A Probabilistic Particle Tracking Framework for Guided and Brownian Motion Systems with High Particle Densities

Herzog, Sebastian; Schiepel, Daniel; Guido, Isabella; Barta, Robin; Wagner, Claus

doi:10.1007/s42979-021-00879-z

Cited by 6 publications

(5 citation statements)

References 52 publications

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“…In §§ 4.3 and 4.4 we pointed out that this provides a new opportunity to identify caustics in numerical data or in experimental data via particle tracking velocimetry (Schanz, Gesemann & Schröder 2016; Herzog et al. 2021). There is a most-likely path along caustics occur.…”

Section: Discussionmentioning

confidence: 99%

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Caustics in turbulent aerosols: an excitable system approach

Barta

Vollmer²

2022

J. Fluid Mech.

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Aerosol particles are inertial particles. They cannot follow the surrounding fluid in a region of high vorticity. These encounters render the particle velocity field ${{\boldsymbol {v}}}$ locally compressible. Caustics occur if the trace of the gradient matrix $\textsf{$\boldsymbol{\sigma}$}$ of the field ${{\boldsymbol {v}}}$ locally diverges. For three-dimensional isotropic and homogeneous turbulence, the dynamics of the gradient matrix can be expressed in terms of three geometric invariants. In the present paper we establish a parametrisation of this problem where the dynamics takes the form of an excitable stochastic dynamical system with a three-dimensional phase space. The deterministic part of the dynamics is solved analytically. We show that the deterministic system has a globally attractive stable fixed point. Small noise induces excursions from the fixed point that typically relax straight back towards the fixed point. Caustics emerge as non-trivial return to a global fixed point when noise excites a trajectory across a stability threshold. The relaxation to the global fixed point will then involve at least one, and it may involve two or even three divergences of $\boldsymbol {Tr}\,\textsf{$\boldsymbol{\sigma}$}$ . Based on a combination of analytical insights and numerical analysis, we determine the rate of occurrence, duration and relative observation probability of caustic events in turbulent aerosols. Our analysis reveals that each approach towards a divergence proceeds along a straight line in the phase space of the dynamical system, which can help identify caustics. Moreover, there are infinite ways in which caustics can arise, namely whenever $\boldsymbol {Tr}\,\textsf{$\boldsymbol{\sigma}$}$ tends to $-\infty$ , so that no two caustics look the same.

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Section: Discussionmentioning

confidence: 99%

“…This is illustrated by the grey bands in figure 3. In § § 4.3 and 4.4 we pointed out that this provides a new opportunity to identify caustics in numerical data or in experimental data via particle tracking velocimetry (Schanz, Gesemann & Schröder 2016;Herzog et al 2021). (vi) There is a most-likely path along caustics occur.…”

Section: Discussionmentioning

confidence: 99%

Caustics in turbulent aerosols: an excitable system approach

Barta

Vollmer²

2022

J. Fluid Mech.

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“…Trajectories are then extracted by successively examining the reconstructions for particles that minimize a certain cost function for each already identified track. The cost functions can be a simple nearest-neighbor approach, more elaborate methods that seek to minimize the acceleration over several past and future time steps (see Malik et al 1993, Ouellette et al 2006, Xu 2008, or probabilistic frameworks (e.g., Herzog et al 2021).…”

Section: D Particle Tracking Velocimetrymentioning

confidence: 99%

3D Lagrangian Particle Tracking in Fluid Mechanics

Schröder

Schanz

2023

Annu. Rev. Fluid Mech.

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In the past few decades various particle image–based volumetric flow measurement techniques have been developed that have demonstrated their potential in accessing unsteady flow properties quantitatively in various experimental applications in fluid mechanics. In this review, we focus on physical properties and circumstances of 3D particle–based measurements and what knowledge can be used for advancing reconstruction accuracy and spatial and temporal resolution, as well as completeness. The natural candidate for our focus is 3D Lagrangian particle tracking (LPT), which allows for position, velocity, and acceleration to be determined alongside a large number of individual particle tracks in the investigated volume. The advent of the dense 3D LPT technique Shake-The-Box in the past decade has opened further possibilities for characterizing unsteady flows by delivering input data for powerful data assimilation techniques that use Navier–Stokes constraints. As a result, high-resolution Lagrangian and Eulerian data can be obtained, including long particle trajectories embedded in time-resolved 3D velocity and pressure fields. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 55 is January 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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“…Barta et al [25] used the Soloff mapping functions [26] with 16 parameters of the 3rd order (3 × 3 × 3) models for triangulation. However, an iterative process was required to determine the LOS by two points as well as the partial derivatives of the mapping functions [27]. This required multiple Z-position planes to obtain sufficiently accurate 3D mapping functions, and the recovery of the 3D particle positions was cumbersome due to the excessive number of iterations.…”

Section: Introductionmentioning

confidence: 99%

A polynomial model with line-of-sight constraints for Lagrangian particle tracking under interface refraction

Zeng,

Qu,

et al. 2024

Meas. Sci. Technol.

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This paper introduces an improvement of the “Shake-The-Box (STB)” (Schanz, Gesemann, and Schröder, Exp. Fluids 57.5, 2016) technique using the polynomial calibration model and the line-of-sight constraints (LOSC) to overcome the refractive interface issues in Lagrangian particle tracking (LPT) measurement. The method (named LOSC-LPT) draws inspiration from the two-plane polynomial camera calibration in tomographic particle image velocimetry (Tomo-PIV) (Worth and Nickels, Thesis, 2010) and the STB-based open-source Lagrangian particle tracking (OpenLPT) framework (Tan, Salibindla, Masuk, and Ni, Exp. Fluids 61.2, 2019). The LOSC-LPT introduces polynomial mapping functions into STB calibration in conditions involving gas–solid–liquid interfaces at container walls exhibiting large refractive index variations, which facilitates the realization of particle stereo matching, three-dimensional (3D) triangulation, iterative particle reconstruction, and further refinement of 3D particle position by shaking the LOS. Performance evaluation based on synthetic noise-free images with a particle image density of 0.05 particle per pixel (ppp) in the presence of refractive interfaces demonstrates that LOSC-LPT can detect a higher number of particles and exhibits lower position uncertainty in the reconstructed particles, resulting in higher accuracy and robustness than that achieved with OpenLPT. In the application to an elliptical jet flow in an octagonal tank with refractive interfaces, the use of polynomial mapping results in smaller errors (mean calibration error < 0.1 px) and thus more long trajectories identified by LOSC-LPT (13,000) compared with OpenLPT (4,500) which uses the pinhole Tsai model (mean calibration error > 1.0 px). Moreover, 3D flow-field reconstructions demonstrate that the LOSC-LPT framework can recover a more accurate 3D Eulerian flow field and capture more complete coherent structures in the flow, and thus holds great potential for widespread application in 3D experimental fluid measurements.

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A Probabilistic Particle Tracking Framework for Guided and Brownian Motion Systems with High Particle Densities

Cited by 6 publications

References 52 publications

Caustics in turbulent aerosols: an excitable system approach

Caustics in turbulent aerosols: an excitable system approach

3D Lagrangian Particle Tracking in Fluid Mechanics

A polynomial model with line-of-sight constraints for Lagrangian particle tracking under interface refraction

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