三维曲面腔顶盖驱动流的MRT-LBM研究

采用多松弛时间格子玻尔兹曼方法(MRT-LBM)的D3Q15模型分别对长方体腔、圆柱腔、半圆柱腔、旋转双曲面腔、旋转椭球面腔、半球腔以及两种组合腔体的三维顶盖驱动腔流进行数值模拟, 比较分析各腔体内流线分布、流速等值线分布和涡心的发展, 对于典型腔体模拟不同雷诺数下的流动情况。结果表明: 在同一雷诺数下, 曲面边界不仅能消除从边界产生的次涡, 还会导致腔内主涡的分离, 增大中心纵剖面纵向回流速度; “上长方体+下半圆柱”腔内流函数分布与边界贴合度最高。当雷诺数不断增大时, 半圆柱腔内主涡逐渐分离成两个同向涡, “上圆柱+下半球”腔内始终保持着圆柱腔与半球腔内的基本流动特征; 而长方体腔内主涡涡心保持在同一高度, 次涡逐渐增强, “上长方体+下半圆柱”腔内流动愈加规则, 主涡逐渐下沉, 流速等值线分布逐渐趋于中心小、四周大。

Flow Patterns in Three-dimensional Lid-driven Cavities with Curved Boundary: MRT-LBM Study

D3Q15 model of multi-relaxation time lattice Boltzmann method(MRT-LBM) is applied to simulate flow in three-dimensional lid-drive cavities with different curved boundaries, including rectangular cavity, cylindrical cavity, semi-cylinder cavity, rotating hyperboloid cavity, ellipsoid cavity, hemisphere cavity and two combined cavities. Streamlines, velocity contours and vortex positions of these cavities are analyzed. Flow characteristics of typical cavities with various Reynolds numbers are compared. It shows that under same Reynolds numbers the curved boundary eliminates the second and third vortices caused by the boundary. It leads to the separation of the main vortex in the cavity and increases the vertical reflux velocity of the central profile. Streamlines of the combined cavity with cuboid up semi-cylinder are fit most with the boundary. As the Reynolds number is increasing, the main vortex in the semi-cylindrical cavity separates gradually into two homodromous vortices, and the basic flow characteristics of the cylindrical cavity and the hemispheric cavity are always maintained in the cavity with cylinder up hemisphere; While the main vortex center in the cuboid cavity remains at the same height, the secondary vortex is gradually enhanced, and the flow in the cavity becomes more and more regular in the combined cavity with cuboid up semi-cylinder, the main vortex gradually sinks, and the flow velocity is smaller at the center and is greater near the boundary in the combined cavity with cuboid up semi-cylinder.