Abstract:

The intra-cavity mixing behavior under the action of a triangular rotor represents a typical mixing problem and has broad engineering application potential. In order to further improve distributive mixing, three enhancement ways were proposed in this paper, including increasing the edge length of the cams, changing cam shapes by perturbation method, and changing the cam topology. Allowing for the rotation periodicity of cams, using the mesh superposition technique, the numerical simulation models of the highly viscous fluid flow under the actions of different cam pairs were established and the instantaneous velocity fields were then solved. The investigations on the mixing dynamics were performed by using the self-developed Runge-Kutta scheme with fourth-order precession. The mixing behaviors were characterized in terms of Lagrangian coherent structures (LCS), interface stretch of tracer lines, and Poincaré cross section. When the edge length equals to 40 mm, two independent Komogorov-Arnold-Moser (KAM) islands turn up surrounding the left and right cams; when the cam edge length is increased up to 45 mm, the mixing mechanism inside the cavity is completely changed where single one KAM island wanders around the left and right sub-cavities along the quasi-periodic orbit of double loop connection orbit, consequently resulting in the best distributive mixing. Compared with changing cam shape, changing cam topology can achieve better mixing with lower power consumption, however, as the edge length of 40 mm does, the mixing mechanism where two independent KAM islands surround the left and right cams remains unchanged.

Key words: mixing, triangular cam, numerical simulation, fluid dynamics, Lagrangian coherent structures

摘要：

三角形转子作用下的腔内混合行为代表了典型的混合问题，具有广泛的工程应用潜力。为进一步改善分布混合，提出了增加转子边长、转子形状摄动变形以及改变转子拓扑结构等三种强化混合的方法。考虑转子运动的周期性，采用有限元叠加网格技术，建立了不同转子作用下的高黏度流体流动的数值模拟模型，求解得到瞬态速度场。采用自行开发的具有4阶精度的Runge-Kutta代码开展流体混合动力学研究。借助拉格朗日相干结构、示踪剂界面拉伸以及Poincaré 截面等对搅拌腔内的分布混合行为进行表征。当转子边长为40 mm时，腔内出现围绕左右转子的两个独立的Komogorov-Arnold-Moser （KAM）岛；当边长增加到45 mm时，腔内的混合机理发生了改变，KAM岛演变为1个，并且沿着联通双环准周期轨道扫掠左右腔，提升分布混合的效果最好。相比改变转子形状，改变拓扑结构更有利于提升分布混合，而且功率消耗更低，但混合机理与转子边长40 mm时相同。

关键词: 混合, 三角形转子, 数值模拟, 流体动力学, 拉格朗日相干结构