Near-wall measurements of turbulence statistics in a fully developed channel flow with a novel laser Doppler velocity profile sensor

This paper reports on the measurements of the near-wall turbulence statistics in a fully developed channel flow. The flow measurements were carried out with a novel laser Doppler velocity profile sensor with a high spatial resolution. The sensor provides both the information of velocity and position of individual tracer particles inside the measurement volume. Hence, it yields the velocity profile inside the measurement volume, in principle, without the sensor being mechanically traversed. Two sensor systems were realized with different techniques. Typically the sensor has a relative accuracy of velocity measurement of 10⁻³ and the spatial resolution of a few micrometers inside the measurement volume of about 500 μm long. The streamwise velocity was measured with two independent sensor systems at three different Reynolds number conditions. The resulting turbulence statistics show a good agreement with available data of direct numerical simulations up to fourth order moment. This demonstrates the velocity profile sensor to be one of the promising techniques for turbulent flow research with the advantage of a spatial resolution more than one magnitude higher than a conventional laser Doppler technique.     

A turbulent plane offset jet with small offset ratio

 Mean velocities and turbulence characteristics of a turbulent plane offset jet with a small offset ratio of 2.125 have been studied using laser Doppler anemometry (LDA). Static pressure measurements highlight the importance of side plates in enhancing two-dimensionality of the jet. The spatial distributions of turbulence intensities and Reynolds shear stress show a high turbulence recirculating flow region close to the nozzle plate between the jet and the offset plate. The LDA results have been used to examine the capability of three different turbulence models (i.e. k–ɛ, RNG and Reynolds stress) in predicting the velocity field of this jet. While all three models are able to predict qualitatively the recirculation, converging and reattachment regions observed experimentally, the standard k–ɛ turbulence model predicts a reattachment length that best agrees with the experimentally determined value. Received: 11 September 1996/Accepted: 30 May 1997     

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.     

Highly spatially resolving laser Doppler velocity measurements of the tip clearance flow inside a hard disk drive model

The flow in the tip clearance of a hard disk drive model has been investigated with laser Doppler techniques. The flow was driven by co-rotating disks inside a cylindrical enclosure in order to simulate a hard disk drive used for data storage devices. The main focus of the investigation was on the understanding of complex flow behavior in the narrow gap region between the disk tip and the outer shroud wall, which is supposed to be one of the causes of flow induced vibration of the disks. Experiments in the past have never been able to examine this region because of the lack of the spatial resolution of sensors in the highly three-dimensional flow in the region. In the present investigation, the flow velocity in the tip clearance region was measured with optical measurement techniques for the first time. The flow behaviors are investigated for four different conditions with two different gap widths and two different shapes of the shroud walls with and without ribs. The velocity measurements were taken both with conventional laser Doppler velocimetry and using a laser Doppler velocity profile sensor with a spatial resolution in the micrometer range. The circumferential velocity component was measured along the axial and radial directions. The steep gradients of the circumferential mean velocity in both directions were successfully captured with a high spatial resolution, which was achieved by the velocity profile sensor. From the supplementary investigations, the existence of vortex structures in the tip clearance region was confirmed with a dependence on the shroud gap width and the shroud shape. The interactions of the two boundary layers seem to be the source of the complex three-dimensional behaviors of the flow in this region.     

Highly spatially resolved velocity measurements of a turbulent channel flow by a fiber-optic heterodyne laser-Doppler velocity-profile sensor

Velocity measurements with a high spatial resolution are important in turbulent flow research. In this paper, we report on the development of a new fiber-optic laser-Doppler velocity-profile sensor exhibiting a spatial resolution of up to 5 μm and its application to turbulent boundary layers. The sensor developed in the present work employs a frequency-division-multiplexing technique in order to separate two measurement signals from the two fringe systems. Velocity measurements close to zero at the solid wall were realized using heterodyne technique. The use of fiber optics improved a robustness of the sensor. The measurement accuracy of the sensor was experimentally investigated with respect to the spatial resolution and velocity. Universal velocity profile of a turbulent flow was obtained in a fully developed channel flow. Mean and fluctuating velocity are presented with a high spatial resolution.     

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).     

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.     

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.     

