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基于虚拟区域法的黏弹性流体中微生物游动的数值模拟和应用

彭方远 潘定一 陈杏藩 林昭武

彭方远, 潘定一, 陈杏藩, 林昭武. 基于虚拟区域法的黏弹性流体中微生物游动的数值模拟和应用. 力学学报, 2023, 55(1): 84-94 doi: 10.6052/0459-1879-22-372
引用本文: 彭方远, 潘定一, 陈杏藩, 林昭武. 基于虚拟区域法的黏弹性流体中微生物游动的数值模拟和应用. 力学学报, 2023, 55(1): 84-94 doi: 10.6052/0459-1879-22-372
Peng Fangyuan, Pan Dingyi, Chen Xingfan, Lin Zhaowu. A numerical algorithm based on fictitious domain method for the simulation of microorganisms swimming in a viscoelastic fluid. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 84-94 doi: 10.6052/0459-1879-22-372
Citation: Peng Fangyuan, Pan Dingyi, Chen Xingfan, Lin Zhaowu. A numerical algorithm based on fictitious domain method for the simulation of microorganisms swimming in a viscoelastic fluid. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 84-94 doi: 10.6052/0459-1879-22-372

基于虚拟区域法的黏弹性流体中微生物游动的数值模拟和应用

doi: 10.6052/0459-1879-22-372
基金项目: 国家自然科学基金(12172327)和国家自然科学基金(12132015)重点项目资助项目
详细信息
    通讯作者:

    林昭武, 副研究员, 主要研究方向为多相流、复杂流体. E-mail: linzhaowu@zju.edu.cn

  • 中图分类号: O35

A NUMERICAL ALGORITHM BASED ON FICTITIOUS DOMAIN METHOD FOR THE SIMULATION OF MICROORGANISMS SWIMMING IN A VISCOELASTIC FLUID

  • 摘要: 微生物是自然生态系统的重要组成部分, 掌握微生物在复杂流体中的运动特性可以为微型器件的设计制造提供理论指导. 壁面效应是微生物游动研究中的重要问题之一, 已有研究表明微生物在壁面附近存在复杂的行为特征. 然而已有研究大多集中于微生物在牛顿流体中的游动模拟, 仅有少数涉及黏弹性流体等非牛顿流体. 本文采用直接力虚拟区域法与乔列斯基分解相结合的数值方法, 引入Squirmer微生物游动模型, 研究了微生物在黏弹性流体中的游动问题. 首先给出求解黏弹性流体本构方程的数值格式; 并将该方法应用于研究微生物游动中的壁面效应. 研究结果表明, 游动方向是影响微生物颗粒壁面效应的重要因素. 流体弹性应力会对微生物产生一个反向转矩, 影响微生物的游动方向, 从而阻碍微生物逃离壁面. 微生物颗粒在黏弹性流体中与壁面作用时间较长, 几乎达到牛顿流体的两倍以上.

     

  • 图  1  网格信息交换示意图

    Figure  1.  Schematic of data exchange

    图  2  并行虚拟区域法流程图

    Figure  2.  Flowchart for the parallel fictitious domain method

    图  3  两种类型粒子游动平均速度${U_{{\rm{GK}}}}$$ We $变化规律: (a)$ \beta = 5 $, (b)$ \beta = - 5 $. (b)插图为$ \beta = - 5,We = 2 $工况下粒子游动速度$ U $随时间的变化曲线; 黑色实线为粗网格$h = 1/16,\Delta t = 0.000\;5$计算结果, 红色实线为细网格$h = 1/32,\Delta t = 0.000\;25$计算结果

    Figure  3.  The average swimming speed ${U_{{\rm{GK}}}}$ of squirmers: (a) $ \beta = 5 $, (b) $ \beta = - 5 $. Inset: squirmer swimming speed computed when using two different meshes at $ \beta = - 5,We = 2 $; black solid line represents the result of coarse grid $h = 1/16,\Delta t = 0.000\;5$, and the red represents the result of fine grid $h = 1/32,\Delta t = 0.000\;25$

    图  4  微生物颗粒($ \beta = 3 $)与壁面作用轨迹图, 粒子与壁面初始距离$ d = 2 $, 游动方向与$ x $轴夹角$\gamma = - \text{π} /4$

