Three-dimensional Particle Tracking Velocimetry Research Articles

Effect of fluid motions on finite spheres released in turbulent boundary layers

This paper extends the work in Tee et al. (Intl J. Multiphase Flow, vol. 133, 2020, 103462) to investigate the effect of turbulent fluid motions on the translation and rotation of lifting and wall-interacting spheres in boundary layers. Each sphere was released from rest in smooth-wall boundary layers with $Re_\tau =670$ and 1300 ( $d^+=56$ and 116, respectively) and allowed to propagate with the incoming fluid. Sphere and surrounding fluid motions were tracked simultaneously via three-dimensional particle tracking velocimetry and stereoscopic particle image velocimetry in streamwise–spanwise planes. Two-point correlations of sphere and fluid streamwise velocities yielded long positive regions associated with long fast- and slow-moving zones that approach and move over the spheres. The related spanwise correlations were shorter due to the shorter coherence length of spanwise fluid structures. In general, spheres lag the surrounding fluid. The less-dense lifting sphere had smaller particle Reynolds numbers varying from near zero up to 300. Its lift-offs coincided with oncoming fast-moving zones and fluid upwash. Wall friction initially retarded the acceleration of the denser sphere. Later, fluid torque associated with approaching high-velocity regions initiated forward rotation. The rotation, which was long-lived, induced sufficient Magnus lift to initiate repeated small lift-offs, reduce wall friction, and accelerate the sphere to higher sustained velocity. Particle Reynolds numbers remained above 200, and vortex shedding was omnipresent such that the spheres clearly altered the fluid motion. Spanwise fluid shear occasionally initiated wall-normal sphere rotation and relatively long-lasting Magnus side lift. Hence the finite sphere size contributed to multiple dynamical effects not present in point-particle models.

Local flow topology of a polymer-laden turbulent boundary layer

Fine-scale flow motions are measured in a Newtonian and polymer drag-reduced turbulent boundary layer (TBL) at a common momentum thickness Reynolds number $Re_{\theta }$ of 2300. Relative to the Newtonian TBL, the polymer-laden flow has a 33 % lower skin-friction coefficient. Three-dimensional (3-D) particle tracking velocimetry is used to measure the components of the velocity gradient tensor (VGT), rate of deformation tensor (RDT) and rate of rotation tensor (RRT). The invariants in these tensors are then used to distinguish the different types of fine-scale flow motions – a method called the $\varDelta$ -criterion. Joint probability density functions (j.p.d.f.s) of the VGT invariants, $Q$ and $R$ , for the Newtonian TBL produce the familiar tear-drop pattern, commonly seen in direct numerical simulations of Newtonian turbulence. Relative to the Newtonian TBL, the polymer-laden flow has significantly attenuated values of $R$ , implying an overall reduction in fluid stretching. The invariants in the RDT, $Q_D$ and $R_D$ , imply that straining motions of the polymeric flow are more two dimensional compared with the Newtonian flow. Moreover, j.p.d.f.s of $Q_D$ and the invariant in the RRT $Q_W$ , suggest that the flow consists of fewer biaxial extensional events and more shear-dominated flow. Few, if any, experimental investigations have measured the 3-D structure of fine-scale motions in a Newtonian and polymer drag-reduced TBL using the $\varDelta$ -criterion. We provide the first experimental evidence that supports the notion that an attenuation of fluid stretching, particularly biaxial straining motions, is central to the mechanism of polymer drag reduction.

