Particle Tracking Velocimetry Algorithm Research Articles

A recursive interpolation algorithm for particle tracking velocimetry

A new type of interpolation algorithm for particle tracking velocimetry is proposed. The algorithm is established based on a combination of ellipsoidal differential equations, i.e. a recursive process from a lower to a higher order interpolation. Each equation is solved as a boundary value problem by using the discrete velocity vector information as boundary conditions. In this paper the performance of the interpolation scheme, such as errors and cross correlations, is examined using the Taylor–Green vortex flow and isotropic turbulent flow. The examination results reveal that the recursive process from linear to hexagonal interpolation provides the best reconstruction in comparison to the single process. A quantitative evaluation is also carried out for integral and derivative information of the velocity vector, such as stream function and vorticity.

Three-dimensional, three-component velocity measurements using stereoscopic micro-PIV and PTV

Two-dimensional, two-component micron resolution particle image velocimetry (micro-PIV) allows measurement of the in-plane velocity components across a single plane within a micro-scale device. The technique has become well established over recent years for the study of micro-scale flows. Stereoscopic micro-PIV uses two cameras and a stereomicroscope to capture all three components of the velocity field. Recently, preliminary results have been published from stereoscopic micro-PIV systems. Here, a complete validation of a stereoscopic micro-PIV system is carried out by comparing results for flow over a micro step with a computational fluid dynamics (CFD) solution. It is found that the accuracy of the correlation-based PIV technique is limited by the degree of overlap of the two focal planes in the stereomicroscope. This prompts the adoption of a ‘super-resolution’ particle tracking velocimetry (PTV) algorithm, which does not require exact alignment of the two focal planes. The PTV is more accurate than the PIV and systematic deviations near to surfaces are greatly reduced. In addition, since the PTV algorithm tracks the three-dimensional coordinates of individual particles the measured velocities are no longer automatically averaged onto the focal plane of the measurement. Thus the PTV data represent a truly three-dimensional, three-component mapping of the flow field, whose resolution is independent of the microscope lens parameters. To demonstrate this, data are presented at a resolution of 10 × 10 × 10 µm across a field of view of 900 × 720 µm, corresponding to the 10× lens used in the experiment. To obtain this out-of-plane resolution with a correlation-based algorithm we would require a numerical aperture more typical of a 20× lens, with a correspondingly smaller field of view. The data agree with the CFD within the experimental uncertainties and it is proposed that the method could be important even in flows where only the in-plane velocity components are of interest. With the current system, a single measurement can determine the in-plane velocity field throughout a 900 × 720 × 45 µm volume, large enough to cover a significant section of a micro-device. The out-of-plane resolution is limited only by the number of images taken and, ultimately, the size of the particles.

Near-surface velocimetry using evanescent wave illumination

Total internal reflection velocimetry (TIRV) is used to measure particle motion in the near-wall region of a microfluidic system. TIRV images are illuminated with the evanescent field of an incident laser pulse and contain only particles that are very close to the channel surface. Sub-micron-sized fluorescent particles suspended in water are used as seed particles and their images are analyzed with a particle tracking velocimetry (PTV) algorithm to extract information about apparent slip velocity. At relatively low shear rates (less than 2,500 s-1), a velocity proportional to the shear rate was observed. The statistical difference between velocities measured over hydrophilic and hydrophobic surfaces was found to be minimal. The results suggest that the slip length, if present, is less than 10 nm, but uncertainty regarding the exact character of the illumination field prevents a more accurate measurement at this time. Numerical simulations are presented to help understand the results and to provide insight into the mechanisms that result in the experimentally observed distributions. Issues associated with the accuracy of the experimental technique and the interpretations of the experimental results are also discussed.

Experimental investigation of interparticle collision rate in particulate flow

Interparticle collision is an important phenomenon in the mechanics of two-phase flow. Most past researches on this problem have been based on the analogy with kinetic theory of gases with few experimental validations of the results. While this paper presents the directly measured experimental data of collision rate in vertical two-phase flow. This research used a high-speed camera and Particle Tracking Velocimetry (PTV) algorithms to focus on the interparticle collisions, especially the collision rate, on a millisecond time scale and a millimeter space scale, which is the particle size (1.8 mm in diameter). The camera speed was normally 2000 frames per second with an exposure of 1/2000 s and a laser power of 25 W for particle velocity of less than 4m/s in the collision region and particle fractions of about 0.015. A manual count of the collision numbers was chosen as the most accurate method for the determination of the collision rate. The PTV algorithms were applied to calculate the particle number density and relative velocities. The correlation between the particle collision rate, the particle number density, the average relative velocity between particles and the measured granular temperature, was compared with commonly used relations based on kinetic theory. The results demonstrated that great differences exist between the theoretical and experimental results for these experimental conditions. The collision rate determined experimentally is much lower than the theoretical estimation based on kinetic theory. This means the theoretical correlations overestimate the collision rate in the gas-particle flows. This discrepancy may be attributed to the assumptions in the theoretical collision model and experimental error.

