Physical modeling represents probably the oldest design tool in hydraulic engineering together with analytical approaches. In free surface flows, the similitude based upon a Froude similarity allows for a correct representation of the dominant forces, namely gravity and inertia. As a result fluid flow properties such as the capillary forces and the viscous forces might be incorrectly reproduced, affecting the air entrainment and transport capacity of a high-speed model flow. Small physical models operating under a Froude similitude systematically underestimate the air entrainment rate and air-water interfacial properties. To limit scale effects, minimal values of Reynolds or Weber number have to be respected. The present article summarizes the physical background of such limitations and their combination in terms of the Morton number. Based upon a literature review, the existing limits are presented and discussed, resulting in a series of more conservative recommendations in terms of air concentration scaling. For other air-water flow parameters, the selection of the criteria to assess scale effects is critical because some parameters (e.g., bubble sizes, turbulent scales) can be affected by scale effects, even in relatively large laboratory models.

中文翻译：

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两相空气水流：物理模型中的比例效应

物理模型可能代表了液压工程中最古老的设计工具以及分析方法。在自由表面流中，基于Froude相似性的相似性允许正确表示主力，即重力和惯性。结果，可能会错误地再现诸如毛细作用力和粘性作用力之类的流体流动特性，从而影响高速模型流的空气夹带和输送能力。在Froude模式下运行的小型物理模型系统地低估了空气夹带率和空气-水界面特性。为了限制比例效应，必须考虑雷诺或韦伯数的最小值。本文根据莫顿数总结了这些限制的物理背景及其组合。根据文献综述，提出并讨论了现有的限值，从而在空气浓度缩放方面提出了一系列更为保守的建议。对于其他空气-水流量参数，选择标准以评估水垢效应至关重要，因为即使在相对较大的实验室模型中，某些参数（例如气泡大小，湍流水垢）也会受到水垢效应的影响。