Theoretical analysis of the onset of gas entrainment from a stratified region through multiple branches

A theoretical analysis has been developed to predict the critical height of the onset of gas entrainment (OGE) during dual and triple discharge from a stratified two-phase region. The two and three discharge branches are mounted on a circular wall, resembling a circular reservoir of a CANDU header–feeder configuration. A point sink model has been developed to predict the critical height and to map the velocities and acceleration flow fields during OGE. The model was verified by comparing the theoretically predicted critical height with the available experimental results. The theoretically predicted critical height is found to be a function of the branch Froude number, the location of the secondary branch with respect to the primary branch, and the angle between the branches. The effect of these variables on the predicted OGE height was investigated and is presented in this paper. Predictions of the critical height were shown to be within 25% of experimental values in both dual and triple discharge.     

Lagrangian coherent structures in the human carotid artery bifurcation

The carotid artery bifurcation is known as a site of atheromatous plaque formation which is closely related to hemodynamics. To investigate the fluid mechanics inside the bifurcation, a transparent model of the carotid geometry was built to estimate the feasibility of using stereoscopic particle image velocimetry (PIV) in a complex three-dimensional geometry. As a first approach, steady inflow conditions are considered. Velocity data are acquired in cross-sectional planes and combined to yield the full three-dimensional velocity vector field in the region of the bifurcation. The finite-time Lyapunov exponent (FTLE) is used as a criterion to reveal the complex flow structure and is found to be particularly efficient in discriminating between reverse flow and recirculation regions. The Lagrangian criterion is also computed with time-resolved, two-component PIV measurements obtained by increasing the Reynolds number up to the onset of unsteadiness. The FTLE field produces in this case a detailed visualization of the instability development.     

Dual-plane stereoscopic particle image velocimetry: system set-up and its application on a lobed jet mixing flow

 The technical basis and system set-up of a dual-plane stereoscopic particle image velocimetry (PIV) system, which can obtain the flow velocity (all three components) fields at two spatially separated planes simultaneously, is summarized. The simultaneous measurements were achieved by using two sets of double-pulsed Nd:Yag lasers with additional optics to illuminate the objective fluid flow with two orthogonally linearly polarized laser sheets at two spatially separated planes, as proposed by Kaehler and Kompenhans in 1999. The light scattered by the tracer particles illuminated by laser sheets with orthogonal linear polarization were separated by using polarizing beam-splitter cubes, then recorded by high-resolution CCD cameras. A three-dimensional in-situ calibration procedure was used to determine the relationships between the 2-D image planes and three-dimensional object fields for both position mapping and velocity three-component reconstruction. Unlike conventional two-component PIV systems or single-plane stereoscopic PIV systems, which can only get one-component of vorticity vectors, the present dual-plane stereoscopic PIV system can provide all the three components of the vorticity vectors and various auto-correlation and cross-correlation coefficients of flow variables instantaneously and simultaneously. The present dual-plane stereoscopic PIV system was applied to measure an air jet mixing flow exhausted from a lobed nozzle. Various vortex structures in the lobed jet mixing flow were revealed quantitatively and instantaneously. In order to evaluate the measurement accuracy of the present dual-plane stereoscopic PIV system, the measurement results were compared with the simultaneous measurement results of a laser Doppler velocimetry (LDV) system. It was found that both the instantaneous data and ensemble-averaged values of the stereoscopic PIV measurement results and the LDV measurement results agree well. For the ensemble-averaged values of the out-of-plane velocity component at comparison points, the differences between the stereoscopic PIV and LDV measurement results were found to be less than 2%. Received: 18 April 2000/Accepted: 2 February 2001     

Experimental study on swirling flow of dilute surfactant solution with deformed free-surface