In vitro investigation of the blood flow downstream of a 3D-printed aortic valve

The hemodynamics in the aorta as well as the durability of aortic valve prostheses vary greatly between different types of devices. Although placement and sizing of surgical aortic valve prostheses are excellent, the valve geometry of common devices cannot be customized to fit the patient’s anatomy perfectly. Similarly, transcatheter aortic valve implantation (TAVI) devices are not customizable and may be orientated unfavorably during implantation. Imperfect fit of an aortic valve prosthesis may result in suboptimal performance and in some cases the need for additional surgery. Leveraging the advent of precision, multi-material 3D-printing, a bioinspired silicone aortic valve was developed. The manufacturing technique makes it fully customizable and significantly cheaper to develop and produce than common prostheses. In this study, we assess the hemodynamic performance of such a 3D-printed aortic valve and compare it to two TAVI devices as well as to a severely stenosed valve. We investigate the blood flow distal to the valve in an anatomically accurate, compliant aorta model via three-dimensional particle tracking velocimetry measurements. Our results demonstrate that the 3D-printed aortic valve induces flow patterns and topology compatible with the TAVI valves and showing similarity to healthy aortic blood flow. Compared to the stenosis, the 3D-printed aortic valve reduces turbulent kinetic energy levels and irreversible energy losses by over 75%, reaching values compatible with healthy subjects and conventional TAVIs. Our study substantiates that the 3D-printed heart valve displays a hemodynamic performance similar to established devices and underscores its potential for driving innovation towards patient specific valve prostheses.

On local isotropy and scale dependence of pair dispersion in turbulent canopy flows

Canopy flows in the atmospheric surface layer play important economic and ecological roles, governing the dispersion of passive scalars in the environment. The interaction of high-velocity fluid and large-scale surface-mounted obstacles in canopy flows produces drag and causes intense, inhomogeneous and anisotropic turbulence. In this work, we focus on the turbulent dispersion of passive scalars by studying the ‘pair dispersion’ – a statistical measure of relative motion between particles. We analyse the results of a three-dimensional particle tracking velocimetry experiment in a wind-tunnel canopy flow, focusing on small scales. We confirm the existence of local isotropy of pair dispersion at scales smaller than a characteristic shear length scale $L_\varGamma =(\epsilon /\varGamma ^3)^{1/2}$ , where $\epsilon$ and $\varGamma$ are the mean dissipation rate and shear rate, respectively. Furthermore, we show that pair dispersion in this locally isotropic regime is a scale-dependent super-diffusive process, similar to what occurs in homogeneous isotropic turbulent flows. In addition, we measure the pair relative velocity correlation function, showing that its de-correlation occurs in the locally isotropic regime, and discuss the implications of this observation for modelling pair dispersion. Thus, our study extends the fundamental understanding of turbulent pair dispersion to the anisotropic inhomogeneous turbulent canopy flow, bringing valuable information for modelling scalar dispersion in the atmospheric surface layer.

Effect of turbulent coherent motion on the onset of particle transport using synchronized 3D PIV and PTV

A series of laboratory experiments was conducted to understand the role of unsteady coherent motions of turbulent flow in the onset of particle motion. Turbulent eddies having coherent structures constantly interact with sediment particles within the bottom boundary layer. Therefore, a 3D turbulent flow field and grain trajectories were obtained by the simultaneous operation of three-dimensional (3D) particle image velocimetry and particle tracking velocimetry. Characteristics of the grain motions were investigated with the various particles in the various flow conditions. Based on the Stokes number of sediments, the spectral density of flow field revealed that turbulent eddies in the production subrange initiate grain motion. The proper orthogonal decomposition extracted the flow fields in the production subrange and the quadrant analysis was used to define dominant turbulent event initiating particle motions in the different flow conditions. The events of outward interaction and sweep initiated particle motion under low-velocity conditions, whereas those of sweep and ejection frequently occurred at the onset of particle motion under high-velocity conditions. Based on the results of the quadrant analysis, we proposed a transition curve that determines the dominant turbulent event depending on the flow condition on the conventional Shields diagram

Experimental study on flow and turbulence characteristics of jet impinging on cylinder using three-dimensional Lagrangian particle tracking velocimetry