Digital imaging and analysis of dusty plasmas

Dust particles immersed within a plasma environment, such as those found in planetary rings or cometary environments, will acquire an electric charge. If the ratio of interparticle potential energy to average kinetic energy is high enough the particles will form either a ‘liquid’ structure with short-range ordering or a crystalline structure with long-range ordering. Since their discovery in laboratory environments in 1994, such crystals have been the subject of a variety of experimental, theoretical, and numerical investigations. Laboratory experiments analyzing the behavior of dust grains in a plasma rely on optical diagnostics to provide data about the system in a non-perturbative manner. In the past, capturing, imaging, and analyzing crystalline structure in dusty plasmas has been a non-trivial problem. Utilizing digital imaging and analysis systems, data capture, image formatting, and analysis can be done quickly. Following data capture, image analysis is conducted using modified Particle Image Velocimetry and Particle Tracking Velocimetry algorithms. The data extracted is then used to construct Voronoi diagrams, calculate particle density, inter-particle spacing, pair correlation functions, and thermal energy. From this data other dust plasma parameters can be inferred such as inter-particle forces and grain charges.

The application of a 3D PTV algorithm to a mixed convection flow

A 3D particle-tracking velocimetry (PTV) algorithm is applied to the wake flow behind a heated cylinder. The method is tested in advance with respect to its accuracy and performance. In the accuracy tests, its capability to locate particles in 3D space is tested. It appears that the algorithm can determine the particle position with an accuracy of less than 0.5 camera pixels, equivalent to 0.3 mm in the present test situation. The performance tests show that for particles located in a 2D plane, the algorithm can track the particles with a vector yield reaching 100%, which means that a velocity vector can be determined for almost all particles detected. The calculated velocity vectors for this situation have a standard deviation of less than 1%. The performance is also tested on a mixed convection flow behind a heated cylinder in which the 2D flow transits into a 3D flow. As there is no exact solution of such a flow available, the 3D PTV results are compared with visualisation results. The results show that the 3D PTV method can capture the main features of the 3D transition of the 2D vortex street.

Development and evaluation of an improved correlation based PTV method

An improved correlation based Particle Tracking Velocimetry (PTV) algorithm was proposed in the present paper. The path tracking of the tracer particles was achieved through a correlation operation of the small interrogation window around the studied tracer particles at two-time steps. The central positions of the tracer particles were determined by the correlation operation of the tracer particle image with a Gaussian particle mask in order to improve the accuracy to identify the central positions of particles up to sub-pixel level. The performance of the present improved correlation based Particle Tracking Velocimetry (PTV) algorithm was evaluated by using both synthetic VSJ standard PIV images and actual PIV images of a self-induced sloshing. Compared with other conventional PTV methods, the present improved correlation based PTV algorithm was found to be able to provide better solution and more robust for suppression the effect of background noise in the PIV images.

A novel algorithm for particle tracking velocimetry using the velocity gradient tensor

Most particle-tracking velocimetry (PTV) algorithms are not suitable for calculating the velocity vectors of a fluid flow subjected to strong deformation, because these algorithms deal only with flows due to translation. Accordingly, it is necessary to develop a novel algorithm applicable to flows subjected to strong deformations such as rotation, shear, expansion and compression. This paper proposes a novel particle tracking algorithm using the velocity gradient tensor (VGT) which can deal with strong deformations and demonstrates that this algorithm is applicable to some basic fluid motions (rigidly rotating flow, Couette flow, and expansion flow). Furthermore, the performance of this algorithm is compared with the binary image cross-correlation method (BICC), the four-consecutive-time-step particle tracking method (4-PTV), and the spring model particle tracking algorithm (SPG) using simulations and experimental data. As a result, it is shown that this novel algorithm is useful and applicable for the highly accurate measurement and analysis of fluid flows subjected to strong deformations.

