Numerical simulation of distributive mixing under a pair of triangular cams

doi:10.11949/0438-1157.20200040

Abstract

Abstract:

The mixing process of a highly viscous Newtonian fluid in a cavity stirred by a pair of triangular cams with different staggered angles was investigated numerically. Owing to the symmetry and period of the moving cams, only one-third of the period was calculated by a transient finite element method (FEM) combined with the mesh superposition technique (MST). A fourth-order Runge-Kutta scheme was developed to execute particle tracking based on periodic velocity fields. Mixing was characterized in terms of Poincaré sections, a Lagragian coherent structure (LCS), and a variance index of mixing. The results showed that mixing and energy consumption were insensitive to the different staggered angles. All cases approached the same asymptotical value of the variance index of mixing and shared a similar mixing mechanism where partially chaotic mixing was embedded with regular laminar Komogorov-Arnold-Moser (KAM) islands.

Key words: computational fluid dynamics, laminar mixing, Lagragian coherent structure, chaos, triangular cams

摘要：

以高黏度牛顿流体为研究对象，采用数值模拟方法研究了不同错列角的三角形转子搅拌作用下的腔内的混合过程。根据运动转子的对称性和周期性，用瞬态有限元法（FEM）结合网格叠加技术（MST）计算了三分之一的周期。提出了一种基于周期速度场的四阶Runge-Kutta算法。采用Poincaré截面、拉格朗日相干结构和混合方差指数等对混合进行表征。结果表明，不同错列角对混合和能耗的影响不明显，所有的混合情况都接近于相同的混合方差指数的渐近值，并具有相似的混合机制，属于部分混沌混合，贴近转子各边嵌入了规则的层流KAM（Komogorov-Arnold-Moser）岛。

关键词: 计算流体力学, 层流混合, 拉格朗日相干结构, 混沌, 三角形转子

CLC Number:

O 315.2

Baiping XU, Biao LIU, Yao LIU, Shouzai TAN, Yaoxue DU, Chuntai LIU. Numerical simulation of distributive mixing under a pair of triangular cams[J]. CIESC Journal, 2020, 71(8): 3545-3555.

徐百平, 刘彪, 刘尧, 谭寿再, 杜遥雪, 刘春太. 不同错列角三角形转子作用下的分布混合数值模拟[J]. 化工学报, 2020, 71(8): 3545-3555.

Figures/Tables 11

Fig.1 Basic geometry of a cavity stirred by a pair of triangular cams with different staggered angles

Fig.2 Meshing for the computational model at t = 0 for a zero staggered angle

Fig.3 The velocity vector distribution of different error angles at time t=0

Fig.4 Different staggered angular velocity vector profiles

Fig.5 Poincaré cross sections of different staggered angles

Fig.6 Sensitivity of FTLE of p3 using different values of time interval, initial circle radius and point number

Fig.7 The distribution of FTLE value of different staggered angles at t = T / 3

Fig.8 Two-period evolution picture of tracer released from p3

Fig.9 Particle evolutions and mixing variance indices until t = 9T (1080s) initially released from the clusters centered at p1

Fig.10 Particle group evolutions initially released from the clusters centered at p4

Fig.11 Power consumptions for different staggered angles

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