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非等温黏弹性复杂流动的改进SPH方法模拟

许晓阳 赵雨婷 李家宇 余鹏

许晓阳, 赵雨婷, 李家宇, 余鹏. 非等温黏弹性复杂流动的改进SPH方法模拟. 力学学报, 2023, 55(5): 1099-1112 doi: 10.6052/0459-1879-22-602
引用本文: 许晓阳, 赵雨婷, 李家宇, 余鹏. 非等温黏弹性复杂流动的改进SPH方法模拟. 力学学报, 2023, 55(5): 1099-1112 doi: 10.6052/0459-1879-22-602
Xu Xiaoyang, Zhao Yuting, Li Jiayu, Yu Peng. Simulations of non-isothermal viscoelastic complex flows by improved SPH method. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1099-1112 doi: 10.6052/0459-1879-22-602
Citation: Xu Xiaoyang, Zhao Yuting, Li Jiayu, Yu Peng. Simulations of non-isothermal viscoelastic complex flows by improved SPH method. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1099-1112 doi: 10.6052/0459-1879-22-602

非等温黏弹性复杂流动的改进SPH方法模拟

doi: 10.6052/0459-1879-22-602
基金项目: 国家自然科学基金(12071367, 12172163)和陕西省“特支计划”青年拔尖人才项目(289890259)资助
详细信息
    通讯作者:

    许晓阳, 教授, 主要研究方向为复杂流体的多尺度建模与计算. E-mail: xiaoyang.xu@xust.edu.cn

  • 中图分类号: O242

SIMULATIONS OF NON-ISOTHERMAL VISCOELASTIC COMPLEX FLOWS BY IMPROVED SPH METHOD

  • 摘要: 非等温黏弹性流体广泛存在于自然界和工业生产中, 准确预测黏弹性流体的非等温流动机理和复杂流变特性有着重要的应用价值. 文章提出一种改进的光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)方法对非等温黏弹性复杂流动进行了数值模拟, 其中流体的黏弹特性通过eXtended Pom-Pom本构模型来表征. 为了提高模拟结果的精度, 采用了一种核函数梯度的修正算法; 为了灵活地施加边界条件, 发展了边界粒子和虚拟粒子相联合的边界处理方法; 为了消除流动过程中的拉伸不稳定性, 施加了粒子迁移技术. 运用改进SPH方法数值模拟了液滴撞击固壁和F型腔注塑成型问题, 通过与Basilisk软件得到的结果进行比较验证了改进SPH方法求解非等温黏弹性流体的有效性. 通过利用不同粒子初始间距进行计算, 评价了改进SPH方法的数值收敛性. 研究了非等温流动相较于等温流动的不同流动特征, 深入分析了不同热流变参数对流动过程的影响. 数值结果表明, 文章提出的改进SPH方法可稳定、准确地描述非等温黏弹性复杂流动的传热机理、复杂流变特性和自由面变化特性.

     

  • 图  1  液滴冲击固体表面的计算模型

    Figure  1.  Computational model of droplet impinging solid wall surface

    图  2  运用改进SPH方法模拟得到的液滴冲击固体表面在不同时刻的温度分布

    Figure  2.  The temperature distribution of droplet impinging solid wall surface at different times obtained by improved SPH method

    图  3  利用改进SPH方法和Basilisk软件得到的液滴铺展宽度随时间变化的比较

    Figure  3.  Comparison of the time changes of the droplet spread width obtained by the improved SPH method and Basilisk software

    图  4  利用不同方法得到的液滴在t* = 2.5时刻的模拟结果

    Figure  4.  The simulation result of droplet at t* = 2.5 obtained by different methods

    图  5  温度依赖系数φ对液滴铺展宽度随时间变化的影响

    Figure  5.  Influence of the temperature dependency coefficient φ on the time change of the droplet spread width

    图  6  不同流变参数下液滴铺展宽度随时间的变化

    Figure  6.  Time change of the droplet spread width under different rheological parameters

    图  7  F型腔注塑成型问题的计算模型

    Figure  7.  Computational model of injection molding process for an F-shaped cavity

    图  8  运用改进SPH方法模拟得到的F型腔注塑成型在不同时刻的温度分布

    Figure  8.  The temperature distribution of F-shaped cavity injection molding at different times obtained by improved SPH method

    图  9  Péclet数对F型腔注塑成型在t = 0.6 s时刻的温度分布的影响

    Figure  9.  Effect of Péclet number on the temperature distribution at t = 0.6 s in F-shaped cavity injection molding

    图  10  运用改进SPH方法模拟得到的F型腔注塑成型在不同时刻的第一法向应力差分布

    Figure  10.  The first normal stress difference distribution of F-shaped cavity injection molding at different times obtained by improved SPH method

    图  11  利用不同粒子间距Δx得到的点A处第一法 向应力差N1随时间变化的比较

    Figure  11.  Comparison of the time change of the first normal stress difference N1 at point A obtained by different particle spacings Δx

    图  12  不同流变参数下点A处的第一法向应力差N1随时间的变化

    Figure  12.  Time change of the first normal stress difference N1 at point A under different rheological parameters

