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Linear stability of the steady flow past rectangular cylinders

Published online by Cambridge University Press:  28 October 2021

A. Chiarini Open the ORCID record for A. Chiarini [Opens in a new window] ,
M. Quadrio Open the ORCID record for M. Quadrio [Opens in a new window]  and
F. Auteri Open the ORCID record for F. Auteri [Opens in a new window]
A. Chiarini
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156Milano, Italy
M. Quadrio
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156Milano, Italy
F. Auteri*
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156Milano, Italy
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Instability: Absolute/convective instability Wakes/Jets: Vortex streets Flow Control: Instability control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 929 , 25 December 2021 , A36
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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