Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion
Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion
复制标题
DOI：
10.1017/jfm.2014.330
复制
发表时间：
2014-06
影响因子：
3.7
通讯作者：
M. Uhlmann;Todor Doychev
中科院分区：
文献类型：
--
作者：
M. Uhlmann;Todor Doychev
摘要 在稀条件下对三周期域中有限尺寸颗粒的重力引起沉降进行了直接数值模拟。对于单个固体与流体密度比 1.5，我们考虑了与稳定垂直运动相对应的伽利略数的两个值 ( $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ga}=121$ ）并在一个孤立球体的情况下稳定倾斜运动（ $\mathit{Ga}=178$ ）。对于多粒子系统，我们仅在后一种情况下观察到强粒子聚类。与聚类相关的几何形状和时间尺度由 Voronoï 曲面细分和粒子条件平均确定。由于聚类，平均颗粒沉降速度与孤立球体的值相比增加了 12%；在非聚类情况下没有观察到这种集体效应。通过定义有限尺寸颗粒附近的局部（瞬时）流体速度平均值，表明观察到的沉降速度的增强是由于在簇区域中引起的向下流体运动（相对于全局平均值）优先被颗粒采样。进一步观察到，在聚类情况下，粒子速度的方差大大增强。借助粒子速度的分解，表明这种增加是由于粒子附近的流体速度波动增强（由于聚类）。最后，我们讨论了对观察到的临界伽利略数的可能解释，该临界伽利略数标志着稀释条件下聚类的开始。
Abstract Direct numerical simulation of the gravity-induced settling of finite-size particles in triply periodic domains has been performed under dilute conditions. For a single solid-to-fluid-density ratio of 1.5 we have considered two values of the Galileo number corresponding to steady vertical motion ( $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ga}=121$ ) and to steady oblique motion ( $\mathit{Ga}=178$ ) in the case of one isolated sphere. For the multiparticle system we observe strong particle clustering only in the latter case. The geometry and time scales related to clustering are determined from Voronoï tessellation and particle-conditioned averaging. As a consequence of clustering, the average particle settling velocity is increased by 12 % as compared with the value of an isolated sphere; such a collective effect is not observed in the non-clustering case. By defining a local (instantaneous) fluid velocity average in the vicinity of the finite-size particles it is shown that the observed enhancement of the settling velocity is due to the fact that the downward fluid motion (with respect to the global average) which is induced in the cluster regions is preferentially sampled by the particles. It is further observed that the variance of the particle velocity is strongly enhanced in the clustering case. With the aid of a decomposition of the particle velocity it is shown that this increase is due to enhanced fluid velocity fluctuations (due to clustering) in the vicinity of the particles. Finally, we discuss a possible explanation for the observation of a critical Galileo number marking the onset of clustering under dilute conditions.