  • [1] Peters GWM, Baaijens FPT. Modelling of non-isothermal viscoelastic flows. Journal of Non-Newtonian Fluid Mechanics, 1997, 68(2-3): 205-224 doi: 10.1016/S0377-0257(96)01511-X
    [2] Li Q, Qu F. A level set based immersed boundary method for simulation of non-isothermal viscoelastic melt filling process. Chinese Journal of Chemical Engineering, 2021, 32: 119-133 doi: 10.1016/j.cjche.2020.09.057
    [3] Fernandes C. A fully implicit log-conformation tensor coupled algorithm for the solution of incompressible non-isothermal viscoelastic flows. Polymers, 2022, 14(19): 4099 doi: 10.3390/polym14194099
    [4] Moreno L, Codina R, Baiges J. Numerical simulation of non-isothermal viscoelastic fluid flows using a VMS stabilized finite element formulation. Journal of Non-Newtonian Fluid Mechanics, 2021, 296: 104640 doi: 10.1016/j.jnnfm.2021.104640
    [5] Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 1977, 181(3): 375-389 doi: 10.1093/mnras/181.3.375
    [6] Lucy LB. A numerical approach to the testing of the fission hypothesis. The Astronomical Journal, 1977, 82: 1013-1024 doi: 10.1086/112164
    [7] 王璐, 徐绯, 杨扬. 完全拉格朗日 SPH 在冲击问题中的改进和应用. 力学学报, 2022, 54(12): 3297-3309 (Wang Lu, Xu Fei, Yang Yang. Improvement of the total Lagrangian SPH and its application in impact problems. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3297-3309 (in Chinese)
    [8] Liu MB, Zhang ZL, Feng DL. A density-adaptive SPH method with kernel gradient correction for modeling explosive welding. Computational Mechanics, 2017, 60(3): 513-529 doi: 10.1007/s00466-017-1420-5
    [9] 王平平, 张阿漫, 彭玉祥等. 近场水下爆炸瞬态强非线性流固耦合无网格数值模拟研究. 力学学报, 2022, 54(8): 2194-2209 (Wang Pingping, Zhang Aman, Peng Yuxiang, et al. Numerical simulation of transient strongly-nonlinear fluid-structure interaction in near-field underwater explosion based on meshless method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(8): 2194-2209 (in Chinese)
    [10] 姚学昊, 陈丁, 武立伟等. 流固耦合破坏分析的多分辨率 PD-SPH 方法. 力学学报, 2022, 54(12): 3333-3343 (Yao Xuehao, Chen Ding, Wu Liwei, et al. A multi-resolution PD-SPH coupling approach for structural failure under fluid-structure interaction. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3333-3343 (in Chinese)
    [11] He F, Zhang H, Huang C, et al. A stable SPH model with large CFL numbers for multi-phase flows with large density ratios. Journal of Computational Physics, 2022, 453: 110944 doi: 10.1016/j.jcp.2022.110944
    [12] Liu MB, Liu GR. Restoring particle consistency in smoothed particle hydrodynamics. Applied Numerical Mathematics, 2006, 56(1): 19-36 doi: 10.1016/j.apnum.2005.02.012
    [13] Xue B, Wang SP, Peng YX, et al. A novel coupled Riemann SPH–RKPM model for the simulation of weakly compressible fluid–structure interaction problems. Ocean Engineering, 2022, 266: 112447 doi: 10.1016/j.oceaneng.2022.112447
    [14] Ng KC, Alexiadis A, Ng YL. An improved particle method for simulating fluid-structure interactions: The multi-resolution SPH-VCPM approach. Ocean Engineering, 2022, 247: 110779 doi: 10.1016/j.oceaneng.2022.110779
    [15] Monaghan JJ, Kajtar JB. SPH particle boundary forces for arbitrary boundaries. Computer Physics Communications, 2009, 180(10): 1811-1820 doi: 10.1016/j.cpc.2009.05.008
    [16] Morris JP, Fox PJ, Zhu Y. Modeling low Reynolds number incompressible flows using SPH. Journal of Computational Physics, 1997, 136(1): 214-226 doi: 10.1006/jcph.1997.5776
    [17] Liu MB, Shao JR, Chang JZ. On the treatment of solid boundary in smoothed particle hydrodynamics. Science China Technological Sciences, 2012, 55(1): 244-254 doi: 10.1007/s11431-011-4663-y
    [18] Yildiz M, Rook RA, Suleman A. SPH with the multiple boundary tangent method. International Journal for Numerical Methods in Engineering, 2009, 77(10): 1416-1438 doi: 10.1002/nme.2458
    [19] Chen C, Zhang AM, Chen JQ, et al. SPH simulations of water entry problems using an improved boundary treatment. Ocean Engineering, 2021, 238: 109679 doi: 10.1016/j.oceaneng.2021.109679
    [20] Yang X, Liu M, Peng S. Smoothed particle hydrodynamics modeling of viscous liquid drop without tensile instability. Computers & Fluids, 2014, 92: 199-208
    [21] Sun PN, Colagrossi A, Marrone S, et al. Multi-resolution Delta-plus-SPH with tensile instability control: Towards high Reynolds number flows. Computer Physics Communications, 2018, 224: 63-80 doi: 10.1016/j.cpc.2017.11.016
