Numerical simulation of mold filling in injection molding using a three‐dimensional finite volume approach

This work presents an implicit finite volume approach to simulate the three-dimensional mold filling problems encountered during the injection molding. The described numerical model deals with the three-dimensional isothermal flow of incompressible, high-viscous Newtonian fluids with moving interfaces. The collocated finite volume method and the SIMPLE segregated algorithm are used to discretize and solve the Navier–Stokes equation. In addition, a bounded compressive high-resolution differencing scheme is adopted to solve the advection equation to capture the interface on a Eulerian framework. This approach effectively solves the flow field in terms of CPU time and memory storage as well as the complicated three-dimensional melt front topology. Several two- and three-dimensional examples are presented to validate the presented approach and illustrate its capabilities. This method can more accurately predict the critical three-dimensional phenomena encountered during mold filling than the existing Hele–Shaw analysis model. The presented numerical approach has been proven to be a highly effective and flexible tool for simulating mold filling problems. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  Vaughan R Voller,et al.  A time-implicit filling algorithm , 1994 .

[2]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[3]  Mark Cross,et al.  Numerical simulation of flows encountered during mold-filling , 1991 .

[4]  C. Rhie,et al.  A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation , 1982 .

[5]  Louis Thomas Manzione,et al.  Applications of Computer Aided Engineering in Injection Molding , 1988 .

[6]  Lars Davidson,et al.  A PRESSURE CORRECTION METHOD FOR UNSTRUCTURED MESHES WITH ARBITRARY CONTROL VOLUMES , 1996 .

[7]  Abhijit Chandra,et al.  An algorithm for handling corners in the boundary element method: Application to conduction-convection equations , 1991 .

[8]  D. B. Kothe,et al.  RIPPLE: A NEW MODEL FOR INCOMPRESSIBLE FLOWS WITH FREE SURFACES , 1991 .

[9]  B. P. Leonard,et al.  The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection , 1991 .

[10]  Mustafa Kamal,et al.  The injection molding of thermoplastics part I: Theoretical model , 1972 .

[11]  Jerzy M. Floryan,et al.  Numerical Methods for Viscous Flows With Moving Boundaries , 1989 .

[12]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[13]  R. C. Mjolsness,et al.  NASA-VOF3D: A three-dimensional computer program for incompressible flows with free surfaces , 1987 .

[14]  D. Kothe Perspective on Eulerian Finite Volume Methods for Incompressible Interfacial Flows , 1998 .

[15]  S. Muzaferija,et al.  Adaptive finite volume method for flow prediction using unstructured meshes and multigrid approach , 1994 .

[16]  Koulis Pericleous,et al.  FREE SURFACE FLOW AND HEAT TRANSFER IN CAVITIES: THE SEA ALGORITHM , 1995 .

[17]  S. Patankar Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[18]  S. G. Rubin,et al.  A diagonally dominant second-order accurate implicit scheme , 1974 .

[19]  Nasser Ashgriz,et al.  FLAIR: fluz line-segment model for advection and interface reconstruction , 1991 .

[20]  Asif Usmani,et al.  Efficient mould filling simulation in castings by an explicit finite element method , 1995 .

[21]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[22]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[23]  Vaughan R Voller,et al.  An algorithm for analysis of polymer filling of molds , 1995 .

[24]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[25]  D. M. Gao A three-dimensional hybrid finite element-volume tracking model for mould filling in casting processes , 1999 .

[26]  J. F. Stevenson A simplified method for analyzing mold filling dynamics† Part I: Theory , 1978 .

[27]  S. Zaleski,et al.  Modelling Merging and Fragmentation in Multiphase Flows with SURFER , 1994 .

[28]  C. A. Hieber,et al.  A unified simulation of the filling and postfilling stages in injection molding. Part I: Formulation , 1991 .

[29]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[30]  J. Murthy,et al.  A PRESSURE-BASED METHOD FOR UNSTRUCTURED MESHES , 1997 .

[31]  Jean-Francois Hetu,et al.  3D finite element method for the simulation of the filling stage in injection molding , 1998 .

[32]  Chaim Gutfinger,et al.  Flow analysis network (FAN)—A method for solving flow problems in polymer processing , 1974 .

[33]  R. I. Issa,et al.  A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes , 1999 .