The fluid flow over three staggered square cylinders at two symmetrical arrangements has been numerically investigated in this study. The numerical calculations are carried out for several values of the Reynolds number (Re) ranging from 1 to 180. The results are presented in the form of vorticity contours and temporal histories of drag and lift coefficients. Furthermore, the physical parameters, namely, the average drag and lift coefficients and Strouhal number are presented as a function of Re. Two different states of flow are found in this work by systematically varying Re: steady and unsteady states. The transition to unsteady state regime is exhibited via Hopf bifurcation first in the second configuration followed consequently by the first one with critical Reynolds number of Re[Formula: see text] and Re[Formula: see text], respectively. It is observed that the bifurcation point of the steady regime to the unsteady one is very much influenced by the change in the geometry of the obstacle. The unsteady periodic wake is characterized by the Strouhal number, which varies with the Reynolds number and the obstacle geometry. Hence, the values of vortex shedding frequencies are estimated for both the considered configurations. Computations obtained also reveal that the spacing in the wake leads to reducing the pressure and enhancing the fluid flow velocity for both arrangements by monotonically strengthening the Reynolds number value. Furthermore, the drag and lift coefficients are determined, which allowed determining; the best configuration in terms of both lift and drag. It is observed that the drag force is dependent on the obstacle geometry and strengthens while lowering the Reynolds number. On the other hand, an opposite trend of the lift drag evolutions is observed for both configurations and considerably affected by the arrangements shape.

中文翻译：

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通过数值研究确定两个对称排列的三个交错方形圆柱体周围的流动状态

本研究对两种对称排列的三个交错方形圆柱体上的流体流动进行了数值研究。数值计算是针对雷诺数 (Re) 范围从 1 到 180 的几个值进行的。结果以涡量等值线和阻力和升力系数的时间历史的形式呈现。此外，物理参数，即平均阻力和升力系数以及 Strouhal 数作为 Re 的函数表示。通过系统地改变 Re，在这项工作中发现了两种不同的流动状态：稳态和非稳态。向不稳定状态的过渡首先在第二种配置中通过 Hopf 分岔表现出来，然后是第一个具有 Re[公式：参见文本]和 Re[公式：参见文本]的临界雷诺数的第一个，分别。可以观察到，稳态到非稳态的分岔点很大程度上受障碍物几何形状变化的影响。非定常周期性尾流以斯特劳哈尔数为特征，随雷诺数和障碍物几何形状而变化。因此，为两种考虑的配置估计了涡旋脱落频率的值。获得的计算还表明，尾流中的间距通过单调增强雷诺数值导致两种布置的压力降低并提高流体流速。此外，确定阻力和升力系数，这允许确定；在升力和阻力方面的最佳配置。据观察，阻力取决于障碍物的几何形状，并在降低雷诺数的同时增强。另一方面，两种配置都观察到升力阻力演变的相反趋势，并且受布置形状的影响很大。