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).     

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.     

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.     

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     

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.     

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.     

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     

Effects of coincidence window and measuring volume size on laser Doppler velocimetry measurement of turbulence

The effects of coincidence window and measuring volume size on two-component laser velocimeter measurement of turbulence in an isothermal liquid flow through a concentric annular channel were studied. Three different coincidence windows (100–500 μs) and three different measuring volume sizes (diameter, 5–9 wall units; spanwise length, 24–91 wall units) were used in a flow of Reynolds number 31,500 and data density spanning the high end of intermediate to the low end of high (3–6). While no significant effects of the coincidence window and measuring volume size were found on the time-mean velocity and turbulence intensities, the streamwise Reynolds shear stress measured near a wall was found to be markedly affected by both. The smallest feasible measuring volume along with an appropriate coincidence window provides good measurement of the shear stress. Received: 8 September 1999/Accepted: 11 July 2000     

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.     

Error quantification of 3D homogeneous and isotropic turbulence measurements using 2D PIV

Particle image velocimetry (PIV) has become a popular non-intrusive tool for measuring various types of flows. However, when measuring three dimensional flows with 2D PIV, there is inherent measurement error due to out-of-plane motion. Errors in the measured velocity field propagate to turbulence statistics. Since this can distort the overall flow characteristics, it is important to understand the effect of this out-of-plane error. In this study, the effect of out-of-plane motion on turbulence statistics is quantified. Using forced isotropic turbulence direct numerical simulation (DNS) flow field data provided by the Johns Hopkins turbulence database (JHTDB), synthetic image tests are performed. Turbulence statistics such as turbulence kinetic energy, dissipation rate, Taylor microscale, Kolmogorov scale, and velocity correlations are calculated. Various test cases were simulated while controlling three main parameters which affect the out-of-plane motion: PIV interrogation window size, camera inter-frame time, and laser sheet thickness. The amount of out-of-plane motion was first quantified, and then the error variation according to these parameters was examined. This information can be useful when examining fully three dimensional flows such as homogeneous and isotropic turbulence via 2D PIV.     

How to estimate the low wavenumber turbulence frequency spectrum

 An estimate of the low wavenumber component of surface turbulence shear stress as a function of frequency has been obtained through measurements of the correlations of the longitudinal component of turbulence velocity made close to the surface at y ⁺=7. The data were acquired in a fully-developed turbulent pipe flow at a Reynolds number (based on centreline velocity and pipe diameter) of 268000, using two single hot-wire anemometer probes. A novel data analysis procedure has been introduced to establish the accuracy limits of the low wavenumber turbulence energy estimate for frequencies in the similarity regime of wall turbulence and the results are compared with other measurement techniques. Received: 18 November 1993/Accepted: 21 April 1997     

Numerical simulation of thermal boundary layer profile measurement

Heat transfer rates from a surface can be determined from the slope of the temperature profile measured with a thermocouple wire traversing within a boundary layer. However, accuracy of such measurement can suffer due to flow distortion and conduction through the thermocouple wire. The present numerical study consists of two parts—a 2D simulation of flow distortion due to a cylinder in cross flow near a solid wall and a 3D simulation defined as a fin problem to calculate the thermal profile measurement error due to conduction through the thermocouple wires. Results show that the measured temperature is lower than the true temperature resulting in a 5% under-prediction of local heat transfer coefficient. A parametric study shows that low thermal conductivity thermocouple (E type) with a small wire diameter (76 micron) is desirable to reduce the measurement error in local Nusselt number.     

Prediction of mono-disperse gas–liquid turbulent flow in a vertical pipe

A two-fluid model in the Eulerian–Eulerian framework has been implemented for the prediction of gas volume fraction, mean phasic velocities, and the liquid phase turbulence properties for gas–liquid upward flow in a vertical pipe. The governing two-fluid transport equations are discretized using the finite volume method and a low Reynolds number $k-\varepsilon$ model is used to predict the turbulence field for the continuous liquid phase. In the present analysis, a fully developed one-dimensional flow is considered where the gas volume fraction profile is predicted using the radial force balance for the bubble phase. The current study investigates: (1) the turbulence modulation terms which represent the effect of bubbles on the liquid phase turbulence in the k–ε transport equations; (2) the role of the bubble induced turbulent viscosity compared to turbulence generated by shear; and (3) the effect of bubble size on the radial forces which results in either a center-peak or a wall-peak in the gas volume fraction profiles. The results obtained from the current simulation are generally in good agreement with the experimental data, and somewhat improved over the predictions of some previous numerical studies.     

Turbulence energy balance in reacting turbulent flows

The turbulence accompanying combustion and the propagation of detonation waves in gases has been studied theoretically and experimentally in many papers [1–8]. The attention of researchers has been concentrated on essential questions like how the turbulent flow field interacts with the kinetics of the chemical reaction and to what extent the process of chemical change is intensified, and how the turbulence itself is deformed by the heat released and the accompanying expansion of the gases. The various mechanisms proposed for these phenomena are based on various hypotheses concerning the structure of the combusion zone and the determinative stage of the interaction of the turbulence with the chemical-reaction kinetics. The mechanism of turbulence generation by combustion proposed in a number of papers [3–6] is based on the observation in turbulent flow of a weakly curved flickering laminar flame. This gives rise to a nonuniform flow field of the gas, part of the energy of which goes over into the energy of turbulent fluctuations. Other authors [7, 8] considered the turbulence field to interact with the chemical-reaction kinetics via a volume mechanism and suggested a criterion of turbulence intensification based on certain physical considerations, e.g., the condition for the intensification of thermogaskinetic oscillations proposed by Rayleigh [9]. In the present paper the problem is analyzed by introducing Kolmogorov's general equation for the turbulence energy balance in reacting turbulent flows [10]. In accordance with, this equation the turbulence energy can vary due to energy exchange between the turbulent motion and the mean gas flow as a result of the work on turbulent mass transport in the acceleration field of the mean flow, and due to the effect of pressure fluctuations on the rate of thermal expansion from the chemical reaction. Each of these effects is considered and analyzed.     

