Multiscale smoothed particle hydrodynamic simulation of injection molding

XU Xiaoyang; TIAN Lingyun

doi:10.16511/j.cnki.qhdxxb.2024.22.004

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Journal of Tsinghua University(Science and Technology) ›› 2024, Vol. 64 ›› Issue (8) : 1401-1413. DOI: 10.16511/j.cnki.qhdxxb.2024.22.004

AEROSPACE AND ENGINEERING MECHANICS

Multiscale smoothed particle hydrodynamic simulation of injection molding

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Abstract

[Objective] Injection molding is an important method in polymer molding processing. Numerical simulations have proven effective in studying viscoelastic injection molding problems. Traditional numerical simulations of injection molding typically rely on macroscale models. However, the performance of plastics is closely related to their micromolecular structure. Understanding the evolution of the micromolecular structure is essential for improving product quality. Therefore, the simulation study of coupling micro- and macroscales has important academic and practical value. [Methods] In this study, a multiscale smoothed particle hydrodynamic (SPH) method based on the bead-spring chain model is used to simulate viscoelastic injection molding. At the macroscale, the conservation equations of mass and momentum are solved using the SPH method, whereas at the microscale, the elastic stress is described using the Brownian configuration field method. The viscoelastic Couette flow is simulated using three types of bead-spring chain models. The effectiveness of the multiscale SPH method is verified by comparing simulation results with analytical solutions of the viscoelastic Couette flow of the Hookean dumbbell model and by comparing the numerical solutions of the viscoelastic Couette flow of the finitely extensible nonlinear elastic dumbbell model with the literature results. The bead-spring dumbbell model is extended to a bead-spring chain model, and the Couette flow is simulated. The influence of different numbers of beads on the viscoelastic flow is analyzed, and an appropriate number of beads is selected for numerical simulations. In addition, the multiscale SPH method is extended to simulate injection molding in C-shaped and N-shaped cavities. Micro- and macro-parameters in injection molding are investigated, including the first normal stress difference, molecular stretch, and mean conformation thickness. The convergence of the multiscale SPH method is evaluated by changing the total number of SPH fluid particles N_f at the macroscale and the total number of bead-spring chain models N_b in each particle at the microscale. The obtained numerical solutions for the velocity are consistent. Furthermore, the effects of different rheological parameters, such as the number of beads of the molecular chain M, the spring maximum extensibility b_max, the viscosity ratio β, the Reynolds number Re, and the Weissenberg number Wi, on the flow behavior of viscoelastic fluid are analyzed. [Results] The results show that the multiscale SPH method can stably and effectively simulate viscoelastic injection molding. This method can obtain micromolecular information that is impossible to obtain using traditional macro closed-form constitutive equations. In addition, different rheological parameters significantly influence the viscoelastic flow behavior. Larger M and b_max values result in increased steady values of molecular stretch and mean conformation thickness. Larger β and Re values result in smaller peak values of the first normal stress difference and weaker overshoot phenomena. Furthermore, larger Wi values yield larger peak values of the first normal stress difference, more oscillating numerical values, smaller molecular stretch values, and greater mean conformational thickness values. [Conclusions] The multiscale method provides a new approach for simulating viscoelastic injection molding.

Key words

smoothed particle hydrodynamics (SPH) / bead-spring chain model / injection molding / viscoelastic fluid / multiscale modeling

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XU Xiaoyang, TIAN Lingyun. Multiscale smoothed particle hydrodynamic simulation of injection molding[J]. Journal of Tsinghua University(Science and Technology). 2024, 64(8): 1401-1413 https://doi.org/10.16511/j.cnki.qhdxxb.2024.22.004