When a round jet impinges on a convex cylindrical surface, complex three-dimensional (3D) flow structures occur, accompanied by the Coanda effect. To characterize the flow and turbulence properties of the general system, ensemble averages of 3D Lagrangian particle tracking velocimetry measurements were taken. The radial bin-averaging method was used in post-processing the tracked particles and corresponding instantaneous velocity vectors to generate appropriate ensemble-averaged statistics. Two impinging angles were selected, and at a fixed Reynolds number, the ensemble-averaged volumetric velocity field and turbulent stress tensor components were measured. The flow and turbulence characteristics of the impinging jet on the cylinder were notably different based on the impinging angle, especially in the downstream region. Surprisingly, the attached wall jet with a half-elliptic shape was abruptly thickened in the wall-normal direction, similar to the axis switching phenomenon observed in elliptic jets in the case of oblique impingement. In the jet-impinging region, the flow spread in all directions with high mean vorticity values. With the development of a 3D curved wall jet, both the Coanda effect and centrifugal force played a significant role in the flow behavior. A notable feature of the self-preserving region was the similarity of mean velocity profiles with scaling by the maximum velocity and the jet half-width for both impinging angle cases. Local isotropy of turbulent normal stresses was observed in this region, supporting the existence of self-preservation in the 3D curved wall jet. The volumetric ensemble-averaged Reynolds stress tensor revealed strong inhomogeneous turbulence in the boundary layer region and the curvature effect on the Reynolds shear stress in the free shear layer.

Volumetric measurement of a Newtonian fluid flow through three-dimensional porous media using Lagrangian particle tracking (Shake-the-Box) technique

This work experimentally investigates the pressure-driven flow of a pure Newtonian fluid through three-dimensional (3D) porous media models. The porous media model consists of square arrays of rods that also could be interpreted as a periodic tandem rod arrangement. We employed a time-resolved three-dimensional particle tracking velocimetry (3D Shake-the-Box) technique for a range of Reynolds numbers 111 ≤ R e ≤ 890 to observe flow structures and vortex formation between the rods in porous media structures with different porosities of ε = 0.7 , 0.8 , and 0.9 , which corresponds to the spacing ratio of L D = 1.75 , 2 , and 3, where L is the distance between the centers of the rods, and D is the diameter of the rods. For all the examined cases, we further analyzed the effect of the Reynolds number and the spacing ratio on the instantaneous and averaged patterns of velocity, vorticity, and the other flow parameters after obtaining the two-dimensional velocity fields using the bin-averaging method. We observed both symmetrical and asymmetrical patterns of structure and recirculation regions between the rods depending on the Reynolds number and spacing ratio. Increasing the Reynolds number reduced the symmetrical patterns of flow structures with respect to the centerline of the gap region, while the spacing ratio was randomly affecting the symmetry degree. Vortex shedding was considerable for the two examined high Reynolds numbers of Re = 444 and Re = 890 behind the upstream rod as the porosity increased. The backward movement of the reattachment point has been observed by increasing the Reynolds number.

Lagrangian particle tracking velocimetry investigation of vortex shedding topology for oscillating heavy spherical pendulums underwater

The vortex shedding topology of a heavy pendulum oscillating in a dense fluid is investigated using time-resolved three-dimensional particle tracking velocimetry (tr-3-D-PTV). A series of experiments with eight different solid to fluid mass ratios $m^*$ in the range $[1.14, 14.95]$ and corresponding Reynolds numbers of up to $Re \sim O(10^4)$ was conducted. The period of oscillation depends heavily on $m^*$ . The relation between amplitude decay and oscillation frequency is non-monotonic, having a damping optimum at $m^* \approx 2.50$ . Moreover, a novel digital object tracking (DOT) method using vorticity-magnitude iso-surfaces is implemented to analyse vortical structures. A similar vortex shedding topology is observed for various mass ratios $m^*$ . Our observations show that first, a vortex ring in the pendulum's wake is formed. Soon after, the initial ring breaks down to two clearly distinguishable structures of similar size. One of the two vortices remains on the circular path of the pendulum, while the other detaches, propagates downwards, and eventually dissipates. The time when the first vortex is shed, and its initial propagation velocity, depend on $m^*$ and the momentum imparted by the spherical bob. The findings further show good agreement between the experimentally determined vortex shedding frequency and the theoretical vortex shedding time scale based on the Strouhal number.

