A level set based immersed boundary method for simulation of non-isothermal viscoelastic melt filling process

doi:10.1016/j.cjche.2020.09.057

Abstract

Abstract: In this work, the polymer melt filling process is simulated by using a coupled finite volume and level-set based immersed boundary (LS-IB) method. Firstly, based on a shape level set (LS) function to represent the mold boundary, a LS-IB method is developed to model the complex mold walls. Then the nonisothermal melt filling process is simulated based on non-Newtonian viscoelastic equations with different Reynolds numbers in a circular cavity with a solid core, and the effects of Reynolds number on the flow patterns of polymer melt are presented and compared with each other. And then for a true polymer melt with a small Reynolds number that varies with melt viscosity, the moving interface, the temperature distributions and the molecular deformation are shown and analyzed in detail. At last, as a commonly used application case, a socket cavity with seven inserts is investigated. The corresponding physical quantities, such as the melt velocity, molecular deformation, normal stresses, first normal stress difference, temperature distributions and frozen layer are analyzed and discussed. The results could provide some predictions and guidance for the polymer processing industry.

Key words: LS-IB method, Non-isothermal filling, Non-Newtonian fluids, Multiscale, Numerical simulation

摘要： In this work, the polymer melt filling process is simulated by using a coupled finite volume and level-set based immersed boundary (LS-IB) method. Firstly, based on a shape level set (LS) function to represent the mold boundary, a LS-IB method is developed to model the complex mold walls. Then the nonisothermal melt filling process is simulated based on non-Newtonian viscoelastic equations with different Reynolds numbers in a circular cavity with a solid core, and the effects of Reynolds number on the flow patterns of polymer melt are presented and compared with each other. And then for a true polymer melt with a small Reynolds number that varies with melt viscosity, the moving interface, the temperature distributions and the molecular deformation are shown and analyzed in detail. At last, as a commonly used application case, a socket cavity with seven inserts is investigated. The corresponding physical quantities, such as the melt velocity, molecular deformation, normal stresses, first normal stress difference, temperature distributions and frozen layer are analyzed and discussed. The results could provide some predictions and guidance for the polymer processing industry.

关键词: LS-IB method, Non-isothermal filling, Non-Newtonian fluids, Multiscale, Numerical simulation

Qiang Li, Fangcao Qu. A level set based immersed boundary method for simulation of non-isothermal viscoelastic melt filling process[J]. Chinese Journal of Chemical Engineering, 2021, 32(4): 119-133.

Qiang Li, Fangcao Qu. A level set based immersed boundary method for simulation of non-isothermal viscoelastic melt filling process[J]. 中国化学工程学报, 2021, 32(4): 119-133.

