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

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.