Three-dimensional Particle Tracking Velocimetry Research Articles

Streamwise and spanwise slip over a superhydrophobic surface

The near-wall turbulent flow over a superhydrophobic surface (SHS) with random texture was studied using three-dimensional Lagrangian particle tracking velocimetry (3D-PTV). The channel was operated at a constant mass flow rate over the SHS and a smooth surface at a Reynolds number of 7000 based on the bulk velocity of $0.93~\text{m}~\text{s}^{-1}$ and the full channel height. The friction Reynolds number was 217, based on the friction velocity and half channel height. The 3D-PTV processing was based on the shake-the-box algorithm applied to images of fluorescent tracers recorded using four high-speed cameras. The SHS was obtained by spray coating, resulting in a root-mean-square roughness of $0.29\unicode[STIX]{x1D706}$ and an average texture width of $5.0\unicode[STIX]{x1D706}$, where $\unicode[STIX]{x1D706}=17~\unicode[STIX]{x03BC}\text{m}$ is the inner flow scale over the SHS. The 3D-PTV measurements confirmed an isotropic slip with a streamwise slip length of $5.9\unicode[STIX]{x1D706}$ and a spanwise slip length of $5.9\unicode[STIX]{x1D706}$. As a result, both the near-wall mean streamwise and spanwise velocity profiles over the SHS were higher than the smooth surface. The streamwise and spanwise slip velocities over the SHS were $0.27~\text{m}~\text{s}^{-1}$ and $0.018~\text{m}~\text{s}^{-1}$, respectively. The near-wall Reynolds stresses over the SHS were larger and shifted towards the wall when normalized by the corresponding inner scaling, despite the smaller friction Reynolds number of 180 over the SHS. The near-wall measurement of streamwise velocity showed that the shear-free pattern consists of streamwise-elongated regions with a length of $800\unicode[STIX]{x1D706}$ and a spanwise width of $300\unicode[STIX]{x1D706}$. The plastron dimensions correspond to the mean distance of the largest roughness peaks $(20~\unicode[STIX]{x03BC}\text{m})$ obtained from profilometry of the SHS. The drag reduction over the SHS was 30 %–38 % as estimated from pressure measurement and the flow field using the 3D-PTV.

A quantitative study of track initialization of the four-frame best estimate algorithm for three-dimensional Lagrangian particle tracking

We introduce a method to improve three-dimensional particle tracking velocimetry (3D-PTV) algorithms. 3D-PTV is an experimental method used to measure the Lagrangian trajectories of individual particles over time. The trajectories are constructed by linking the particle positions from a sequence of images. Different 3D-PTV algorithms have been proposed in the literature, ranging from simply taking the nearest neighbor in the next frame to using multiframe schemes. This work focuses on the initialization of the four-frame best estimate (4BE) method introduced by Ouellette et al (2006 Exp. Fluids 40 301–13). Previously, tracking algorithms have been initialized by using the particle’s nearest neighbor(s) in the next frame or by using a velocity guess to predict the particle’s location in the next frame. We propose a more robust initialization, coupled with 4BE, that performs better than existing methods in the literature, in the sense of yielding a higher number of correct tracks. The performance of the proposed initialization method is compared to the 4BE method that uses nearest neighbor initialization by applying both methods on direct numerical simulation data from the Johns Hopkins turbulence databases. We show that the modified initialization greatly improves tracking in two canonical cases, homogeneous isotropic turbulence and turbulent channel flow (inhomogenous and anisotropic), greatly increasing the percentage of correct tracks found even under challenging seeding/particle displacement conditions.