References

[1] LI X J, HE J H. Variational multi-scale finite element method for the two-phase flow of polymer melt filling process[J]. International Journal of Numerical Methods for Heat and Fluid Flow, 2020, 30(3):1407-1426.
[2] QUAGLIATO L, LEE J, FONSECA J H, et al. Influences of stress triaxiality and local fiber orientation on the failure strain for injection-molded carbon fiber reinforced polyamide-6[J]. Engineering Fracture Mechanics, 2021, 250:107784.
[3] XIONG M X, WANG Y H, LIEW J Y R. Evaluation on thermal behavior of concrete-filled steel tubular columns based on modified finite difference method[J]. Advances in Structural Engineering, 2016, 19(5):746-761.
[4] RANADE R, HILL C, PATHAK J. DiscretizationNet:A machine-learning based solver for Navier-Stokes equations using finite volume discretization[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 378:113722.
[5] GUO Q, RUI H X, LI X L. Modified marker and cell schemes for Stokes equations with Dirichlet boundary condition[J]. Mathematical Methods in the Applied Sciences, 2022, 45(16):10384-10407.
[6] 魏建国,韩江,侯庆志,等.声道中气动声学问题的光滑粒子动力学模拟[J].清华大学学报(自然科学版), 2016, 56(11):1242-1248. WEI J G, HAN J, HOU Q Z, et al. SPH simulations of aeroacoustic problems in vocal tracts[J]. Journal of Tsinghua University (Science and Technology), 2016, 56(11):1242-1248.(in Chinese)
[7] LUCY L B. A numerical approach to the testing of the fission hypothesis[J]. Astronomical Journal, 1977, 82:1013-1024.
[8] GINGOLD R A, MONAGHAN J J. Smoothed particle hydrodynamics:Theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society, 1977, 181(3):375-389.
[9] MONAGHAN J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics, 1994, 110(2):399-406.
[10] ELLERO M, TANNER R I. SPH simulations of transient viscoelastic flows at low Reynolds number[J]. Journal of Non-Newtonian Fluid Mechanics, 2005, 132(1-3):61-72.
[11] LIU M B, LIU G R. Smoothed particle hydrodynamics (SPH):An overview and recent developments[J]. Archives of Computational Methods in Engineering, 2010, 17(1):25-76.
[12] GHYSELS P, SAMAEY G, VAN LIEDEKERKE P, et al. Multiscale modeling of viscoelastic plant tissue[J]. International Journal for Multiscale Computational Engineering, 2010, 8(4):379-396.
[13] HASHEMI M R, FATEHI R, MANZARI M T. SPH simulation of interacting solid bodies suspended in a shear flow of an Oldroyd-B fluid[J]. Journal of Non-Newtonian Fluid Mechanics, 2011, 166(21-22):1239-1252.
[14] VÁZQUEZ-QUESADA A, ELLERO M. SPH simulations of a viscoelastic flow around a periodic array of cylinders confined in a channel[J]. Journal of Non-Newtonian Fluid Mechanics, 2012, 167-168:1-8.
[15] BAO Y D, WU D M. Virtual training system with physical viscoelastic model and blood flow simulation based on a range-based SPH method[J]. Journal of Biomimetics, Biomaterials and Biomedical Engineering, 2015, 25:41-53.
[16] HECK T, SMEETS B, VANMAERCKE S, et al. Modeling extracellular matrix viscoelasticity using smoothed particle hydrodynamics with improved boundary treatment[J]. Computer Methods in Applied Mechanics and Engineering, 2017, 322:515-540.
[17] DOS SANTOS BRITO C J, VIEIRA-E-SILVA A L B, ALMEIDA M W S, et al. Large viscoelastic fluid simulation on GPU[C]//2017 16th Brazilian Symposium on Computer Games and Digital Entertainment (SBGames). Curitiba, Brazil:IEEE, 2017:134-143.
[18] VAHABI M, KAMKARI B. Simulating gas bubble shape during its rise in a confined polymeric solution by WC-SPH[J]. European Journal of Mechanics-B/Fluids, 2019, 75:1-14.
[19] MOINFAR Z, VAHABI S, VAHABI M. Numerical simulation of drop deformation under simple shear flow of Giesekus fluids by SPH[J]. International Journal of Numerical Methods for Heat and Fluid Flow, 2023, 33(1):263-281.
[20] CLEARY P W, HA J, PRAKASH M, et al. 3D SPH flow predictions and validation for high pressure die casting of automotive components[J]. Applied Mathematical Modelling, 2006, 30(11):1406-1427.
[21] VESENJAK M, REN Z. Application aspects of the meshless SPH method[J]. Journal of the Serbian Society for Computational Mechanics, 2007, 1(1):74-86.
[22] HOU Q, ZHANG L X, TIJSSELING A S, et al. Rapid filling of pipelines with the SPH particle method[J]. Procedia Engineering, 2012, 31:38-43.
[23] XU X Y, OUYANG J, YANG B X, et al. SPH simulations of three-dimensional non-Newtonian free surface flows[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 256:101-116.
[24] ROBINSON M, LUDING S, RAMAIOLI M. SPH-DEM simulations of grain dispersion by liquid injection[J]. AIP Conference Proceedings, 2013, 1542(1):1122-1125.
[25] HE L P, LU G, CHEN D C, et al. Three-dimensional smoothed particle hydrodynamics simulation for injection molding flow of short fiber-reinforced polymer composites[J]. Modelling and Simulation in Materials Science and Engineering, 2017, 25(5):055007.
[26] XU X Y, YU P. A multiscale SPH method for simulating transient viscoelastic flows using bead-spring chain model[J]. Journal of Non-Newtonian Fluid Mechanics, 2016, 229:27-42.
[27] KAILASHAM R, CHAKRABARTI R, PRAKASH J R. Shear viscosity for finitely extensible chains with fluctuating internal friction and hydrodynamic interactions[J]. Journal of Rheology, 2023, 67(1):105-123.
[28] SUN P N, PILLOTON C, ANTUONO M, et al. Inclusion of an acoustic damper term in weakly-compressible SPH models[J]. Journal of Computational Physics, 2023, 483:112056.
[29] MUTA A, RAMACHANDRAN P. Efficient and accurate adaptive resolution for weakly-compressible SPH[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 395:115019.
[30] XU X Y, OUYANG J, LI W M, et al. SPH simulations of 2D transient viscoelastic flows using Brownian configuration fields[J]. Journal of Non-Newtonian Fluid Mechanics, 2014, 208-209:59-71.
[31] SHAO S D, LO E Y M. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface[J]. Advances in Water Resources, 2003, 26(7):787-800.
[32] BONVIN J C. Numerical simulation of viscoelastic fluids with mesoscopic models[D]. Lausanne, Switzerland:EPFL, 2000.
[33] LIU M B, LIU G R. Restoring particle consistency in smoothed particle hydrodynamics[J]. Applied Numerical Mathematics, 2006, 56(1):19-36.
[34] LIU M B, SHAO J R, LI H Q. An SPH model for free surface flows with moving rigid objects[J]. International Journal for Numerical Methods in Fluids, 2014, 74(9):684-697.
[35] 许晓阳,周亚丽,余鹏. eXtended Pom-Pom黏弹性流体的改进光滑粒子动力学模拟[J].物理学报, 2023, 72(3):034701. XU X Y, ZHOU Y L, YU P. Improved smoothed particle dynamics simulation of eXtended Pom-Pom viscoelastic fluid[J]. Acta Physica Sinica, 2023, 72(3):034701.(in Chinese)
[36] LASO M, ÖTTINGER H C. Calculation of viscoelastic flow using molecular models:The CONNFFESSIT approach[J]. Journal of Non-Newtonian Fluid Mechanics, 1993, 47:1-20.