Numerical validation of velocity gradient tensor particle trackingvelocimetry for highly deformed flow fields

Particle tracking velocimetry (PTV) has recently been recognized asquite an effective engineering research tool for understandingmulti-dimensional fluid flow structures. There are, however, still a number ofunsettled problems in the practical use of PTV, i.e. the lack of generalityof the PTV algorithm for various types of flows and the measurementuncertainty with respect to spatial resolution. The authors have developed ageneralized PTV algorithm named the velocity gradient tensor (VGT) method inorder to accurately track the tracer particles in a flow field with stronglocal deformation rates. The performance of the VGT method has already beenexamined for several simple flow fields, such as linear shearing andTaylor-Green vortex flows. In this paper, the applicability of the VGT methodfor complicated flows, which include a wide dynamic range in wavenumber, isquantitatively examined by simulation of Rankine vortex flows, Karmanvortex-shedding flows around a rectangular cylinder and homogeneous turbulentflows, which are numerically solved by using the unsteady Navier-Stokesequations. The results show that the VGT technique, using only two frames toestimate velocity, performs better than does the four-frame PTV technique andhas a remarkably higher tracking performance than those of typicalconventional PTV algorithms.

B102濃度相関ベースの粒子追跡法の改良

An improved correlation based Particle Tracking Velocimetry (PTV) algorithm was proposed in the present paper. The path tracking of the tracer particles was achieved through a recursive correlation operation of the small interrogation window at two-time steps. The central positions of the tracer particles were determined by the correlation operation of the tracer particle image with a gauss particle mask in order to improve the accuracy to identify the central positions of particles up to sub-pixel level. The performance of the present improved correlation based Particle Tracking Velocimetry (PTV) algorithm was evaluated by using both artifical VSJ standard PIV images and actual PIV images of a self-induced sloshing. Compared with other conventional PTV methods, the present improved correlation based PTV algorithm was found to be able to provide better solution.

B107ネットワークモデルを用いた粒子追跡法

Particle tracking velocimetry (PTV) is one of the methods that measure flow velocity fields. This paper proposes a new method that solves the correspondence problem of particle tracking velocimetry using a network model. The PTV offers many advantages for the study of fluid flows. The flow visualization images are analyzed to obtain the velocity distribution of the flow. Several PTV algorithm has been proposed in the past. The most of the method assumes that the fluid motion, within small regions of the flow fields, is parallel over short time intervals. However, actual flow fields may have some detoured motion, such as rotation and expansion. The proposed pairing particles method using the networks model is based on a connection of particles according as the weights between particles on a 1st image and 2nnd image. The technique is applied to the PTV standard images distributed through the web site (http : //www.vsior.jp/piv). The simulation results demonstrate the effectiveness of the present technique.

B211 濃度相関による粒子追跡法のPIV標準画像による評価

In the present paper, a new algorithm for particle tracking velocimetry (PTV) has been proposed. The algorithm consists on the following two main parts: (1) detection of particle's positions by a multi-steps of thresholding, and (2) particle tracking over a two time steps of images by a density cross-correlation method. The performance of present PTV technique was evaluated by using the PIV standard images which distributed with using the internet The results show a good performance to get the high spatial resolution of velocities with a reliable accuracy.

A new two-frame particle tracking algorithm using match probability

A new particle tracking algorithm using the concept of match probability between two consequent image frames has been developed to obtain an instantaneous 2-dimensional velocity field. Our proposed algorithm for correctly tracking particle paths from only two image frames is based on iterative estimation of match probability and no-match probability as a measure of the matching degree. A computer simulation has been carried out to study the performance of the developed algorithm by comparing with the conventional 4-frame Particle Tracking Velocimetry (PTV) method. The effect of various thresholds used in the developed algorithm on the recovery ratio and the error ratio were also investigated. Although the new algorithm relies on the iterative updating process of match probability which is time consuming, computation time is relatively short compared to that of the 4-frame PTV method. Additionally, the new 2-frame PTV algorithm recovers more velocity vectors and has a higher dynamic range and a lower error ratio.

Estimation of Fluid Velocity by Tracking a Particle which Does Not Follow the Flow.

A new method has been developed in order to estimate fluid velocity using tracer particles which do not follow the flow. The present PTV (particle tracking velocimetry) algorithm is an extension of Kalman filter-type velocimetry reported by Yagoh et al. (Yagoh, K., Ogawara, K. and Iida, S., Trans. Jpn. Soc. Mech. Eng., Vol. 57, No. 542, B (1991), p.3622) by which particle position measured in the presence of noise can be used to determine particle velocity. Although PTV is a common technique for flow measurements, one obvious shortcoming is noted. Namely, ordinary PTV algorithms could not be used when the particle density is different from the fluid density, because of ill-trackability of tracer particles. This may cause serious loss in accuracy when some forces cannot be neglected, for example, centrifugal forces of gravitational force. This study has proven that the new algorithm successfully identifies fluid velocity, and that it also has the ability to estimate particle diameter during the course of the tracking process.