focal length collimator and a large focal length front lens. For measurement of turbulence intensities smaller than 1%, it may become necessary to collect the signals in the side scatter and to use a frequency-domain signal processor. For such an application, temperature control may also be necessary, but it should be applied to the entire diode-collimator assembly and not just to the laser diode as suggested in previous publications.     

Shadow Doppler velocimetry with double fiber-array sensors

Shadow Doppler velocimetry (SDV) systems with double fiber-array sensors were developed for the measurements of particle trajectory angles and for the stereoscopic investigation of particles. The parallel two-line fiber-array configuration improves the accuracy of the trajectory angle measurement in a plane perpendicular to the optical axis, which contributes to the high accuracy of the particle shape reconstruction process. It also provides information on the other trajectory angle in a plane parallel to the two laser beams. Furthermore, it realizes "time-of-flight" velocity measurement, which provides the possibility to simplify the original SDV setup by removing the laser Doppler velocimetry (LDV) components. On the other hand, stereoscopic SDV was also developed, which is effective in cases where three-dimensional characteristics of shape, orientation, or behavior of particles are important.     

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.     

Irregular particle sizing using speckle pattern for continuous wave laser applications

We present velocity power spectra computed by the so-called direct method from burst-type laser Doppler anemometer (LDA) data, both measured in a turbulent round jet and generated in a computer. Using today’s powerful computers, we have been able to study more properties of the computed spectra than was previously possible, and we noted some unexpected features of the spectra that we now attribute to the unavoidable influence of a finite measurement volume (MV). The most prominent effect, which initially triggered these studies, was the appearance of damped oscillations in the higher frequency range, starting around the cutoff frequency due to the finite size of the MV. Using computer-generated data mimicking the LDA data, these effects have previously been shown to appear due to the effect of dead time, i.e., the finite time during which the system is not able to acquire new measurements. These dead times can be traced back to the fact that the burst-mode LDA cannot measure more than one signal burst at a time. Since the dead time is approximately equal to the residence time for a particle traversing a measurement volume, we are dealing with widely varying dead times, which, however, are assumed to be measured for each data point. In addition, the detector and processor used in the current study introduce a certain amount of fixed processing and data transfer times, which further contribute to the distortion of the computed spectrum. However, we show an excellent agreement between a measured spectrum and our modeled LDA data, thereby confirming the validity of our model for the LDA burst processor.     

Evaluation of the effect of variable refraction index on the path of a laser beam

The use of a laser-Doppler anemometer to measure velocities in a fluid with a larger variation in its refractive index perpendicular to the laser beams may introduce appreciable errors. This situation is commonly encountered in convective heat transfer studies. The beams are refracted as they pass through the fluid and the distance of the intersection of the beams, control volume, from the surface may be significantly different than the distance of the beams from the surface when they entered the fluid. If the flow is unsteady or turbulent, the relative movement of the beams may be such that the size and location of the control volume is constantly changing causing appreciable errors.     

A high-resolution laser Doppler anemometer: design, qualification, and uncertainty

A new high-resolution laser Doppler anemometer (LDA) has been developed with a working distance of 350 mm, allowing operation in lab-scale wind tunnels. The measurement volume size is 35 μm in diameter by 60 μm in length, allowing resolution of the smallest turbulence scales even at fairly high Reynolds numbers. The controversial question of velocity and validation bias in LDA data is resolved with an experimental method for measuring and removing those effects. Uncertainty estimates are also derived for all the mean and Reynolds stress measurements. Received: 27 June 1999/Accepted: 30 August 2000     

光束穿越搅拌槽圆形壁面时对LDA中控制体和测点的影响

本文利用光线跟踪法，分析和计算了利用激光多普勒测速仪（ＬＤＡ）测速时，光束穿越圆形壁面对控制体和测点位置带来的影响，并定性给出了ＬＤＡ对诸如圆形搅拌槽之类流场测试的一些有关参数，为测点定位和数据分析提供了依据。     

Grating holographic interferometry

A holographic interferometric technique, combining an image hologram with a grating approach, is proposed for three-dimensional deformation measurements on opaque planar object surfaces. In this technique, the holographic plate is brought close to the object surface, onto which a high-frequency crossed-line diffraction grating has been replicated. The grating surface produces multiple object waves rather than the usual diffusely reflected object waves. The double-exposed single holograms can be reconstructed at multiple off-axis angles. Four independent high-contrast fringe patterns are extracted simultaneously. Displacement vectors over the entire measurement area are separated in three orthogonal directions. The resultant displacements are presented as three-dimensional meshed plots and topographic contour maps. The optical system for both recording and reconstruction of the holograms has been simplified compared to conventional holographic interferometry. Experimental errors associated with fringe readout and system geometry are reduced because of the sharp images and the well-defined spatial orientation in the reconstruction system.     

Multi-mode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers

A novel LDA system using laser diode arrays and multi-mode fibers in the transmitting optics is presented. The use of high numerical aperture multi-mode step-index fibres results in measurement volumes with, for example, 80 µm length and minimal speckle effects. Because of the high spatial resolution and low relative fringe spacing variation of d/d5×10^–4 the multi-mode fibre LDA is predestined for investigating turbulent flows. Boundary layer measurements carried out show excellent agreement with theoretical velocity profiles.     

Development of a double-beam rheo-optical analyzer for full tensor measurement of optical anisotropy in complex fluid flow

The design and testing of the Double-Beam Rheo-Optical Analyzers, DB-ROA is described. The DB-ROA contains the two optically modulated laser beams that are transmitted through a sheared sample in different angles. The full components of the stress tensor can be evaluated simultaneously by a single measurement of the birefringence and orientation angle of each beam. The mechanical properties are also measured simultaneously with the optical properties. This system can be applied to both steady and transient shear flows. Three types of DB-ROAs are designed. They are distinguished by the optical modulation system, that is (1) a single modulator system, (2) a synchronization of two modulators, and (3) a two individual modulator system. The performance tests were carried out and its validity was demonstrated by comparison between the optical and the mechanical measurements of the first normal stress difference. The signal-to-noise ratio was strongly affected by the choice of the oblique angle of the second beam. The design features for the different optical modulation systems are discussed.     

Laser-dual-focus system for measuring the flow through narrow rod bundles

A non-disturbing optical instrument for the measurement of flow velocity in complicated flow channels, e.g. inclined flow through rod bundles is described. The measuring probe based on the laser-dual-focus principle is brought inside one of the plexiglass tubes forming the grid. A mirror which is situated inside the probe deflects the two laser beams producing the measuring volume into the flow field to be examined. An optical system for a thin probe has been developed which has to fit into one of the rods and which enables one both to produce the measuring volume as well as to receive the back-scattered light. The required laser power can be reduced to 2 mW. The photo-multiplier necessary for the evaluation of scattered light signals can be separated from the optical head by using light wave conductors. Examples are presented by which the applicability of the new probe to the described flow situation is demonstrated.