# Lattice gas automaton modelling of a vortex flow meter: Strouhal-Reynolds number dependence

## TL;DR

This study uses two-dimensional lattice gas automaton models to investigate vortex shedding behind a trapezoid-shaped object, aiming to understand the Reynolds-Strouhal number relationship and its dependence on three-dimensional flow structures.

## Contribution

It demonstrates that in a two-dimensional setting, the Strouhal number remains nearly independent of Reynolds number, highlighting the role of three-dimensional effects in flow behavior.

## Key findings

- Strouhal number is nearly Reynolds-independent in 2D models.
- Three-dimensional vortex structures influence the Reynolds-Strouhal dependence.
- Supports the hypothesis that pipe diameter affects vortex flow meter accuracy.

## Abstract

Motivated by recent experimental and computational results concerning the three-dimensional structure of vortices behind a vortex shedding flow meter [M. Reik et al., Forsch. Ingenieurwes. 74, 77 (2010)], we study the Strouhal-Reynolds number dependence in the vortex street in two dimensions behind a trapezoid-shaped object by employing two types of Frisch-Hasslacher-Pomeau (FHP) models. Our geometry is intended to reproduce the operation of the vortex shedding flow meter in a two-dimensional setting, thus preventing the formation of three-dimensional vortex structure. In particular, we check if the anomalous Reynolds-Strouhal number dependence reported for three dimensions can also be found in our two-dimensional simulation. As we find that the Strouhal number is nearly independent of the Reynolds number in this particular setup, our results provide support for the hypothesis that three-dimensional flow structures are responsible for that dependence, thus hinting at the importance of the pipe diameter to the accurate operation of industrial vortex flow meters.