复杂型腔充模过程中分子构型演化的数值模拟

李强; 邵水军; 李世顺

doi:10.7498/aps.65.244601

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摘要

基于充模过程的两相黏弹性流体模型，采用有限体积、浸入边界和复合水平集流体体积方法，数值模拟了聚合熔体在复杂型腔中的充模过程.首先，借助一类特殊函数（R-functions）将基于基本几何体的水平集函数组合成描述复杂型腔的形状水平集函数.然后，采用浸入边界法处理复杂型腔问题，有限体积方法求解熔体控制方程，利用复合水平集流体体积方法对熔体前沿界面进行隐式追踪.基于有限伸展非线性弹性哑铃本构方程模型，计算熔体分子构型张量，通过取向椭圆描述分子的取向及拉伸行为，实现了充模过程中分子构型的可视化.最后，对带有两个圆形嵌件的环状型腔内的充模过程进行数值模拟研究，得到了充模过程中型腔内的温度、应力及分子构型的变化情况，并重点分析了充模速度、熔体温度和模具温度等对分子构型的影响.数值结果表明：本文提出的耦合模型可以成功模拟复杂型腔内充模过程中的温度、应力和分子取向等物理量的动态变化；适当提高注射速度可以增大熔接痕的强度；提升熔体温度和模具温度，可以有效改善甚至消除熔接痕.

关键词:

作者及机构信息

1.
河南理工大学数学与信息科学学院, 焦作 454000;

2.
河南理工大学机械与动力工程学院, 焦作 454000

通信作者: 邵水军, shaosj@hpu.edu.cn

基金项目: 国家自然科学基金（批准号：11401177）、河南省科技攻关项目（批准号：162102210230）、河南省教育厅基础研究计划（批准号：15A110001）和河南理工大学博士基金（批准号：B2013-057，B2012-030）资助的课题.

参考文献

[1]	Kim S W, Turng L S 2006 Polym. Eng. Sci. 46 1263
[2]	Shen C Y 2009 Simulation of Injection Molding and Theories and Methods for Optimization of Moulds Designing (Beijing:Science Press) p4(in Chinese)[申长雨2009注塑成型模拟及模具优化设计理论与方法(北京:科学出版社)第4页]
[3]	Yuan R F, Zhong C W, Zhang H 2015 J. Comput. Phys. 296 184
[4]	Cai L, Gao H, Luo X Y, Nie Y F 2015 Sci. China:Phys. Mech. Astron. 45 024702(in Chinese)[蔡力, 高昊, 罗小玉, 聂玉峰2015中国科学:物理学力学天文学 45 024702]
[5]	Ruan C L 2011 Ph. D. Dissertation (Xi'an:Northwestern Polytechnical University) (in Chinese)[阮春蕾2011博士学位论文(西安:西北工业大学)]
[6]	Baaijens H P W, Peters G W M, Baaijens F P T, Han E H M 1995 J. Rheol. 39 1243
[7]	Jiang T, Ouyang J, Ren J L 2012 Comp. Phys. Comm. 183 50
[8]	Dai J F, Fan X P, Meng B, Liu J F 2015 Acta Phys. Sin. 64 094704 (in Chinese)[戴剑锋, 樊学萍, 蒙波, 刘骥飞2015物理学报 64 094704]
[9]	Li Q 2016 Comput. Fluids 132 94
[10]	Li Q, Ouyang J, Yang B X, Li X J 2012 Appl. Math. Model. 36 2262
[11]	Ren J L, Lu W G, Jiang T 2015 Acta Phys. Sin. 64 080202 (in Chinese)[任金莲, 陆伟刚, 蒋涛2015物理学报 64 080202]
[12]	Hetu J F, Gao D M, Rejon A G, Salloum G 1998 Polym. Eng. Sci. 38 223
[13]	Mu Y, Zhao G Q, Chen A, Dong G W, Li S 2014 Comput. Chem. Eng. 63 91
[14]	Zheng S P, Ouyang J, Zhao Z F, Zhang L 2012 Comput. Math. Appl. 64 2860
[15]	Li Q, Li W M 2016 Acta Phys. Sin. 65 064601 (in Chinese)[李强, 李五明2016物理学报 65 064601]
[16]	Wang Y, Shu C, Yang L M 2016 J. Comput. Phys. 306 237
[17]	Boronat T, Segui V J, Peydro M A, Reig M J 2009 J. Mater. Process Tech. 209 2735
[18]	Isayev A I, Shyu G D, Li C T 2006 J. Polym. Sci. Pol. Phys. 44 622
[19]	Cai S Y, Zhang W H 2015 Comput. Method. Appl. M. 289 267

