The mixing in three-dimensional enclosures is investigated numerically using flow in cubical cavity as a geometrically simple model of various natural and engineering flows. The mixing rate is evaluated for up to the value of Reynolds number $$\hbox {Re}=2000$$ Re = 2000 for several representative scenarios of moving cavity walls: perpendicular motion of the parallel cavity walls, motion of a wall in its plane along its diagonal, motion of two perpendicular walls outward the common edge, and the parallel cavity walls in motion either in parallel directions or in opposite directions. The mixing rates are compared to the well-known benchmark case in which one cavity wall moves along its edge. The intensity of mixing for the considered cases was evaluated for (i) mixing in developing cavity flow initially at rest, which is started by the impulsive motion of cavity wall(s), and (ii) mixing in the developed cavity flow. For both cases, the initial interface of the two mixing fluids is a horizontal plane located at the middle of the cavity. The mixing rates are ranked from fastest to slowest for twenty time units of flow mixing. The pure convection mixing is modeled as a limit case to reveal convective mechanism of mixing. Mixing of fluids with different densities is modeled to show the advantage in terms of mixing rate of genuinely 3D cases. Grid convergence study and comparison with published numerical solutions for 3D and 2D cavity flows are presented. The effects of three-dimensionality of cavity flow on the mixing rate are discussed.

中文翻译：

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通过移动腔壁在三维腔中混合

使用立方体腔中的流动作为各种自然和工程流动的几何简单模型，对三维外壳中的混合进行了数值研究。对于移动腔壁的几种代表性场景，混合率的评估高达雷诺数 $$\hbox {Re}=2000$$ Re = 2000：平行腔壁的垂直运动，壁在其内部的运动沿其对角线的平面，两个垂直壁在公共边缘外的运动，以及平行的空腔壁在平行方向或相反方向运动。混合速率与众所周知的基准案例进行比较，其中一个腔壁沿其边缘移动。对所考虑情况的混合强度进行评估，用于 (i) 最初在静止状态下发展腔流中的混合，这是由腔壁的脉冲运动开始的，以及（ii）在发展的腔流中混合。对于这两种情况，两种混合流体的初始界面是位于空腔中间的水平面。对于二十个时间单位的流动混合，混合速率从最快到最慢排列。纯对流混合被建模为一个极限情况，以揭示混合的对流机制。对不同密度流体的混合进行建模，以显示真正 3D 案例在混合率方面的优势。介绍了网格收敛研究以及与已发表的 3D 和 2D 腔流数值解的比较。讨论了空腔流动的三维度对混合速率的影响。两种混合流体的初始界面是位于空腔中部的水平面。对于二十个时间单位的流动混合，混合速率从最快到最慢排列。纯对流混合被建模为一个极限情况，以揭示混合的对流机制。对不同密度流体的混合进行建模，以显示真正 3D 案例在混合率方面的优势。介绍了网格收敛研究以及与已发表的 3D 和 2D 腔流数值解的比较。讨论了空腔流动的三维度对混合速率的影响。两种混合流体的初始界面是位于空腔中部的水平面。对于二十个时间单位的流动混合，混合速率从最快到最慢排列。纯对流混合被建模为一个极限情况，以揭示混合的对流机制。对不同密度流体的混合进行建模，以显示真正 3D 案例在混合率方面的优势。介绍了网格收敛研究以及与已发表的 3D 和 2D 腔流数值解的比较。讨论了空腔流动的三维度对混合速率的影响。纯对流混合被建模为一个极限情况，以揭示混合的对流机制。对不同密度流体的混合进行建模，以显示真正 3D 案例在混合率方面的优势。介绍了网格收敛研究以及与已发表的 3D 和 2D 腔流数值解的比较。讨论了空腔流动的三维度对混合速率的影响。纯对流混合被建模为一个极限情况，以揭示混合的对流机制。对不同密度流体的混合进行建模，以显示真正 3D 案例在混合率方面的优势。介绍了网格收敛研究以及与已发表的 3D 和 2D 腔流数值解的比较。讨论了空腔流动的三维度对混合速率的影响。