A Unified Strouhal-Reynolds Number Relationship for Laminar Vortex Streets Generated by Different Shaped Obstacles

TL;DR

This study experimentally confirms a universal Strouhal-Reynolds number relationship for laminar vortex shedding across different obstacle shapes, showing that the relation applies broadly beyond circular cylinders.

Contribution

It provides experimental evidence that the $St=1/(A+B/Re)$ relation applies to various obstacle shapes, extending its validity beyond circular cylinders.

Findings

The $St=1/(A+B/Re)$ relation holds for different obstacle shapes.

In the limit of high Reynolds number, $St$ approaches approximately 0.21.

Shape influences the parameter B, but not the asymptotic Strouhal number.

Abstract

A new Strouhal-Reynolds number relationship, $St=1/(A+B/Re)$, has been recently proposed based on observations of laminar vortex shedding from circular cylinders in a flowing soap film. Since the new $St$-$Re$ relation was derived from a general physical consideration, it raises the possibility that it may be applicable to vortex shedding from bodies other than circular ones. The work presented herein provides experimental evidence that this is the case. Our measurements also show that in the asymptotic limit ($Re\rightarrow\infty$), $St_{\infty}=1/A\simeq0.21$ is constant independent of rod shapes, leaving $B$ the only parameter that is shape dependent.