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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.Abstract: Non-spherical particle-laden flows are commonly seen and important in nature and industrial processes. The particle's rotational and orientational behaviors could affect the forces and torques acting on the particle from ambient fluid flow. To accurately capture the motion of non-spherical particles, especially for angular particle dynamics, most numerical studies of non-spherical particle-laden flows are carried out in the Euler-Lagrange frame. There are two most popular numerical approaches: the point-particle method and the particle-resolved method. This paper comprehensively and systematically summarizes these methods and significant recent findings about non-spherical particles in simple and turbulent flows. The mechanism of particle orientation and rotation by suspended non-spherical particles, as well as the modulation effect of particles on turbulent drag reduction, are discussed. Furthermore, the key and unsolved problems of non-spherical particle-laden flows for future study are proposed at the end of the paper.
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图 1 描述颗粒运动的参考系: 惯性参考系
$ \left\langle{{x},{y},{z}}\right\rangle $ , 颗粒参考系$\left\langle{{{x}}',{{y}}',{z}'}\right\rangle$ 以及随动参考系$\left\langle{{{x}}'',{{y}}'',{z}''}\right\rangle$ 
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 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 13 椭球颗粒在槽道湍流中的取向分布. (a)(b)无惯性椭球颗粒(Challabotla et al. 2015b); (c)(d)St = 30椭球颗粒
图 14 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 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 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 $-\dfrac{ {{B} }-\pi}{2\left(1-\lambda^{2}\right)^{{3}/{2} } }-\dfrac{\lambda}{1-\lambda^{2} }$ $ \dfrac{2}{3} $ $-\dfrac{{A} }{2{\left({{\lambda } }^{2}-1\right)}^{{3}/{2} } }+\dfrac{\lambda }{ {\lambda }^{2}-1}$ γ $-\dfrac{{B}-{\pi } }{ {\left(1-{\boldsymbol{\lambda } }^{2}\right)}^{{3}/{2} } }+\frac{2}{\left(1-{\lambda }^{2}\right)\lambda }$ $ \dfrac{2}{3} $ $\dfrac{{A} }{ {\left({{\lambda } }^{2}-1\right)}^{{3}/{2} } }-\dfrac{2}{\left({\lambda }^{2}-1\right)\lambda }$ χ $-\dfrac{ { {B} }-\pi}{\left(1-\lambda^{2}\right)^{ {1}/{2} } }$ $ 2 $ $\dfrac{{A} }{ {\left({{\lambda } }^{2}-1\right)}^{{1}/{2} } }$ 其中 ${A}=2{\ln}\left({\lambda }+\sqrt{ {\lambda }^{2}-1}\right),\;{ {{B} } }=2{\rm{arctan} }\dfrac{\lambda}{\sqrt{1-\lambda^{2}} }$ 
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表 2 有限尺寸杆状颗粒在剪切流中不同
$ {{Re}}_{\mathrm{s}} $ 对应的转动模态$ \mathrm{\lambda }=2 $(Huang et al. 2012) $\mathrm{\lambda }=4$(Rosén et al. 2014) ${{Re} }_{\mathrm{s} }$ 状态 ${Re}_{\mathrm{s} }$ 状态 0 Jeffery 轨迹 0 Jeffery 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
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表 3 有限尺寸碟状颗粒在剪切流中不同
$ {{R}{e}}_{\mathrm{s}} $ 对应的转动模态$ \mathrm{\lambda }=1/2 $(Huang et al. 2012) ${{R}{e} }_{\mathrm{s} }$ 状态 0 Jeffery 轨迹 0 ~ 112 自旋 112 ~ 168 翻转/倾斜自旋 168 ~ 520 静止朝向
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