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Numerical simulations of flow past three circular cylinders in equilateral-triangular arrangements

Published online by Cambridge University Press:  23 March 2020

Weilin Chen
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin300350, China
Chunning Ji*
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin300350, China Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration, Tianjin University, Tianjin300350, China
Md. Mahbub Alam
Institute for Turbulence-Noise-Vibration Interaction and Control, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China
John Williams
School of Engineering and Material Science, Queen Mary University of London, LondonE1 4NS, UK State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu610065, China
Dong Xu
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin300350, China Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration, Tianjin University, Tianjin300350, China
Email address for correspondence:


Flow past three identical circular cylinders is numerically investigated using the immersed boundary method. The cylinders are arranged in an equilateral-triangle configuration with one cylinder placed upstream and the other two side-by-side downstream. The focus is on the effect of the spacing ratio $L/D(=1.0{-}6.0)$, Reynolds number $Re(=50{-}300)$ and three-dimensionality on the flow structures, hydrodynamic forces and Strouhal numbers, where $L$ is the cylinder centre-to-centre spacing and $D$ is the cylinder diameter. The fluid dynamics involved is highly sensitive to both $Re$ and $L/D$, leading to nine distinct flow structures, namely single bluff-body flow, deflected flow, flip-flopping flow, steady symmetric flow, steady asymmetric flow, hybrid flow, anti-phase flow, in-phase flow and fully developed in-phase co-shedding flow. The time-mean drag and lift of each cylinder are more sensitive to $L/D$ than $Re$ while fluctuating forces are less sensitive to $L/D$ than $Re$. The three-dimensionality of the flow affects the development of the wake patterns, changing the $L/D$ ranges of different flow structures. A diagram of flow regimes, together with the contours of hydrodynamic forces, in the $Re-L/D$ space, is given, providing physical insights into the complex interactions of the three cylinders.

JFM Papers
© The Author(s), 2020. Published by Cambridge University Press

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