Lagrangian turbulence statistics using 3D-PTV: Realistic virtual experiment assessment

The outcome of a three-dimensional particle tracking velocimetry (3D-PTV) experiment can be significantly improved if the influence of the camera locations, calibration, and light volume can be determined before conducting the experiment. Such a-priory assessment will also reduce the time for troubleshooting a 3D-PTV experiment. In this paper, we report a “virtual experiment” approach. Multiple frames of synthetic particle images are generated using triangulation and optical spread functions based on the Lagrangian trajectories in 3D velocity fields with known spatio-temporal characteristics. We use an analytical 3D Burger’s vortex, and the homogeneous isotropic turbulence (HIT) data-set from the turbulence database hosted by Johns Hopkins University (JHU). The 3D particle positions are projected on two-dimensional (2D) images using artificial extrinsic and intrinsic camera matrices, depth of field, and volume illumination. These 2D images served as images taken by a four-camera 3D-PTV system in a virtual experiment. Blind test calibration using OpenPTV, an open source software, reconstructs the camera positions for a simulated experimental set-up and the calibrated set-up is used to create Lagrangian trajectories from the particle image sequences. Finally, we compare the turbulent statistics reconstructed from the virtual experiment with that of the ground truth data. We show that reconstruction from a virtual 3D-PTV experiment reproduces the mean flow and turbulent statistics faithfully; however, the disparity increases for higher order and multi-point statistics. The proposed approach can be used to fine-tune the camera parameters and the light volume in order to increase the fidelity of turbulent flow measurements using 3D-PTV.

A parametric study of 3D PTV algorithms based on a two-view collimated imaging model

Volumetric Lagrangian measurements of droplet or turbulent flow using particle tracking methods have attracted intensive attention recently. The performance of three-dimensional particle tracking velocimetry (3D PTV) is highly reliant on the algorithms. Most existing 3D PTV algorithms are developed for multi-view systems, which cannot be applied directly to two-view systems due to the insufficient geometry constraints. In the current study, three different 3D PTV algorithms applicable for two-view systems are investigated parametrically using synthetic data. The imaging model is established on a two-view collimated shadowgraph imaging setup, which features a high framing rate, large test volume and long depth focus. The performances of the three algorithms are tested under different image particle densities and displacement–spacing ratios. The correctness of 3D reconstruction and tracking, as well as the number of ghost particles, are obtained and compared comprehensively. The results indicate that significant improvement is achieved through the dedicated designed algorithms. The comparative study reveals the potential of each algorithm with extremely limited geometry constraints in two-view systems, which may serve as guidance for choosing appropriate algorithms under different test conditions.

An experimental study of flow–structure interaction regimes of a freely falling flexible cylinder

The fluid–structure interaction problem composed of an elongated, finite-length, flexible cylinder falling in a fluid at rest is investigated experimentally. Tomographic reconstruction of the cylinder and three-dimensional particle tracking velocimetry of the surrounding fluid, based on the Shake-The-Box algorithm, are used jointly to capture both solid and fluid motions. Starting from the rectilinear vertical fall characterized by a steady wake, focus is placed on subsequent regimes involving, mainly in the horizontal direction, periodic rigid-body motions (RBM) of weak amplitude or periodic large-amplitude bending oscillations (BO). Two RBM regimes are explored: the TRA regime where the cylinder exhibits translational oscillations in a plane perpendicular to its axis, and the AZI regime in which the body displays an azimuthal oscillation around its centre. The associated unsteady wakes are composed of counter-rotating vortices bending near the body ends to connect with the adjacent vortex rows. Specific organizations of the vortical structures are uncovered, depending on the regime. In particular, in the AZI regime, they present an antisymmetrical distribution relative to the midspan point. For a sufficiently long cylinder, BO regimes emerge, resembling the structural modes of an unsupported beam. The associated wakes exhibit a cellular organization. Within each cell delimited by two deformation nodes, two counter-rotating vortex rows are shed per oscillation cycle. Flow velocity fluctuations are in phase opposition on each side of a deformation node. For both RBM and BO regimes, frequency and phase analyses of cylinder and wake behaviours, along the span, highlight the spatio-temporal synchronization of the unsteady flow and moving body.

