Generalization of the JTZ model to open plane wakes

TL;DR

This paper extends the JTZ model to open plane wakes by adding a double row of vortices, aligning well with simulations and experiments, and explores particle transport dynamics influenced by vortex interactions.

Contribution

The paper introduces an extended JTZ model for open plane wakes, incorporating vortices to better match real flow conditions and analyze particle trajectories.

Findings

Extended JTZ model qualitatively matches numerical and experimental flow patterns.

Particle size significantly affects trajectory patterns around vortices.

Model predictions align with experimental results for typical particle sizes.

Abstract

The JTZ model [C. Jung, T. T\'el and E. Ziemniak, Chaos {\bf 3}, (1993) 555], as a theoretical model of a plane wake behind a circular cylinder in a narrow channel at a moderate Reynolds number, has previously been employed to analyze phenomena of chaotic scattering. It is extended here to describe an open plane wake without the confined narrow channel by incorporating a double row of shedding vortices into the intermediate and far wake. The extended JTZ model is found in qualitative agreement with both direct numerical simulations and experimental results in describing streamlines and vorticity contours. To further validate its applications to particle transport processes, the interaction between small spherical particles and vortices in an extended JTZ model flow is studied. It is shown that the particle size has significant influences on the features of particle trajectories, which have two characteristic patterns: one is rotating around the vortex centers and the other accumulating in the exterior of vortices. Numerical results based on the extended JTZ model are found in qualitative agreement with experimental ones in the normal range of particle sizes.