Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method

Abstract

Abstract: A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.

Key words: injection molding, Level Set Method, two-phase flow, non-isothermal, non-Newtonian flow

摘要： A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.

关键词: injection molding, Level Set Method, two-phase flow, non-isothermal, non-Newtonian flow

YANG Binxin, OUYANG Jie, LIU Chuntai, LI Qiang. Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method[J]. , 2010, 18(4): 600-608.

杨斌鑫, 欧阳洁, 刘春太, 李强. Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method[J]. , 2010, 18(4): 600-608.

References

1 Kumar,A.,Ghoshdastidar,P.S.,Muju,M. K.,“Computer simulation of transport processes during injection mold-filling and optimization of the molding conditions”,J. Mater.Process.Technol.,120(1-3),428-449 (2002).
2 Chiang,H.H.,Hieber,C.A.,Wang,K. K.,“A unified simulation of the filling and post filling stages in injection molding(I)Formulation”,Polym.Eng.Sci.,31(2),116-123(1991).
3 Hieber,C.A.,Shen,S. F.,“A finite-element/finite-difference simulation of the injection molding filling process”,J.Non-Newton.Fluid Mech.,7(1),1-32(1980).
4 Hétu,J. F.,Gao,D. M.,Garcia-Rejon,A.,Salloum,G.,“3D finite element method for the simulation of the filling stage in injection molding”,Polym.Eng.Sci.,38(2),223-236(1998).
5 Zheng,S. P.,Ouyang,J.,Zhang,H.P.,Zhang,L.,“Dynamic simulation for weldlines in thin mold with rectangle cylinder”,J.Chem.Ind.Eng.(China),59(1),232-238(2008).(in Chinese)
6 Cui,K.,Ouyang,J.,Zheng,S. P.,Zhao,Z. F.,Ruan,C. L.,“Level setmethod for 3D melt front surface”,J.Chem.Ind.Eng.(China),59 (12),3020-3026(2008).(in Chinese) 7 Yang,B.X.,Ouyang,J.,Zheng,S. P.,Zhao,Z.F.,“Simulation of injection molding process with level set two-phase flow method”,J.Chem.Ind.Eng.(China),60(11),2729-2736 (2009).(in Chinese)
8 Sethian,J. A.,“Fast marching methods”,SIAM Review,41(2), 199-235(1999).
9 Sussman,M.,Fatemi,E.,Smereka,P.,Osher,S.,“An improved level set method of incompressible two-phase flows”,Comput.Fluid.,27(5/6),663-680(1998).
10 Sussman,M.,Pucket,E. G.,“A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressibletwo-phase flows”,J.Comput.Phys.,162(2),301-337(2000).
11 Sussman,M.,Smereka,P.,“Axisymmetric free boundary problems”,J.Fluid Mech.,341(1),269-294(1997).
12 Sussman,M.,Smereka,P.,Osher,S.,“A level set approach to computing solutions to incompressible two-phase flow”,J.Comput.Phys.,114(1),146-159(1994).
13 Yang,C.,Mao,Z. S.,“An improved level set approach to the simulation of drop and bubble motion”,Chin.J.Chem.Eng.,10(3),263-272(2002).
14 Wang,J. F.,Yang,C.,Mao,Z. S.,“A simple weighted integration method for calculating surface tension force to suppress parasitic flow in the level set approach”,Chin.J.Chem.Eng.,14(6),740-746(2006).
15 El Otmani,R.,Zinet,M.,Boutaous,M.,Chantrenne,P.,Benhadid,H.,”Numerical simulation of the filling phase in the polymer injection molding process with a conservative level set method”,Int. J. Mater.Form.,1(Suppl.1),731-734(2008).
16 Osher,S.,Fedkiw,R.P.,“Level set methods:An overview and some recent results”,J.Comput.Phys.,169(2),463-502(2001).
17 Liu,C. T.,“Simulation-based studies on processing optimization and part performance in injection molding”,Ph.D.Thesis,Zhengzhou Univ.,China(2003).(in Chinese)
18 Boronat,T.,Segui,V.J.,Peydro,M. A.,Reig,M. J.,“Influence of temperature and shear rate on the rheology and processability of reprocessed ABS in injection molding process”,J.Mater.Process.Tech.,209(5),2735-2745(2009).
19 Tao,W. Q.,Numerical Heat Transfer,2nd edition,Xi'an Jiaotong University Press,Xi'an (2001).(in Chinese)
20 Rhie,C. M.,Chow,W.L.,“Numerical study of the turbulent flow past an airfoil with trailing edge separation”,AIAA J.,21(11),1525-1532 (1983).
21 Darwish,M. S.,Whiteman,J.R.,Bevis,M.J.,“Numerical modelling of viscoelastic liquids using a finite-volume method”,J.Non-Newton.Fluid
Mech.,45(3),311-337(1992).
22 Osher,S.,Shu,C. W.,“High-order essentially non-oscillatory schemes for Hamilton-Jacobi equations”,SIAM J.Numer.Anal.,28 (4),907-922(1991).
23 Jiang,G. S.,Peng,D.P.,“Weighted ENO schemes for Hamilton-Jacobi equations”,SIAM J.Sci.Comput.,21(6),2126-2143(2002).
24 Shu,C.W.,Osher,S.,“Efficient implementation of essentially non-oscillatory shock-capturing schemes II”,J.Comput.Phys.,83(1),32-78(1989).
25 Wu,Q. Y.,Wu,J. A.,Polymer Rheology,Higher Education Press,Beijing (2004).(in Chinese)

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