Particle Tracking Velocimetry Data Research Articles

One-shot omnidirectional pressure integration through matrix inversion

Abstract In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now ``fast-forwarded'' to the ``infinity'' iteration, leading to a different matrix equation that can be solved in a single {\color{blue}step}, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of $\sim10^6$ when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of $\sim 10^9$ points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements {\color{blue} a boundary condition where the boundary points are treated as interior points to the extent that information is available}. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.

Simultaneous flow and particle measurements for multiphase flows in hydraulic engineering: A review and synthesis of current state

While multiphase flows are abundant in both natural environments and engineering applications, their analysis and quantification present challenges. In particular, simultaneously measuring the flow field and quantifying particle behavior pose many challenges. Methods based on Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) principles have been used in the last two decades to measure flow fields and dispersed (particle) phases, respectively. Despite the extensive application of these principles to multiphase flow, there are numerous approaches and techniques used to synchronize and combine PIV and PTV measurements. Combined PIV and PTV data acquisition also requires consideration of phase discrimination to obtain distinct data for the fluid and dispersed phases. In the literature, various methods have been proposed and applied to achieve phase discrimination. This review paper aims to consolidate and classify various phase discrimination techniques used in specialized applications in hydraulic engineering. These methods are categorized into optical (spectral, temporal, and hybrid) and post-processing methods, with a particular emphasis on their applicability within the realm of hydraulic engineering. Moreover, this review expands on several emerging PIV/PTV technologies and applications, where the combination of equipment and algorithms has led to significant strides in the non-intrusive measurement of multiphase flow. By consolidating and critically evaluating current methods for particle discrimination, this paper aims to enhance the scientific community's understanding of simultaneous phase velocity measurements, thereby setting the stage for advancements in multiphase flow visualization techniques.

Assimilating Sparse 3D-PTV Data Of A Pulsed Jet Using Physics-Informed Neural Networks

Phase-resolved volumetric velocity measurements of a pulsed jet are conducted by means of three-dimensional particle tracking velocimetry (PTV). The resulting scattered and relatively sparse data are densely reconstructed by adopting physics-informed neural networks (PINNs), here regularized by the Navier-Stokes equations. It is shown that the assimilation yields a higher spatial resolution, and the process remains robust, even at low particle densities ( 𝑝𝑝𝑝 < 0.001). This is achieved by enforcing compliance with the governing equations, thus leveraging the spatiotemporal evolution of the measured flow field. The results indicate that the PINN reconstructs unambiguously velocity, vorticity and pressure fields with a level of detail not attainable with conventional methods (binning) or more advanced data assimilation techniques (vortex-in-cell). The results of this article support the findings of Clark di Leoni (2023) suggesting that the PINN methodology is inherently suited to the assimilation of PTV data, in particular under conditions of severe sparsity or during experiments with limited control of seeding concentration.

Meshless track assimilation (MTA) of 3D PTV data

We propose a data assimilation algorithm to improve the resolution of 3D particle tracking velocimetry (PTV) data and, as a byproduct, it estimates the pressure field. The proposed method, called meshless tracking assimilation (MTA), does not rely on a mesh to compute derivatives. Instead, it exploits the analytical formulation of the obtained field to extract the gradients of the involved quantities in arbitrary points. MTA actively constraints PTV data points to satisfy the Navier–Stokes equations in both time and space at user-defined spatial locations. Three test cases are investigated. The first one is a synthetic dataset reconstructed from a direct numerical simulation and it serves to ensure that the method is properly implemented and working. The second one is the 2020 data assimilation challenge which gives a qualitative comparison with other data assimilation methods. Finally, MTA is used on a Tomographic PTV experiment of a Jet Flow with ReD≃3000 to ensure it can be implemented successfully on experimental data. The first and third test cases show a significant performance boost compared to the classic linear interpolation. This improvement allows for a higher level of structural resolution without sacrificing the temporal and spatial smoothness of the solution. The second test case generally aligns well with other state-of-the-art data assimilation techniques in terms of performance, but there are some noticeable differences.

