Settling experiments were conducted in a turbulence column to investigate the effect of turbulence on the effective fall velocity of solid particles slightly denser than the fluid $({\rho }_p\gtrsim {\rho }_f)$. Five types of particles of different materials and shapes were tested, their size ranging between $o\left(1\right)\eta$ and $o\left(10\right)\eta$, where $\eta$ is the Kolmogorov viscous length scale. Thus, the particles were of finite size with an unknown analytical form for the fluid-particle forces. The density ratio ranged as $({\rho }_p-{\rho }_f)/{\rho }_f=\{0.13:1.6\}$, and the still-fluid particle Reynolds number as ${\text{Re}}_p^0=\{75:981\}$. The turbulence levels characterized with the integral-scale Reynolds number ranged as ${\text{Re}}_L=\{34:510\}$. Two-dimensional (2D) particle image velocimetry was used to obtain flow statistics, the residual mean circulation, and the turbulence statistics, while 2D particle tracking was performed to measure particle settling velocities. For all types of particles tested, settling retardation is observed as the turbulence intensity is increased. It is found that if both the effective fall velocity $W_s$ and the turbulent fluid velocity $W_{f,\text{rms}}$ are nondimensionalized by the still-fluid particle terminal velocity $W_0$, the settling retardation can be described by a unique relation independent of the particle type, $W_s/W_0=f(W_{f,\text{rms}}/W_0)$, for the given range of flow regimes. Using analytical descriptions of the loitering and nonlinear drag effects, this scaling is shown to have a solid physical basis.

中文翻译：

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湍流塔中沉降延迟的实验证据

在湍流柱中进行沉降实验，以研究湍流对比流体稍致密的固体颗粒的有效下落速度的影响 $（{\rho }_p\gtrsim {\rho }_F）$。测试了五种类型的不同材料和形状的颗粒，它们的大小在$Ø（\mathrm{1个}）\eta$ 和 $Ø（10）\eta$，在哪里 $\eta$是Kolmogorov粘性长度标尺。因此，粒子具有有限的大小，并且对流体粒子力的解析形式未知。密度比范围为$（{\rho }_p-{\rho }_F）/{\rho }_F=\{0.13：1.6\}$，并且静态流体雷诺数为 ${\text{回覆}}_p^0=\{75：981\}$。以积分尺度雷诺数为特征的湍流水平范围为${\text{回覆}}_{\mathrm{大号}}=\{34：510\}$。使用二维（2D）粒子图像测速仪获得流量统计数据，残留平均循环和湍流统计数据，同时执行2D粒子跟踪以测量粒子沉降速度。对于测试的所有类型的颗粒，随着湍流强度的增加，观察到沉降延迟。发现如果同时有效下降速度${\mathrm{w\; ^}}_s$ 和湍流速度 ${\mathrm{w\; ^}}_{F，\text{均方根}}$ 通过静止流体的粒子终极速度无量纲化 ${\mathrm{w\; ^}}_0$，沉降延迟可以通过与颗粒类型无关的唯一关系来描述， ${\mathrm{w\; ^}}_s/{\mathrm{w\; ^}}_0=F（{\mathrm{w\; ^}}_{F，\text{均方根}}/{\mathrm{w\; ^}}_0）$，对于给定的流量范围。通过使用游荡和非线性阻力效应的分析描述，表明这种缩放比例具有坚实的物理基础。