Experimental and numerical study of the separation angle for flow around a circular cylinder at low Reynolds number

Abstract

The separation point of the flow around a circular cylinder has been numerically and experimentally investigated in the regime of Reynolds number less than 280. The present results reveal that the long-existing discrepancy in the data concerning the time-averaged separation angles reported in the literature results mainly from the oscillating characteristics of the flow separation on the cylinder surface and the experimental methodologies rather than the commonly mentioned blockage-ratio effect. In the present experiment, the time-averaged separation angles are obtained by averaging the instantaneous images from a soap-film flow visualization instead of from the commonly used streakline images from finite time exposures. Excellent agreement has been achieved between the present experimental results and numerical simulations by the spectral element method. Particle-streak visualization in a towing tank has also been conducted to compare with that of the two-dimensional soap-film experiments. It reveals that the separation angle is insensitive to the three-dimensional effect. Variations of the time-averaged separation angles with Reynolds number can be represented by a four-term $\theta _{s}\hbox{--}{\it Re}^{-1/2}$ relationship in the range of $7\,{\le}\,{\it Re}\,{\le}\,200$. Moreover, if the data in the very low Reynolds number region are excluded, a simple linear $\theta_{s}\hbox{--}{\it Re}^{-1/2}$ relationship can be derived for $10\,{\le}\,{\it Re}\,{\le}\,200$. Since the dimensionless boundary layer thickness and the Strouhal–Reynolds number relationship for the circular cylinder are also known to be proportional to ${\it Re}^{-1/2}$, this linear relationship offers direct evidence that the flow characteristics of the boundary layer extend downstream along the cylinder surface to the separation point in this ${\it Re}$-range. The blockage effect on the separation angle has also been quantitatively analysed.