四螺杆扰动下粘性流体混沌动力学特性研究
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摘要
在螺杆的周期性扰动下,聚合粘性物流体在螺杆挤出机内的运动具有混沌特性。区别于传统欧拉方法,从Lagrangian新视角分析了四螺杆扰动下粘性流体的混沌动力学特性。基于有限时间不变流形理论,计算了四螺杆挤出机不同初始时刻位的有限时间Lyapunov指数FTLE和拉格朗日拟序结构LCS;利用LCS准边界特性分析了四螺杆挤出系统不同区域的流体运动的动力学特性,指出了抑制和促进四螺杆流体输运的局部区域;结合Poincaré截面验证了分析结果的正确性。结果表明,在同向旋转四螺杆的周期性扰动作用下,四螺杆挤出机中心区由LCS包围,成为流体输运的死区。通过改变螺杆的扰动方向,可以消除中心区LCS的封闭结构,强化异向旋转四螺杆挤出机的物质交换,有效提高了设备的混合效率。
Under the periodic disturbance of the screws,the fluid motion of viscous polymer melt in the screw extruder has the characteristics of chaos.Different from the traditional Euler method,in this paper,the Lagrangian method was used to investigate the fluid transport properties in the four-screw extruders.Based on the finite time invariant manifold theory,the finite time Lyapunov exponent(FTLE) and Lagrangian coherent structures(LCS) of the four-screw extruders were calculated considering the different initial time.The LCS as a boundary separated three regions with different mixing characteristics in the screw extruders,in which the local regions with poor or good mixing performances were also identified.The accuracy of LCS patterns was verified by comparing with Poincaré section.The results show that the center region of the co-rotating four-screw extruder is surrounded by a closed LCS under the periodic disturbance of the co-rotating four screws.Therefore,the center region is a dead region of fluid transportation.By changing the rotating direction of the four screws,the closed LCS surrounding the center region is eliminated.This results in the increase of material exchange and mixing efficiency in the counter-rotating four-screw extruder.
Under the periodic disturbance of the screws,the fluid motion of viscous polymer melt in the screw extruder has the characteristics of chaos.Different from the traditional Euler method,in this paper,the Lagrangian method was used to investigate the fluid transport properties in the four-screw extruders.Based on the finite time invariant manifold theory,the finite time Lyapunov exponent(FTLE) and Lagrangian coherent structures(LCS) of the four-screw extruders were calculated considering the different initial time.The LCS as a boundary separated three regions with different mixing characteristics in the screw extruders,in which the local regions with poor or good mixing performances were also identified.The accuracy of LCS patterns was verified by comparing with Poincaré section.The results show that the center region of the co-rotating four-screw extruder is surrounded by a closed LCS under the periodic disturbance of the co-rotating four screws.Therefore,the center region is a dead region of fluid transportation.By changing the rotating direction of the four screws,the closed LCS surrounding the center region is eliminated.This results in the increase of material exchange and mixing efficiency in the counter-rotating four-screw extruder.
引文
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[4] Nakayama Y,Takeda E,Shigeishi T,et al.Melt-mi-xing by novel pitched-tip kneading disks in a co -rotating twin-screw extruder [J].Chemical Engineering Science,2011,66(1):103-110.
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[6] 焦哲,符松.高速转动圆盘流动数值模拟研究[J].计算力学学报,2016,33(4):588-593.(JIAO Zhe,FU Song.Numerical investigation of flows between rotating disks[J].Chinese Journal of Computational Mechanics,2016,33(4):588-593.(in Chinese))
[7] Polyflow.User’s guide,Version 3.10.0.Chapter 20,2003.
[8] Tang J N,Tseng C C,Wang N F.Lagrangian-based investigation of multiphase flows by finite -time Lyapunov exponents [J].Acta Mechanica Sinica,2012,28(3):612-624.
[9] Farazmand M,Haller G.Attracting and repelling Lagrangian coherent structures from a single computation [J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2013,23(2):023101.
[10] Robinson M,Cleary P W.The influence of cam geo -metry and operating conditions on chaotic mixing of viscous fluids in a twin cam mixer[J].AIChE Journal,2011,57(3):581-598.
[11] Ryrie S C.Mixing by chaotic advection in a class of spatially periodic flows[J].Journal of Fluid Mechanics,1992,236:1-26.
[12] Rubion G,Borgogno D,Veranda M,et al.Detection of magnetic barriers in a chaotic domain:First application of finite time Lyapunov exponent method to a magnetic confinement configuration [J].Plasma Physics and Controlled Fusion,2015,57(8):085004.
[13] Anderson P D,Galaktiono O S,Peters G W M,et al.Mixing of non-Newtonian fluids in time-periodic cavity flows [J].Journal of Non -Newtonian Fluid Mechanics,2000,93(2-3):265-286.