Experimental study of inelastic strain patterns in a model of a tube-plate ligament using an interferometric moiré technique

A sensitive moiré interferometer has been developed for measuring elasto-plastic strain distributions. No rigid connection with the specimen was required, and the fringe patterns could be seen by eye as loading progressed. The system has been applied to the measurement of strain patterns in a stainless-steel model of a tube-plate ligament. The model was loaded in tension and in bending, with the eventual aim of measuring strain-intensification factors which could be used as basic design data.     

Modelling of the diffusion of fluid particles in turbulent flows approaching a circular cylinder by random Fourier modes and random flight

To investigate the diffusion of fluid particles around a cylinder in a turbulent flow, we have developed two new types of model for simulating the trajectory of particles:(1) a model combining random Fourier modes and random flight (RF); (2) a pure kinematic simulation (KS) by random Fourier modes. In model 1 the large-scale turbulence is simulated by a sum of random Fourier modes varying in space and time, and the small-scale random motion of particles is simply modelled by an Itô type of stochastic differential equation with a memory time comparable to the Lagrangian time scaleT _s ^L of the small-scale motion. In model 2, both large- and small-scale turbulence is simulated using random Fourier modes. The change of turbulence around the cylinder is modelled by rapid distortion theory (RDT), although the small-scale motion of particles in the RF model is simply assumed to keep the homogeneous random behaviour. These models give very similar and realistic trajectories showing rapid changes of direction due to the small-scale motion.     

The Oriented-Eddy Collision Turbulence Model

The Oriented-Eddy Collision (OEC) model treats turbulent flow as a non-Newtonian fluid where the average behavior of turbulence is modeled as a collection of interacting fluid particles which have inherent orientation. The model is derived from the two-point velocity correlation transport equation, and has the form of a collection of Reynolds-stress transport equations, with one set of transport equations for each representative eddy direction. The addition of eddy orientation information adds important physics to the model and allows the model to represent structural (two-point) information about the turbulence. This structural information is sufficient to allow the model to capture the effect of external forces and imposed mean strains (such as rapid distortion theory) exactly. The only physical effects that must be empirically modeled are those that are due to turbulence-turbulence interactions, referred to as eddy collisions. The performance of the model in a number of canonical flow situations is presented.     

Effect of the measurement volume in turbulent pipe flow measurement by the ultrasonic velocity profile method (mean velocity profile and Reynolds stress measurement)

 The ultrasonic velocity profile measurement method has some favorable advantages over the conventional flow measurement methods, such as measurement of the instantaneous velocity profile over the measuring line and its applicability to opaque liquids. The method has another advantage of being non-intrusive. Hence, it is applicable to various flow conditions, although it requires a relatively large measurement volume. In this paper, the effects of the measurement volume on the mean velocity profile and the Reynolds stress measurement have been investigated for fully developed turbulent flows in a vertical pipe. The results were then compared with data obtained by direct numerical simulation. Received: 9 March 2000 / Accepted: 27 March 2001 Published online: 29 November 2001     

On the analysis of an impinging jet on ground effects

Laser Doppler measurements and flow visualization are presented for a turbulent circular jet emerging into a low-velocity cross-stream and, then, impinging on a flat surface perpendicular to the jet-nozzle axis. The experiments were performed for a Reynolds number based on the jet-exit conditions of 6 × 10⁴, a jet-to-crossflow velocity ratio of 30 and for an impingement height of 5 jet diameters and include mean and turbulent velocity characteristics along the two normal directions contained in planes parallel to the nozzle axis. The results, which have relevance to flows found beneath VSTOL aircraft in ground effect, show the presence of a complex 3-D scarf vortex formed around the impinging jet. In zones where measurement data are not available, the flow details are numerically-visualized using a solution of the finite difference form of the fully threedimensional Reynolds-averaged Navier-Stokes equations, incorporating the turbulence viscosity concept. The turbulent structure of the flow is affected by flow distortion at the impinging zone, which results in an unconventional behaviour of the dimensionless structure parameters that determine the empirical constants in engineering models of turbulence. The relative magnitude of the terms involved in the transport equations for the turbulent stresses is quantified from the experimental data in order to assess the importance of these effects and show the extent to which the turbulent structure of the impingement zone is affected by extra rates of strain.     

Non-equilibrium turbulent phenomena in the ?ow over a backward-facing ramp

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid turbulence, turbulent wakes, and homogeneous isotropic turbulence(HIT). The non-equilibrium turbulence in non-canonical flows, however, has rarely been studied due to the complexity of the flows. In the present contribution, a directnumerical simulation(DNS) database of a turbulent flow is analyzed over a backwardfacing ramp, the flow near the boundary is demonstrated, and the non-equilibrium turbulent properties of the flow in the wake of the ramp are presented by using the characteristic parameters such as the dissipation coefficient C and the skewness of longitudinal velocity gradient Sk, but with opposite underlying turbulent energy transfer properties. The equation of Lagrangian velocity gradient correlation is examined, and the results show that non-equilibrium turbulence is the result of phase de-coherence phenomena, which is not taken into account in the modeling of non-equilibrium turbulence. These findings are expected to inspire deeper investigation of different non-equilibrium turbulence phenomena in different flow conditions and the improvement of turbulence modeling.