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.

中文翻译：

---

流过等边三角形排列的三个圆柱体的数值模拟

使用浸入边界法对通过三个相同圆柱体的流动进行数值研究。气缸排列成等边三角形配置，一个气缸放置在上游，另外两个并排放置在下游。重点是间距比 $L/D(=1.0{-}6.0)$ 、雷诺数 $Re(=50{-}300)$ 和三维度对流动结构、水动力和 Strouhal 的影响数字，其中 $L$ 是圆柱中心距，$D$ 是圆柱直径。所涉及的流体动力学对 $Re$ 和 $L/D$ 高度敏感，导致九种不同的流动结构，即单钝体流、偏转流、翻转流、稳态对称流、稳态非对称流、混合流、反相流、同相流和完全发展的同相共脱落流。每个气缸的时间平均阻力和升力对 $L/D$ 比 $Re$ 更敏感，而波动力对 $L/D$ 的敏感度低于 $Re$。流动的三维度影响尾流模式的发展，改变不同流动结构的 $L/D$ 范围。给出了 $Re-L/D$ 空间中的流态图以及流体动力的轮廓，提供了对三个圆柱体复杂相互作用的物理见解。