Flow-induced motions of flexible plates: fluttering, twisting and orbital modes

The unsteady dynamics of wall-mounted flexible plates under inclined flows was fundamentally described using theoretical arguments and experiments under various Cauchy numbers $Ca=\unicode[STIX]{x1D70C}_{f}bL^{3}U_{0}^{2}/(EI)\in [7,81]$ (where $\unicode[STIX]{x1D70C}_{f}$ is the fluid density, $b$ and $L$ are the plate width and length, $U_{0}$ is the incoming velocity, $E$ is Young’s modulus and $I$ is the second moment of the area) and inclination angles $\unicode[STIX]{x1D6FC}$. Three-dimensional particle tracking velocimetry and a high-resolution force sensor were used to characterize the evolution of the plate dynamics and aerodynamic force. We show the existence of three distinctive, dominant modes of tip oscillations, which are modulated by the structure dynamic and flow instability. The first mode is characterized by small-amplitude, planar fluttering-like motions occurring under a critical Cauchy number, $Ca=Ca_{c}$. Past this condition, the motions are dominated by the second mode consisting of unsteady twisting superimposed onto the fluttering patterns. The onset of this mode is characterized by a sharp increase of the force fluctuation intensity. At sufficiently high $Ca$ and $\unicode[STIX]{x1D6FC}$, the plate may undergo a third mode given by large-scale tip orbits about the mean bending. Using the equation of motion and first-order approximations, we propose a formulation to estimate $Ca_{c}$ as a function of $\unicode[STIX]{x1D6FC}$; it exhibits solid agreement with experiments.

Single-camera three-dimensional tracking of natural particulate and zooplankton

We develop and characterize an image processing algorithm to adapt single-camera defocusing digital particle image velocimetry (DDPIV) for three-dimensional (3D) particle tracking velocimetry (PTV) of natural particulates, such as those present in the ocean. The conventional DDPIV technique is extended to facilitate tracking of non-uniform, non-spherical particles within a volume depth an order of magnitude larger than current single-camera applications (i.e. 10 cm × 10 cm × 24 cm depth) by a dynamic template matching method. This 2D cross-correlation method does not rely on precise determination of the centroid of the tracked objects. To accommodate the broad range of particle number densities found in natural marine environments, the performance of the measurement technique at higher particle densities has been improved by utilizing the time-history of tracked objects to inform 3D reconstruction. The developed processing algorithms were analyzed using synthetically generated images of flow induced by Hill’s spherical vortex, and the capabilities of the measurement technique were demonstrated empirically through volumetric reconstructions of the 3D trajectories of particles and highly non-spherical, 5 mm zooplankton.

Three-dimensional particle tracking velocimetry algorithm based on tetrahedron vote

A particle tracking velocimetry algorithm based on tetrahedron vote, which is named TV-PTV, is proposed to overcome the limited selection problem of effective algorithms for 3D flow visualisation. In this new cluster-matching algorithm, tetrahedrons produced by the Delaunay tessellation are used as the basic units for inter-frame matching, which results in a simple algorithmic structure of only two independent preset parameters. Test results obtained using the synthetic test image data from the Visualisation Society of Japan show that TV-PTV presents accuracy comparable to that of the classical algorithm based on new relaxation method (NRX). Compared with NRX, TV-PTV possesses a smaller number of loops in programming and thus a shorter computing time, especially for large particle displacements and high particle concentration. TV-PTV is confirmed practically effective using an actual 3D wake flow.

Experimental study of the surface oscillations induced by a shallow flow past a lateral cavity

The present work presents an experimental study in which resonant surface oscillations inside a lateral cavity are reconstructed, often denoted as se- iching, which are excited by a shallow main stream flowing past the horizontal basin. Firstly, the flow configurations that trigger transverse and/or longitu- dinal seiching are studied using pressure measurements in the corners of the cavity, which shows that a transitional Froude number exists, approximately 0.63, at which the dominant seiching mode changes from transverse to longi- tudinal seiching. For both types of resonant conditions, the surface shape is analyzed in detail using a three-dimensional particle tracking velocimetry (3D- PTV) setup. Based upon floating seeding particles, the 3D surface is recon- structed with a superior spatial resolution compared to traditional measurement techniques, which confirms the multimodal aspect of the surface oscillations.

