NORTE-07-0162-FEDER-000086 and the Minho Advanced
Computing Center (MACC) for providing HP

Fernandes, C.

Nóbrega, J. M.

Pedro, João Luís Oliveira

Ramôa, Bruno Manuel Oliveira

English

Universidade do Minho: RepositoriUM

On the simulation of the filling stage of thermoplastic injection molding using the open-source solver openInjMoldSim

     On the simulation of the Filling Stage of Thermoplastic Injection Molding using the Open-Source Solver openInjMoldSim   João Pedro, Bruno Ramôa, João Miguel Nóbrega, Célio Fernandes  Institute for Polymers and Composites, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal; b8389@dep.uminho.pt (J.P.); bruno.ramoa@dep.uminho.pt (B.R.); mnobrega@dep.uminho.pt (J.M.N.); cbpf@dep.uminho.pt (C.F.)  1. Introduction  In the present study, the simulation of the three-dimensional (3D) non-isothermal, non-Newtonian fluid flow of polymer melts is investigated. In particular, the filling stage of thermoplastic injection molding (IM) [ROS] is numerically studied with a solver implemented in the open-source computational library OpenFOAM® [KRE, MOL].   2. Governing equations  In the approach employed, the air and the polymer melt phases are assumed to be immiscible and compressible, unless otherwise stated. During the filling stage, the flow is governed by the mass, momentum, and energy conservation equations, which can be written as follows:   The simulation of the IM filling stage requires solving the fluid flow equations and capturing the melt front location at every time step. For that purpose, an advanced free-surface capturing model, based on the volume-of-fluid (VoF) [HIR] method is used. In this method, a species transport equation is used to track the relative volume fraction of the two phases, or phase fraction, α, distribution. The phase fraction ranges from zero to one, zero being for air and one for the polymer melt. In this way, the fluid interface is located in regions where 0 < α < 1, and the physical properties can be calculated as an average weighted by α, as follows:  𝜓𝜓 =  𝜓𝜓𝑚𝑚α +  𝜓𝜓𝑎𝑎(1 − 𝛼𝛼),  where the subscripts m and a denote the melt and air phases' properties, respectively, and 𝜓𝜓 represents all the relevant fluid properties, namely 𝜌𝜌, 𝜂𝜂, 𝑐𝑐𝑃𝑃, and 𝑘𝑘. The governing equation for the phase fraction, 𝛼𝛼, is defined as:  ∂α𝜕𝜕𝜕𝜕 + ∇ ⋅(α𝐮𝐮) + ∇ ⋅ [α(1− α)𝐮𝐮𝑟𝑟] =  Sp +  Su,  where 𝐮𝐮𝑟𝑟 is the relative velocity vector, commonly denominated by “compression velocity”. 𝑆𝑆𝑝𝑝 and 𝑆𝑆𝑢𝑢 represent two terms that arise from considering a compressible material.  The rheological behavior of the melt and air phases is defined by a single-fluid two-phase model. For the air phase, the kinematic viscosity is assumed to be constant, i.e., a Newtonian fluid. For the polymer melt, the Cross-WLF constitutive model is employed. This constitutive model is widely adopted for studying both the filling and packing stages of the IM process and is given by:  𝜂𝜂𝑚𝑚(𝑇𝑇, 𝑝𝑝, γ̇) =  𝜂𝜂0(𝑇𝑇, 𝑝𝑝)1 + �𝜂𝜂0(𝑇𝑇, 𝑝𝑝)?̇?𝛾 τ∗ �1−𝑛𝑛 ,  In this work, we adopted the Williams-Landel-Ferry (WLF) model to describe the dependence of 𝜂𝜂0 on 𝑇𝑇 and 𝑝𝑝, given by:  𝜂𝜂0(𝑇𝑇,𝑝𝑝) =  D1exp �−C1(𝑇𝑇 − 𝑇𝑇0)C2 + 𝑇𝑇 − 𝑇𝑇0�  where T0 = D2 + D3𝑝𝑝 and 𝐷𝐷1, 𝐷𝐷2, 𝐷𝐷3, 𝐶𝐶1, and 𝐶𝐶2 are parameters determined by experimental characterization. The relation of specific volume, pressure, and temperature is designated by the pressure-volume-temperature behavior (PVT). In this work, we have employed the modified Tait model where the specific volume, 𝑉𝑉�, is given by:   𝑉𝑉� = 𝑉𝑉0� �1 − 𝐶𝐶ln �1 + �𝑝𝑝𝐵𝐵��� + 𝑉𝑉𝑡𝑡�   3. Case studies  3.1. Case Study 1: Filling of a Rectangular Cavity with a Cylindrical Insert  This case study covers the filling of a rectangular cavity with a cylindrical insert, illustrated in Figure 1. The cavity geometry has a constant thickness of 4 mm, a width of 40 mm, and a length of 150 mm, while the cylindrical insert has a diameter of 15 mm, and its center is located at 55 mm from the inlet.   