An experimental investigation was performed on a swirling flow of dilute surfactant solution with deformed free-surface in a cylindrical container driven by the constantly rotating bottom wall. The purpose of the experiment was to estimate weak viscoelasticity in the tested surfactant solutions as well as to investigate the flow characteristics. The tested fluid was an aqueous solution of CTAC (CTAC: cetyltrimethyl ammonium chloride), which is a cationic surfactant. Water, 40 ppm, 60 ppm and 200 ppm CTAC solution flows were tested at Froude numbers ranging from 2.59 to 16.3. Particle image velocimetry (PIV) was used to measure the secondary velocity field in the meridional plane. The deformed free-surface level was extracted from the PIV images. At a similar Froude number, the depth of the dip formed at the center region of the free surface was decreased for CTAC solution flow compared with water flow. The inertia-driven vortex at the up-right corner in the meridional plane becomes more and more weakened with increase of the solution concentration or viscoelasticity. Through analyzing the overall force balance compared with water flow, the first normal stress difference characterizing the viscoelasticity was estimated for the dilute CTAC solution flows. The result supports the viscoelasticity-based turbulent drag-reduction mechanism of surfactant solution flow.     

NUMERICAL MODELLING AND PARTICLE IMAGE VELOCIMETRY MEASUREMENT OF THE LAMINAR FLOW FIELD INDUCED BY AN ENCLOSED ROTATING DISC

The fluid flow field within an enclosed cylindrical chamber with a rotating flat disc was calculated using a finite volume computational fluid dynamics (CFD) model and compared with particle image velocimetry (PIV) measurements. Two particular laminar cases near the Transitional flow regime were investigated: Reynolds number Re=2.5×1 ⁴, chamber aspect ratio G (h/R_d)=0.2 and Re=4.2×10⁴, G (h/R_d)=0.217. This enabled direct comparison with the numerical and experimental results reported by other researchers. The computational details and some major factors that affect the computed accuracy and convergence speed are also discussed in detail. PIV results containing some 4300 velocity vector points in each of seven planes for each case were obtained from the flow field parallel to the rotating disc. It was found that PIV results could be obtained in planes within the boundary layers as well as the core flow by careful use of a thin laser illumination sheet and correct choice of laser pulse separation. There was close agreement between numerical results, the present PIV measurements and other reported experimental and numerical results.     

Evaluation of aero-optical distortion effects in PIV

Aero-optical distortion effects on the accuracy of particle image velocimetry (PIV) are investigated. When the illuminated particles are observed through a medium that is optically inhomogeneous due to flow compressibility, the resulting particle image pattern is subjected to deformation and blur. In relation to PIV two forms of error can be identified: position error and velocity error. In this paper a model is presented that describes these errors and particle image blur in relation to the refractive index field of the flow. In the case of 2D flows the model equations can be simplified and, furthermore, the background oriented schlieren technique (BOS) can be applied as a means to assess and correct for the optical error in PIV. The model describing the optical distortion is validated by both computer simulation and real experiments of 2D flows. Two flow features are considered: one with optical distortion normal to the velocity (shear layer) and one with optical distortion in the direction of the flow (expansion fan). Both simulation and experiments demonstrate that the major source for the velocity error is the second derivative of the refractive index in the direction of the velocity vector. The aero-optical distortion effect is less critical for shearing interfaces in comparison with compression/expansion fronts, the most critical case being represented by shock waves. Based on the results from the simulated experiments, it is concluded that for the 2D flow case the BOS method allows a measurement of the mean velocity error in PIV and can reduce it to a large extent.     

A method for automatic estimation of instantaneous local uncertainty in particle image velocimetry measurements

The uncertainty of any measurement is the interval in which one believes the actual error lies. Particle image velocimetry (PIV) measurement error depends on the PIV algorithm used, a wide range of user inputs, flow characteristics, and the experimental setup. Since these factors vary in time and space, they lead to nonuniform error throughout the flow field. As such, a universal PIV uncertainty estimate is not adequate and can be misleading. This is of particular interest when PIV data are used for comparison with computational or experimental data. A method to estimate the uncertainty from sources detectable in the raw images and due to the PIV calculation of each individual velocity measurement is presented. The relationship between four error sources and their contribution to PIV error is first determined. The sources, or parameters, considered are particle image diameter, particle density, particle displacement, and velocity gradient, although this choice in parameters is arbitrary and may not be complete. This information provides a four-dimensional “uncertainty surface” specific to the PIV algorithm used. After PIV processing, our code “measures" the value of each of these parameters and estimates the velocity uncertainty due to the PIV algorithm for each vector in the flow field. The reliability of our methodology is validated using known flow fields so the actual error can be determined. Our analysis shows that, for most flows, the uncertainty distribution obtained using this method fits the confidence interval. An experiment is used to show that systematic uncertainties are accurately computed for a jet flow. The method is general and can be adapted to any PIV analysis, provided that the relevant error sources can be identified for a given experiment and the appropriate parameters can be quantified from the images obtained.     