Measuring three-dimensional flow structures in the conductive airways using 3D-PTV

Detailed information about flow patterns and mass transport in the conductive airways is of crucial interest to improve ventilation strategies as well as targeted drug delivery. Despite a vast number of flow studies in this field, there is still a dearth in experimental data of three-dimensional flow patterns, in particular for the validation of numerical results. Therefore, oscillating flow within a realistic model of the upper human conductive airways is studied here experimentally. The investigated range of Reynolds numbers is Re = 250–2000 and the Womersley number is varied between $$\alpha$$ = 1.9–5.1, whereby physiological flow at rest conditions is included. In employing the three-dimensional particle tracking velocimetry measurement technique, we can directly visualize airway specific flow structures as well as examine Lagrangian trajectory statistics, which has not been covered to date. The systematic variation of characteristic flow parameters in combination with the advanced visualization technique sheds new light on the mechanisms of evolving flow patterns. By determining Lagrangian properties such as pathline curvature and torsion, we find that both strongly depend on the Reynolds number. Moreover, the probability density function of the curvature reveals a unique shape for certain flow regions and resembles a turbulent like behavior at the small scales.

Concentration and velocity statistics of inertial particles in upward and downward pipe flow

Three-dimensional particle tracking velocimetry is applied to particle-laden turbulent pipe flows at a Reynolds number of 10 300, based on the bulk velocity and the pipe diameter, for developed fluid flow and not fully developed flow of inertial particles, which favours assessment of the radial migration of the inertial particles. Inertial particles with Stokes number ranging from 0.35 to 1.11, based on the particle relaxation time and the radial-dependent Kolmogorov time scale, and a ratio of the root-mean-square fluid velocity to the terminal velocity of order 1 have been used. Core peaking of the concentration of inertial particles in up-flow and wall peaking in down-flow have been found. The difference in mean particle and Eulerian mean liquid velocity is found to decrease to approximately zero near the wall in both flow directions. Although the carrier fluid has all of the characteristics of the corresponding turbulent single-phase flow, the Reynolds stress of the inertial particles is different near the wall in up-flow. These findings are explained from the preferential location of the inertial particles with the aid of direct numerical simulations with the point-particle approach.

Short-term exposure to gold nanoparticle suspension impairs swimming behavior in a widespread calanoid copepod

Calanoid copepods play an important role in the functioning of marine and brackish ecosystems. Information is scarce on the behavioral toxicity of engineered nanoparticles to these abundant planktonic organisms. We assessed the effects of short-term exposure to nonfunctionalized gold nanoparticles on the swimming behavior of the widespread estuarine copepod Eurytemora affinis. By means of three-dimensional particle tracking velocimetry, we reconstructed the trajectories of males, ovigerous and non-ovigerous females. We quantified changes in their swimming activity and in the kinematics and geometrical properties of their motion, three important descriptors of the motility patterns of zooplankters. In females, exposure to gold nanoparticles in suspension (11.4 μg L−1) for 30 min caused depressed activity and lower velocity and acceleration, whereas the same exposure caused minimal effects in males. This response differs clearly from the hyperactive behavior that is commonly observed in zooplankters exposed to pollutants, and from the generally lower sensitivity of female copepods to toxicants. Accumulation of gold nanoparticles on the external appendages was not observed, precluding mechanical effects. Only very few nanoparticles appeared sporadically in the inner part of the gut in some samples, either as aggregates or as isolated nanoparticles, which does not suggest systemic toxicity resulting from pronounced ingestion. Hence, the precise mechanisms underlying the behavioral toxicity observed here remain to be elucidated. These results demonstrate that gold nanoparticles can induce marked behavioral alterations at very low concentration and short exposure duration. They illustrate the applicability of swimming behavior as a suitable and sensitive endpoint for investigating the toxicity of nanomaterials present in estuarine and marine environments. Changes in swimming behavior may impair the ability of planktonic copepods to interact with their environment and with other organisms, with possible impacts on population dynamics and community structure.

