In this study, numerical simulations of bubbly flows in an infinitely long vertical channel were performed. Generally, the upper and lower boundaries of such channels are simplified as periodic boundary conditions. Unlike horizontal channel flows, the presence of gravity in the streamwise direction complicates the establishment of periodic boundary conditions. Therefore, a specialized treatment is required to prevent fluid acceleration. Here, we developed a novel treatment for the imposition of periodic boundaries and proposed a new microbubble model to consider the surface tension effect of microbubbles. To detect each bubble in the flow field, we implemented a bubble identification algorithm, which facilitates a thorough statistical analysis of bubble number, size, and spatial distribution. Validation tests were conducted, and good agreement was achieved between our results and reference data. We also confirmed that the results obtained with periodic boundaries are consistent with those achieved without them. Finally, we simulated the evolution of rising bubble swarms in a quiescent liquid. The method presented here contributes to the numerical simulations of bubbly flows in industrial systems, including oil-gas transportation, bubble columns, and nuclear reactors.

中文翻译：

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垂直周期通道中气泡流的数值模拟

在这项研究中，对无限长垂直通道中的气泡流进行了数值模拟。通常，此类通道的上下边界被简化为周期性边界条件。与水平河道流不同，流向重力的存在使周期性边界条件的建立变得复杂。因此，需要专门的处理来防止流体加速。在这里，我们开发了一种施加周期性边界的新颖处理方法，并提出了一种新的微泡模型来考虑微泡的表面张力效应。为了检测流场中的每个气泡，我们实现了气泡识别算法，这有助于对气泡数量、大小和空间分布进行彻底的统计分析。进行了验证测试，我们的结果与参考数据之间取得了良好的一致性。我们还证实，使用周期性边界获得的结果与没有周期性边界时获得的结果是一致的。最后，我们模拟了静止液体中上升的气泡群的演化。这里提出的方法有助于工业系统中气泡流的数值模拟，包括油气运输、泡罩塔和核反应堆。