Linear stability of the steady flow past rectangular cylinders. (25th December 2021)

• Record Type: Journal Article
• Authors: Chiarini, A.; Quadrio, M.; Auteri, F.
• Is Part Of: Journal of fluid mechanics. Volume 929(2021)
• Publication Date: 2021-12-25
• Subjects: absolute/convective instability -- vortex streets -- instability control; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2021.819
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : The primary instability of the flow past rectangular cylinders is studied to comprehensively describe the influence of the aspect ratio $AR$ and of rounding the leading- and/or trailing-edge corners. Aspect ratios ranging between $0.25$ and $30$ are considered. We show that the critical Reynolds number ( $\textit {Re}_c$ ) corresponding to the primary instability increases with the aspect ratio, starting from $\textit {Re}_c \approx 34.8$ for $AR=0.25$ to a value of $\textit {Re}_c \approx 140$ for $AR = 30$ . The unstable mode and its dependence on the aspect ratio are described. We find that positioning a small circular cylinder in the flow modifies the instability in a way strongly depending on the aspect ratio. The rounded corners affect the primary instability in a way that depends on both the aspect ratio and the curvature radius. For small $AR$, rounding the leading-edge corners has always a stabilising effect, whereas rounding the trailing-edge corners is destabilising, although for large curvature radii only. For intermediate $AR$, instead, rounding the leading-edge corners has a stabilising effect limited to small curvature radii only, while for $AR \geqslant 5$ it has always a destabilising effect. In contrast, for $AR \geqslant 2$ rounding the trailing-edge corners consistently increases $\textit {Re}_c$ . Interestingly, when all the corners are rounded, the flow becomes more stable, at all aspect ratios. An explanation for the stabilising and destabilising effect of the rounded corners is provided.