Exploring the geostrophic regime of rapidly rotating convection with experiments

Rapidly rotating Rayleigh–Bénard convection is studied using time-resolved particle image velocimetry and three-dimensional particle tracking velocimetry. Approaching the geostrophic regime of rotating convection, where the flow is highly turbulent and at the same time dominated by the Coriolis force, typically requires dedicated setups with either extreme dimensions or troublesome working fluids (e.g., cryogenic helium). In this study, we explore the possibilities of entering the geostrophic regime of rotating convection with classical experimental tools: a table-top conventional convection cell with a height of 0.2 m and water as the working fluid. In order to examine our experimental measurements, we compare the spatial vorticity autocorrelations with the statistics from simulations of geostrophic convection reported earlier in [D. Nieves et al., “Statistical classification of flow morphology in rapidly rotating Rayleigh-Bénard convection,” Phys. Fluids 26, 086602 (2014)]. Our findings show that we have indeed access to the geostrophic convection regime and can observe the signatures of the typical flow features reported in the aforementioned simulations.

Shear-scaling-based approach for irreversible energy loss estimation in stenotic aortic flow – An in vitro study

Today, the functional and risk assessment of stenosed arteries is mostly based on ultrasound Doppler blood flow velocity measurements or catheter pressure measurements, which rely on several assumptions. Alternatively, blood velocity including turbulent kinetic energy (TKE) may be measured using MRI. The aim of the present study is to validate a TKE-based approach that relies on the fact that turbulence production is dominated by the flow’s shear to determine the total irreversible energy loss from MRI scans. Three-dimensional particle tracking velocimetry (3D-PTV) and phase-contrast magnetic resonance imaging (PC-MRI) simulations were performed in an anatomically accurate, compliant, silicon aortic phantom. We found that measuring only the laminar viscous losses does not reflect the true losses of stenotic flows since the contribution of the turbulent losses to the total loss become more dominant for more severe stenosis types (for example, the laminar loss is 0.0094±0.0015W and the turbulent loss is 0.0361±0.0015W for the Remax=13,800 case, where Remax is the Reynolds number based on the velocity in the vena-contracta). We show that the commonly used simplified and modified Bernoulli’s approaches overestimate the total loss, while the new TKE-based method proposed here, referred to as “shear scaling” approach, results in a good agreement between 3D-PTV and simulated PC-MRI (mean error is around 10%). In addition, we validated the shear scaling approach on a geometry with post-stenotic dilatation using numerical data by Casas et al. (2016). The shear scaling-based method may hence be an interesting alternative for irreversible energy loss estimation to replace traditional approaches for clinical use. We expect that our results will evoke further research, in particular patient studies for clinical implementation of the new method.

Improvements on digital inline holographic PTV for 3D wall-bounded turbulent flow measurements

Three-dimensional (3D) particle image velocimetry (PIV) and particle tracking velocimetry (PTV) provide the most comprehensive flow information for unraveling the physical phenomena in a wide range of fluid problems, from microfluidics to wall-bounded turbulent flows. Compared with other 3D PIV techniques, such as tomographic PIV and defocusing PIV, the digital inline holographic PTV (DIH-PTV) provides 3D flow measurement solution with high spatial resolution, low cost optical setup, and easy alignment and calibration. Despite these advantages, DIH-PTV suffers from major limitations including poor longitudinal resolution, human intervention (i.e. requirement for manually determined tuning parameters during tracer field reconstruction and extraction), limited tracer concentration, small sampling volume and expensive computations, limiting its broad use for 3D flow measurements. In this study, we present our latest developments on minimizing these challenges, which enables high-fidelity DIH-PTV implementation to larger sampling volumes with significantly higher particle seeding densities suitable for wall-bounded turbulent flow measurements. The improvements include: (1) adjustable window thresholding; (2) multi-pass 3D tracking; (3) automatic wall localization; and (4) continuity-based out-of-plane velocity component computation. The accuracy of the proposed DIH-PTV method is validated with conventional 2D PIV and double-view holographic PTV measurements in smooth-wall turbulent channel flow experiments. The capability of the technique in characterization of wall-bounded turbulence is further demonstrated through its application to flow measurements for smooth- and rough-wall turbulent channel flows. In these experiments, 3D velocity fields are measured within sampling volumes of 14.7 × 50.0 × 14.4 mm3 (covering the entire depth of the channel) with a velocity resolution of <1.1 mm/vector. Overall, the presented DIH-PTV method and measurements highlight the applicability of DIH-PTV to obtain 3D characterization of the turbulent structures with velocity spatial resolution and within sampling volume sizes comparable to other the-state-of-the-art 3D whole-field flow measurement techniques.