Automated topology classification method for instantaneous velocity fields

Topological concepts provide highly comprehensible representations of the main features of a flow with a limited number of elements. This paper presents an automated classification method of instantaneous velocity fields based on the analysis of their critical points distribution and feature flow fields. It uses the fact that topological changes of a velocity field are continuous in time to extract large scale periodic phenomena from insufficiently time-resolved datasets. This method is applied to two test-cases : an analytical flow field and PIV planes acquired downstream a wall-mounted cube.     

The onset of gas entrainment from a flowing stratified gas–liquid regime in dual discharging branches: Part II: Critical conditions at low to moderate branch Froude numbers

This is the second of a two part investigation. Experiments were performed in a 50.8 mm diameter horizontal pipe with three 6.35 mm diameter branches located at the test section mid-span. The inlet length was 1.8 m, and three branch orientations were tested at 0° (side), 45° (inclined), and 90° (bottom) from horizontal. Water and air, operating at 206 kPa, were used and both fluids flowed co-currently within the inlet in the smooth-stratified regime. The inlet superficial velocity of the liquid phase ranged between 0.04 and 0.15 m/s while in the gas phase values of 0.3, 0.4, and 1 m/s were tested. Three different dual discharge combinations were tested and included side-inclined, side-bottom, and inclined-bottom. The tested branch flow Froude numbers were limited between low to moderate values which ranged between 1 and 23. Extensive experimental data are reported for the critical conditions at the onset of gas entrainment during dual discharge. A novel map was developed for the inclined-bottom branch configuration showing the relationship between the inlet superficial liquid velocity and branch Froude numbers. This map was used to quantify the three observed modes of gas entrainment during dual discharge. These modes were classified as onset of gas entrainment in the inclined branch only, in the bottom branch only, or both the inclined and bottom branches simultaneously. The critical height at the onset of gas entrainment results are compared to published models and data sets and poor agreement was found with studies conducted in stratified gas–liquid reservoirs.     

Simultaneous velocity field measurements in two-phase flows for turbulent mixing of sprays by means of two-phase PIV

This paper describes a novel derivative of the PIV method for measuring the velocity fields of droplets and gas phases simultaneously using fluorescence images rather than Mie scattering images. Two-phase PIV allows the simultaneous and independent velocity field measurement of the liquid phase droplets and ambient gas in the case of two-phase flow mixing. For phase discrimination, each phase is labelled by a different fluorescent dye: the gas phase is seeded with small liquid droplets, tagged by an efficient fluorescent dye while the droplets of the liquid phases are tagged by a different fluorescent dye. For each phase, the wavelength shift of fluorescence is used to separate fluorescence from Mie scattering and to distinguish between the fluorescence of each phase. With the use of two cross-correlation PIV cameras and adequate optical filters, we obtain two double frame images, one for each phase. Thus standard PIV or PTV algorithms are used to obtain the simultaneous and independent velocity fields of the two phases. Because the two-phase PIV technique relies on the ability to produce two simultaneous and independent images of the two phases, the choice of the labelling dyes and of the associated optical filter sets is relevant for the image acquisition. Thus a spectroscopic study has been carried out to choose the optimal fluorescent dyes and the associated optical filters. The method has been evaluated in a simple two-phase flow: droplets of 30–40 μm diameter, produced by an ultrasonic nozzle are injected into a gas coflow seeded with small particles. Some initial results have been obtained which demonstrate the potential of the method.     

