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Linear global and asymptotic stability analysis of the flow past rectangular cylinders moving along a wall

Published online by Cambridge University Press:  29 June 2023

Alessandro Chiarini Open the ORCID record for Alessandro Chiarini [Opens in a new window]  and
Franco Auteri Open the ORCID record for Franco Auteri [Opens in a new window]
Alessandro Chiarini*
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Franco Auteri
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
Email address for correspondence: alessandro.chiarini@polimi.it
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Abstract

The primary instability of the steady two-dimensional flow past rectangular cylinders moving parallel to a solid wall is studied, as a function of the cylinder length-to-thickness aspect ratio ${A{\kern-4pt}R} =L/D$ and the dimensionless distance from the wall $g=G/D$. For all ${A{\kern-4pt}R}$, two kinds of primary instability are found: a Hopf bifurcation leading to an unsteady two-dimensional flow for $g \ge 0.5$, and a regular bifurcation leading to a steady three-dimensional flow for $g < 0.5$. The critical Reynolds number $Re_{c,2\text{-}D}$ of the Hopf bifurcation ($Re=U_\infty D/\nu$, where $U_\infty$ is the free stream velocity, $D$ the cylinder thickness and $\nu$ the kinematic viscosity) changes with the gap height and the aspect ratio. For ${A{\kern-4pt}R} \le 1$, $Re_{c,2\text{-}D}$ increases monotonically when the gap height is reduced. For ${A{\kern-4pt}R} >1$, $Re_{c,2\text{-}D}$ decreases when the gap is reduced until $g \approx 1.5$, and then it increases. The critical Reynolds number $Re_{c,3\text{-}D}$ of the three-dimensional regular bifurcation decreases monotonically for all ${A{\kern-4pt}R}$, when the gap height is reduced below $g < 0.5$. For small gaps, $g < 0.5$, the hyperbolic/elliptic/centrifugal character of the regular instability is investigated by means of a short-wavelength approximation considering pressureless inviscid modes. For elongated cylinders, ${A{\kern-4pt}R} > 3$, the closed streamline related to the maximum growth rate is located within the top recirculating region of the wake, and includes the flow region with maximum structural sensitivity; the asymptotic analysis is in very good agreement with the global stability analysis, assessing the inviscid character of the instability. For cylinders with $AR \leq 3$, however, the local analysis fails to predict the three-dimensional regular bifurcation.

JFM classification

Instability: Absolute/convective instability Wakes/Jets: Vortex streets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 966 , 10 July 2023 , A22
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

†

Present address: Complex Fluids and Flows Unit, Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna-son, Okinawa 904-0495, Japan.

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