Unsteady separation and oscillations in a compressible wake of a cylinder

TL;DR

This paper analyzes oscillations in the supersonic wake of cylinders, revealing a Reynolds number threshold for unsteadiness and proposing a universal Strouhal number based on wake momentum thickness for high-speed wakes.

Contribution

It introduces a new interpretation of wake oscillations, emphasizing the Reynolds number dependence and proposing a universal Strouhal number for hypersonic and high supersonic wakes.

Findings

Oscillations depend strongly on Reynolds number.

A threshold Reynolds number exists below which unsteadiness does not occur.

A universal Strouhal number based on wake momentum thickness is proposed.

Abstract

The paper presents a new analysis and a new interpretation of oscillations observed in the experiments of near wakes of cylinders at Mach 4 and Mach 6 and Reynolds number range 2 $\times$ 10$^4$ to 5 $\times$ 10$^5$ by \cite{schmidt2015oscillations} and \cite{thasu2022strouhal}. It is shown that the presence of such oscillations is strongly Reynolds number dependent. It is further shown that there is a threshold Reynolds number below which wake unsteadiness and oscillations do not appear. Attention is drawn to the earlier experimental investigation of supersonic wakes behind cylinders and spheres by \cite{kendall1962exp} which discusses cylinder oscillations and confirms the concept of threshold Reynolds number. Following the earlier work of \cite{goldburg1965strouhal} on hypersonic wakes of spheres and cones, a Strouhal number($St_\theta$) based on total wake momentum thickness ($\theta$) is shown to be the relevant similarity parameter for correlating the hypersonic and high supersonic wakes of spheres, cones, as well as cylinders. In this limited sense, $St_\theta$ can be said to be `universal'. A universal Strouhal number based on only one geometry (\textit{i.e.,} a circular cylinder) and over a limited Reynolds number range as proposed by \cite{schmidt2015oscillations} is much too restrictive.