Low-Cost 3D-PTV Utilizing Rainbow Light Illumination And Artificial Neural Network Applied To Rayleigh-Bénard Convection

Building on the novel methodology for three-dimensional (3D) color particle tracking velocimetry (PTV) proposedearlier by our research group, an improvement and an evaluation of the method is presented in this study. The method utilizes only a color camera and a consumer-grade liquid crystal display projector (LCDP), and thus cost for implementation is greatly lower than that required for a tomographic system. Employment of artificial neural network system enables to eliminate human decisions in constructing a color-to-depth conversion function. That is, the calibration can be performed automatically once relationship between particle color and depth are associated in actual measurement environments. The method was tested in a Rayleigh–Bénard convection of water, which is expected to have horizontally isotropic structures. Two different flow states were successfully measured. The results showed that the 3D color PTV can measure the same statistics of velocity components in the in-plane and out-of-plane directions. Considering all the results, the proposed method using only a single camera and an LCDP has a potential to be an alternative to the state-of-art tomographic measurements.

Force on inertial particles crossing a two layer stratified turbulent/non-turbulent interface

We study the peculiar motion of inertial solid particles across stratified turbulent/non-turbulent interfaces (STNTI). Previous studies in quiescent stratified layers demonstrated that inertial particles slow down substantially due to an additional force term related to the stratification. Here we report for the first time a similar effect on inertial particles moving across a two-layer STNTI of finite thickness. This problem is addressed both experimentally and numerically: we utilize the three-dimensional particle tracking velocimetry (3D-PTV) in a index-matched STNTI experiment under an oscillating grid, and two direct numerical simulation (DNS) cases of STNTI. The DNSs test the effects of different turbulent forcings on inertial spheres in the turbulent layer and across STNTI and extends the parameter ranges of Reynolds and Froude numbers unfeasible in the experiments. Turbulence is produced in the DNSs using a convective forcing (heat source at the domain boundary) in one case, and a forcing that mimics a vertically oscillating grid in the other. The numerical spheres are tracked, through one-way coupling approach, using a modified Basset–Boussinesq–Oseen equation which includes a stratification-induced term. The stratification force is modelled as an additional buoyancy of a caudal wake with varying density. This algorithm creates Lagrangian trajectories that resemble the motion of inertial particles across stratified interfaces in quiescent and turbulent experiments. Furthermore, numerical results for the STNTI cases help to distinguish the essential features observed in the experiments that are caused by stratification from those that relate to turbulence–particle interactions.

Particle radial velocity and concentration kernels estimation in isotropic grid turbulence experiments of inertialess particles at small separation distances

We report experimental measurements of kinematic and dynamic particle concentration kernels conditioned by the separation distances of solid inertialess particles in isotropic turbulence by three-dimensional particle tracking velocimetry with particle diameters smaller than the Kolmogorov length scale. Particle radial relative velocity statistics are measured from the dissipation to the integral length-scale range. The radial scaling of particle and fluid relative velocity variance $\langle w_r(r)^{2} \rangle \sim r^{2/3}$ in the inertial subrange, consistent with Kolmogorov's theory, is reported, while a new scaling is found for small distances due to finite-size effects between particles. The measured concentration kernels at small separation distances therefore deviate from those in the theory of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) at small inter-particle distances due to hydrodynamic interactions. A real kernel taking into account the history of the particle tracks and excluding multiple events is also calculated, while the normalised particle concentration kernels are found to be essentially insensitive to the flow Reynolds number.

The Presence of a Substrate Strengthens The Jet Generated by Upside-Down Jellyfish

Upside-down jellyfish, Cassiopea, are prevalent in warm and shallow parts of the oceans throughout the world. They are unique among jellyfish in that they rest upside down against the substrate and extend their oral arms upwards. This configuration allows them to continually pull water along the substrate, through their oral arms, and up into the water column for feeding, nutrient and gas exchange, and waste removal. Although the hydrodynamics of the pulsation of jellyfish bells has been studied in many contexts, it is not clear how the presence or absence of the substrate alters the bulk flow patterns generated by Cassiopea medusae. In this paper, we use three-dimensional (3D) particle tracking velocimetry and 3D immersed boundary simulations to characterize the flow generated by upside-down jellyfish. In both cases, the oral arms are removed, which allows us to isolate the effect of the substrate. The experimental results are used to validate numerical simulations, and the numerical simulations show that the presence of the substrate enhances the generation of vortices, which in turn augments the upward velocities of the resulting jets. Furthermore, the presence of the substrate creates a flow pattern where the water volume within the bell is ejected with each pulse cycle. These results suggest that the positioning of the upside-down jellyfish such that its bell is pressed against the ocean floor is beneficial for augmenting vertical flow and increasing the volume of water sampled during each pulse.

