基于拉格朗日的单螺杆销钉挤出机混沌混合分析
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摘要
从拉格朗日理论的新视角,分析了高分子聚合物熔体在单螺杆销钉挤出机内的流型结构以及流动行为,揭示了销钉强化聚合物熔体输运和混沌混合的机理。使用有限元软件Polyflow计算了流场的速度分布和混合指数;借助Matlab数学软件进行自主编程对速度场进行积分得到了三种不同销钉挤出机模型的有限时间李雅普诺夫指数。结果显示,在加入销钉之后,单螺杆销钉挤出机流域中出现了圆柱绕流现象,绕流产生的尾迹将撞击螺棱,销钉和螺棱的这种相互作用将加剧聚合物熔体的拉伸作用。每个销钉都将产生尾迹,随着销钉数量的增加,导致流域中产生了更多的尾迹。尾迹与销钉相互作用得到了增强,导致流域中产生了更多的涡结构,说明流域中的大部分熔体处于混沌混合的状态。混沌混合使销钉挤出机内的流体拉伸作用得到了增强,流体的混合指数得到增加,混合效率也逐渐增大。
The flow pattern of high molecular polymer fluid in a single screw extruder was analyzed from the new viewpoint of Lagrange theory,which revealed the mechanism of the pin strengthing polymer melt transport and chaotic mixing of the flow field.The velocity distribution and mixing index of the flow field were calculated by the finite element software Polyflow. Besides,with the help of Matlab software,autonomous programming was used to intergrate the velocity field and then the finite time Lyapunov exponent of three pin screw extruder models was obtained. The results show that after the pin is added,the flow around the circular cylinder appear in the basin of the extruder of the single screw pin. The wake generated by the flow will impact the spirial,and the interaction between the pin and the screw will aggrarate the tensile effect of the polymer melt. Each pin will generate the wake and with the increase of pin number,more wakes will be generated in the basin. The interaction between the wake and the pin is enhanced, resulting in more vortex structure in the basin which suggest the polymer melt is in a state of chaotic mixing. Chaotic mixing enhances the fluid stretching effect,mixing index and the mixing efficiency in the pin screw extruder.
The flow pattern of high molecular polymer fluid in a single screw extruder was analyzed from the new viewpoint of Lagrange theory,which revealed the mechanism of the pin strengthing polymer melt transport and chaotic mixing of the flow field.The velocity distribution and mixing index of the flow field were calculated by the finite element software Polyflow. Besides,with the help of Matlab software,autonomous programming was used to intergrate the velocity field and then the finite time Lyapunov exponent of three pin screw extruder models was obtained. The results show that after the pin is added,the flow around the circular cylinder appear in the basin of the extruder of the single screw pin. The wake generated by the flow will impact the spirial,and the interaction between the pin and the screw will aggrarate the tensile effect of the polymer melt. Each pin will generate the wake and with the increase of pin number,more wakes will be generated in the basin. The interaction between the wake and the pin is enhanced, resulting in more vortex structure in the basin which suggest the polymer melt is in a state of chaotic mixing. Chaotic mixing enhances the fluid stretching effect,mixing index and the mixing efficiency in the pin screw extruder.
引文
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[3]徐百平,瞿金平,刘跃军,等.单螺杆挤出机中三维流动有限体积数值模拟[J].化工学报,2008,59(12):3 055–3 060.Xu Baiping,Qu Jinping,Liu Yuejun,et al.Numerical simulation of three-dimensional flow in single screw extruder by finite volume method[J].Journal of chemical industry and engineering(China),2008,59(12):3 055–3 060.
[4]毕超,江波.往复式单螺杆销钉挤出机停留时间分布研究[J].工程塑料应用,2007,35(12):72–76.Bi Chao,Jiang Bo.Study on residence time distribution of reciprocating single screw pin screw[J].Engineering Plastics Application,2007,35(12):72–76.
[5]刘倩楠,毕超.往复式单螺杆销钉挤出机往复运动传动机理与混炼性能关系的研究[J].工程塑料应用,2013(8):66–71.Liu Qiannan,Bi Chao.Study of drive mechanism of reciprocating motion and mixing performance of reciprocating single screw pinbarrel extruder[J].Engineering plastics application,2013(8):66–71.
[6]陈晋南,姚慧,彭炯.销钉机筒挤出机混合段的混合性能[J].北京理工大学学报,2008,28(1):90–94.Chen Jinnan,Yao Hui,Peng Jiong.Mixing performance of the mixing section in a pin barrel extruder[J].Transaction of beijing institute of technology,2008,28(1):90–94.
[7]Chen Jinnan,Dai Pan,Yao Hui,et al.Numerical analysis of mixing performance of mixing section in pin-barrel single-screw extruder[J].Journal of Polymer Engineering,2001,31(1):53–62.
[8]Kim S J,Kwon T H.Enhancement of mixing performance of singlescrew extrusion processes via chaotic flow:PartⅠ.Basic concepts and experimental study[J].Advances in Polymer Technology,1996,15(1):55–69.
[9]Kim S J,Kwon T H.Enhancement of mixing performance of single-screw extrusion processes via chaotic flow:PartⅡ.Numerical study[J].Advances in Polymer Technology,1996,15(1):55–69.
[10]Lee T H,Kwon T H.A new representative measure of chaotic mixing in a chaos single-screw extruder[J].Advances in Polymer Technology,1999,18(1):53–68.
[11]Hwang W R,Jun H S,Kwon T H.Experiments on chaotic mixing in a screw channel flow[J].Aiche Journal,2002,48(8):1 621–1 630.
[12]Haller G.A variational theory of hyperbolic Lagrangian Coherent Structures[J].Physica D:Nonlinear Phenomena,2011,240(7):574–598.
[13]陆启韶.常微分方程与动力系统[M].北京:北京航空航天大学出版社,2010.Lu Qishao.Ordinary differential equations and dynamic systems[M].Beijing:Beijing University of Aeronautics and Astronautics Press,2010.
[14]Wu Jun,Pan Chong,Li Tian.Experimental investigation on coherent structures at early stage of boundary layer bypass transition induced by wake impingement[J].Science China Technological Sciences,2012,55(11):2 981–2 989.
[15]崔光耀,潘翀,高琪,等.沟槽方向对湍流边界层流动结构影响的实验研究[J].力学学报,2017,49(6):1 201–1 212.Cui Guangyao,Pan Chong,Gao Qi,et al.Flow structure in the turbulent boundary layer over directional riblets surfaces[J].Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1 201–1 212.