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A corrected smoothed particle hydrodynamics (SPH) method for viscoelastic fluid is proposed and used to tentatively simulate and predict the behavior of the molecule near the weld line in the filling process of the FENE-P fluid in this paper. And the corrected SPH scheme for the viscoelastic fluid is simultaneously presented. Firstly, a coupled macro-micro model based on the SPH method for the viscoelatic fluid is set up. Then, some benchmarks, such as the flow behavior of the periodic cylinders of FENE-P fluid and the non-isothermal Poiseuille flow based on the Oldroyd-B model which is a simplified model of FENE-P model, are simulated to verify their validity and the convergence of the corrected SPH method of solving the coupled macro-micro problem of the polymer and the discrete SPH temperature model for viscoelastic fluid. Finally, the filling process of the viscoelastic fluid based on the FENE-P model in a ring-shaped mold is simulated, and the behavior of the micro molecules in the filling process is tentatively shown by orientation ellipse. Meanwhile the non-isothermal filling process of the FENE-P fluid is also implemented. The numerical results show clearly the behavior of the molecules in the filling process of the FENE-P fluid, the weld line is indeed observed in the filling process of the FENE-P fluid in the ring-shaped mold, and the non-isothermal filling process can improve the weld line to some extent. In order to further discuss the improvement of the weld line, the filling processes of different cases are simulated in the multiple-gating C-shaped mold by using the pattern of the hot runner and valve gates, and the obtained results are compared with other available data. Moreover, the effect of the delay time needed for the fluid to be injected on the flow is also investigated. The numerical results show that the pattern of the hot runner and valve gates can improve and even remove the weld-line in the filling process of the polymer melt, especially for the big-sized product, and the shorter the delay time is, the faster the flow is, and the bigger the appearance probability of the weld line is.
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Keywords:
- smoothed particle hydrodynamics method /
- FENE-P viscoelastic model /
- filling process /
- weld line
[1] Xiao C J, Liu C T, Shen C Y 2003 Eng. Plast. Appl. 3 17 (in Chinese) [肖长江, 刘春太, 申长雨 2003 工程塑料应用 3 17]
[2] Dong L 2007 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese) [董林 2007 博士研究生学位论文 (长春: 吉林大学)]
[3] Tomé M F, Duffy B, McKee S 1996 J. Non-Newton. Fluid Mech. 62 9
[4] John D, Anderson J R 2002 Computational Fluid Dynamics: the Basics with Applications (Beijing: Tsinghua University Press)
[5] Yang B X, Ouyang J 2012 Acta Phys. Sin. 61 234602 (in Chinese) [杨斌鑫, 欧阳洁 2012 61 234602]
[6] Fu D X, Ma Y W 2002 Computational Fluid Mechanics (Beijing: Higher Education Press) (in Chinese) [傅德薰, 马延文 2002 计算流体力学 (北京: 高等教育出版社)]
[7] Li Q 2012 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [李强 2012 博士研究生学位论文 (西安: 西北工业大学)]
[8] Chen R J, Ge H X 2010 Chin. Phys. B 19 090201
[9] Gingold R A, Monaghan J J 1977 Mon. Not. Roy. Astron. Soc. 181 375
[10] Ma L Q, Chang J Z, Liu H T, Liu M B 2012 Acta Phys. Sin. 61 054701 (in Chinese) [马理强, 常建忠, 刘汉涛, 刘谋斌 2012 61 054701]
