New approach to develop a 3D non-isothermal computational framework for injection molding process based on level set method

doi:10.1016/j.cjche.2016.04.014

Abstract

Abstract: The simulation of three-dimensional (3D) non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled with transient heat transfer. This paper presents a full 3D non-isothermal two-phase flow model to predict the complex flowinmelt filling process,where the Cross-WLFmodel is applied to characterize the rheological behavior of polymer melt. The governing equations are solved using finite volume method with SIMPLEC algorithm on collocated grids and the melt front is accurately captured by a high resolution level set method. A domain extension technique is adopted to dealwith the complex cavities, which greatly reduces the computational burden. To verify the validity of the developed 3D approach, the melts filling processes in two thin rectangular cavities (one of them with a cylindrical insert) are simulated. The predicted melt front interfaces are in good agreement with the experiment and commercial software prediction. For a case with a rather complex cavity, the dynamic filling process in a hemispherical shell is successfully simulated. All of the numerical results show that the developed numerical procedure can provide a reasonable prediction for injection molding process.

Key words: Injection molding, Non-isothermal, Finite volume/SIMPLEC method, Domain extension technique, High resolution level set method

摘要： The simulation of three-dimensional (3D) non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled with transient heat transfer. This paper presents a full 3D non-isothermal two-phase flow model to predict the complex flowinmelt filling process,where the Cross-WLFmodel is applied to characterize the rheological behavior of polymer melt. The governing equations are solved using finite volume method with SIMPLEC algorithm on collocated grids and the melt front is accurately captured by a high resolution level set method. A domain extension technique is adopted to dealwith the complex cavities, which greatly reduces the computational burden. To verify the validity of the developed 3D approach, the melts filling processes in two thin rectangular cavities (one of them with a cylindrical insert) are simulated. The predicted melt front interfaces are in good agreement with the experiment and commercial software prediction. For a case with a rather complex cavity, the dynamic filling process in a hemispherical shell is successfully simulated. All of the numerical results show that the developed numerical procedure can provide a reasonable prediction for injection molding process.

关键词: Injection molding, Non-isothermal, Finite volume/SIMPLEC method, Domain extension technique, High resolution level set method

Xin Zhuang, Jie Ouyang, Chuntao Jiang, Qingsheng Liu. New approach to develop a 3D non-isothermal computational framework for injection molding process based on level set method[J]. , 2016, 24(7): 832-842.

