黏弹性流体充模过程中凝固现象的数值模拟

王芳; 李俊林; 杨斌鑫

doi:10.7498/aps.63.084601

摘要

建立了黏弹性流体在充模过程中带有相变的气-液两相模型，该模型分别由气、液两相的质量守恒方程、动量守恒方程、能量守恒方程描述，并通过引入Heaviside函数将气-液两相的方程组统一为一个方程组；建立了一个对型腔内熔体和气体都适用的修正的焓方法来描述充模过程中的相变. 采用基于同位网格的有限体积方法对模型进行求解，水平集方法捕捉充模过程中的界面演化，模拟出了黏弹性流体在充模过程中的凝固现象，得出了充模过程中型腔内的温度、压力、第一法向应力差等随时间的变化；并讨论了型腔壁面温度、熔体温度、注射速度对充模过程中凝固现象的影响. 研究结果表明：型腔壁面温度越高，凝固层越薄；熔体温度越高，凝固层越薄；注射速度越高，凝固层越薄，故提高型腔壁面温度、熔体温度、注射速度可以减少或消除型腔壁面附近的凝固层.

关键词:

Abstract

A gas-liquid two-phase model for the simulation of viscoelastic fluid mold filling process with the consideration of phase change is proposed, in which the governing equations for the melt and air in the cavity, including the mass conservation, momentum conservation and energy conservation equations, are unified into one system of equations. A revised enthalpy method, which can be used for both the melt and air in the mold cavity, is proposed to describe the phase change during the mold filling. Finite volume method on non-staggered grid is used to solve the system. The level set method is used to capture the interface evolution in the mold filling process. The distributions of physical quantities such as velocity, pressure and temperature and so on are given. The "frozen skin" layers under different temperatures and velocities are discussed in detail. Numerical results show that increasing the temperatures of the melt and cavity is a better way to get rid of the "frozen skin" layer than increasing the injection velocity.

Keywords:

作者及机构信息

1.
太原科技大学应用科学学院, 太原 030024

基金项目: 国家自然科学基金（批准号：51078250）、山西省自然科学基金（批准号：2012011019-2，2011011021-3）、山西省研究生优秀创新项目（批准号：20133117）和太原科技大学博士基金（批准号：20112011）资助的课题.

Authors and contacts

1.
School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51078250), the Natural Science Foundation of Shanxi Province, China (Grant Nos. 2012011019-2, 2011011021-3), the Outstanding Graduate Innovation Project in Shanxi Province, China (Grant No. 20133117), and the Doctoral Sustentation Fund of Taiyuan University of Science and Technology, China (Grant No. 20112011).

参考文献

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[43]	Shen C Y 2009 Simulation of Injection Molding and Mold Optimization Design Theory and Method (Beijing: Science Press) p53 (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53页]