Numerical and experimental comparison of complete three-dimensional particle tracking velocimetry algorithms for indoor airflow study

The experimental data retrieved from three-dimensional particle tracking velocimetry (3D PTV) are crucial for indoor environment engineering when designing ventilation strategies or monitoring airborne pollutants dispersion in inhabited spaces as well as in livestock compounds. The performance of the measurement algorithm, as the core part of the 3D PTV technology, has a strong influence on the final results. This study presents a method to select the better 3D PTV algorithm depending on the application targeted. This study first compared the performance of seven 3D PTV algorithms on two types of 3D laminar macro scale flows of known Navier–Stokes solutions, namely the Kovasznay and Beltrami flows. The comparison was based on the accuracy, the measuring volume coverage and the achievable trajectory length of each algorithm with respect to the particle tracking density and the total number of frames. Then, the measurement algorithms with better performances were further compared with the experimental measurement of real 3D airflows in a cubic cavity. The results suggest that different measurement algorithms have different advantages and drawbacks depending on the application targeted, and that the algorithms using the epipolar constraint as the method of spatial matching generally perform better.

Three-dimensional flow observation on the air entrainment into a vertical-wet-pit pump

The authors consider the air entrainment into a suction pipe which is vertically inserted down into a suction sump across a mean free-water surface. This configuration is often referred to as the “vertical wet-pit pump,” and has many practical advantages in construction, maintenance and operation. Most of the flows appearing in various industrial and environmental problems like the present suction- sump flow become often complicated owing to both of their unsteadiness with poor periodicity and their fully-three-dimensionality. In order to understand the complicated flow inside a suction sump in the vertical-wet-pit-pump configuration, the authors experimentally observe the flow using the three-dimensional particle tracking velocimetry (3D-PTV) technique, which includes more unknown factors in accuracy and reliability than other established measuring techniques. So, the authors examine the simultaneous measurement by the 3D-PTV with another velocimetry the ultrasonic velocity profiler. As a result, under the suitable condition with high accuracy, the authors have revealed the complicated flow.

Experimental study of forces on freely moving spherical particles during resuspension into turbulent flow

Turbulent resuspension, a process of lifting solid particles from the bottom by turbulent flow, is ubiquitous in environmental and industrial applications. The process is a sequence of events that starts with an incipient motion of the particle being dislodged from its place, continues as sliding or rolling on the surface, ending with the particle being detached from the surface and lifted up into the flow. We study the resuspension of solid spherical particles with the density comparable to that of the fluid, and the diameter comparable with the Kolmogorov length scale. Three-dimensional particle tracking velocimetry (3D-PTV) tracks particle motion during the lift-off events in an oscillating grid turbulent flow. We measure simultaneously the Lagrangian trajectories of both the particles freely moving along the bottom smooth wall and the surrounding flow tracers. Different force terms acting on particles were estimated based on particle motion and local flow parameters. The results show that: i) the lift force is dominant; ii) the drag force on freely moving particles is less relevant in this type of resuspension; iii) the Basset (history or viscous-unsteady) force is a non-negligible component and plays an important role before the lift-off event. Although we cannot estimate very accurately the magnitude of the force terms, we find that during the resuspension the dominant forces are 2−10 times the buoyancy force magnitude. The findings cannot be extrapolated to particles, which are much smaller than the Kolmogorov length scale, or much denser than the fluid. Nevertheless, the present findings can assist in modeling of the sediment transport, particle filtration, pneumatic conveying and mixing in bio-reactors.

