Abstract In the present paper, an Euler-Euler two-fluid model combined with the baseline model, which is a set of closures for the interfacial momentum and turbulence transfer, is validated against experimental data for low Reynolds number bubbly flows in vertical pipes. The model has already been validated for high Reynolds number pipe flows and bubble columns in the previous work (Liao et al., 2019, Chem. Eng. Sci. 202, 55–69). To further substantiate the k − ω SST model with consideration of bubble-induced source included in the baseline model, it is of interest to examine it for low Reynolds number pipe flows, where the bulk is laminar and the transition to turbulence is induced sorely by the agitation of bubbles. Simulations are configured and carried out in the open source CFD code OpenFOAM for eight test cases. Each of them has a different combination of gas and liquid volumetric flow rates. The numerical results are then compared with the experimental data taken from the literature. The comparison is based on different parameters including air void fraction, mean bubble velocity, mean liquid velocity, turbulent kinetic energy and Reynolds shear stress. Although, confirming results with the experimental data are presented but further improvement of the model for turbulent transition as well as inter-phase momentum transfer is necessary. Reliable prediction of the velocity profile in single-phase and extremely sparse bubbly flow cases is shown, and the phase distribution in fully-developed cases is well captured. In addition to the bulk Reynolds number and void fraction, the pipe-to-bubble size ratio is found to have definite influence on the laminar-turbulent transition.

中文翻译：

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层流气泡管流的欧拉-欧拉双流体模型：基线模型的验证

摘要 在本文中，欧拉-欧拉二流体模型与基线模型相结合，该模型是一组界面动量和湍流传递的闭包，针对垂直管道中低雷诺数气泡流的实验数据进行了验证。该模型已经在之前的工作中针对高雷诺数管流和气泡柱进行了验证（Liao 等，2019，Chem. Eng. Sci. 202, 55-69）。为了进一步证实 k − ω SST 模型并考虑到包含在基线模型中的气泡引起的源，有兴趣检查低雷诺数管流，其中体积是层流的，并且向湍流的过渡是由以下原因引起的气泡的搅动。在开源 CFD 代码 OpenFOAM 中为八个测试用例配置和执行模拟。它们中的每一个都有不同的气体和液体体积流量组合。然后将数值结果与文献中的实验数据进行比较。比较基于不同的参数，包括空气空隙率、平均气泡速度、平均液体速度、湍流动能和雷诺剪切应力。虽然，提供了与实验数据的确认结果，但需要进一步改进湍流转变和相间动量传递模型。显示了单相和极其稀疏的气泡流情况下速度剖面的可靠预测，并且很好地捕获了完全发展情况下的相分布。除了体积雷诺数和空隙率之外，