施引文献

[1]	Wang V W, Hieber C A, Wang K K 1986 J. Polym. Eng. 7 21
[2]	Chiang H H, Hieber C A, Wang K K 1991 Polym. Eng. Sci. 31 116
[3]	Kabanemi K K, Vaillancourt H, Wang H, Salloum G 1998 Polym. Eng. Sci. 38 21
[4]	Smith D E, Tortorelli D A, Tucker C L 1998 Comput. Method Appl. M. 167 325
[5]	Hetu J F, Gao D M, Garcia-Rejon A, Salloum G 1998 Polym. Eng. Sci. 38 223
[6]	Pichelin E, Coupez T 1998 Comput. Method Appl. M. 163 359
[7]	Kim S W, Turng L S 2006 Polym. Eng. Sci. 46 1263
[8]	Zhou H M, Geng T, Li D Q 2005 J. Reinf. Plast. Comp. 24 823
[9]	Chang R Y, Yang W H 2001 Int. J. Numer. Meth. Fl. 27 125
[10]	Zhou J, Turng L S 2007 Adv. Polym. Tech. 25 247
[11]	Khayat R E, Elsin W, Kim K 2000 Int. J. Numer. Meth. Fl. 33 847
[12]	Holm E J, Langtangen H P 1999 Comput. Method Appl. M. 178 413
[13]	Luoma J A, Voller V R 2000 Appl. Math. Model. 24 575
[14]	Soukane S, Trochu F 2006 Compos. Sci. Technol. 66 1067
[15]	Ayad R, Rigolot A 2002 J. Mech. Design 124 813
[16]	Geng T, Li D Q, Zhou H M 2006 Eng. Comput. Germany 21 289
[17]	Kim M S, Park J S, Lee W I 2003 Int. J. Numer. Meth. Fl. 42 791
[18]	Zhou H M, Yan B, Zhang Y 2008 J. Mater. Process. Tech. 204 475
[19]	Au C K 2005 Int. J. Mach. Tool. Manu. 45 115
[20]	Khor C Y, Ariff Z M, Che Ani F, Abdul Mujeebu M, Abdullah M K, Abdullah M Z, Joseph M A 2010 Int. Commun. Heat Mass 37 131
[21]	Yang B X, Ouyang J, Liu C T, Li Q 2010 Chinese J. Chem. Eng. 18 600 (in Chinese) [杨斌鑫, 欧阳洁, 刘春太, 李强 2010 化工学报 18 600]
[22]	Ao L, Wang W H, Chen J L, Gao S X, Wu G H 2001 Acta Phys. Sin. 50 793 (in Chinese) [敖玲, 王文洪, 陈京兰, 高淑侠, 吴光恒 2001 物理学报 50 793]
[23]	Zhang H Q 2001 Acta Phys. Sin. 50 528 (in Chinese) [张红群2001 物理学报 50 528]
[24]	Liu P, Yang T Q, Zhang L Y, Yao X 2000 Acta Phys. Sin. 49 2300 (in Chinese) [刘鹏, 杨同青, 张良莹, 姚熹 2000 物理学报 49 2300]
[25]	Li R X, Cheng Y M, Peng M J 2012 Chin. Phys. B 21 090205
[26]	Yang F, Zhu K Q 2010 Chin. Phys. Lett. 27 034601
[27]	Sussman M, Fatemi E, Smereka P, Osher S 1998 Comput. Fluids 27 663
[28]	Yang B X, Ouyang J 2012 Acta Phys. Sin. 61 234602 (in Chinese) [杨斌鑫, 欧阳洁 2012 物理学报 61 234602]
[29]	Verbeeten W M H, Peters G W M, Baaijens F T P 2001 J. Rheol. 45 823
[30]	Aboubacar M, Aguayo J P, Phillips P M, Phillips T N, Tamaddon-Jahromi H R, Snigerev B A, Webster M F 2005 J. Non-Newton. Fluid 126 207
[31]	Rubinstein L I 1994 The Stefan Problem (Providence: Providence Press) p56
[32]	Carslaw H S, Jaeger J S 1959 Conduction of Heat in Solids (Oxford: Oxford University Press) p113
[33]	Cahn J W, Hilliard J E 1958 J. Chem. Phys. 28 1015
[34]	Du L F, Zhang R, Xing H, Zhang L M, Zhang Y, Liu L 2013 Acta Phys. Sin. 62 106401 (in Chinese) [杜立飞, 张蓉, 邢辉, 张利民, 张洋, 刘林 2013 物理学报 62 106401]
[35]	Wang T, Li J J, Wang J C 2013 Acta Phys. Sin. 62 106402 (in Chinese) [王陶, 李俊杰, 王锦程 2013 物理学报 62 106402]
[36]	Krabbenhoft K, Damkilde L, Nazem M 2007 Int. Commun. Heat Mass 43 233
[37]	Kim S, Kim M C, Chun W G 2001 Korean J. Chem. Eng. 18 40
[38]	Caldwell J, Date A W 2003 Commun. Numer. Meth. En. 19 865
[39]	Luoma J A, Voller V R 2000 Appl. Math. Model. 24 575
[40]	Cao Y, Faghri A, Chang W S 1989 Int. Commun. Heat Mass 32 1289
[41]	Yang B, Fu X R, Yang W, Liang S P, Hu S, Yang M B 2009 Polym. Eng. Sci. 49 1234
[42]	Boronat T, Segui V J, Peydro M A, Reig M J 2009 J. Mater. Process Tech. 209 2735
[43]	Shen C Y 2009 Simulation of Injection Molding and Mold Optimization Design Theory and Method (Beijing: Science Press) p53 (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53页]

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