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非球形颗粒两相流的数值模拟研究进展

崔智文 王泽 蒋新宇 赵立豪

崔智文, 王泽, 蒋新宇, 赵立豪. 非球形颗粒两相流的数值模拟研究进展. 力学进展, 待出版 doi: 10.6052/1000-0992-22-006
引用本文: 崔智文, 王泽, 蒋新宇, 赵立豪. 非球形颗粒两相流的数值模拟研究进展. 力学进展, 待出版 doi: 10.6052/1000-0992-22-006
Cui Z W, Wang Z, Jiang X Y, Zhao L H. Numerical study of non-spherical particle-laden flows. Advances in Mechanics, in press doi: 10.6052/1000-0992-22-006
Citation: Cui Z W, Wang Z, Jiang X Y, Zhao L H. Numerical study of non-spherical particle-laden flows. Advances in Mechanics, in press doi: 10.6052/1000-0992-22-006

非球形颗粒两相流的数值模拟研究进展

doi: 10.6052/1000-0992-22-006
详细信息
    作者简介:

    赵立豪, 清华大学长聘副教授 (特别研究员) , 博士生导师, 国家级青年人才项目入选者. 主要从事湍流两相流相关问题的理论与应用研究, 在Journal of Fluid Mechanics、Physical Review Letters、Science Advances等流体力学和综合性主流学术期刊上发表SCI论文60余篇, 担任数个国际SCI期刊编委, 包括国际多相流杂志International Journal of Multiphase Flow编委、Acta Mechanica编委、Acta Mechanica Sinica青年编委及客座编辑等. 现任中国力学学会环境力学专委会副主任、对外交流与合作委员会秘书长、中国空气动力学学会计算空气动力学专委会委员等

    通讯作者:

    zhaolihao@tsinghua.edu.cn

Numerical study of non-spherical particle-laden flows

More Information
  • 摘要: 非球形颗粒两相流是多相流的重要研究方向之一, 常见于自然界及工业生产过程中. 不同于球形颗粒, 由于非球形颗粒形状的各向异性, 除了颗粒平动行为, 还需要考虑颗粒的转动与取向行为, 颗粒的取向与转动行为会影响颗粒所受的力和力矩. 为了准确地模拟非球形颗粒的运动行为, 目前非球形颗粒两相流的数值模拟研究主要基于欧拉−拉格朗日的求解框架展开, 常见的非球形颗粒两相流数值模拟方法主要包括点颗粒法与全分辨颗粒法. 本文将对这两类方法进行介绍, 同时会全面介绍非球形颗粒两相流研究的基础理论模型, 并系统地总结非球形颗粒在简单基本流和复杂湍流中的研究进展, 包括对于非球形颗粒在湍流中的取向与转动行为机理, 以及颗粒对湍流减阻调制作用的研究. 最后, 本文提出了非球形颗粒两相流研究存在的问题及未来研究方向.

     

  • 图  1  描述颗粒运动的参考系: 惯性参考系$ \left\langle{\boldsymbol{x},\boldsymbol{y},\boldsymbol{z}}\right\rangle $, 颗粒参考系$\left\langle{{\boldsymbol{x}}',{\boldsymbol{y}}',\boldsymbol{z}'}\right\rangle$以及随动参考系$\left\langle{{\boldsymbol{x}}'',{\boldsymbol{y}}'',\boldsymbol{z}''}\right\rangle$

    图  2  椭球颗粒模型示意图.(a)三轴不等颗粒, (b)杆状颗粒, (c)碟状颗粒

    图  3  全分辨颗粒两相流问题示意图

    图  4  网格方法示意图. (a)贴体网格类方法, (b)非贴体类网格方法

    图  5  浸没边界方法的欧拉网格和拉格朗日网格

    图  6  格子结构与速度的示意图. (a) D2Q9, (b) D3Q19

    图  7  细针以任意取向在流体中沉降示意图

    图  8  (a)颗粒在简单剪切流示意图; (b-g)椭球颗粒在剪切流中的转动时代表椭球颗粒方向的轨迹图. 其中(b-d)无惯性椭球颗粒, (e-g)以最长轴定义的颗粒转动惯性分布为${\mathrm{S}\mathrm{t}}_{\mathrm{r}}=669, 646, 100$; 形状参数(b, e)$ \mathrm{\lambda }=5 $, (c, f)$ \mathrm{\lambda }=1/5 $, (d, g)$ {\mathrm{k}}_{\mathrm{a}}=1,{k}_{b}={10}^{-0.65},{k}_{c}=0.1 $

    图  9  颗粒在剪切流中转动的不同模态(Rosén et al. 2014)

    图  10  颗粒中心处滑移速度非零时的剪切流模型示意图

    图  11  无惯性椭球颗粒的(a)转动率随形状变化的关系(数据来自Byron 等 (2015), 两处实验数据分别来自Marcus等 (2014)与Parsa 等(2012))与(b)在湍流中运动示意图

    图  12  有限尺寸杆状颗粒在湍流中分布示意图(a)与(b)自适应网格加密(Schneiders et al. 2019)

