Thin disks falling in air
Thin disks falling in air
复制标题
DOI：
10.1017/jfm.2023.209
复制
发表时间：
2023-04
影响因子：
3.7
通讯作者：
Amy Tinklenberg;M. Guala;F. Coletti
中科院分区：
文献类型：
--
作者：
Amy Tinklenberg;M. Guala;F. Coletti
摘要本文对毫米级薄圆盘在静止空气中的沉降进行了实验研究。选择的物理参数范围与沉降在大气中的片状晶体相关：直径与厚度的纵横比为$\chi =25\unicode{x2013}60$，基于圆盘直径和下落速度的雷诺数为$Re=O（10^2）$，惯性比为$I^*=O（1）$。使用Baker & Coletti（J. Fluid Mech.，第943卷，2022，A27）。大多数圆盘要么垂直下落，其最大投影面积垂直于重力，要么翻滚，同时以小于20 °的角度横向漂移。两个考虑的三个磁盘大小表现出双峰行为，与非翻滚和翻滚模式发生显着的概率，这强调了需要一个统计表征的过程。较小的圆盘（直径为1 mm，$Re=96$）比较大的圆盘（直径为3 mm，$Re=360$）具有更强的翻滚倾向，这与人们普遍认为的$Re=100$是一个阈值的观点不一致，低于该阈值，下落的圆盘保持水平。较大的下降速度（和，因此，较小的阻力系数）被发现相对于现有的相关性的基础上在液体中的实验，演示的密度比在设置的垂直速度的作用。这些数据支持一个简单的缩放的旋转频率的基础上的阻力和重力之间的平衡，这仍有待于在进一步的研究中，磁盘厚度和密度比是不同的。
Abstract We experimentally investigate the settling of millimetre-sized thin disks in quiescent air. The range of physical parameters is chosen to be relevant to plate crystals settling in the atmosphere: the diameter-to-thickness aspect ratio is $\chi =25\unicode{x2013}60$, the Reynolds numbers based on the disk diameter and fall speed are $Re=O(10^2)$ and the inertia ratio is $I^*=O(1)$. Thousands of trajectories are reconstructed for each disk type by planar high-speed imaging, using the method developed by Baker & Coletti (J. Fluid Mech., vol. 943, 2022, A27). Most disks either fall straight vertically with their maximum projected area normal to gravity or tumble while drifting laterally at an angle $<20^\circ$. Two of the three disk sizes considered exhibit bimodal behaviour, with both non-tumbling and tumbling modes occurring with significant probabilities, which stresses the need for a statistical characterization of the process. The smaller disks (1 mm in diameter, $Re=96$) have a stronger tendency to tumble than the larger disks (3 mm in diameter, $Re=360$), at odds with the diffused notion that $Re=100$ is a threshold below which falling disks remain horizontal. Larger fall speeds (and, thus, smaller drag coefficients) are found with respect to existing correlations based on experiments in liquids, demonstrating the role of the density ratio in setting the vertical velocity. The data supports a simple scaling of the rotational frequency based on the equilibrium between drag and gravity, which remains to be tested in further studies where disk thickness and density ratio are varied.