Volumetric particle tracking velocimetry with improved algorithms using a two-view shadowgraph system

Determining the time-resolved three-dimensional (3D) three-component (3C) velocity is essential for complex turbulent flow measurements. The current study is an extension of a recently developed temporal-spatial three-dimensional particle tracking velocimetry (TS 3D-PTV) technique established for two-view imaging systems. Two improvements have been embedded in TS 3D-PTV algorithm to improve the accuracy at high particle image densities (up to 0.03 ppp). One is using the neighboring particle information to correct the predicted positions and select the temporal particles with higher probability; the other is to iteratively optimize the 2D particle positions during the tracking process using the temporal and image information. The synthetic particle tests indicate that the correctness can be increased by 4.7%–5.8%, to reach a value about 92% with the improved algorithm around 0.03 ppp. The comparative results also indicate that using an advanced particle identification algorithm can improve the correctness over 20%. Two experiments, including a buoyancy jet in water and a transient droplet splashing process, have been conducted with a two-view shadowgraph imaging system. Different tracking algorithms have been conducted to determine the 3D trajectories of seeding particles or secondary droplets comparatively. The new algorithm has shown the best performance with much longer and more reliable trajectories, which indicates the tracking interruption caused by particle overlapping is reduced. The newly developed algorithms have further improved the performance under high seeding density conditions, which makes the two-view shadowgraph 3D PTV system adaptable to more experimental conditions.

Wake characteristics of complex-shaped snow particles: Comparison of numerical simulations with fixed snowflakes to time-resolved particle tracking velocimetry experiments with free-falling analogs

Experimental and numerical approaches have their own advantages and limitations, in particular, when dealing with complex phenomena such as snow particles falling at moderate Reynolds numbers (Re). Time-resolved, three-dimensional particle tracking velocimetry (4D-PTV) experiments of free-falling, three-dimensional (3D)-printed snowflakes' analogs shed light on the elaborate falling dynamics of irregular snow particles but present a lower resolution (tracer seeding density) and a limited field of view (domain size) to fully capture the wake flow. Delayed-detached eddy simulations of fixed snow particles do not realistically represent all the physics of a falling ice particle, especially for cases with unsteady falling attitudes, but accurately predict the drag coefficient and capture the wake characteristics for steadily falling snowflakes. In this work, we compare both approaches on time- and space-averaged flow quantities in the snowflake wake. First, we cross validate the two approaches for low Re cases, where close agreement of the wake features is expected, and second, we assess how strongly the unsteady falling motion perturbs the average wake pattern as compared to a fixed particle at higher Re. For steadily falling snowflakes, the fixed-particle model can properly represent the wake flow with errors within the experimental uncertainty (±15%). At moderate/high Re (unsteady falling motion), larger differences are present. Applying a co-moving frame to the experimental data to account for the particle movement or filtering the numerical data on larger grids reduces these differences only to some extent, implying that an unsteady fall significantly alters the average wake structure as compared to a fixed particle model.

Effect of the aspect ratio on the dynamics of air bubbles within Rayleigh–Bénard convection