Dense velocity, pressure and Eulerian acceleration fields from single-instant scattered velocities through Navier–Stokes-based data assimilation

In this study, a reconstruction procedure to infer full 3D instantaneous velocity and pressure fields from sparse velocity measurements is proposed, here focusing on the case of scattered data as provided by particle tracking velocimetry (PTV). A key characteristic of the present approach is that it only relies on single-instant velocity measurements, and does not require any time-resolved or acceleration information. It is based on a strong enforcement of the Navier–Stokes equations where the partial time derivative of the velocity field, namely Eulerian acceleration, is considered as a control vector to minimize the discrepancies between the single-instant measurements and the reconstructed flow. Eulerian acceleration is thus a byproduct of the present methodology in addition to the identification of the full velocity and pressure fields. The reconstruction performances of the proposed Navier–Stokes-based data-assimilation approach for single-instant velocity measurements (NS-DA-SIM) are assessed using a numerical dataset for the 3D flow past a cylinder. Comparisons with existing data assimilation methodologies allow to further illustrate the merits of the present approach. The latter is finally applied to the instantaneous reconstruction of an experimental air jet flow from volumetric PTV data, confirming its robustness and high efficacy.

An end-to-end KNN-based PTV approach for high-resolution measurements and uncertainty quantification

We introduce a novel end-to-end approach to improving the resolution of Particle Image Velocimetry (PIV) measurements. We conceptualised the algorithm as a tool that is able, starting from raw pictures, to obtain high-resolution flow fields and uncertainty estimations with minimal intervention from the user. The method blends information from different snapshots without the need for time-resolved measurements on grounds of similarity of flow regions in different snapshots. The main hypothesis is that, with a sufficiently large ensemble of statistically-independent snapshots, the identification of flow structures that are morphologically similar but occurring at different time instants is feasible. Since the particles randomly seed the flow, a randomised sampling of such structures is naturally achieved, providing different views of the same region. Measured individual vectors from different snapshots with similar flow organisation can thus be merged, resulting in an artificially increased particle concentration. This allows refining the interrogation region and, consequently, increasing the spatial resolution. The measurement domain is split in subdomains. The similarity is enforced only on a local scale, i.e. morphologically-similar regions are sought only among subdomains corresponding to the same flow region. The identification of locally-similar snapshots is based on K-nearest neighbours search in a space of significant flow features. Such features are defined in terms of a Proper Orthogonal Decomposition, performed in subdomains on the original low-resolution data, obtained either with standard cross-correlation or with binning of Particle Tracking Velocimetry data with a relatively large bin size. A refined bin size is then selected according to the number of “sufficiently close” snapshots identified. The more neighbours identified, the higher the “virtual” particle image density and the smaller is the bin size, provided that the number of particles to be contained in it is fixed. The statistical dispersion of the velocity vectors within the bin is then used to estimate the uncertainty and to select the optimal K which minimises it. The method is tested and validated against datasets with a progressively increasing level of complexity: two virtual experiments based on direct numerical simulations of the wake of a fluidic pinball and a channel flow and the experimental data collected in a turbulent boundary layer.

Physics-Driven PTV Interpolation Through Learned Regularization

This paper deals with spatial interpolation of instantaneous Particle Tracking Velocimetry (PTV) data. Such a task can be handled using generic signal processing tools like B-splines, radial basis functions (RBF) or Kriging. We deal with non time-resolved PTV as gathered by dual frame particle image velocimetry (PIV) systems followed by dual frame PTV algorithms. In such a dual frame context, Physics-based interpolation techniques typically rely on enforcement of divergence free constraints on the interpolated field. The aim of this communication is to explore the wider field of Physics-based PTV interpolators based on learning a deep neural network. These interpolators are learned on a database of flow examples that may be generated by high resolution PIV or DNS. We propose an instance of such a Physics-based PTV interpolator based on the machine learning concept of unrolled optimization. This concept is extended in order to deal with random measurement location, characteristic of PTV data. We also show how to use this concept to perform pressure estimation from PTV data, along with velocity interpolation. The concept is illustrated on a 2D laminar flow, DNS data is used to train and benchmark the proposed method against RBF interpolation. The proposed method is shown to be much more robust than RBF interpolation against low density seeding and noise.

