Abstract A three-dimensional phase-field lattice Boltzmann method has been applied to investigate the rise of Taylor bubbles within annular pipes. The approach couples the conservative phase-field model with a velocity-based lattice Boltzmann scheme. The implementation uses 27 discrete velocities to resolve both the interfacial dynamics and the hydrodynamics. To assist numerical stability for the high-density ratio, two-phase flows a weighted multiple-relaxation-time collision operator is employed. This paper makes contributions in three areas. First, the model is employed to capture the behaviour of Taylor bubbles in five combinations of vertical annular pipes, with results compared to experimental findings from the literature for air-water flows. From this, shortcomings were identified in the ability of existing correlations to accurately predict rise velocities for bubbles in various liquids. Second, the effect of pipe inclination on the rise behaviour of the bubbles was investigated. From the findings, a preliminary correlation describing the rise velocity was proposed. The first two components of the study were conducted with the Taylor bubble rising in stagnant fluid. The final component of this study imposed liquid flow in a concentric annular pipe to determine the impact of this on the bubble’s dynamics. The liquid velocity was defined through a Reynolds number based on the average inlet velocity up to an absolute value of 10. The viscosity was varied to examine Morton numbers from 2.56e-3 to 6.55e-5. To this end both co- and counter-current flow was analysed and a distribution parameter proposed to capture the liquid-gas interaction. To extend this work, future investigations will look to extend the parameter range assessed to ensure the universality of the correlations identified.

中文翻译：

---

环形管道中泰勒气泡的上升特性

摘要 三维相场格子玻尔兹曼方法已被应用于研究环形管内泰勒气泡的上升。该方法将保守的相场模型与基于速度的格子 Boltzmann 方案相结合。该实现使用 27 个离散速度来解析界面动力学和流体动力学。为了帮助高密度比的数值稳定性，两相流采用了加权多重松弛时间碰撞算子。本文在三个方面做出了贡献。首先，该模型用于捕捉五种垂直环形管道组合中泰勒气泡的行为，并将结果与​​空气-水流文献中的实验结果进行比较。由此，现有相关性在准确预测各种液体中气泡上升速度的能力方面存在缺陷。其次，研究了管道倾斜对气泡上升行为的影响。根据这些发现，提出了描述上升速度的初步相关性。研究的前两个部分是在泰勒气泡在停滞的流体中上升的情况下进行的。这项研究的最后一个组成部分是在同心环形管中施加液体流动，以确定这对气泡动力学的影响。液体速度通过基于平均入口速度的雷诺数定义，绝对值最高为 10。改变粘度以检查从 2.56e-3 到 6.55e-5 的莫顿数。为此，对顺流和逆流进行了分析，并提出了一个分布参数来捕获液-气相互作用。为了扩展这项工作，未来的调查将寻求扩展评估的参数范围，以确保确定的相关性的普遍性。