    图  14  椭球颗粒在槽道湍流中的取向分布. (a,b)无惯性椭球颗粒, 数据来自Challabotla等(2015b); (c,d)St=30椭球颗粒

    图  15  颗粒在近壁流向涡结构影响下的取向行为及区域划分(Cui Z et al. 2021). (a, b)分别为细长杆状与扁平颗粒在瞬时流向涡附近的取向分布; (c-d)条件系综平均后的颗粒取向分布, 其中(c)细长杆状颗粒与流向夹角余弦值$ \left|\mathrm{cos}{\theta }_{x}\right| $, (d) 扁平颗粒与展向夹角余弦值$ \left|\mathrm{cos}{\theta }_{z}\right| $. (e)依据颗粒取向行为特点进行的区域划分示意图

    图  13  杆状颗粒在雷诺数$ {\mathrm{R}\mathrm{e}}_{\mathrm{\tau }}=1000 $槽道湍流分布图. 其中云图为流向速度, 白色等值线代表0.95倍槽流中心平均速度

    图  16  无惯性杆状颗粒在壁面取向行为与流体拉格朗日拉伸方向的差异(Cui Z et al. 2020)

    图  17  竖直槽道示意图.(a)向下流动, (b)向上流动

    图  18  不同形状和颗粒惯性的非球形颗粒回转轴方向与涡量的夹角分布(Zhao et al. 2015). (a)槽道中部, (b)近壁区.

    图  19  纤维与拉格朗日拉伸结构的关系. (a)周期流动(Parsa et al. 2011), (b)非周期流动(Parsa et al. 2011),(c)拉格朗日拉伸(黑色箭头)与压缩(红色箭头)与拉格朗日结构的关系(Cui Z & Zhao, 2021)

    图  20  纤维减阻机制示意图(Paschkewitz et al. 2004)

    表  1  轴对称椭球颗粒相关的形状参数

    碟状椭球颗粒
    (${\bf{0} } < \boldsymbol{\lambda } < {\bf{1} }$)
    球形颗粒
    (${\lambda }={\bf{1} }$)
    杆状椭球颗粒
    (${\lambda } > {\bf{1} }$)
    α=β$-\dfrac{ {\rm{B} }-\pi}{2\left(1-\lambda^{2}\right)^{\frac{3}{2} } }-\dfrac{\lambda}{1-\lambda^{2} }$$ \dfrac{2}{3} $$-\dfrac{\rm{A} }{2{\left({{\lambda } }^{2}-1\right)}^{\frac{3}{2} } }+\dfrac{\lambda }{ {\lambda }^{2}-1}$
    γ$-\dfrac{\rm{B}-{\pi } }{ {\left(1-{\boldsymbol{\lambda } }^{2}\right)}^{\frac{3}{2} } }+\frac{2}{\left(1-{\lambda }^{2}\right)\lambda }$$ \dfrac{2}{3} $$\dfrac{\rm{A} }{ {\left({{\lambda } }^{2}-1\right)}^{\frac{3}{2} } }-\dfrac{2}{\left({\lambda }^{2}-1\right)\lambda }$
    χ$-\frac{{\rm{B}}-\pi}{\left(1-\lambda^{2}\right)^{\frac{1}{2}}}$$ 2 $$\dfrac{\rm{A} }{ {\left({{\lambda } }^{2}-1\right)}^{\frac{1}{2} } }$
    其中 $\rm{A}=2{\ln}\left({\lambda }+\sqrt{ {\lambda }^{2}-1}\right),\;{ {\rm{B} } }=2{\rm{arctan} }\dfrac{\lambda}{\sqrt{1-\lambda^{2}} }.$
    下载: 导出CSV

    表  2  有限尺寸杆状颗粒在剪切流中不同$ {\mathrm{R}\mathrm{e}}_{\mathrm{s}} $对应的转动模态

    $ \mathrm{\lambda }=2 $(Huang et al. 2012)$ \mathrm{\lambda }=4 $(Rosén et al.2014)
    $ {\mathrm{R}\mathrm{e}}_{\mathrm{s}} $状态$ {\mathrm{R}\mathrm{e}}_{\mathrm{s}} $状态
    0Jeffery 轨迹0Jeffery 轨迹
    0 ~ 120翻转0 ~ 14翻转
    120 ~ 235翻转或自旋15 ~ 62翻转或自旋
    235 ~ 305翻转或倾斜自旋63 ~ 71翻转或倾斜自旋
    305 ~ 345翻转或倾斜摇摆72 ~ 74翻转或倾斜摇摆
    345 ~ 385翻转或摇摆75翻转或摇摆
    385 ~ 445翻转76 ~ 89翻转
    445 ~ 700翻转或静止朝向90 ~ 150翻转或静止朝向
    下载: 导出CSV

    表  3  有限尺寸碟状颗粒在剪切流中不同$ {\mathrm{R}\mathrm{e}}_{\mathrm{s}} $对应的转动模态

    $ \mathrm{\lambda }=1/2 $(Huang et al. 2012)
    $ {\mathrm{R}\mathrm{e}}_{\mathrm{s}} $状态
    0Jeffery 轨迹
    0 ~ 112自旋
    112 ~ 168翻转/倾斜自旋
    168 ~ 520静止朝向
    下载: 导出CSV
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  • 收稿日期:  2014-01-02
  • 录用日期:  2014-03-04
  • 网络出版日期:  2014-05-06

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