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

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.