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