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.     

Effective particle size range in laser-Doppler anemometry

The present paper points out that all existing laser-Doppler anemometer systems do not only operate within a finite range of Doppler frequencies but also work within a relatively narrow range of signal amplitudes. It is shown that this corresponds to a finite, and usually to an extremely small, range of particle diameters which contributes to the final LDA measurements. Because of this, the particle size distribution has to be matched to the LDA-system used for measuring particle velocities. If this is not taken into account in particle seeding, low data rates will result in spite of very high particle passage rates through the measuring control volume. This is shown experimentally and is supported by theoretical considerations.The present investigation results in conclusions regarding optimum particle size distributions for laser-Doppler anemometry. If fluid velocity measurements are attempted rather than particle velocity measurements, the particles still have to satisfy well known size requirements that are flow, fluid and particle density dependent.The experimental study employs a combined optical system for simultaneous measurements of particle velocity, particle size and particle concentration. The system is used to measure those particles of a spectrum of oil droplets that contribute to the validated signal output of counter and transient recorder based LDA-electronic signal processing systems.     

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.     

An LDA technique for in situ simultaneous velocity and size measurement of large spherical particles in a two-phase suspension flow

A relatively simple optical scheme using the reference-mode laser Doppler anemometry for the in situ measurement of flow properties of a dilute particle-fluid two-phase suspension having a predominant flow direction is hereby proposed. It is an extension of the established technique of optical gating for particle sizing which is fully integrated into the established technique of laser Doppler anemometry for velocity measurement. Particles that can be measured by this scheme are limited to those with sizes greater than the smaller dimension of the optical measuring volume. Inherent in the methodology is a procedure for providing information on the local particle number density and velocity distributions for each size range of the particles and the local velocity distribution of the continuous phase. The accompanying electronics and interfaces are also established for data processing and analysis in a mini computer. Validation of the scheme has been accomplished by controlled experiments using stainless steel balls and water droplets of 1 mm and greater in diameter.     

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.     

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.     

The effect of astigmatism due to beam refractions on the formation of the measurement volume in LDA measurements

The accuracy of LDA measurements depends on the optical alignment of the laser beams. Improperly designed optical systems lead to fringe distortion in the measurement volume and in earlier investigations this effect has always been taken as the main cause of optical inaccuracy in LDA measurements. In the present work a different cause of fringe distortion is considered: astigmatism due to beam refractions. A quantitative theory for the astigmatism of laser beams is derived for both single and multiple refractions. Parameter calculations with regard to the size of the astigmatism effect have been carried out. It is shown that astigmatism is a relevant parameter which influences the fringe uniformity and fringe distortion in an LDA measurement volume and affects the measurement accuracy of measurements in internal flow. The equations derived enable the change in cross sections of the refracted laser beams to be determined. The spatial deviations of the diverse focusing points of refracted laser beams relative to the position of the LDA measurement volume are found to depend strongly on the incident angle of the beams and therefore on the off-axis alignment angle of the LDA probe (off-axis from the normal to the flow-wall-interface).     

In situ calibration of hot wires close to highly heat-conducting walls

A calibration procedure has been derived that permits reliable hot-wire measurements close to walls. When hot wires are calibrated in a free flow and subsequently used for near-wall velocity measurements, erroneous velocity information results because of additional heat losses to the wall. On the other hand, laser-Doppler anemometry (LDA) measurements of local time mean velocities are very little affected by the presence of the wall and this readily suggests in situ calibration of hot wires located just behind the LDA measuring volume and at the same distance from the wall. Calibrations of this kind are described for highly heat-conducting walls and the results show good agreement with corresponding data obtained through numerical investigations. The present investigations permit a generally applicable correction curve to be suggested for hot-wire velocity measurements close to walls of high thermal conductivity. Received: 3 May 2000/Accepted: 24 November 2000     

A transient laser Doppler anemometry for measurement of rapidly changing velocities of solid bodies

A transient laser Doppler anemometry (LDA) is developed to extract the velocity history of a solid body that is transient in nature. A digital storage oscilloscope was used in place of the conventional counter to allow postprocessing of the recorded Doppler signals. By sliding a rectangular window with a length on the order of 1μs, frequencies of the rapidly changing Doppler signals were extracted using a refined signal processing method. This method, which incorporates the chirp-Z transform algorithm to the short-time Fourier transform routine for frequency enhancement, has proved its superiority over the conventional short-time Fourier transform and the zero-crossing methods; the latter was used in the authors' previously published works. The transient LDA was then applied to record transient responses of projectiles with different masses during impact on plates of various thicknesses, and interesting impact phenomena were discovered. From these applications, it is found that this method is robust and reliable for extracting the velocity history of a solid body during a transient event.     