Deformation modes of an oil-water interface under a local electric field: From Taylor cones to surface dimples

Fluidic interfaces disintegrate under sufficiently strong electric fields, leading to electrohydrodynamic (EHD) tip streaming. Taylor cones, which emit charged droplets from the tip of a conical cusp, are among the most prominent and well-studied examples of EHD instabilities. In liquid-liquid systems, more complex interface deformation modes than simple Taylor cones can be observed, with the interface being pushed away from the electrode, and additional cone structures emerging from the rim of the dimple. In this article, we investigate the mechanisms behind these deformation modes experimentally and numerically, and demonstrate that the presence of droplets triggers the dimple at the interface. In order to characterize the underlying processes, we replace the pin electrode by a hollow metallic needle with a prescribed electrolyte volume flow. The submerged electrospray introduces droplets of an aqueous KCl solution with varying ion concentrations into silicone oils with varying viscosities. By measuring the corresponding electric current and by optical investigation of the interface deformation, we study the system response to variations of the ionic concentration, viscosity, applied voltage as well as flow rate. In addition to the experiments, we use a finite element solver and compute the charge transport due to the droplets in the oil phase. Further, we compute the electric potential distribution, flow field and interface deformation. After calibration of our model with particle tracking velocimetry data of the flow inside the oil phase, we reproduce the experimentally observed dimple at the liquid-liquid interface. In summary, this work highlights the importance of charged droplets for the complex dynamic modes observed when a liquid-liquid interface is exposed to a local electric field.

Pressure calculation for flows with moving surface boundaries from particle tracking velocimetry (PTV)

The examples of flow conditions, where an object of a fixed or deformable body moves in a fluid, or the interface between the flow phases instantaneously changes its topology, are numerous in industry and natural sciences. The advent of particle image velocimetry (PIV) [1] and particle tracking velocimetry (PTV) [2] enabled the measurement of the instantaneous velocity fields in these types of complicated flow fields. As a next step, several methodologies have been developed in the past decade to calculate the pressure fields from PIV or PTV data [3,4]. These methods were developed based on the assumption of a stationary flow domain, with surface boundaries that are fixed and independent of time. This makes the current pressure calculation methods inapplicable to a flow domain with deformable moving surface boundaries. Also, for most of the two-phase flows, the capillary forces are significant and the pressure drop over the two-phase interface must be considered. Therefore, the current pressure calculators require an improvement in the formulation of the algorithms to account for the deformable volume conditions and the effect of the surface tension force. For the calculation of pressure from sparse PTV velocity data, firstly, a tessellation method is required to interconnect the irregularly spaced vectors in the flow field using a highquality mesh grid. The mesh must be dynamic and adjust itself to the moving boundaries. This tessellation method has already been developed by the current authors [5]. As the next step, equations of motion for a deformable C.V. need to be coupled with the tessellation method to calculate the instantaneous pressures in a two-phase flow field, with a moving interface, which will be the ultimate goal of the current study.

Dense flow field interpolations from PTV data in the presence of generic solid boundaries

Three-dimensional flow measurements by Particle Tracking Velocimetry (PTV) provide scattered flow information, that often needs to be interpolated onto a regular grid. Therefore, the use of experimental data assimilation approaches such as VIC+ (Schneiders and Scarano, 2016) were proposed to enhance the instantaneously available spatial resolution limits beyond that of the PTV measurements. Nevertheless, there exists no prior attempt to perform the data assimilation when the flow is in direct contact with physical objects. Thus, in order to handle generic solid body intrusions within the flow fields of VIC+ application, the utilization of Arbitrary Lagrangian-Eulerian and immersed boundary treatment approaches of the computational fluid-structure interaction (FSI) frameworks are proposed. The introduced variants over the standard VIC+ are assessed with a high fidelity numerical test case of flow over periodic hills. The accuracy superiority of the flow field reconstructions with the proposed approaches are denoted especially in close proximity of the interaction surface. An experimental application of the introduced methods is demonstrated to compute the pressure distribution over an unsteadily moving elastic membrane surface, revealing the time-resolved interaction between the flow structures and the membrane deformations.

