Quantifying instantaneous flow reversal of tracer particles in subsonic, transonic and supersonic flows past a circular cylinder

Abstract

Tracer pathline statistics have rarely, if at all, been used in the investigation of compressible subsonic, transonic and supersonic flows past a circular cylinder. Here, we report pathline histogram, conditional histogram and zonal histogram data, focusing on the characteristics of particle instantaneous flow reversal and their dependencies on Mach number and tracer release position. The far-upstream Mach number and the diameter-based Reynolds number used for these three flow regimes are $(0.2,10000),(0.9,3900)$ and $(1.2,10000)$, respectively. The subsonic surface-release histogram profiles display unexpected persistent oscillations at a frequency $50$ times of the periodic vortex shedding frequency, reflecting the effect of a very small magnitude zig-zagging type of particle motion in a region very close to the wall and slightly behind the mean flow separation location. No similar high-frequency oscillation is observed in the corresponding transonic and supersonic histograms likely because, at $\text{Ma}\ge 0.9$, periodic vortex shedding ceases to exist and the near-wake becomes a quasi-laminar recirculation zone bounded by a pair of converging slip-layers with a neck opening to the far-wake. At the instant of $5$ subsonic vortex-shedding periods after being released from the cylinder surface, there are $1.67\mathrm{\%}$, $35.2\mathrm{\%}$ and $39.7\mathrm{\%}$ particles that experience flow reversal in the subsonic, transonic and supersonic flows, respectively. Surprisingly, in the present transonic flow, growth of the turbulent far-wake behind the pair of lambda-shocks is constrained over a considerable streamwise distance.

KEYWORDS:

• Tracer particle
• cylinder
• transonic
• supersonic
• subsonic

Acknowldgment

The support by the Natural Science and Engineering Research Council of Canada and Compute Canada is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The support by the Natural Science and Engineering Research Council of Canada and Compute Canada is gratefully acknowledged.