Flow over periodic hills: an experimental study

Two-dimensional flow over periodically arranged hills was investigated experimentally in a water channel. Two-dimensional particle image velocimetry (PIV) and one-dimensional laser Doppler anemometry (LDA) measurements were undertaken at four Reynolds numbers ( \text5,600 ￡ Re ￡ \text37,000\text{5,600} \le Re \le \text{37,000}). Two-dimensional PIV field measurements were thoroughly validated by means of point-by-point 1D LDA measurements at certain positions of the flow. A detailed study of the periodicity and the homogeneity was undertaken, which demonstrates that the flow can be regarded as two-dimensional and periodic for Re 3 \text10,000Re \ge \text{10,000}. We found a decreasing reattachment length with increasing Reynolds number. This is connected to a higher momentum in the near-wall zone close to flow separation which comes from the velocity speed up above the obstacle. This leads to a velocity overshoot directly above the hill crest which increases with Reynolds number as the inner layer depth decreases. The flow speed up above that layer is independent of the Reynolds number which supports the assumption of inviscid flow disturbance in the outer layer usually made in asymptotic theory for flow over small hills.     

Closed-loop-manipulated wake of a stationary square cylinder

Vortex shedding from a fixed rigid square cylinder in a cross flow was manipulated by perturbing the cylinder surface using piezo-ceramic actuators, which were activated by a feedback hot-wire signal via a proportional–integral–derivative (PID) controller. The manipulated flow was measured at a Reynolds number (Re) of 7,400 using particle image velocimetry (PIV), laser-induced fluorescence (LIF) flow visualisation, two-component laser Doppler anemometry (LDA), hot wires and load cells. It is observed that the vortex circulation, fluctuating streamwise velocity, lift and drag coefficients and mean drag coefficient may decrease by 71%, 40%, 51%, 42% and 20%, respectively, compared with the unperturbed flow, if the perturbation velocity of the cylinder surface is anti-phased with the flow lateral velocity associated with vortex shedding. On the other hand, these quantities may increase by 152%, 90%, 60%, 67% and 37%, respectively, given in-phased cylinder surface perturbation and vortex shedding. Similar effects are obtained at Re=3,200 and 9,500, respectively. The relationship between the perturbation and flow modification is examined, which provides insight into the physics behind the observation.     

Heterodyne Doppler global velocimetry

Doppler Global Velocimetry (DGV) is an imaging flow measurement technique which allows the measurement of the velocity distribution in a plane. In DGV the frequency shift of scattered light from moving particles within the flow is used to determine the local flow velocity. Heterodyne Doppler Global Velocimetry (HDGV) is a new approach which combines the imaging and geometrical characteristics of DGV with the measurement principles of reference beam laser Doppler anemometry. The frequency shifted scattered light from the flow tracers is heterodyned with a reference beam from the same light source. Due to interference the result of this superposition is a harmonic intensity modulated signal. This signal is detected using a smart pixel detector array to obtain the velocity distribution. Two different experiments are presented. The first experiment compares the measured velocity distribution of a rotating disk with its actual velocity. The second experiment demonstrates the capability of the technique to measure a real flow.     

Unsteady velocity measurements in a realistic intracranial aneurysm model

The initiation, growth and rupture of intracranial aneurysms are intensively studied by computational fluid dynamics. To gain confidence in the results of numerical simulations, validation of the results is necessary. To this end the unsteady flow was measured in a silicone phantom of a realistic intracranial aneurysm. A flow circuit was built with a novel unsteady flow rate generating method, used to model the idealised shape of the heartbeat. This allowed the measurement of the complex three-dimensional velocity distribution by means of laser-optical methods such as laser doppler anemometry (LDA) and particle image velocimetry (PIV). The PIV measurements, available with high temporal and spatial distribution, were found to have good agreement with the control LDA measurements. Furthermore, excellent agreement was found with the numerical results.     

