The characterization of the shape of liquid elements in a spray is a good way to analyze atomization processes. Experimental approaches based on common imaging techniques suffer from partial information given by 2D images to characterize intrinsically 3D objects such as liquid droplets. In this paper, we address the question, To what extent can the shape parameters measured on 2D images reveal the 3D content of the droplet shape? An analytical approach is first adopted to determine relationships between 2D and 3D shape parameters for two families of objects, the oblate and prolate spheroids. Two numerical databases obtained from direct numerical simulation of two-phase flows are then explored for their ability to give complete 3D shape information and extrapolate 2D parameter values from projections on planes selected according to flow characteristics. Focus is put on one shape parameter particularly sensitive to 3D to 2D projection effects, namely the uniformity parameter introduced by Blaisot and Yon (2005). Statistics obtained from the numerical databases are used to guide the analysis of results extracted from experimental images. It is shown that statistics on a 3D shape parameter could be induced from the ones for the 2D parameters. Two conditions are necessary: (1) the 2D projection is performed perpendicularly to the main flow direction, which is always the case in experiments; and (2) a particular care must be put on the determination of the statistics of orientations of the main axis of the liquid elements. This last point should be tackled in future experimental analyzes to estimate 3D shape parameter statistics from 2D images.

中文翻译：

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二维投影对水滴形状参数影响的分析

表征喷雾中液体元素的形状是分析雾化过程的好方法。基于常见成像技术的实验方法受到 2D 图像给出的部分信息的影响，以表征本质上的 3D 对象，例如液滴。在本文中，我们解决了这样一个问题：在 2D 图像上测量的形状参数在多大程度上可以揭示液滴形状的 3D 内容？首先采用分析方法来确定两个对象族（扁球体和长球体）的 2D 和 3D 形状参数之间的关系。然后探索从两相流的直接数值模拟中获得的两个数值数据库，了解它们提供完整的 3D 形状信息并从根据流动特性选择的平面上的投影推断 2D 参数值的能力。重点放在对 3D 到 2D 投影效果特别敏感的一个形状参数上，即 Blaisot 和 Yon (2005) 引入的均匀性参数。从数值数据库中获得的统计数据用于指导从实验图像中提取的结果的分析。结果表明，可以从 2D 参数的统计中得出关于 3D 形状参数的统计。需要两个条件：（1）二维投影垂直于主流方向进行，实验中总是如此；(2) 必须特别注意确定液体元素主轴方向的统计数据。最后一点应该在未来的实验分析中解决，以从 2D 图像估计 3D 形状参数统计。