References

[1] H.M. Zhou, Computer Modeling for Injection Molding:Simulation, Optimization, and Control, John Wiley & Sons, Hoboken, 2013.
[2] J. Ren, T. Jiang, W.G. Lu, G. Li, An improved parallel SPH approach to solve 3D transient generalized Newtonian free surface flows, Comput. Phys. Commu. 205(2016) 87-105.
[3] T. Jiang, Z.C. Chen, W.G. Lu, J.Y. Yuan, D.S. Wang, An efficient split-step and implicit pure mesh-free method for the 2D/3D nonlinear Gross-Pitaevskii equations, Comput. Phys. Commun. 231(2018) 19-30.
[4] J.L. Ren, T. Jiang, Simulation of the 3D viscoelastic free surface flow by a parallel corrected particle scheme, Chin. Phys. B 25(2) (2016), 020204-1-14.
[5] S. Tiwari, J. Kuhnert, Modeling of two-phase flows with surface tension by finite pointset method (FPM), J. Comput. Appl. Math. 203(2) (2007) 376-386.
[6] E.O. Reséndiz-Flores, F.R. Saucedo-Zendejo, Meshfree numerical simulation of free surface thermal flows in mould filling processes using the Finite Pointset Method, Int. J. Therm. Sci. 127(2018) 29-40.
[7] C.M. Oishi, F.P. Martins, R.L. Thompson, The "avalanche effect" of an elastoviscoplastic thixotropic material on an inclined plane, J. Non-Newtonian Fluid Mech. 247(2017) 165-177.
[8] G.Y. Soh, G.H. Yeoh, V. Timchenko, An algorithm to calculate interfacial area for multiphase mass transfer through the volume-of-fluid method, Int. J. Heat Mass Transf. 100(2016) 573-581.
[9] M. Shams, A.Q. Raeini, M.J. Blunt, B. Bijeljic, A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method, J. Comput. Phys. 357(2018) 159-182.
[10] S. Mukherjee, A. Zarghami, C. Haringa, K. van As, Simulating liquid droplets:A quantitative assessment of lattice Boltzmann and Volume of Fluid methods, Int. J. Heat Fluid Flow 70(2018) 59-78.
[11] A. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer, New York, (2003) 17-22.
[12] H.Y. Li, Y.F. Yap, J. Lou, J.C. Chai, Z. Shang, Conjugate heat transfer in stratified two-fluid flows with a growing deposit layer, Appl. Therm. Eng. 113(2017) 215-228.
[13] R. Broglia, D. Durante, Accurate prediction of complex free surface flow around a high speed craft using a single-phase level set method, Comput. Mech. 62(3) (2018) 421-437.
[14] Q. Li, S.L. Shao, S.S. Li, Numerical simulation of molecular configuration evolution in complex cavity filling process, Acta Phys. Sin. 65(24) (2016) 98-108.
[15] Q. Li, Numerical simulation of melt filling process in complex mold cavity with insets using IB-CLSVOF method, Comput. Fluids 132(2016) 94-105.
[16] G. Son, Efficient implementation of a coupled level-set and volume-of-fluid method for three-dimensional incompressible two-phase flows, Numer. Heat Tranf. B-Fundam. 43(6) (2003) 549-565.
[17] Z. Wang, J. Yang, B. Koo, F. Stern, A coupled level set and volume-of-fluid method for sharp interface simulation of plunging breaking waves, Int. J. Multiphase Flow 35(3) (2009) 227-246.
[18] N.K. Singh, B. Premachandran, A coupled level set and volume of fluid method on unstructured grids for the direct numerical simulations of two-phase flows including phase change, Int. J. Heat Mass Transf. 122(2018) 182-203.
[19] D.L. Son, S.Y. Bo, Y.P. Wang, W.J. Liu, A VOSET method combined with IDEAL algorithm for 3D two-phase flows with large density and viscosity ratio, Int. J. Heat Mass Transf. 114(2017) 155-168.
[20] Z. Cao, D. Sun, J. Wei, B. Yu, A coupled volume-of-fluid and level set method based on multi-dimensional advection for unstructured triangular meshes, Chem. Eng. Sci. 176(2018) 560-579.
[21] K. Ling, W.Q. Tao, A sharp-interface model coupling VOSET and IBM for simulations on melting and solidification, Comput. Fluids 178(2019) 113-131.
[22] T. Yamamoto, Y. Okano, S. Dost, Quantitative benchmark computations of twodimensional bubble dynamics, Int. J. Numer. Methods Fluids 83(2016) 23-25.
[23] Q. Li, H.F. Niu, Three-dimensional simulations of non-isothermal flow for gas penetration in complex cavity during gas assisted injection moulding process, Can. J. Chem. Eng. 96(4) (2018) 978-988.
[24] C.S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys. 25(3) (1977) 220-252.
[25] M.C. Lai, C.S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys. 160(2) (2000) 705-719.
[26] K. Khadra, P. Angot, S. Parneix, J.P. Caltagirone, Fictitious domain approach for numerical modelling of Navier-Stokes equations, Int. J. Numer. Meth. Fluids 34(8) (2000) 651-684.
[27] E.A. Fadlun, R. Verzicco, P. Orlandi, J. Mohd-Yusof, Combined immersedboundary finite-difference methods for three-dimensional complex flow simulations, J. Comput. Phys. 161(1) (2000) 35-60.
[28] A. Gilmanov, F. Sotiropoulos, E. Balaras, A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids, J. Comput. Phys. 191(2003) 660-669.
[29] M. Shrivastava, A. Agrawal, A. Sharma, A novel level set-based immersedboundary method for CFD simulation of moving-boundary problems, Numer. Heat Tranf. B-Fundam. 63(4) (2013) 304-326.
[30] T. Patel, A. Lakdawala, A dual grid, dual level set based cut cell immersed boundary approach for simulation of multi-phase flow, Chem. Eng. Sci. 177(2018) 180-194.
[31] Z. Cui, Z. Yang, H.Z. Jiang, W.X. Huang, L. Shen, A sharp-interface immersed boundary method for simulating incompressible flows with arbitrarily deforming smooth boundaries, Int. J. Comput. Meth-Sing. 15(01) (2018), 1750080-1-27.
[32] M. Chai, K. Luo, C. Shao, J. Fan, An efficient level set remedy approach for simulations of two-phase flow based on sigmoid function, Chem. Eng. Sci. 172(2017) 335-352.
[33] C.L. Ruan, J. Ouyang, Microstructures of polymer solutions of flow past a confined cylinder, Polym-Plast. Tech. 49(5) (2010) 510-518.
[34] 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. Tech. 209(5) (2009) 2735-2745.
[35] X. Li, J. Ouyang, Q. Li, J.L. Ren, Simulations of a full three-dimensional packing process and flow-induced stresses in injection molding, J. Appl. Polym. Sci. 126(5) (2012) 1532-1545.
[36] S.Y. Cai, W.H. Zhang, Stress constrained topology optimization with free-form design domains, Comput. Method Appl. Mech. 289(2015) 267-290.
[37] 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.
[38] J.L. Ren, W.G. Lu, T. Jiang, Improved smooth particle dynamics simulation and prediction of weld line in mold filling process, Acta Phys. Sin. 64(8) (2015), 080202-1-12(in Chinese).
[39] C.Y. Shen, Simulation of Injection Molding and Theories and Methods for Optimization of Moulds Designing, Science Press, Beijing, 2009(in Chinese).
[40] S.P. Zheng, J. Ouyang, Z.F. Zhao, L. Zhang, An adaptive method to capture weldlines during the injection mold filling, Comput. Math. Appl. 64(2012) 2860-2870.