施引文献

[1]	Kim S W, Turng L S 2006 Polym. Eng. Sci. 46 1263
[2]	Shen C Y 2009 Simulation of Injection Molding and Theories and Methods for Optimization of Moulds Designing (Beijing:Science Press) p4(in Chinese)[申长雨2009注塑成型模拟及模具优化设计理论与方法(北京:科学出版社)第4页]
[3]	Yuan R F, Zhong C W, Zhang H 2015 J. Comput. Phys. 296 184
[4]	Cai L, Gao H, Luo X Y, Nie Y F 2015 Sci. China:Phys. Mech. Astron. 45 024702(in Chinese)[蔡力, 高昊, 罗小玉, 聂玉峰2015中国科学:物理学力学天文学 45 024702]
[5]	Ruan C L 2011 Ph. D. Dissertation (Xi'an:Northwestern Polytechnical University) (in Chinese)[阮春蕾2011博士学位论文(西安:西北工业大学)]
[6]	Baaijens H P W, Peters G W M, Baaijens F P T, Han E H M 1995 J. Rheol. 39 1243
[7]	Jiang T, Ouyang J, Ren J L 2012 Comp. Phys. Comm. 183 50
[8]	Dai J F, Fan X P, Meng B, Liu J F 2015 Acta Phys. Sin. 64 094704 (in Chinese)[戴剑锋, 樊学萍, 蒙波, 刘骥飞2015物理学报 64 094704]
[9]	Li Q 2016 Comput. Fluids 132 94
[10]	Li Q, Ouyang J, Yang B X, Li X J 2012 Appl. Math. Model. 36 2262
[11]	Ren J L, Lu W G, Jiang T 2015 Acta Phys. Sin. 64 080202 (in Chinese)[任金莲, 陆伟刚, 蒋涛2015物理学报 64 080202]
[12]	Hetu J F, Gao D M, Rejon A G, Salloum G 1998 Polym. Eng. Sci. 38 223
[13]	Mu Y, Zhao G Q, Chen A, Dong G W, Li S 2014 Comput. Chem. Eng. 63 91
[14]	Zheng S P, Ouyang J, Zhao Z F, Zhang L 2012 Comput. Math. Appl. 64 2860
[15]	Li Q, Li W M 2016 Acta Phys. Sin. 65 064601 (in Chinese)[李强, 李五明2016物理学报 65 064601]
[16]	Wang Y, Shu C, Yang L M 2016 J. Comput. Phys. 306 237
[17]	Boronat T, Segui V J, Peydro M A, Reig M J 2009 J. Mater. Process Tech. 209 2735
[18]	Isayev A I, Shyu G D, Li C T 2006 J. Polym. Sci. Pol. Phys. 44 622
[19]	Cai S Y, Zhang W H 2015 Comput. Method. Appl. M. 289 267

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复杂型腔充模过程中分子构型演化的数值模拟

1. 河南理工大学数学与信息科学学院, 焦作 454000;

2. 河南理工大学机械与动力工程学院, 焦作 454000

通信作者: 邵水军, shaosj@hpu.edu.cn

基金项目:

国家自然科学基金（批准号：11401177）、河南省科技攻关项目（批准号：162102210230）、河南省教育厅基础研究计划（批准号：15A110001）和河南理工大学博士基金（批准号：B2013-057，B2012-030）资助的课题.