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     

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     

An inclined wall jet: Mean flow characteristics and effects of acoustic excitation

 The mean velocity field of a 30° inclined wall jet has been investigated using both hot-wire and laser Doppler anemometry (LDA). Provided that the nozzle aspect ratio is greater than 30 and the inclined wall angle (β) is less than 50°, LDA measurements for various β show that the reattachment length is independent of the nozzle aspect ratio and the nozzle exit Reynolds number (in the range 6670–13,340). There is general agreement between the reattachment lengths determined by LDA and those determined using wall surface oil film visualisation technique. The role of coherent structures arising from initial instabilities of a 30° wall jet has been explored by hot-wire spectra measurements. Results indicate that the fundamental vortex roll-up frequency in both the inner and outer shear layer corresponds to a Strouhal number (based on nozzle exit momentum thickness and velocity) of 0.012. The spatial development of instabilities in the jet has been studied by introducing acoustic excitation at a frequency corresponding to the shear layer mode. The formation of the fundamental and its first subharmonic has been identified in the outer shear layer. However, the development of the first subharmonic in the inner shear layer has been severely suppressed. Distributions of mean velocities, turbulence intensities and Reynolds shear stress indicate that controlled acoustic excitation enhances the development of instabilities and promotes jet reattachment to the wall, resulting in a substantially reduced recirculation flow region. Received: 24 November 1998/Accepted: 24 August 1999     

Local liquid velocity measurements in air-water bubbly flow

Local measurements of axial liquid velocity were performed for vertical upward air-water bubbly flow in a 101.6-mm inner-diameter round pipe by using a laser Doppler anemometer (LDA) and a hot-film anemometer (HFA). The data reduction approaches for both the LDA and HFA are discussed in detail. A threshold scheme with the information of local void fraction and velocity distribution in single-phase flow was applied to the LDA to approximately discriminate liquid velocity signals from those of the bubble interface velocity. Furthermore, a formulation was given to account for the effect of the bubble relative velocity on the liquid in the front and wake regions of the bubbles. For the HFA, an amplitude threshold scheme and a slope criterion were used to extract liquid velocity information. To reduce the measurement uncertainty, the experiments were performed in flow conditions where the area-averaged void fraction was less than 20%. The experimental results showed satisfactory agreement between the liquid volumetric flow rates calculated by area integration of the local liquid velocity and void fraction measurements, and the measured value by a magnetic flow meter. Also, the area-averaged relative velocity between the gas and liquid phases obtained from the current measurements agreed well with previous research.     

On the spatial resolution of velocity and velocity gradient-based turbulence statistics measured with multi-sensor hot-wire probes

A highly resolved turbulent channel flow direct numerical simulation with Re _τ = 200 has been used to investigate the ability of 12-sensor hot-wire probes to accurately measure velocity and velocity gradient based turbulence statistics. Various virtual sensor separations have been tested in order to study the effects of spatial resolution on the measurements. First, the effective cooling velocity has been determined for each sensor for (1) an idealized probe where the influence of the velocity component tangential to the sensors and flow blockage by the presence of the prongs and the finite lengths of and thermal cross-talk between the sensors are neglected and, (2) for a real probe, the characteristics of which have been determined experimentally. Then, simulating the response of the virtual probes for these two cases to obtain the effective velocities cooling the sensors, velocity and vorticity component statistics have been calculated by assuming the velocity gradients to be constant over the probe sensing area.     

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.     

On the directional dependence of turbulence properties in anisotropic turbulent flows

 An examination is made of the consequences of a zero correlation between fluctuations in velocity level and flow direction in a stationary anisotropic turbulent flow. This zero correlation results from the fact that in a stationary turbulent flow fluctuations in both velocity level and flow direction are entirely random processes. In this paper this is considered to be an inherent property of stationary flow and utilised to simplify both the computation and the measurement of anisotropic turbulence. This new method shows several advantages compared to earlier methods. First, the spatial distribution of the flow turbulence has been shown to be a trigonometric function of the spatial parameter. Second, the relationship between Reynolds normal and shear stresses has been established. Third, when a two-dimensional flow field is concerned, two measurements using a one-component LDA system are sufficient to identify the turbulence. Until now it has been considered that three such measurements were necessary. The feasibility of the method, known as zero correlation method, has been analysed and demonstrated by experiment. Received: 29 January 1997/Accepted: 30 July 1997     

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.     

Characteristics of film condensation of supersaturated steam–air mixture on a flat plate

Experimental and numerical work was performed for the laminar film condensation of steam–air mixture flow over a flat plate. For small temperature difference between the gas mixture and the cold wall, the gas mixture in the boundary layer can be treated as superheated gas. When the temperature difference is large, the gas mixture becomes supersaturated near the interface. In that case, mist formed near the interface, the temperature profile of the gas mixture was greatly concaved toward the interface and the heat transfer was enhanced. However the velocity profile measured by the laser Doppler anemometer (LDA) showed the same trend without mist formation. A calculation model is proposed and compared with the experimental data and previous models for the superheated or the saturated conditions.     

