The Lattice Boltzmann method (LBM) has been applied for the simulation of lid-driven flows inside cavities with internal two-dimensional circular obstacles of various diameters under Reynolds numbers ranging from 100 to 5000. With the LBM, a simplified square cross-sectional cavity was used and a single relaxation time model was employed to simulate complex fluid flow around the obstacles inside the cavity. In order to made better convergence, well-posed boundary conditions should be defined in the domain, such as no-slip conditions on the side and bottom solid-wall surfaces as well as the surface of obstacles and uniform horizontal velocity at the top of the cavity. This study focused on the flow inside a square cavity with internal obstacles with the objective of observing the effect of the Reynolds number and size of the internal obstacles on the flow characteristics and primary/secondary vortex formation. The current LBM has been successfully used to precisely simulate and visualize the primary and secondary vortices inside the cavity. In order to validate the results of this study, the results were compared with existing data. In the case of a cavity without any obstacles, as the Reynolds number increases, the primary vortices move toward the center of the cavity, and the secondary vortices at the bottom corners increase in size. In the case of the cavity with internal obstacles, as the Reynolds number increases, the secondary vortices close to the internal obstacle become smaller owing to the strong primary vortices. In contrast, depending on the sizes of the obstacles ( $R/L$ = 1/16, 1/6, 1/4, and 2/5), secondary vortices are induced at each corner of the cavity and remain stationary, but the secondary vortices close to the top of the obstacle become larger as the size of the obstacle increases.

中文翻译：

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带有内部圆形障碍物的盖驱动腔流的模拟

Lattice Boltzmann方法（LBM）已用于模拟腔内盖驱动的流动，在雷诺数范围为100到5000的情况下，腔体内具有各种直径的内部二维圆形障碍物。有了LBM，简化了的方形横截面腔使用单个松弛时间模型来模拟围绕腔体内障碍物的复杂流体流动。为了更好地收敛，应在域中定义适当的边界条件，例如侧面和底部实心壁表面以及障碍物表面的防滑条件以及障碍物顶部的均匀水平速度。腔。这项研究的重点是带有内部障碍物的方腔内部的流动，目的是观察内部障碍物的雷诺数和大小对流动特性和一次/二次涡流形成的影响。当前的LBM已成功用于精确模拟和可视化腔体内的初级和次级涡旋。为了验证这项研究的结果，将结果与现有数据进行了比较。在腔体没有任何障碍的情况下，随着雷诺数的增加，初级涡流向腔体中心移动，并且位于底角的次级涡流的大小增加。对于带有内部障碍物的空腔，随着雷诺数的增加，由于强大的初级涡旋，靠近内部障碍物的次级涡旋变得更小。相反，根据障碍物的大小（ $\mathrm{[R}/\mathrm{大号}$ = 1 / 16、1 / 6、1 / 4和2/5），在空腔的每个角处都产生了次级涡流，并保持静止，但是随着障碍物的大小，靠近障碍物顶部的次级涡流变得更大。障碍增加了。