收稿日期: 2016-05-19

修回日期: 2016-07-21

刊出日期: 2016-12-05

摘要: 基于充模过程的两相黏弹性流体模型，采用有限体积、浸入边界和复合水平集流体体积方法，数值模拟了聚合熔体在复杂型腔中的充模过程.首先，借助一类特殊函数（R-functions）将基于基本几何体的水平集函数组合成描述复杂型腔的形状水平集函数.然后，采用浸入边界法处理复杂型腔问题，有限体积方法求解熔体控制方程，利用复合水平集流体体积方法对熔体前沿界面进行隐式追踪.基于有限伸展非线性弹性哑铃本构方程模型，计算熔体分子构型张量，通过取向椭圆描述分子的取向及拉伸行为，实现了充模过程中分子构型的可视化.最后，对带有两个圆形嵌件的环状型腔内的充模过程进行数值模拟研究，得到了充模过程中型腔内的温度、应力及分子构型的变化情况，并重点分析了充模速度、熔体温度和模具温度等对分子构型的影响.数值结果表明：本文提出的耦合模型可以成功模拟复杂型腔内充模过程中的温度、应力和分子取向等物理量的动态变化；适当提高注射速度可以增大熔接痕的强度；提升熔体温度和模具温度，可以有效改善甚至消除熔接痕.

关键词:

Numerical simulation of molecular conformation evolution during mold filling process in a complex cavity

1.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;

2.
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China

Fund Project:

Project supported by National Natural Science Foundation of China (Grant No. 11401177), the Key Science and Technology Program of Henan Province, China (Grant No. 162102210230), the Henan Provincial Research Foundation for Basic Research, China (Grant No. 15A110001), and the Research Fund for the Doctoral Program of Henan Polytechnic University, China (Grant Nos. B2013-057, B2012-030).

Received Date: 19 May 2016

Accepted Date: 21 July 2016

Published Online: 05 December 2016

Abstract: In the mold filling process, polymer melt will suffer the shear stress and stretch, which has important influences on the mechanical properties and surface quality of the final plastic products. In this paper a gas-liquid two-phase flow model for a viscoelastic fluid is proposed and used to simulate the mold filling process, in which the finitely extensible nonlinear elastic dumbbell with Peterlin closure (FENE-P) model and cross-WLF viscosity model combined with Tait state equation are used to describe the constitutive relationship and viscosity change of the viscoelastic melt, respectively. Meanwhile, the improved coupled level-set and volume-of-fluid method is used to trace the melt front, and the finite volume method on non-staggered grid is used to solve the mass, momentum, and energy conservation equations. Firstly, the R-function, an excellent implicit modeling tool of constructive solid geometry, is employed to establish the shape level-set function to describe the complex mold cavities based on the signed distance functions that represent basic geometries. And the immersed boundary method is applied to dealing with the complex mold cavities by using the shape level-set function. The benchmark problem of the flow past a cylinder is simulated to verify the validity of the FENE-P model, where the orientational ellipses are used to describe the molecular orientation and deformation. Moreover, the visualization of polymer molecular deformation is achieved. Then, the non-isothermal filling process of the viscoelastic fluid is simulated in an annular mold cavity with two circular insets, and the behaviors of the molecular orientation, temperature and stress in the filling process are shown and analyzed in detail. Finally, the problems are also discussed that how the injection velocity, melt and mold temperatures influences on the molecular conformation and solidified layer thickness. Numerical results show that the computational framework proposed in this paper can be successfully used to simulate the non-isothermal mold filling process in the complex mold cavity. Increasing properly the injection velocity can reduce the heat loss and improve the strength of the weld line. The higher the melt or mold temperature, the thinner the solidified layer is. Thus, increasing the injection velocity, as well as raising the melt and the mold temperatures will improve or remove the weld line in melt filling process.

Keywords:

shape level-set function /
coupled level-set and volume-of-fluid method /
weld line /
molecular conformation

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