Experimental testing of Taylor's hypothesis by L.D.A. in highly turbulent flow

A new configuration for the transmitting optics of a laser Doppler anemometer has been developed in order to measure the velocity at two different points at the same time. From the simultaneous measurements at two points along the mean flow direction it is possible to evaluate the spatial correlations and to compare them with the temporal correlation to verify the validity limits of Taylor's hypothesis also known as the frozen turbulence hypothesis. The transfer function between the velocity signals at two different points has been introduced to better explain the differences between Taylor's hypothesis and non frozen flow. The analysis is carried out in a flow with high turbulence levels.     

Doppler picture velocimetry applied to hypersonics: automated DPV fringe pattern analysis using the FFT method

Doppler picture velocimetry (DPV) is a tool for visualizing and measuring the flow velocity distribution of tracer particles in a laser light sheet. A frequency sensitive Michelson interferometer, tuned for detecting the velocity distribution by the Doppler effect, visualizes the velocity information of tracer particles crossing an illuminating laser light sheet as interference fringe patterns. Many efforts have been done to evaluate best these DPV patterns, in order to obtain the frequency distribution and, by applying the Doppler formula, the velocity profile of the tracers. The first processing method, developed in 1982, relied on manual processing of the pictures by the user, due to the unavailability of suitable high performance picture processing algorithms. This drawback made DPV being considered as a rather time-consuming measurement technique with limited accuracy, compared to existing commercial velocity measurement systems (e.g. PIV). This is no more the state of the art: The new DPV analysis software, presented in this paper, allows automated processing of the interference fringe samples obtained by two images, a reference picture without frequency shift and a Doppler picture containing the frequency shift, using single beam velocimetry. Based on Fast Fourier transformation (FFT), the presented algorithm determines the corresponding velocity profile (in pseudo colours) within only a few seconds on a standard personal computer without user intervention.     

Mean velocity and moments of turbulent velocity fluctuations in the wake of a model ship propulsor

Pod drives are modern outboard ship propulsion systems with a motor encapsulated in a watertight pod, whose shaft is connected directly to one or two propellers. The whole unit hangs from the stern of the ship and rotates azimuthally, thus providing thrust and steering without the need of a rudder. Force/momentum and phase-resolved laser Doppler anemometry (LDA) measurements were performed for in line co-rotating and contra-rotating propellers pod drive models. The measurements permitted to characterize these ship propulsion systems in terms of their hydrodynamic characteristics. The torque delivered to the propellers and the thrust of the system were measured for different operation conditions of the propellers. These measurements lead to the hydrodynamic optimization of the ship propulsion system. The parameters under focus revealed the influence of distance between propeller planes, propeller frequency of rotation ratio and type of propellers (co- or contra-rotating) on the overall efficiency of the system. Two of the ship propulsion systems under consideration were chosen, based on their hydrodynamic characteristics, for a detailed study of the swirling wake flow by means of laser Doppler anemometry. A two-component laser Doppler system was employed for the velocity measurements. A light barrier mounted on the axle of the rear propeller motor supplied a TTL signal to mark the beginning of each period, thus providing angle information for the LDA measurements. Measurements were conducted for four axial positions in the slipstream of the pod drive models. The results show that the wake of contra-rotating propeller is more homogeneous than when they co-rotate. In agreement with the results of the force/momentum measurements and with hypotheses put forward in the literature (see e.g. Poehls in Entwurfsgrundlagen für Schraubenpropeller, 1984; Schneekluth in Hydromechanik zum Schiffsentwurf, 1988; Breslin and Andersen in Hydrodynamics of ship propellers, 1996; Schneekluth and Bertram in Ship design for efficiency and economy, 1998), the co-rotating propellers model showed a much stronger swirl in the wake of the propulsor. The anisotropy of turbulence was analyzed using the anisotropy tensor introduced by Lumley and Newman (J Fluid Mech 82(1):161–178, 1977). The invariants of the anisotropy tensor of the wake flow were computed and were plotted in the Lumley–Newman-diagram. These measurements revealed that the anisotropy tensor in the wake of ship propellers is located near to the borders of the invariant map, showing a large degree of anisotropy. They will be presented and will be discussed with respect to applications of turbulence models to predict swirling flows.