A hybrid method for bubble geometry reconstruction in two-phase microchannels

Understanding bubble dynamics is critical to the design and optimization of two-phase microchannel heat sinks. This paper presents a hybrid experimental and computational methodology that reconstructs the three-dimensional bubble geometry, as well as provides other critical information associated with nucleating bubbles in microchannels. Rectangular cross-section silicon microchannels with hydraulic diameters less than 200 μm were fabricated with integrated heaters for the flow experiments, and the working liquid used was water. Bubbles formed via heterogeneous nucleation and were observed to grow from the silicon side walls of the channels. Two-dimensional images and two-component liquid velocity field measurements during bubble growth were obtained using micron-resolution particle image velocimetry (μPIV). These measurements were combined with iterative three-dimensional numerical simulations using finite element software, FEMLAB. The three-dimensional shape and location of the bubble were quantified by identifying the geometry that provided the best match between the computed flow field and the μPIV data. The reconstructed flow field through this process reproduced the experimental data within an error of 10–20%. Other important information such as contact angles and bubble growth rates can also be estimated from this methodology. This work is an important step toward understanding the physical mechanisms behind bubble growth and departure.     

Simultaneous PIV and concentration measurements in a gas-turbine combustor model

Simultaneous velocity and concentration measurements have been performed in a gas-turbine combustor model. Particle image velocimetry (PIV) was used to acquire planar velocity information and to identify coherent flow structures. The Mie scattering technique, based on a slightly modified experimental setup, was used for concentration measurements in this mixing flow. The degree of mixing was assessed by examining local concentration measurements while inhomogeneously seeding the primary and secondary stream of the mixing layer. Connections between flow field and concentration distribution were highlighted using the proper orthogonal decomposition algorithm (POD). Uncertainties and systematic errors for the PIV measurements due to the suboptimal seeding are discussed using a comparison with a second test series at optimal seeding conditions. Results are presented for several flow parameters and at various lateral planes.     

Particle image velocimetry in a variable density flow: application to a dynamically evolving microburst

A fondamental difficulty in the experimental study of gravity-driven flows using particle image velocimetry (PIV) and other optical diagnostic techniques is the problem associated with variations in thé refractive index within the fluid. This paper discusses a method by which the refractive indices of two fluids are matched while maintaining density differences of up to 4%. Aqueous solutions of glycerol and potassium phosphate are used to achieve precise index matching in the presence of mixed and unmixed constituents. The effectiveness of the method is verified in a PIV study of a laboratory-scale model of an atmospheric microburst where planes of two-dimensional velocity vectors are obtained in thé evolving flow field.This work was sponsored by the National Science Foundation under grant CTS-9209948. We also thank TSI, Inc. for the use of its facility     

Flow Characterization Through a Network Cell Using Particle Image Velocimetry

Particle image velocimetry (PIV) with refractive index matching was developed to map pore-scale fluid flow through a clear, acrylic two-dimensional network flow cell. A microscope objective lens was incorporated in the PIV set up so that flow in micro-scale throats could be measured. The flow cell consists of 20 × 20, equal-size cylindrical pore bodies, 2.5mm in diameter and 1.0mm in height, connected on a diamond lattice by 2.5 mm long, square cross-section throats of widths that varied randomly among 0.2, 0.6, and 1.0 mm. Micro-PIV data was used to obtain the two-dimensional streamline pattern of fluid flow and the velocity field over the field of view (FOV) by periodically illuminating seed particles following the flow and cross correlating particle positions to determine displacements over time. Refractive index matching of the flow cell and test fluid minimizes extraneous scattering of light at solid--liquid interfaces improving image resolution. Experimentally determined velocity vectors for single-phase flow through three pore bodies and their adjoining throats as well as for the outlet of the flow cell were compared with numerical simulations of flow through the cell.     

Viscous flow through microfabricated hyperbolic contractions

We study the flow of a Newtonian fluid through microfabricated hyperbolic contractions followed by a sudden expansion, with the aim of investigating the potential of this geometry to serve as an extensional microrheometer. A set of planar converging geometries, with total Hencky strains ranging from 1.0 to 3.7, were fabricated in order to produce a homogeneous extensional flow field within the contraction. The velocity field in various planes of the hyperbolic contraction was quantified by means of microparticle image velocimetry (μPIV) and the pressure drop across the converging geometry was also measured and found to vary approximately linearly with the flow rate. Additionally, an extensive range of numerical calculations were carried out using a finite-volume method to help assess the performance of this geometry as a microfluidic elongational rheometer. The measured velocity fields in the contraction and associated pressure drops compare very well (to within 10%) with the numerical predictions. For the typical dimensions used in the microfluidic devices, the steady viscous flow through the contraction is shown to be three-dimensional and it is demonstrated that regions with nearly constant strain rate can only be achieved using geometries with large total Hencky strains under Hele–Shaw (potential-like) flow conditions.     

