[论文解读] An analytical and experimental study of secondary atomization for vibrational and bag breakup modes

Varun Kulkarni|arXiv (Cornell University)|Jun 17, 2023

Laser-induced spectroscopy and plasma被引用 3

一句话总结

本研究通过理论与实验相结合的方法，对液滴在振动破碎和袋状破碎模式下的二次雾化现象进行了研究。推导出袋状破碎的理论韦伯数边界，验证了袋状结构和液滴形变随韦伯数呈指数增长的规律，并通过PDA测量发现Sauter平均直径（D32）低于以往估计值，揭示了在粘性流体中液滴尺寸向更大的方向偏移的现象。

ABSTRACT

Bag breakup of drops has been a subject of interest for almost over a century. Several issues such as theoretical estimation of the regime boundary marking the onset of such breakup, bag growth rates, drop size distribution, and the effect of Weber number, $We$, and Ohnesorge number, $Oh$, on these quantities remains unaddressed. The current study aims to clarify aspects of the atomization process through experiments and theory. We examine bag breakup of a single drop of various inviscid and low viscosity fluids as it deforms in the presence of a continuous horizontal air jet. The We boundary at which bag breakup begins is theoretically determined and the expression obtained, $We = 12(1 + \frac{2}{3} Oh^2)$, is found to match well with existing experimental data. An exponential growth in the radial extent of the deformed drop and the streamline dimension of the bag is predicted by the theoretical model and confirmed by experimental findings. These quantities are observed to strongly depend on $We$. However, their dependence on $Oh$ is weak for the range of $Oh$ considered in this study. Subsequent to drop deformation, bag formation and expansion is the bursting process. This is marked by the disintegration of the bag owing to instability of the Rayleigh-Taylor type, followed by collapse of the liquid rim bounding this bag by Plateau-Rayleigh instability. The sizes of the drops thus produced are measured using Phase Doppler Anemometry (PDA) which is in contrast to shadowgraphs used in earlier studies. A discernible shift in the peak of the drop size distribution for viscous drops is seen which indicates a preponderance of drops of higher diameters vis-à-vis fragment size distribution for inviscid drops. Furthermore, an estimate of the Sauter mean diameter ($D_{32}$) is presented which is somewhat lower than earlier predictions.

研究动机与目标

• 阐明液滴袋状破碎起始的理论与实验基础。
• 量化袋状结构与液滴形变对韦伯数（We）和奥内索尔格数（Oh）的依赖关系。
• 研究二次雾化机制，包括瑞利-泰勒不稳定性与拉普拉斯-雷利不稳定性。
• 利用相位多普勒测速仪（PDA）测量液滴尺寸分布，相较于传统阴影照相法更具优势。
• 估算Sauter平均直径（D32），并与先前的理论预测进行比较。

提出的方法

• 基于流体力学原理，推导袋状破碎的韦伯数边界：We = 12(1 + (2/3)Oh²)。
• 实验装置通过水平气流作用于单个液滴，诱导其发生袋状破碎。
• 利用相位多普勒测速仪（PDA）测量液滴破裂后的尺寸分布。
• 分析液滴径向形变及袋状结构流线尺寸随时间的变化。
• 应用瑞利-泰勒不稳定性与拉普拉斯-雷利不稳定性模型，解释袋状结构破裂与液膜边缘坍塌机制。
• 将理论预测与不同韦伯数和奥内索尔格数范围内的实验数据进行对比。

实验结果

研究问题

• RQ1 袋状破碎的理论韦伯数临界值是多少？其与实验观测结果的吻合程度如何？
• RQ2 液滴形变的径向范围及袋状结构流线尺寸如何随时间演变？其对韦伯数和奥内索尔格数的依赖关系如何？
• RQ3 粘度（Oh）如何影响袋状破碎后二次雾化过程中的液滴尺寸分布？
• RQ4 所得液滴的Sauter平均直径（D32）是多少？其与先前理论估算相比有何差异？
• RQ5 基于PDA的液滴尺寸分布测量方法与传统阴影照相法相比，在捕捉破裂后液滴特征方面有何不同？

主要发现

• 理论推导的袋状破碎韦伯数边界 We = 12(1 + (2/3)Oh²) 与现有实验数据高度吻合。
• 液滴形变的径向范围及袋状结构流线尺寸均表现出指数增长，主要依赖于韦伯数。
• 在研究范围内，奥内索尔格数的影响微弱，表明粘度对形变动力学的影响较小。
• PDA测量结果显示，与无粘性液滴相比，粘性液滴的液滴尺寸分布峰值向更大直径方向发生明显偏移。
• 估算的Sauter平均直径（D32）低于早期理论预测，表明雾化程度比先前假设更细。
• 袋状结构的破裂由瑞利-泰勒不稳定性驱动，随后液膜边缘通过拉普拉斯-雷利不稳定性发生坍塌，与观测到的液滴形成过程一致。