Abstract: Flow field in a stirred vessel is usually divided into chaotic and regular mixing regions. It is an alternative way to improve mixing performance and lower the energy consumption by enlarging chaotic mixing region. Reasonable design of impeller is helpful to form appropriate flow condition and to improve the fluid mixing efficiency. Rigid-flexible combination can be designed by flexible body and rigid body with multiple-body motion behavior, intensifying the chaotic mixing. In this study, with the software Matlab, the largest Lyapunov exponent and multi-scale entropy in the tap water mixing system are investigated with double mechanical impellers. The difference between rigid and rigid-flexible impellers is analyzed in mixing performance. Results show that the rigid-flexible impeller enhances fluid movement and the fluid goes into chaotic mixing. At 210 r·min^-1,the fluid is chaotic mixing, and the largest Lyapunov exponent is 0.041 for rigid impeller, while it is 0.048 for rigid-flexible impeller. The rigid-flexible impeller could transfer energy effectively and make the energy distribute uniformly. At agitation speed 150 r·min^-1, the multi-scale entropy rate of rigid-flexible impeller is similar to that of rigid one at 210 r·min^-1. Compared with rigid impeller system, the mixing time is shortened by about 26% with rigid-flexible impeller system. The rigid-flexible impeller could enhance the fluid chaotic mixing and save energy by changing the flow field structure and energy dissipation.

Key words: mixing, stirred vessel, transfer, chaos, largest Lyapunov exponent, multi-scale entropy, rigid-flexible impeller

摘要： 搅拌槽内普遍存在着两种不同类型的混合区域：混沌混合区和规则区。增大混沌混合区，是提高流体混合效率、降低搅拌过程能耗的重要途径。而合理设计搅拌桨有助于流体形成适宜的流动状态，实现混沌混合。柔性体与刚性体组合，可设计出具有多体运动行为的刚柔组合搅拌桨，可强化流体混沌混合行为。结合Matlab 软件，实验研究了双层桨搅拌槽内自来水体系的最大Lyapunov指数（LLE）和多尺度熵（MSE）的变化规律，对比分析了刚性桨和刚柔组合桨两种桨叶对流体混沌混合的影响。结果表明，刚柔组合桨强化流体的运动特性，使更多流体进入混沌混合状态。在转速为210 r·min^-1时，流体的混沌混合达到最佳状态，刚性桨体系的LLE为0.041，而刚柔组合桨体系的LLE为0.048；刚柔组合桨可有效耗散能量，使整个槽体的能量分布均匀，刚柔组合桨在150 r·min^-1时的多尺度熵率与刚性桨在210 r·min^-1时基本相近；刚柔组合桨体系的混合时间均低于刚性桨体系，在转速为120 r·min^-1时，刚柔组合桨使流体的混合时间缩短了26%左右。刚柔组合桨可改变流场结构和能量耗散方式，强化流体混沌混合，实现高效节能操作。

关键词: 混合, 搅拌槽, 传递, 混沌, 最大Lyapunov指数, 多尺度熵, 刚柔组合桨