平行三螺杆挤出机聚合物混沌混合的拉格朗日拟序结构分析
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摘要
从拉格朗日拟序结构的新视角,对三螺杆挤出机二维流场的动力学特性进行有限元分析。采用4阶Runge-Kutta法计算粒子的运动轨迹,验证了时间步长对计算结果精确度的影响。利用有限时间李雅普诺夫指数(FTLE),Poincaré截面和粒子可视化技术分析了三螺杆挤出机流场的混沌混合机理。结果表明,拉伸和折叠作用促进了流体粒子的物质交换。由于在啮合区存在双曲不动点,混合效率较高,啮合区是流场混沌混合的主要区域;在紧靠螺杆壁区域,物质线的闭合导致流体输运受阻,近螺杆区混合效果较差。通过与双螺杆挤出机进行拉格朗日拟序结构(LCS)结构的比较发现,由于啮合区的增加,强化了挤出机流场的混沌混合;通过对数拉伸值的比较,三螺杆挤出机的混合能力优于双螺杆挤出机。
From a new viewpoint of Lagrangian coherent structure,the ?nite element analysis of dynamic characteristics was used to analyze the two-dimensional ?ow ?eld of a tri-screw extruder. The trajectory of particles was calculated by using the fourth order Runge-Kutta scheme to validate the time step of the simulation method. Finite-time Lyapunov exponent(FTLE),Poincaré section and particle visualization technology were adopted to analyze the ?ow chaotic mixing mechanism in the tri-screw extruder. The results show that stretching and folding actions promote the material exchange of ?uid particles. In nip region,which is the main area of chaotic mixing,the mixing ef?ciency is high due to the existence of hyperbolic ?xed point.In the near wall region,the mixing effect is poor due to the ?uid transposition is hampered by the closed material line. Compared with the Lagrangian coherent structure(LCS) of twin screw extruder ?ow ?eld,the tri-screw extruder has more meshing arear to strengthen the chaotic mixing of the extruder.In the end,the logarithmic stretching was used to analyze the mixing ability,which demonstrate the mixing ability in the triscrew extruder is better than that of the twin screw extruder.
From a new viewpoint of Lagrangian coherent structure,the ?nite element analysis of dynamic characteristics was used to analyze the two-dimensional ?ow ?eld of a tri-screw extruder. The trajectory of particles was calculated by using the fourth order Runge-Kutta scheme to validate the time step of the simulation method. Finite-time Lyapunov exponent(FTLE),Poincaré section and particle visualization technology were adopted to analyze the ?ow chaotic mixing mechanism in the tri-screw extruder. The results show that stretching and folding actions promote the material exchange of ?uid particles. In nip region,which is the main area of chaotic mixing,the mixing ef?ciency is high due to the existence of hyperbolic ?xed point.In the near wall region,the mixing effect is poor due to the ?uid transposition is hampered by the closed material line. Compared with the Lagrangian coherent structure(LCS) of twin screw extruder ?ow ?eld,the tri-screw extruder has more meshing arear to strengthen the chaotic mixing of the extruder.In the end,the logarithmic stretching was used to analyze the mixing ability,which demonstrate the mixing ability in the triscrew extruder is better than that of the twin screw extruder.
引文
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[15]王佳男,王嘉骏,冯连芳,等.弯曲微通道中液滴内混合过程的数值模拟研究[J].高校化学工程学报,2014,28(2):218-222.Wang Jianan,Wang Jiajun,Feng Lianfang,et al.Numerical study on fluids mixing based on droplet flows in serpentine microchannels[J].Journal of Chemical Engineering of Chinese Universities,2014,28(2):218-222.
[2]Jones C,Winkler S.Handbook of dynamical systems[M].Towards Application,World Scientific,2002.55-92.
[3]朱向哲,袁惠群.三螺杆挤出机挤出特性的数值模拟[J].高分子材料科学与工程,2008,24(3):32-35.Zhu Xiangzhe,Yuan Huiqun.Numerical simulation of extrusion characteristics of intermeshing co-rotating tri-screw extruder[J].Polymer Materials Science and Engineering.2008,24(3):32-35.
[4]程志飞,何延东,朱向哲,等.Roller转子密炼机聚合物流体的混沌混合特性[J].高分子材料科学与工程,2013,43(12):128-132.Cheng Zhifei,He Yandong,Zhu Xiangzhe,et al.Chaotic mixing of polyer melt in internal mixer with roller rotors[J].Polymer Materials Science and Engineering,2013,43(12):128-132.
[5]Xu Baiping,Kuang Tangqing,Yu Huiwen,et al.Enhancement of mixing by different baffle arrays in cavity flows[J].Chemical Engineering Science,2015,137:837-851.
[6]Haller G,Yuan G.Lagrangian coherent structures and mixing in two-dimensional turbulence[J].Chaos,2000,10(1):99-108.
[7]Haller G,Yuan G.Lagrangin coherent structures and mixing in twodimensional turbulence[J].Physica D Nonlinear Phenomena,2000,147:352-370.
[8]Shadden S C,Lekien F,Marsden J E.Definition and properties of Lagrangian coherent structures from-finite Lyapunov exponents in two-dimensional aperiodic flows[J].Physica D Nonlinear Phenomena,2005,212(3):271-304.
[9]Lekien Francois,Shadden Shawn C,Marsden Jerrold E.Lagrangian coherent structures in n-dimensional systems[J].Journal of Mathematical Physics,2007,48:1-19.
[10]高鹤,朱向哲,佟莹,等.4WS转子密炼机聚合物混沌混合的拉格朗日拟序结构分析[J].高校化学工程学报,2016,30(6):1 274-1 283.Gao He,Zhu Xiangzhe,Tong Ying,et al.Lagrangian coherent structure analysis of chaotic mixing in an internal batch mixer with 4ws rotors[J].Journal of Chemical Engineering of Chinese Universities,2016,30(6):1 274-1 283.
[11]佟莹,高鹤,朱向哲,等.三螺杆挤出机啮合块端面二维流场混沌混合拉格朗日拟序结构分析[J].化工学报,2016,67(10):4 378-4 388.Tong Ying,Gao He,Zhu Xiangzhe,et al.Analysis of 2D flow chaotic mixing at cross section of tri-screw extruder by Lagrangian coherent structure[J].CIESC Journal,2016,67(10):4 378-4 388.
[12]Green M A,Rowley C W,Haller G.Detection of Lagrangian coherent structures in three-dimensional turbulence[J].Journal of Fluid Mechanics,2007,572(1):111-120.
[13]Ottino J M.The kinematics of mixing:stretching,chaos,and transport[M].New York:Cambridge University Press;1989.
[14]孟宇,朱向哲,刘俭.棱顶间隙对4WS密炼机流体混合特性影响[J].石油化工高等学校校报,2018,31(5):77-83.Meng Yu,Zhu Xiangzhe,Liu Jian.Effects of different clearance on the mixing characteristics in the 4WS internal mixer[J].Journal of Petrochemical Universities,2018,31(5):77-83.
[15]王佳男,王嘉骏,冯连芳,等.弯曲微通道中液滴内混合过程的数值模拟研究[J].高校化学工程学报,2014,28(2):218-222.Wang Jianan,Wang Jiajun,Feng Lianfang,et al.Numerical study on fluids mixing based on droplet flows in serpentine microchannels[J].Journal of Chemical Engineering of Chinese Universities,2014,28(2):218-222.