双螺杆挤出机强化三角形转子作用下的腔内分布混合模拟

doi:10.11949/0438-1157.20231005

摘要/Abstract

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40mm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

Abstract:

The mixing in a cavity stirred by a pair of triangular cams belongs to the representative mixing problem, which has wide engineering potentials. In order to further improve distributive mixing, the 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 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 maps. When the edge length is equal to 40 mm, two independent Komogorov-Arnold-Moser (KAM) islands turns 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

中图分类号:

O313

徐百平, 梁瑞凤, 喻慧文, 吴桂群, 肖书平. 双螺杆挤出机强化三角形转子作用下的腔内分布混合模拟[J]. 化工学报, DOI: 10.11949/0438-1157.20231005.

Baiping XU, Ruifeng LIANG, Huiwen YU, Guiqun WU, Shuping XIAO. Numerical simulation of enhancement of distributive mixing in cavity stirred by triangular cams of corotating twin screw extruders[J]. CIESC Journal, DOI: 10.11949/0438-1157.20231005.

图/表 12

图1 三角形转子对搅拌腔几何模型

Fig.1 Geometrical model of a triangular rotor pair mixing chamber

图2 三角形转子对搅拌腔几何模型，(a)流域网格划分，(b)转子网格划分

Fig.2 Triangular rotor-to-mixing chamber geometry model, (a) domain meshing, (b) rotor meshing

图3 示踪剂混合图像与可视化实验结果对比

Fig.3 Comparison of tracer mixing images and visualisation of experimental results

图4 新型转子几何结构，(a)Cam45，(b)FanS，(c)Camhole

Fig.4 New rotor geometry,(a) Cam45,(b) FanS,(c) Camhole

图5 Camhole转子叠加网格结果，(a)网格叠加t=0，(b)转子网格划分局部

Fig.5 Camhole rotor superimposed mesh results, (a) mesh superimposed t = 0, (b) local rotor meshing

图6 Cam45拉格朗日相干结构(Δt=T/3), (a) repelling LCS, (b) attracting LCS

Fig.6 Cam45 Lagrangian coherent structure (Δt=T/3), (a) repelling LCS, (b) attracting LCS

图7 Camhole位于p1点示踪粒子混合图像, (a) 0-320 s, (b) 480-600 s

Fig.7 Camhole tracer particle mixing image at point p1, (a) 0-320 s, (b) 480-600 s

图8 示踪剂s在Camhole内不同时刻混合图像, (a)0~120 s, (b) 200 s, (c) 280 s

Fig.8 Tracer s mixed images at different moments within Camhole, (a) 0~120 s, (b) 200 s, (c) 280 s

图9 不同转子混合图像对比，(a)Cam45, t=280 s, (c)FanS, t=360 s, (d)Camhole, t=360 s

Fig.9 Comparison of mixing patterns with different rotors, (a) Cam45, t=280 s, (c) FanS, t=360 s, (d) Camhole, t=360 s

图10 不同转子示踪剂s界面拉伸对比

Fig.10 Comparison of interfacial stretching of the tracer s by different rotors

图11 不同转子作用下混合过程的Poincarè截面，(a) Cam45，(b) FanS，(c) Camhole

Fig.11 Poincarè cross section of the mixing process under different rotor actions, (a) Cam45, (b) FanS, (c) Camhole

图12 不同转子作用下功率消耗

Fig.12 Power consumption with different rotor actions

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