Experimental study and large eddy simulation for the turbulent flow around four cylinders in an in-line square configuration

The turbulent flows around four cylinders in an in-line square configuration with different spacing ratios of 1.5, 2.5, 3.5 and 5.0 have been investigated experimentally at subcritical Reynolds numbers from 11,000 to 20,000. The mean and fluctuating velocity distributions were obtained using the laser Doppler anemometry (LDA) measurement. The digital particle image velocimetry (DPIV) was employed to characterize the full field vorticity and velocity distributions as well as other turbulent quantities. The experimental study indicated that several distinct flow patterns exist depending on the spacing ratio and subcritical Reynolds number for turbulent flow. The three-dimensional numerical simulations were also carried out using the large eddy simulation (LES) at Reynolds number of 15,000 with the spacing ratio of 1.5 and 3.5. The results show that the LES numerical predictions are in good agreement with the experimental measurements. Therefore, the three-dimensional vortex structures and the full field instantaneous and mean quantities of the flow field such as velocity field, vorticity field, etc., which are very difficult to obtain experimentally, can be extracted from the simulation results for the deepening of our understanding on the complex flow phenomena around four cylinders in in-line configuration.     

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.     

Slip velocity measurements in an upward bubbly flow by combined LDA and electrodiffusional techniques

 An experimental technique for the measurement of the local slip velocity of spherical bubbles is reported. It is based on the measurement of the local liquid velocity by an electrodiffusional method, and the bubble velocity by a specially adapted LDA (Laser Doppler anemometer) with a short measuring volume. The bubble velocity is measured taking into account the shift between the bubble centre and the centre of the LDA measuring volume. The slip velocity is obtained by subtracting the liquid velocity from the bubble velocity at the point corresponding to the bubble centre. The technique is applicable for flows with high velocity gradients. Results of the slip velocity measurements in an upward bubbly flow at laminar pipe Reynolds numbers are presented. Received: 25 July 1996/Accepted: 13 April 1998     

A new method to measure particle turbulent dispersion using laser doppler anemometer

A laser doppler anemometer (LDA) was used to measure local dispersion coefficients of particles in turbulent flow. The experimental set-up is described along with the data acquisition equipment and processing procedures. Results for 5 particles dispersing from a point source in pipe flow are shown. A second estimate for the diffusivity was obtained from mean square dispersion measurements.List of symbols A projected area of LDA measuring volume, normal to pipe axis - B ₀ – B ₂ coefficients used in concentration curve fits - C particle number density, concentration - d _f fringe spacing - f _B Bragg cell frequency shift - f _D frequency of Doppler signal - H LDA measuring volume dimension in pipe axial direction - h random variation in H - J particle flux - J ₀, J ₁ bessel function of zeroth and first order - r radial location - t time - U axial velocity - u fluctuating component of axial velocity - v_p average particle radial velocity - x axial coordinate - y position of particle in the direction normal to the mean flow relative to the centerline - mean square dispersion Greek Symbols _2,3 roots of Bessel functions - _p turbulent diffusivity of particles - laser wave length - laser beam intersection angle     

Propagation of shear-layer structures in the near-wall region of a turbulent boundary layer

Two non-intrusive techniques, namely laser Doppler anemometry (LDA) and the electrochemical method, have been used for simultaneous measurements of the instantaneous streamwise velocity (U) and longitudinal wall shear stress (S), evaluated in a zero pressure gradient turbulent boundary layer. The space-time correlation between the fluctuating velocity and shear stress suggests that the coherent flow structures are propagated (i) under a slight angle of 5° in the near-wall region and (ii) at an average angle of 15.5° for y⁺>30. It is shown that the time shift obtained from the correlation between the LDA and the electrochemical signals is due to the dynamic behaviour of the electrodiffusion probe, but also to the leaning character of the coherent structures.     

On the motion of particles in a fluid under the influence of a large velocity gradient

The motion of seeding particles as used in laser Doppler anemometry is investigated in the presence of a large velocity gradient across aerodynamic shocks under different flow conditions. Experimentally obtained results are presented and compared with theoretical predictions based upon the size distribution of the seeding particles used. It is found that the agreement of experimental and theoretical results depends on the flow conditions as well as on the particle material.