References

[1] S.W. Kim, L.S. Turng, Developments of three-dimensional computer-aided engineering simulation for injection moulding, Model. Simul. Mater. Sci. Eng. 12(2004) S151-S173.
[2] D. Cardozo, Three models of the 3D filling simulation for injection molding:A brief review, J. Reinf. Plast. Compos. 27(2008) 1963-1974.
[3] H.H. Chiang, C.A. Hieber, K.K.Wang, A unified simulation of the filling and post filling stages in injection molding. Part I:Formulation, Polym. Eng. Sci. 31(2) (1991) 116-124.
[4] H.M. Zhou, D.Q. Li, Filling simulation and gas penetration modeling for gas-assisted injection molding, Appl. Math. Model. 27(2003) 849-860.
[5] J.F. Hetu, D.M. Gao, A. Garcia-Rejon, G. Salloum, 3D finite element method for the simulation of the filling stage in injection molding, Polym. Eng. Sci. 38(2) (1998) 223-236.
[6] H.M. Zhou, T. Geng, D.Q. Li, Numerical filling simulation of injection molding based on 3D finite element model, J. Reinf. Plast. Compos. 24(2005) 823-830.
[7] X.P. Wang, X.K. Li, Numerical simulation of three dimensional non-Newtonian free surface flows in injection molding using ALE finite element method, Finite Elem. Anal. Des. 46(2010) 551-562.
[8] R.E. Khayat, C. Plaskos, D. Genouvrier, An adaptive boundary-element approach for 3D transient free surface cavity flow, as applied to polymer processing, Int. J. Numer. Methods Eng. 50(2001) 1347-1368.
[9] R.Y. Chang, W.H. Yang, Numerical simulation of mold filling in injection molding using a three-dimensional finite volume approach, Int. J. Numer. Methods Fluids 37(2001) 125-148.
[10] B.J. Araújo, J.C.F. Teixeira, A.M. Cunha, C.P.T. Groth, Parallel three-dimensional simulation of the injection molding process, Int. J. Numer. Methods Fluids 59(2009) 801-815.
[11] S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed:Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys. 79(1988) 12-49.
[12] S. Osher, R. Fedkiw, Level set methods and dynamic implicit surfaces, Springer-Verlag, New York, 2002.
[13] B.X. Yang, J. Ouyang, C.T. Liu, Q. Li, Simulation of non-isothermal injection molding for a non-Newtonian fluid by level set method, Chin. J. Chem. Eng. 18(4) (2010) 600-608.
[14] M. Sussman, E. Fatemi, P. Smereka, S. Osher, An improved level set method for incompressible two-phase flows, Comput. Fluids 27(5-6) (1998) 663-680.
[15] C. Yang, Z.S.Mao, An improved level set approach to the simulation of drop and bubble motion, Chin. J. Chem. Eng. 10(3) (2002) 263-272.
[16] T. Boronat, V.J. Segui, M.A. Peydro,M.J. Reig, Influence of temperature and shear rate on the rheology and processability of reprocessed ABS in injection molding process, J. Mater. Process. Technol. 209(2009) 2735-2745.
[17] J.P. Van Doormaal, G.D. Raithby, Enhancements of the SIMPLEmethod for predicting incompressible fluid flows, Numer. Heat Transfer 7(1984) 147-163.
[18] Q. Li, J. Ouyang, X.J. Li, G.R. Wu, B.X. Yang, Numerical simulation of gas-assisted injection molding process for a door handle, Comput. Model. Eng. Sci. 74(4) (2011) 247-267.
[19] P.J. Oliveira, F.T. Pinho, G.A. Pinto, Numerical simulation of non-linear elastic flows with a general collocated finite-volume method, J. Non-Newtonian Fluid Mech. 79(1998) 1-43.
[20] C. Yang, Z.S. Mao, Numerical simulation of interphase mass transfer with the level set approach, Chem. Eng. Sci. 60(2005) 2643-2660.
[21] G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126(1996) 202-228.
[22] G.S. Jiang, D.P. Peng,Weighted ENO schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput. 21(6) (2000) 2126-2143.
[23] J.H. Nie, B.F. Armaly, Three-dimensional convective flow adjacent to backwardfacing step-effects of step height, Int. J. Heat Mass Transf. 45(2002) 2431-2438.
[24] A. Korichi, L. Oufer, Numerical heat transfer in a rectangular channel with mounted obstacles on the upper and lower walls, Int. J. Therm. Sci. 44(2005) 644-655.
[25] C. Yang, Z.S.Mao, Mirror fluid method for numerical simulation of sedimentation of a solid particle in a Newtonian fluid, Phys. Rev. E 71(2005) 036704.
[26] L.K. Jiao, L.X.Wang, Q. Li, C.Y. Shen, 3D simulation of filling stage in injection molding based on ANSYS CFX, Polym. Mater. Sci. Eng. 28(3) (2012) 156-160(in Chinese).
[27] C.Y. Shen, Theory and method of numerical simulation and mold optimization design for injection molding, Science Press, Beijing, 2009(in Chinese).
[28] C.D. Han, Rheology and processing of polymeric materials, Oxford University Press, Oxford, 2007.
[29] S. Fathi, A.H. Behravesh, Real-time measurement of flow front kinematics using quantitative visualization in injection molding process, Polym. Eng. Sci. 48(2008) 598-605.
[30] S. Fathi, A.H. Behravesh, Visualization analysis of flow behavior during weld-line formation in injection molding process, Polym. Plast. Technol. 47(2008) 666-672.