    Figure  4.  Trajectory of puller ($ \beta = 3 $) contact with wall, the initial distance between particles and wall $ d = 2 $, the angle between swimming direction and$ x $-axis $\gamma = - \text{π} /4$

    图  5  微生物颗粒自由游动流场结构图. 坐标系为随体坐标; 黑色箭头表示颗粒游动方向, 背景云图表示构型张量的迹${\rm{Tr}}\left( {{{\boldsymbol{C}}}} \right)$. 左半部分图为$ We = 0 $结果; 右半部分图为$ We = 4 $结果

    Figure  5.  Flow field around squirmer particles free swimming in viscoelastic fluids with comoving frame; the black arrow represents the swimming direction of particles, and the background cloud chart represents the trace of the configuration tensor ${\rm{Tr}}\left( {\boldsymbol{C}} \right)$. The left part of figure shows the result at $ We = 0 $; the right part shows the result at $ We = 4 $

    图  6  不同类型微生物颗粒与壁面间隔距离$ d $随时间变化曲线. 黏弹性流体的参数为: $ Re = 0.01 $, $ We = 0\sim 4 $, $ \alpha = 0.2 $, $ {\mu _r} = 0.5 $, $ {\rho _r} = 1.0 $

    Figure  6.  The distance between squirmer particles and the wall in the y direction as a function of time. Parameters of viscoelastic fluid: $ Re = 0.01 $, $ We = 0\sim 4 $, $ \alpha = 0.2 $, $ {\mu _r} = 0.5 $, $ {\rho _r} = 1.0 $

    图  7  微生物颗粒游动方向与$ x $轴夹角随时间变化曲线. 黏弹性流体的参数为: $ Re = 0.01 $, $ We = 0\sim 4 $, $ \alpha = 0.2 $, $ {\mu _r} = 0.5 $, $ {\rho _r} = 1.0 $

    Figure  7.  Angle between squirmer particles swimming direction and the $ x $-axis as a function of time. Parameters of the viscoelastic fluid: $ Re = 0.01 $, $ We = 0\sim 4 $, $ \alpha = 0.2 $, $ {\mu _r} = 0.5 $, $ {\rho _r} = 1.0 $

    图  8  微生物颗粒在$ x - y $平面内受到的水动力转矩$ {T_z} $随时间变化曲线. 其中, $ {T_{v,z}} $表示黏性转矩$ z $方向分量, $ {T_{e,z}} $表示弹性转矩$ z $方向分量, 计算公式见式(33). 黏弹性流体的参数为: $ Re = 0.01 $, $ We = 0,4 $, $ \alpha = 0.2 $, $ {\mu _r} = 0.5 $, $ {\rho _r} = 1.0 $

    Figure  8.  Hydrodynamic torque in the z direction computed using Eq. (33). $ {T_{v,z}} $ represents the viscous torque and $ {T_{e,z}} $ the elastic torque. Parameters of the viscoelastic fluid: $ Re = 0.01 $, $ We = 0,4 $, $ \alpha = 0.2 $, $ {\mu _r} = 0.5 $, $ {\rho _r} = $1.0

    图  9  微生物颗粒在壁面方向受到的水动力$ {F_y} $随时间变化曲线. 其中, $ {F_{v,y}} $表示黏性应力$ y $方向分量, $ {F_{e,y}} $表示弹性应力$ y $方向分量, 计算公式见式(33). 黏弹性流体的参数为: $ Re = 0.01 $, $ We = 0,4 $, $ \alpha = 0.2 $, $ {\mu _r} = 0.5 $, $ {\rho _r} = 1.0 $

    Figure  9.  Hydrodynamic forces in the y direction computed using Eq. (33). $ {F_{v,y}} $ represents the viscous force and $ {F_{e,y}} $ the elastic force. Parameters of viscoelastic fluid: $ Re = 0.01 $, $ We = 0,4 $, $ \alpha = 0.2 $, $ {\mu _r} = 0.5 $, $ {\rho _r} = 1.0 $

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出版历程
  • 收稿日期:  2022-08-14
  • 录用日期:  2022-11-04
  • 网络出版日期:  2022-11-05
  • 刊出日期:  2023-01-18

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