    [22] Chalk CM, Pastor M, Peakall J, et al. Stress-Particle smoothed particle hydrodynamics: An application to the failure and post-failure behaviour of slopes. Computer Methods in Applied Mechanics and Engineering, 2020, 366: 113034 doi: 10.1016/j.cma.2020.113034
    [23] Lyu HG, Sun PN. Further enhancement of the particle shifting technique: Towards better volume conservation and particle distribution in SPH simulations of violent free-surface flows. Applied Mathematical Modelling, 2022, 101: 214-238 doi: 10.1016/j.apm.2021.08.014
    [24] Rafiee A, Manzari MT, Hosseini M. An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows. International Journal of Non-Linear Mechanics, 2007, 42(10): 1210-1223 doi: 10.1016/j.ijnonlinmec.2007.09.006
    [25] 杨波, 欧阳洁, 蒋涛等. PTT 黏弹性流体的光滑粒子动力学方法模拟. 力学学报, 2011, 43(4): 667-673 (Yang Bo, Ouyang Jie, Jiang Tao, et al. Numerical simulation of the viscoelastic flows for PTT model by the SPH method. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 667-673 (in Chinese)
    [26] Xu X, Deng XL. An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids. Computer Physics Communications, 2016, 201: 43-62 doi: 10.1016/j.cpc.2015.12.016
    [27] King JRC, Lind SJ. High weissenberg number simulations with incompressible smoothed particle hydrodynamics and the log-conformation formulation. Journal of Non-Newtonian Fluid Mechanics, 2021, 293: 104556 doi: 10.1016/j.jnnfm.2021.104556
    [28] Duque-Daza C, Alexiadis A. A simplified framework for modelling viscoelastic fluids in discrete multiphysics. Chem Engineering, 2021, 5(3): 61
    [29] Vahabi M, Hadavandmirzaei H, Kamkari B, et al. Interaction of a pair of in-line bubbles ascending in an Oldroyd-B liquid: A numerical study. European Journal of Mechanics-B/Fluids, 2021, 85: 413-429 doi: 10.1016/j.euromechflu.2020.11.004
    [30] Moinfar Z, Vahabi S, Vahabi M. Numerical simulation of drop deformation under simple shear flow of Giesekus fluids by SPH. International Journal of Numerical Methods for Heat & Fluid Flow, 2023, 33(1): 263-281
    [31] Meburger S, Niethammer M, Bothe D, et al. Numerical simulation of non-isothermal viscoelastic flows at high weissenberg numbers using a finite volume method on general unstructured meshes. Journal of Non-Newtonian Fluid Mechanics, 2021, 287: 104451 doi: 10.1016/j.jnnfm.2020.104451
    [32] Verbeeten WMH, Peters GWM, Baaijens FPT. Differential constitutive equations for polymer melts: The extended Pom–Pom model. Journal of Rheology, 2001, 45(4): 823-843 doi: 10.1122/1.1380426
    [33] Tanner RI. Engineering Rheology. OUP Oxford, 2000
    [34] O'connor J, Domínguez JM, Rogers BD, et al. Eulerian incompressible smoothed particle hydrodynamics on multiple GPUs. Computer Physics Communications, 2022, 273: 108263 doi: 10.1016/j.cpc.2021.108263
    [35] Liu GR, Liu MB. Smoothed Particle Hydrodynamics: A Meshfree Particle Method. Singapore: World Scientific, 2003
    [36] Shao S, Lo EYM. Incompressible SPH method for simulating newtonian and non-newtonian flows with a free surface. Advances in Water Resources, 2003, 26(7): 787-800 doi: 10.1016/S0309-1708(03)00030-7
    [37] Bonet J, Lok TSL. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Computer Methods in Applied Mechanics and Engineering, 1999, 180(1-2): 97-115 doi: 10.1016/S0045-7825(99)00051-1
    [38] Lind SJ, Xu R, Stansby PK, et al. Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. Journal of Computational Physics, 2012, 231(4): 1499-1523 doi: 10.1016/j.jcp.2011.10.027
    [39] Wang PP, Meng ZF, Zhang AM, et al. Improved particle shifting technology and optimized free-surface detection method for free-surface flows in smoothed particle hydrodynamics. Computer Methods in Applied Mechanics and Engineering, 2019, 357: 112580 doi: 10.1016/j.cma.2019.112580
    [40] Yang L, Rakhsha M, Hu W, et al. A consistent multiphase flow model with a generalized particle shifting scheme resolved via incompressible SPH. Journal of Computational Physics, 2022, 458: 111079 doi: 10.1016/j.jcp.2022.111079
    [41] Popinet S. An accurate adaptive solver for surface-tension-driven interfacial flows. Journal of Computational Physics, 2009, 228(16): 5838-5866 doi: 10.1016/j.jcp.2009.04.042
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出版历程
  • 收稿日期:  2022-12-29
  • 录用日期:  2023-03-29
  • 网络出版日期:  2023-03-30
  • 刊出日期:  2023-05-18

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