Abstract

The ratio between bubble velocity and mean velocity of the two-phase flow is a key parameter in Taylor flow. Correlations for this characteristic velocity ratio that are valid over the entire range of attainable capillary numbers are missing so far. Here, we develop such a correlation for laminar gas–liquid Taylor flow in circular capillary channels. The proposed model is a two-parameter logistic function, which approaches the theoretical asymptotic limit of Bretherton at low capillary number. The correlation relies on prior known parameters such as channel diameter, fluid properties and gas/liquid volumetric flow rates only. In comparison with numerical and experimental data, it is accurate within ±5 and ±18%, respectively. The correlation should be useful to estimate various prior unknown hydrodynamics features of Taylor flow such as bubble velocity, mean liquid velocity, gas holdup, uniform liquid film thickness, bubble diameter, and streamline patterns in the liquid slug. The derived two-parameter logistic function may be useful to develop similar correlations for non-circular channels and liquid–liquid Taylor flow.

中文翻译：

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特征速度比与预测毛细管气液泰勒流动流体动力学的相关性

摘要

气泡速度与两相流平均速度之间的比率是泰勒流的关键参数。到目前为止，在整个可达到的毛细管数范围内都没有有效的该特征速度比相关性。在这里，我们为圆​​形毛细管通道中的层状气液泰勒流量建立了这种相关性。所提出的模型是一个两参数对数函数，它在低毛细管数下接近布雷瑟顿的理论渐近极限。该相关仅依赖于先前已知的参数，例如通道直径，流体性质和气体/液体体积流量。与数值和实验数据相比，其准确度分别在±5％和±18％之内。该相关性对于估计泰勒流的各种先前未知的流体动力学特征（例如气泡速度，平均液体速度，气体滞留率，均匀的液膜厚度，气泡直径和液团中的流线型态）应该是有用的。导出的两参数对数函数可能有助于开发非圆形通道和液-液泰勒流量的相似相关性。