层流搅拌流动中的混合动力学与输运机制

中文摘要 AI 辅助

我们研究了在充满牛顿流体的无限二维域中，被动染料的层流混合，通过模拟一个沿圆形路径以恒定速度旋转的圆柱形搅拌器来搅拌初始静止的流体。流体在下半部分被被动染料标记，从而能够系统分析染料界面的演化和混合动力学。通过在层流范围内改变搅拌雷诺数，我们确定了流动拓扑的转变如何控制混合，并区分了涵盖扩散主导混合和对流混合的三个混合区域。在扩散主导区域，混合的特征是形成充分混合的中心区域，以及以近似自相似方式演化的螺旋染料图案的发展。对流混合的标志是中心区域之外染料界面的显著变形。我们通过将混合事件与特定的流动特征联系起来，提供了对流混合的机理解释：（i）搅拌器与染料界面的直接相互作用，以及（ii）搅拌器附近和中心区域之外的涡脱落。当涡结构能够逃离中心区域并非局域地输运标量梯度时，混合得到增强。当涡活动仍局限于搅拌器路径附近时，尽管搅拌强度增加，每个搅拌周期的混合仅表现出对搅拌速度的弱依赖性。只有当逃逸的涡引入一种新的输运机制，将标量梯度携带到远超搅拌器路径的地方时，每个周期的混合才会显著增强。总体而言，我们通过识别流动特征控制标量演化的输运机制，提出了流动拓扑与混合之间的机理联系，为混合的运动学与底层流体动力学之间架起了桥梁。

英文摘要

We investigate laminar mixing of a passive dye in an infinite, two-dimensional domain filled with a Newtonian fluid by simulating a cylindrical stirrer that rotates at constant speed along a circular path, stirring an initially quiescent fluid. The fluid is marked by a passive dye in the lower half of the domain, enabling a systematic analysis of dye-interface evolution and mixing dynamics. By varying the stirring Reynolds number within the laminar regime, we identify how transitions in flow topology govern mixing and distinguish three mixing regimes spanning diffusion-dominated and advective mixing. In the diffusion-dominated regime, mixing is characterized by the formation of a well-mixed central region and the development of a spiral dye pattern that evolves in an approximately self-similar manner. Advective mixing is marked by substantial deformation of the dye interface beyond the central region. We provide a mechanistic interpretation of advective mixing by relating mixing events to specific flow features: (i) direct interaction between the stirrer and the dye interface, and (ii) vortex shedding near the stirrer and away from the central region. Enhanced mixing occurs when vortical structures are able to escape the central region and transport scalar gradients nonlocally. When vortical activity remains confined near the stirrer's path, mixing per stirrer period exhibits only weak dependence on stirring speed despite increasing stirring intensity. Significant enhancement of mixing per period occurs only when escaping vortices introduce a new transport mechanism that carries scalar gradients far beyond the stirrer's path. Overall, we present a mechanistic link between flow topology and mixing by identifying the transport mechanisms through which flow features govern scalar evolution, providing a bridge between the kinematics of mixing and the underlying fluid dynamics.

发表机构

• Concordia University（康考迪亚大学）

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