On the Lagrangian features of circular and semicircular jets via 3D Particle Tracking Velocimetry

Three-dimensional Particle Tracking Velocimetry was employed to characterize jets from circular and semi-circular pipes in the intermediate and far fields. Grid-interpolated velocity were used to validate the measurements, and confirmed the negligible effect of the pipe shape on the mean flow in the intermediate field. Several volumetric regions were defined to get Lagrangian statistical description of the flow from categorized particle trajectories. Probability density functions of the velocity fluctuations, particle acceleration, and curvature of the trajectories revealed common and distinctive features of the jets. The first one showed departure from the Gaussian distribution away from the core, and the acceleration exhibited heavy tails in the two jets; however the curvature pdf revealed distinctive footprint of the pipe shape.

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow.

3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using stereoscopic recording of image sequences. The basic components, features, constraints and optimization tips of a 3D-PTV topology consisting of a high-speed camera with a four-view splitter are described and discussed in this article. The technique is applied to the intermediate flow field (5 <x/d <25) of a circular jet at Re ≈ 7,000. Lagrangian flow features and turbulence quantities in an Eulerian frame are estimated around ten diameters downstream of the jet origin and at various radial distances from the jet core. Lagrangian properties include trajectory, velocity and acceleration of selected particles as well as curvature of the flow path, which are obtained from the Frenet-Serret equation. Estimation of the 3D velocity and turbulence fields around the jet core axis at a cross-plane located at ten diameters downstream of the jet is compared with literature, and the power spectrum of the large-scale streamwise velocity motions is obtained at various radial distances from the jet core.

Breakup of Finite-Size Colloidal Aggregates in Turbulent Flow Investigated by Three-Dimensional (3D) Particle Tracking Velocimetry.

Aggregates grown in mild shear flow are released, one at a time, into homogeneous isotropic turbulence, where their motion and intermittent breakup is recorded by three-dimensional particle tracking velocimetry (3D-PTV). The aggregates have an open structure with a fractal dimension of ∼2.2, and their size is 1.4 ± 0.4 mm, which is large, compared to the Kolmogorov length scale (η = 0.15 mm). 3D-PTV of flow tracers allows for the simultaneous measurement of aggregate trajectories and the full velocity gradient tensor along their pathlines, which enables us to access the Lagrangian stress history of individual breakup events. From this data, we found no consistent pattern that relates breakup to the local flow properties at the point of breakup. Also, the correlation between the aggregate size and both shear stress and normal stress at the location of breakage is found to be weaker, when compared with the correlation between size and drag stress. The analysis suggests that the aggregates are mostly broken due to the accumulation of the drag stress over a time lag on the order of the Kolmogorov time scale. This finding is explained by the fact that the aggregates are large, which gives their motion inertia and increases the time for stress propagation inside the aggregate. Furthermore, it is found that the scaling of the largest fragment and the accumulated stress at breakup follows an earlier established power law, i.e., dfrag ∼ σ(-0.6) obtained from laminar nozzle experiments. This indicates that, despite the large size and the different type of hydrodynamic stress, the microscopic mechanism causing breakup is consistent over a wide range of aggregate size and stress magnitude.

Characterization of intermittency in zooplankton behaviour in turbulence.

We consider Lagrangian velocity differences of zooplankters swimming in still water and in turbulence. Using cumulants, we quantify the intermittency properties of their motion recorded using three-dimensional particle tracking velocimetry. Copepods swimming in still water display an intermittent behaviour characterized by a high probability of small velocity increments, and by stretched exponential tails. Low values arise from their steady cruising behaviour while heavy tails result from frequent relocation jumps. In turbulence, we show that at short time scales, the intermittency signature of active copepods clearly differs from that of the underlying flow, and reflects the frequent relocation jumps displayed by these small animals. Despite these differences, we show that copepods swimming in still and turbulent flow belong to the same intermittency class that can be modelled by a log-stable model with non-analytical cumulant generating function. Intermittency in swimming behaviour and relocation jumps may enable copepods to display oriented, collective motion under strong hydrodynamic conditions and thus, may contribute to the formation of zooplankton patches in energetic environments.