Local flow dynamics in the motion of slug bubbles in a flowing mini square channel

For a slug flow flowing in a square capillary, the surrounding liquid flows through a thin film between the slug bubble and the wall and the corners of the channel and generates an asymmetric two-phase flow field with significant spatial variations. The current literature mainly discusses the bulk features of such a flow field, while local phenomena in these flows are not well known yet. In this study, the local dynamics of the liquid film and corner flows in a flowing square channel with a width of 3 mm were investigated by experiments and numerical simulations. Instantaneous velocity fields in the liquid flow were measured at the channel's central plane using particle tracking velocimetry (PTV). The obtained data were utilized to calculate the axial variations of the film and corner velocities. Three-dimensional numerical simulations with adaptive mesh refinement of the interface were performed for a series of flow conditions. Comparing the film velocity obtained from PTV and simulations demonstrates an overall good agreement between the results, with discrepancies close to the solid walls, where the PTV data is sporadic. Film and corner flows show rapid velocity changes adjacent to the minimum film area. Both experiments and simulations elucidate the backflow phenomena in the analyzed flow fields, where the liquid locally flows in the opposite streamwise direction. The backflow region shrinks as the liquid flow rate and speed of the bubble increase. Film flow shows significant pressure drops as it passes through the minimum film area. On the contrary, the corner flow does not demonstrate any rapid pressure fluctuations. The vortex structures’ identification revealed dominant vortex loops inside the gas and small-scale vortex filaments along the channel walls, generated from the liquid film rupture.

On the three-dimensional features of a confined slug bubble in a flowing square capillary

The motion of long bubbles in tubular capillaries has typically been described by bulk characteristics. However, the dynamics of slug bubbles in square capillaries are more complex due to a corner flow and a thin film flow. The physics can be correctly explained by elucidating local 3D features of the two-phase flow field. To this aim, an experimental study based on particle tracking velocimetry (PTV) and a numerical simulation based on the volume-of-fluid method were conducted to investigate the dynamics of slug bubbles rising in a flowing square capillary with a cross-sectional area of 3 × 3 mm2. To precisely analyze the phases' interaction, interfacial flow data were mapped onto a radial-tangential coordinate system on central and diagonal planes. The simulated interface topology and velocity fields show a good agreement with the experimental PTV data on the central plane, with an absolute error of less than 1.2% for terminal bubble speed. Tangential speeds show their maxima occurring in the channel corners, where pressure is maximum. The thin liquid film flow that occurs where the bubble approaches the wall applies noticeable shear stress on the channel walls, where high and low-pressure regions are generated. Structures of vortices inside the bubble were identified using isosurfaces of the Q-criterion, and their cores were detected based on the parallel vector method. Results reveal a dominant vortex ring adjacent to the liquid film flow and two oblique vortex tubes close to the bubble's nose.