Figure 1. Geometry and boundary patches for Case Study 1 (dimensions in mm).  Figure 2 shows the distribution of the pressure field on the mold cavity, computed for both compressible (C) and incompressible (I) formulations, at the switch-over point (98% of volume filled cavity). These results showed that the maximum pressure required to fill the cavity, predicted by both formulations, was quite similar, with a difference of approximately 3.7%, and the computational cost is 5% smaller for the incompressible formulation.   Figure 2. Distribution of the pressure field on the mold cavity, for the two formulations, compressible (C) and incompressible (I), at the switch-over point. run time40 hoursrun time42 hours3.2. Case Study 2: Filling of a Tensile Test Specimen  This second case study comprises the simulation of the filling stage of a tensile test specimen. The aim of this case study is to compare the accuracy and performance of openInjMoldSim with the proprietary software Moldex3D®. This case study geometry is illustrated in Figure 3.  Figure 3. Geometry and boundary patches for Case Study 2 (dimensions in mm).  Figure 4 shows the contour of the pressure field distribution in the cavity at the switch-over point. The pressure profiles obtained in both software are qualitatively identical. However, as also shown in Figure 4, the melt flow front predicted by the open-source software seemed more realistic than that of the proprietary counterpart, which present a plug-like surface.   Figure 4. Pressure distribution at the switch-over point and melt flow front shape predicted by the most refined mesh of both software.    openInjMoldSim (M3) Moldex3D® (M4)4. Conclusions  A numerical formulation available in the open-source computational library OpenFOAM®, the openInjMoldSim solver, was assessed in different test cases related to the simulation of the filling stage of the injection molding process. In summary, the results presented here showed that the injection molding code can be used to model the filling stage of injection molding processes accurately.  Acknowledgments: The authors would like to acknowledge the Minho University cluster under the project NORTE-07-0162-FEDER-000086 and the Minho Advanced Computing Center (MACC) for providing HPC resources that contributed to the research results reported within this abstract.  References  [HIR] Hirt, C.W.; Nichols, B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 1981, 39, 201–225, doi:10.1016/0021-9991(81)90145-5.  [KRE] Krebelj, K.; Turk, J. An open–source injection molding simulation. A solver for OpenFOAM. https://github.com/krebeljk/openInjMoldSim, 2019.  [MOL] Mole, N.; Krebelj, K.; Stok, B. Injection molding simulation with solid semi-crystalline polymer mechanical behavior for ejection analysis. Int. J. Adv. Manuf. Technol. 2017, 93, 4111–4124, doi:10.1007/s00170-017-0847-3.  [ROS] Rosato, D.V.; Rosato, M.G. Injection Molding Handbook; Springer: Cham, Switzerland, 2000.  

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On the simulation of the filling stage of thermoplastic injection molding using the open-source solver openInjMoldSim

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