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基于2D网格的轴对称浸没边界法

蔡政刚 潘君华 倪明玖

蔡政刚, 潘君华, 倪明玖. 基于2D网格的轴对称浸没边界法. 力学学报, 2022, 54(7): 1-12 doi: 10.6052/0459-1879-22-110
引用本文: 蔡政刚, 潘君华, 倪明玖. 基于2D网格的轴对称浸没边界法. 力学学报, 2022, 54(7): 1-12 doi: 10.6052/0459-1879-22-110
Cai Zhenggang, Pan Junhua, Ni Mingjiu. An axisymmetric immersed boundary method based on 2D mesh. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1-12 doi: 10.6052/0459-1879-22-110
Citation: Cai Zhenggang, Pan Junhua, Ni Mingjiu. An axisymmetric immersed boundary method based on 2D mesh. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1-12 doi: 10.6052/0459-1879-22-110

基于2D网格的轴对称浸没边界法

doi: 10.6052/0459-1879-22-110
基金项目: 国家自然科学基金(52006212), 中国科学院基础前沿科学研究计划(ZDBS-LY-JSC033), 中国科学院战略性先导科技专项B类(XDB22040201)和中国博士后科学基金(2019M650815)资助项目
详细信息
    作者简介:

    潘君华, 助理研究员, 主要研究方向: 磁流体力学. E-mail: panjunhua@ucas.ac.cn

  • 中图分类号: O361.3

AN AXISYMMETRIC IMMERSED BOUNDARY METHOD BASED ON 2D MESH

  • 摘要: 浸没边界法是处理颗粒两相流中运动边界问题的一种常用数值模拟方法. 当研究的物理问题的无量纲参数满足一定要求时, 该流场结构呈现轴对称状态. 为此本文提出了一种基于2D笛卡尔网格和柱坐标系的轴对称浸没边界法. 该算法采用有限体积法(FVM)对动量方程进行空间离散, 并通过阶梯状锐利界面替代真实的固体浸没边界来封闭控制方程. 为了提高计算效率, 本文采用自适应网格加密技术提高浸没边界附近网格分辨率. 由于柱坐标系的使用, 使得动量方程中的黏性项产生多余的源项, 我们对其作隐式处理. 此外, 在对小球匀速近壁运动进行直接数值模拟时, 由于球壁间隙很小, 间隙内的压力变化比较剧烈. 因此想要精确地解析流场需要很高的网格分辨率. 此时, 需要在一个时间步内多次实施投影步来保证计算的稳定性. 而在小球自由碰壁运动中, 我们通过引入一个润滑力模型使得低网格分辨率下也能模拟小球近壁处的运动. 最后通过小球和圆盘绕流、Stokes流小球近壁运动以及小球自由下落碰壁弹跳算例验证本算法对于轴对称流的静边界和动边界问题均是适用和准确的.

     

  • 图  1  浸没边界和网格单元划分示意图

    Figure  1.  Schematic diagram of immersed boundary and dividing cells type

    图  2  柱坐标系下的体积微元

    Figure  2.  Volume element in cylindrical coordinates

    图  3  流体方程计算流程图

    Figure  3.  Flow chart of fluid equation calculation

    图  4  2D自适应网格

    Figure  4.  An 2D AMR grid around immersed boundary

    图  5  小球绕流几何参数

    Figure  5.  Configuration for flow past a fixed sphere

    图  6  不同雷诺数流线对比

    Figure  6.  Streamline at different Re with IBM

    图  7  小球回流区长度和阻力系数对比

    Figure  7.  Comparisons of the length of recirculation zone $ {L}_{re} $ and drag coefficient$ {C}_{d} $ of sphere

    图  8  圆盘绕流几何参数

    Figure  8.  Configuration for flow past a circular disk

    图  9  不同雷诺数流线对比

    Figure  9.  Comparison of streamline at different Re

    图  10  圆盘回流区长度和阻力系数对比

    Figure  10.  Comparisons of the length of recirculation zone $ {L}_{re} $ and drag coefficient$ {C}_{d} $ of circular disk

    图  11  小球匀速靠近壁面几何参数

    Figure  11.  Configuration for a sphere with a constant velocity approaching a wall

    图  12  压力云图间隙为(a) $ \varepsilon = 1.1 $和(b) $ \varepsilon = 0.1 $

    Figure  12.  Contour of pressure around sphere with (a) $\varepsilon =1.1$ and (b)$\varepsilon =0.1$

    图  13  数值模拟阻力和理论结果对比

    Figure  13.  Comparison of numerical and theoretical results

    图  14  小球与壁面正碰过程

    Figure  14.  Process of a sphere impacting normally on a wall

    图  15  颗粒碰撞轨迹

    Figure  15.  Trajectory of the sphere after colliding with a wall

    表  1  雷诺数Re = 200网格无关性验证

    Table  1.   Grid independence test at Re = 200

    Case$D/\Delta x$$ {C_d} $$ {L_{re}} $
    coarse mesh1600.7681.435
    fine mesh3200.7701.430
    下载: 导出CSV

    表  2  雷诺数Re = 100网格无关性验证

    Table  2.   Grid independence test at Re = 100

    Case$D/\Delta x$$ {C_d} $$ {L_{re}} $
    coarse mesh1601.3271.960
    fine mesh3201.3291.965
    下载: 导出CSV

    表  3  物理计算参数

    Table  3.   Physical and computational parameters

    CaseAB
    $ S{t_c} $ 27 152
    $ {Re} $ 30 165
    $ {U_{in}} $/(m·s−1) 0.518 0.585
    $ D $/m 0.006 0.003
    $ {\rho _p} $/(kg·m−3) 7800 7800
    $ {\rho _f} $/(kg·m−3) 965 935
    $ \nu $/(s·m−2) $1.036\;3 \times {10^{ - 4} }$ $1.069\;5 \times {10^{ - 5} }$
    $ D/\Delta x $ 32 32
    $ {\varepsilon _{al}} $ 0.5 0.5
    $ {\varepsilon _w} $ 0.001 0.001
    下载: 导出CSV
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  • 收稿日期:  2022-03-07
  • 录用日期:  2022-05-07
  • 网络出版日期:  2022-05-08

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