Laboratory experiments and numerical simulations were performed to quantify the effect of the aspect ratio, Γ, in the dynamics of air bubbles within turbulent Rayleigh–Bénard (RB) convection. We explored four scenarios defined by Γ=1.25, 1.5, 2, and 2.5 under Rayleigh numbers ranging from 2.0×109 to 1.6×1010. Continuous 1-mm bubbles were released at two locations from the bottom along the roll path. Three-dimensional particle tracking velocimetry was used to track a large number of bubbles and determine features of the trajectories and pair dispersion, R2(t), for various initial separations, rp within H/10≤rp≤5H/10; here, H is the height. The R2(t) of the bubbles within a quiescent medium was included for reference. Characterization of the bubble streams, namely, the center of mass (Lc), mean deviation (Rc) to Lc, vertical (vz) and lateral (vL) velocities, and their ratios reveal the strong modulation of the roll structure and Γ. In particular, Lc exhibited an approximately symmetric distribution around the maximum, which occurred at the middle height only in the Γ=1.25 case. Maximum Lc was near the wall top with the highest aspect ratio. However, Rc did not vary substantially among the cases. Bubbles' lateral pair dispersion RL2 shows correlated trends with Γ, particularly at large initial separations and times, whereas the vertical pair dispersion is mainly dominated by buoyancy. The RL2 decreased as Γ increased. It indicates the effect of different-sized roll structures modulated by Γ. In general, R2 embodies distinct features of Γ-modulated bubble dynamics in RB convection.

Lagrangian coherent track initialization

Advances in time-resolved three-dimensional Particle Tracking Velocimetry (4D-PTV) techniques have consistently revealed more accurate Lagrangian particle motions. A novel track initialization technique as a complementary part of 4D-PTV, based on local temporal and spatial coherency of neighbor trajectories, is proposed. The proposed Lagrangian Coherent Track Initialization (LCTI) applies physics-based Finite Time Lyapunov Exponent (FTLE) to build four frame coherent tracks. We locally determine Lagrangian coherent structures among neighbor trajectories by using the FTLE boundaries (i.e., ridges) to distinguish the clusters of coherent motions. To evaluate the proposed technique, we created an open-access synthetic Lagrangian and Eulerian dataset of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900 obtained from three-dimensional direct numerical simulation. Performance of the proposed method based on three characteristic parameters, temporal scale, particle concentration (i.e., density), and noise ratio, showed robust behavior in finding true tracks compared to the recent initialization algorithms. Sensitivity of LCTI to the number of untracked and wrong tracks is also discussed. We address the capability of using the proposed method as a function of a 4D-PTV scheme in the Lagrangian particle tracking challenge. We showed that LCTI prevents 4D-PTV divergence in flows with high particle concentrations. Finally, the LCTI behavior was demonstrated in a jet impingement experiment. LCTI was found to be a reliable tracking tool in complex flow motions, with a strength revealed for flows with high velocity and acceleration gradients.

Kalman filtering approach to particle track filtering and track uncertainty quantification for 3D PTV measurement

Three-dimensional Particle Tracking Velocimetry (3D-PTV) is a non-invasive flow measurement technique that computes the velocity field by reconstructing 3D particle positions of individual tracer particles and by subsequently tracking those positions. The particle velocity measurement accuracy depends on the faithful reconstruction of 3D particle positions. The complex measurement chain in 3D-PTV involves several steps, from calibration to 3D position reconstruction and particle position tracking, each having its own source of error. Additionally, higher seeding density increases the uncertainty in particle reconstruction and tracking, which in turn, increases the noise in the estimated tracks. A noisy track decreases the measurement accuracy and amplifies any noise in the PTV-derived quantities of interest, which includes acceleration, pressure and vorticity. Thus, track filtering techniques are critical in a 3D-PTV measurement. Track fitting using polynomial functions, filtering methods adopted from signal processing and object tracking are among the well-established techniques used to achieve smooth position, velocity estimates from reconstructed particle trajectories. The Kalman filter is one such filtering technique that is widely used in various applications. The strength of the Kalman filter lies in its ability to perform noise reduction that is informed by existing physical models and the uncertainty estimates of recorded measurements. However, the measurement uncertainty input to the Kalman filter needs to be known at priori, which in many cases may not be available or could be difficult to estimate. In the literature on Kalman filters and their variants applied to 2D-PIV/PTV, the position uncertainty data fed to the filter is either user-defined or estimated based on global noise levels in the PTV measurements. But instantaneous position and velocity uncertainty quantification for individual particle positions/tracks has been challenging in the 3D PTV community. Recent work by Bhattacharya and Vlachos (2020) provides an estimate of the uncertainty in the reconstructed particle positions for a 3D PTV measurement. This position uncertainty estimate dynamically updates the filter gain for each track and enables the evaluation of the performance of the Kalman filter in 3D PTV track filtering.