Foam flow, distinguished by its low density and extensive specific surface area, is employed for the cleaning of plant systems. However, its dual nature as a gas-liquid mixture and a non-Newtonian fluid complicates the prediction of the frictional pressure drop. This study constructed a laboratory-scale experimental setup to illustrate the upward flow behavior of aqueous foam in a vertical circular pipe, capturing the foam flow using a high-speed camera. Utilizing the collected data and images, a model was developed for the friction factor to predict the frictional pressure drop of the foam flow, under the assumption that the foam flow is a non-Newtonian, quasi-homogeneous, steady, and fully developed laminar flow. Wet foam, characterized by small, uniformly distributed spherical bubbles, is observed at lower foam quality levels. In contrast, dry foam, marked by a larger mean bubble diameter, non-uniform bubble distributions, and slugs, is observed at higher foam quality levels. A notable inflection point in the frictional pressure drop is observed during the transition from wet to dry foam within a vertical pipe. The foam regime and frictional pressure drop characteristics of the foam flow show limited sensitivity to surfactant concentration within the experimental range. A correlation for friction factors, applicable to both wet and dry foam flows in vertical circular pipes, was developed based on the Reynolds number, exhibiting a prediction error of 23.6 %.

中文翻译：

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开发适用于圆形垂直管道中的湿泡沫和干泡沫流动的摩擦系数相关性

泡沫流以其低密度和大比表面积而著称，用于清洁工厂系统。然而，其作为气液混合物和非牛顿流体的双重性质使摩擦压降的预测变得复杂。本研究构建了一个实验室规模的实验装置，以说明水性泡沫在垂直圆形管道中的向上流动行为，并使用高速摄像机捕获泡沫流。利用收集到的数据和图像，假设泡沫流是非牛顿、准均匀、稳定且充分发展的层流，则开发了摩擦系数模型来预测泡沫流的摩擦压降。湿泡沫的特征是小而均匀分布的球形气泡，在较低的泡沫质量水平下观察到。相比之下，干泡沫以较大的平均气泡直径、不均匀的气泡分布和段塞为特征，在较高的泡沫质量水平下观察到。在垂直管道内从湿泡沫过渡到干泡沫期间，观察到摩擦压降的显着拐点。泡沫流的泡沫状态和摩擦压降特征在实验范围内对表面活性剂浓度的敏感性有限。基于雷诺数开发了适用于垂直圆形管道中的湿泡沫和干泡沫流的摩擦系数相关性，预测误差为 23.6%。