A neural network particle finding algorithm and a new four-frame predictive tracking algorithm are proposed for three-dimensional Lagrangian particle tracking (LPT). A quantitative comparison of these and other algorithms commonly used in three-dimensional LPT is presented. Weighted averaging, one-dimensional and two-dimensional Gaussian fitting, and the neural network scheme are considered for determining particle centers in digital camera images. When the signal to noise ratio is high, the one-dimensional Gaussian estimation scheme is shown to achieve a good combination of accuracy and efficiency, while the neural network approach provides greater accuracy when the images are noisy. The effect of camera placement on both the yield and accuracy of three-dimensional particle positions is investigated, and it is shown that at least one camera must be positioned at a large angle with respect to the other cameras to minimize errors. Finally, the problem of tracking particles in time is studied. The nearest neighbor algorithm is compared with a three-frame predictive algorithm and two four-frame algorithms. These four algorithms are applied to particle tracks generated by direct numerical simulation both with and without a method to resolve tracking conflicts. The new four-frame predictive algorithm with no conflict resolution is shown to give the best performance. Finally, the best algorithms are verified to work in a real experimental environment.

A quantitative study of three-dimensional Lagrangian particle tracking algorithms

The connection between fluid flow and optical flow is explored in typical flow visualizations to provide a rational foundation for application of the optical flow method to image-based fluid velocity measurements. The projected-motion equations are derived, and the physics-based optical flow equation is given. In general, the optical flow is proportional to the path-averaged velocity of fluid or particles weighted with a relevant field quantity. The variational formulation and the corresponding Euler–Lagrange equation are given for optical flow computation. An error analysis for optical flow computation is provided, which is quantitatively examined by simulations on synthetic grid images. Direct comparisons between the optical flow method and the correlation-based method are made in simulations on synthetic particle images and experiments in a strongly excited turbulent jet.

Fluid flow and optical flow

Defocusing digital particle image velocimetry (DDPIV) is the natural extension of planar PIV techniques to the third spatial dimension. In this paper we give details of the defocusing optical concept by which scalar and vector information can be retrieved within large volumes. The optical model and computational procedures are presented with the specific purpose of mapping the number density, the size distribution, the associated local void fraction and the velocity of bubbles or particles in two-phase flows. Every particle or bubble is characterized in terms of size and of spatial coordinates, used to compute a true three-component velocity field by spatial three-dimensional cross-correlation. The spatial resolution and uncertainty limits are established through numerical simulations. The performance of the DDPIV technique is established in terms of number density and void fraction. Finally, the velocity evaluation methodology, using the spatial cross-correlation technique, is described and discussed in terms of velocity accuracy.

/pdf/defocusing-digital-particle-image-velocimetry-and-the-three-16f9u5efor.pdf

Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows

A whole-field three-dimensional (3D) particle tracking velocimetry (PTV) tool for diagnostics in fluid mechanics is presented. Specifically, it is demonstrated why and when PTV is the natural choice in 3D applications compared to particle image velocimetry (PIV). Three different tracking methods are investigated, namely the nearest neighbour, the neural network and the relaxation method. In order to demonstrate the use of PTV for 3D applications, the selected tracking schemes are implemented for use with the defocusing digital particle image velocimetry (DDPIV) technique. The performance of the tracking algorithms is evaluated based on synthetic 3D information. Furthermore, the potential benefit of a merging between the PIV and PTV approaches is explored within the DDPIV framework. The results show that the relaxation tracking method is the most robust and efficient, while the combined PIV/PTV analysis brings significant improvements solely with the neural network scheme. In terms of errors, PTV is found to be more sensitive to particle reconstruction errors than the DDPIV cross-correlation analysis.

/pdf/two-frame-3d-particle-tracking-m0tyorb89f.pdf

Two-frame 3D particle tracking

Three-dimensional particle tracking velocimetry (3D PTV) is a flow measurement technique for the determination of velocity vectors and trajectories within a three-dimensional observation volume. This makes this technique suitable not only for Eulerian but also for Lagrangian investigation of flow phenomena, especially in the field of turbulence and turbulent diffusion. The principle and the application on open channel flow of 3D PTV are briefly described in the first part of this paper. By decomposition of the velocity vectors velocity profiles and turbulence intensities are derived and presented in the second part. Turbulent energy dissipation, Kolmogorov length and time scales and Taylor micro scales are computed from the measured data sets. In the Lagrangian analysis pdf's of the Lagrangian acceleration, correlation coefficients and Taylor micro scales are determined. The individual determination of the particle positions and displacements allows finally the application on the one and two particle approaches for turbulent diffusion from Taylor (1921), Richardson (1926) and Batchelor (1949, 1952).

https://iopscience.iop.org/article/10.1088/0957-0233/8/12/017/pdf

3D PTV and its application on Lagrangian motion

Particle Tracking Velocimetry (PTV) is one of the oldest measuring techniques in fluid mechanics. It is often called low particle number density Particle Image Velocimetry (PIV) (Adrian, 1991). The two methods have indeed in common that they determine the velocity from the displacement of particles in a moving fluid during a prescribed time interval. In contrast to PIV, in which the mean displacement of a small group of particles is sought for, PTV tracks the trajectories of individual particles in three-dimensional space. Particle identification and determination of its position in space is a very important step in PTV. This is only possible if the number density, i.e. the number of particles per unit volume, ρ N = N / V, where N is the number of particles in an observation volume V, is not too high.

Particle Tracking Velocimetry (PTV)

The photogrammetric procedure described in the previous chapter yields coordinates of particle positions in space at successive time steps. These coordinates have inevitably true errors of which the root mean square values σ i, rms in x, y and z-directions have been estimated in the photogrammetric part (Maas, this chapter). Hence particle positions are determined with some known noise. Noise depends mainly on: 


The optical properties of the media involved, e.g. index of refraction of air, water, oil, glass, etc.


The imaging arrangement used and the quality of the particle images


The spatial camera resolution and imaging scale


The quality of the calibration

Particle Tracking in Three-Dimensional Space

Videogrammetric Methods in Velocimetry

Interpolation Schemes for Three-Dimensional Velocity Fields from Scattered Data Using Taylor Expansions

In this chapter, we consider the simultaneous flow of liquids and gases through porous media. We shall assume that cohesive forces in these fluids exceed the adhesion ones, and that the fluids are immiscible and separated from each other by stable abrupt interfaces. Air, water and oil are immiscible under normal conditions (atmospheric pressure, room temperature, etc.). This does not mean that solubility (or volatility) is zero, but that they are so small that a sharp interface forms and that the physical properties of the fluids are not affected.

Th. Dracos

Papers

Particle Tracking Velocimetry (PTV)

Particle Tracking in Three-Dimensional Space

Videogrammetric Methods in Velocimetry

Interpolation Schemes for Three-Dimensional Velocity Fields from Scattered Data Using Taylor Expansions

Multiphase Flow in Porous Media