[11] Fan X J., Tanner R I, Zheng R 2010 J. Non-Newton. Fluid Mech. 165 219
[12] Han X, Yang G, Long X Y 2007 J. Hunan Univ. 34 28 (in Chinese) [韩旭, 杨刚, 龙述尧 2007 湖南大学学报 34 28]
[13] Batra R C, Zhang G M 2007 Comput. Mech. 40 531
[14] Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[15] Ren J L, Ouyang J, Jiang T 2012 Comput. Mech. 49 643
[16] Jiang T, Ren J L, Xu L, Lu L G 2014 Acta Phys. Sin. 63 210203 (in Chinese) [蒋涛, 任金莲, 徐磊, 陆林广 2014 63 210203]
[17] Ruan C L 2011 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [阮春蕾 2011 博士研究生学位论文 (西安: 西北工业大学)]
[18] Colagrossi A, Landrini M 2003 J. Comput. Phys. 191 448
[19] Cleary P W 2010 Appl. Math. Model. 34 3189
[20] Han X H 2007 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese) [韩先洪 2007 博士学位论文 (大连: 大连理工大学)]
[21] Monaghan J J, Kajtar J B 2009 Comput. Phys. Commun. 180 1811
[22] Liu A W, Bornside D E, Amstrong R C, Brown R A 1998 J. Non-Newton. Fluid Mech. 77 153
[23] Ahsan A 2011 Evaporation, Condensation and Heat Transfer (Croatia: InTech)
[24] Liu Y 2009 Ph. D. Dissertation (Guangzhou: South China University of Technology) (in Chinese) [刘毅2009 博士研究生学位论文 (广州: 华南理工大学)]
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[1] Xiao C J, Liu C T, Shen C Y 2003 Eng. Plast. Appl. 3 17 (in Chinese) [肖长江, 刘春太, 申长雨 2003 工程塑料应用 3 17]
[2] Dong L 2007 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese) [董林 2007 博士研究生学位论文 (长春: 吉林大学)]
[3] Tomé M F, Duffy B, McKee S 1996 J. Non-Newton. Fluid Mech. 62 9
[4] John D, Anderson J R 2002 Computational Fluid Dynamics: the Basics with Applications (Beijing: Tsinghua University Press)
[5] Yang B X, Ouyang J 2012 Acta Phys. Sin. 61 234602 (in Chinese) [杨斌鑫, 欧阳洁 2012 61 234602]
[6] Fu D X, Ma Y W 2002 Computational Fluid Mechanics (Beijing: Higher Education Press) (in Chinese) [傅德薰, 马延文 2002 计算流体力学 (北京: 高等教育出版社)]
[7] Li Q 2012 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [李强 2012 博士研究生学位论文 (西安: 西北工业大学)]
[8] Chen R J, Ge H X 2010 Chin. Phys. B 19 090201
[9] Gingold R A, Monaghan J J 1977 Mon. Not. Roy. Astron. Soc. 181 375
[10] Ma L Q, Chang J Z, Liu H T, Liu M B 2012 Acta Phys. Sin. 61 054701 (in Chinese) [马理强, 常建忠, 刘汉涛, 刘谋斌 2012 61 054701]
[11] Fan X J., Tanner R I, Zheng R 2010 J. Non-Newton. Fluid Mech. 165 219
[12] Han X, Yang G, Long X Y 2007 J. Hunan Univ. 34 28 (in Chinese) [韩旭, 杨刚, 龙述尧 2007 湖南大学学报 34 28]
[13] Batra R C, Zhang G M 2007 Comput. Mech. 40 531
[14] Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[15] Ren J L, Ouyang J, Jiang T 2012 Comput. Mech. 49 643
[16] Jiang T, Ren J L, Xu L, Lu L G 2014 Acta Phys. Sin. 63 210203 (in Chinese) [蒋涛, 任金莲, 徐磊, 陆林广 2014 63 210203]
[17] Ruan C L 2011 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [阮春蕾 2011 博士研究生学位论文 (西安: 西北工业大学)]
[18] Colagrossi A, Landrini M 2003 J. Comput. Phys. 191 448
[19] Cleary P W 2010 Appl. Math. Model. 34 3189
[20] Han X H 2007 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese) [韩先洪 2007 博士学位论文 (大连: 大连理工大学)]
[21] Monaghan J J, Kajtar J B 2009 Comput. Phys. Commun. 180 1811
[22] Liu A W, Bornside D E, Amstrong R C, Brown R A 1998 J. Non-Newton. Fluid Mech. 77 153
[23] Ahsan A 2011 Evaporation, Condensation and Heat Transfer (Croatia: InTech)
[24] Liu Y 2009 Ph. D. Dissertation (Guangzhou: South China University of Technology) (in Chinese) [刘毅2009 博士研究生学位论文 (广州: 华南理工大学)]
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