PTV measurements of oscillating grid turbulence in water and polymer solutions

Particle Tracking Velocimetry (PTV) is applied to measure the flow in an oscillating grid stirred tank filled with either water or shear thinning dilute polymer solutions (DPS) of Xanthan Gum (XG). There are many interests of studying turbulence in such complex non-Newtonian fluids (e.g. in the pharmaceutical, cosmetic, or food industry), and grid stirred tanks are commonly used for fundamental studies of turbulence in Newtonian fluids. Yet the case of oscillating grid flows in shear thinning solutions has been addressed recently by Lacassagne et al. (Exp Fluids 61(1):15, Phys Fluids 31(8):083102, 2019a, b), with only a single two dimensional (2D) Particle Image Velocimetry (PIV) characterization of mean flow and turbulence properties in the central vertical plane of the tank. Here, PTV data processed by the Shake The Box algorithm allows for the time resolved, three dimensional (3D) 3 components (3C) measurement of Lagrangian velocities for a large number of tracked particles in a central volume of interest of the tank. The possibility of projecting this Lagrangian information on an Eulerian grid is explored, and projected Eulerian results are compared with 2D PIV data from the previous work. Even if the mean flow is difficult to reproduce at the lowest polymer concentrations, a good agreement is found between measured turbulent decay laws, thus endorsing the use of this 3D-PTV metrology for the study of oscillating grid turbulence in DPS. The many possibilities of further analysis offered by the 3D3C nature of the data, either in the original Lagrangian form or in the projected Eulerian one, are finally discussed.Graphic

Structured illumination microscopy: a new way to improve the axial spatial resolution of microscale particle velocimetry

Many visualizations of microchannel flows illuminate a significant portion, if not all, of the channel. This volume illumination degrades the axial spatial resolution of microscale particle velocimetry measurements because signal from out-of-focus tracer particles “contaminates” the image. We present here a novel way to improve the axial spatial resolution of such velocimetry measurements, structured illumination microscopy (SIM) particle-tracking velocimetry (PTV). In these initial proof of concept experiments, double-exposure SIM PTV was used to measure velocities in plane Poiseuille flow. The velocity results obtained from the SIM images have significantly less error and standard deviation than standard microscale PTV data obtained with volume illumination. Our estimates also suggest that the axial spatial resolution of the SIM results is a twofold improvement over those obtained with “standard” microscale PTV.

Surface flow profiles for dry and wet granular materials by Particle Tracking Velocimetry; the effect of wall roughness

.Two-dimensional Particle Tracking Velocimetry (PTV) is a promising technique to study the behaviour of granular flows. The aim is to experimentally determine the free surface width and position of the shear band from the velocity profile to validate simulations in a split-bottom shear cell geometry. The position and velocities of scattered tracer particles are tracked as they move with the bulk flow by analyzing images. We then use a new technique to extract the continuum velocity field, applying coarse-graining with the postprocessing toolbox MercuryCG on the discrete experimental PTV data. For intermediate filling heights, the dependence of the shear (or angular) velocity on the radial coordinate at the free surface is well fitted by an error function. From the error function, we get the width and the centre position of the shear band. We investigate the dependence of these shear band properties on filling height and rotation frequencies of the shear cell for dry glass beads for rough and smooth wall surfaces. For rough surfaces, the data agrees with the existing experimental results and theoretical scaling predictions. For smooth surfaces, particle-wall slippage is significant and the data deviates from the predictions. We further study the effect of cohesion on the shear band properties by using small amount of silicon oil and glycerol as interstitial liquids with the glass beads. While silicon oil does not lead to big changes, glycerol changes the shear band properties considerably. The shear band gets wider and is situated further inward with increasing liquid saturation, due to the correspondingly increasing trend of particles to stick together.Graphical abstract

Hierarchy of hybrid unsteady-flow simulations integrating time-resolved PTV with DNS and their data-assimilation capabilities

Data-assimilation capabilities of hybrid-type simulations integrating time-resolved particle image velocimetry with unsteady computational fluid dynamics (CFD) are characterized, and a series of algorithms developed previously are evaluated in terms of four criteria: (i) compatibility with the governing equations; (ii) completeness of a set of flow quantities; (iii) temporal and spatial filtering functions; and (iv) spatial resolution. This study specifically introduces a hierarchy of three hybrid simulations combining time-resolved particle tracking velocimetry (PTV) and direct numerical simulation (DNS) from low to high fidelities: the proper orthogonal decomposition–Galerkin-projection approach with proportional feedback of PTV data, the DNS solver with similar feedback, and the DNS solver with the extended Kalman filter. By solving a planar-jet problem at , we demonstrate that the resultant hybrid flow fields essentially (i) satisfy the governing equations spatially and approximately temporally, and (ii) can provide instantaneous pressure fields (iii) with the noise levels substantially lower than those of the original PTV data and (iv) the resolution comparable to CFD. The results show that increasing the feedback gain improves replicability, i.e. the agreement between the simulation and the data; however, it degrades temporal compatibility and filtering functions. On the other hand, the fidelity enhances both replicability and spatial filtering, but increases computational cost.