Local gas and liquid phase velocity measurement in a miniature stirred vessel using PIV combined with a new image processing algorithm

A method which combines standard two-dimensional particle image velocimetry (PIV) with a new image processing algorithm has been developed to measure the average local gas bubble velocities, as well as the local velocities of the liquid phase, within small stirred vessel reactors. The technique was applied to measurements in a gas–liquid high throughput experimentation (HTE) vessel of 45 mm diameter, but it is equally suited to measurements in larger scale reactors. For the measurement of liquid velocities, 3 μm latex seeding particles were used. For gas velocity measurements, a separate experiment was conducted which involved doping the liquid phase with fluorescent Rhodamine dye to allow the gas–liquid interfaces to be identified. The analysis of raw PIV images enabled the detection of bubbles within the laser plane, their differentiation from obscuring bubbles in front of the laser plane, and their use in lieu of tracer particles for gas velocity analysis using cross-correlation methods. The accuracy of the technique was verified by measuring the velocity of a bubble rising in a vertical glass column. The new method enabled detailed velocity fields of both phases to be obtained in an air–water system. The overall flow patterns obtained showed a good qualitative agreement with previous work in large scale vessels. The downward liquid velocities above the impeller were greatly reduced by the addition of the gas, and significant differences between the flow patterns of the two-phases were observed.     

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).     

PIV measurements in a weakly separating and reattaching turbulent boundary layer

A high Reynolds number flat plate turbulent boundary layer was studied in a wind-tunnel experiment using particle image velocimetry (PIV). The flow is subjected to an adverse pressure gradient (APG) which is designed such that the boundary layer separates and reattaches, forming a weak separation bubble. With PIV we are able to get a more complete picture of this complex flow phenomenon. The view of a separation bubble being composed of large scale coherent regions of instantaneous backflow occurring randomly in a three-dimensional manner in space and time is verified by the present PIV measurements. The PIV database was used to test the applicability of various velocity scalings around the separation bubble. We found that the mean velocity profiles in the outer part of the boundary layer, and to some extent also the Reynolds shear-stress, are self-similar when using a velocity scale based on the local pressure gradient. The same can be said for the so called Perry–Schofield scaling, which suggests that the two velocity scales are connected. This can also be interpreted as an experimental evidence of the claimed relation between the latter velocity scale and the maximum Reynolds shear-stress.     

水气两相流中稀疏气泡流动速度场的数字图像测量初探

由空压机提供的气体通过—排微小直径的喷嘴进入静止水体，形成水气两相流流场。在单相PIV和PTV技术的基础上，研究稀疏气液两相流情况下气泡的速度场分布。PIV算法采用快速傅立叶互相关分析法，而PTV算法需要获得每幅图像中每个气泡的形心，根据连续图像中的粒子对，计算速度。用PIV和PTV两种算法处理求出气泡的速度并对两种方法进行比较，其最终研究成果可应用于流体及多相流的流量测技术，提高我们进行低密度气液两相流相关研究的测量水平。同时为水气两相流的数值分析和理论研究提供流场测试的数据。     

The turbulence structure of drag-reduced boundary layer flow

The structure of turbulence in a drag-reduced flat-plate boundary layer flow has been studied with particle image velocimetry (PIV). Drag reduction was achieved by injection of a concentrated polymer solution through a spanwise slot along the test wall at a location upstream of the PIV measurement station. Planes of velocity were measured parallel to the wall (x–z plane), for a total of 30 planes across the thickness of the boundary layer. For increasing drag reduction, we found a significant modification of the near-wall structure of turbulence with a coarsening of the low-speed velocity streaks and a reduction in the number and strength of near-wall vortical structures.