Application of full flow field reconstruction to a viscoelastic liquid in a 2D cross-slot channel

High quality flow kinematics reconstruction from noisy and spatially scattered data requires the use of a regularization technique. Enforcing incompressibility, we employ the recently proposed Tikhonov regularization method combined with a high-order finite element approximation in its stream function formulation. The method is applied to experimental particle tracking velocimetry data, obtained for an incompressible polymer melt in a cross-slot channel. To overcome a potential regularization bias, where the velocity changes rapidly over small distances, regularization is performed on the departure of the velocity field from its Newtonian counterpart. It is compared with a more trivial approach, in which the data are smoothed locally and the velocity gradient fields computed using finite differences. The reconstructions are evaluated in terms of the quality of the streamlines and the velocity gradient histories. Regularization leads to significant noise reduction and to an improved utility of existing data for subsequent applications as we demonstrate by analyzing the principal stress-difference obtained by applying a constitutive equation to the reconstructed flow fields.

Quantitative assessment of flow and electric fields for electrophoretic focusing at a converging channel entrance with interfacial electrode

The electric field and flow field gradients near an electrified converging channel are amenable to separating and focusing specific classes of electrokinetic material, but the detailed local electric field and flow dynamics in this region have not been thoroughly investigated. Finite elemental analysis was used to develop a model of a buffer reservoir connected to a smaller channel to simulate the electrophoretic and flow velocities (which correspond directly to the respective electric and flow fields) at a converging entrance. A detailed PTV (Particle Tracking Velocimetry) study using charged fluorescent microspheres was performed to assess the model validity both in the absence and presence of an applied electric field. The predicted flow velocity gradient from the model agreed with the PTV data when no electric field was present. Once the additional forces that act on the large particles required for tracing (dielectrophoresis) were included, the model accurately described the velocity of the charged particles in electric fields.

Nonparametric estimation of non-stationary velocity fields from 3D particle tracking velocimetry data

Nonparametric estimation of nonstationary velocity fields from 3D particle tracking velocimetry data is considered. The velocities of tracer particles are computed from their positions measured experimentally with random errors by high-speed cameras observing turbulent flows in fluids. Thus captured discrete data is plugged into a smoothing spline estimate which is used to estimate the velocity field at arbitrary points. The estimate is further smoothed over several time frames using the fixed design kernel regression estimate. Consistency of the resulting estimate is investigated. Its performance is validated on the real data obtained by measuring a fluid flow of a liquid in a (rotating) square tank agitated by an oscillating grid.

Instability waves in a low-Reynolds-number planar jet investigated with hybrid simulation combining particle tracking velocimetry and direct numerical simulation

Instability waves in a laminar planar jet are extracted using hybrid unsteady-flow simulation combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS). Unsteady velocity fields on a laser sheet in a water tunnel are measured with time-resolved PTV; subsequently, PTV velocity fields are rectified in a least squares sense so that the equation of continuity is satisfied, and they are transplanted to a two-dimensional incompressible Navier–Stokes solver by setting a multiple of the computational time step equal to the frame rate of the PTV system. As a result, the unsteady hybrid velocity field approaches that of the measured one over time, and we can simultaneously acquire the unsteady pressure field. The resultant set of flow quantities satisfies the governing equations, and their resolution is comparable to that of numerical simulation with the noise level much lower than the original PTV data. From hybrid unsteady velocity fields, we extract eigenfunctions using bi-orthogonal decomposition as a spatial problem for viscous instability. We also investigate stability/convergence characteristics of the hybrid simulation referring to linear stability analysis.