This study analyses the flow of Taylor bubbles through vertical and inclined annular pipes using high-fidelity numerical modeling. A recently developed phase-field lattice Boltzmann method is employed for the investigation. This approach resolves the two-phase flow behavior by coupling the conservative Allen–Cahn equation to the Navier–Stokes hydrodynamics. This paper makes contributions in three fundamental areas relating to the flow of Taylor bubbles. First, the model is used to determine the relationship between the dimensionless parameters (Eotvos and Morton numbers) and the bubble rise velocity (Froude number). There currently exists no surrogate model for the rise of a Taylor bubble in an annular pipe that accounts for fluid properties. Instead, relations generally include the diameter of the outer and inner pipes only. This study covered Eotvos numbers between 10 and 700 and Morton numbers between 10−6 and 100. As such, the proposed correlation is applicable to concentric annular pipes within this range of parameters. An assessment of the correlation to parameters outside of this range was made; however, this was not the primary scope for the investigation. Following this, the effect of pipe inclination was introduced with the impact on rise velocity measured. A correlation between the inclination angle and the rise velocity was proposed and its performance quantified against the limited experimental data available. Finally, the high-fidelity numerical results were analyzed to provide key insights into the physical mechanisms associated with annular Taylor bubbles and the shape they form. To extend this work, future studies on the effect of pipe eccentricity, diameter ratios, and pipe fittings (e.g., elbows and risers) on the flow of Taylor bubbles will be conducted.

中文翻译：

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使用高保真数值模型开发垂直和倾斜环形管道中泰勒气泡运动的闭合关系

本研究使用高保真数值建模分析了泰勒气泡通过垂直和倾斜环形管道的流动。最近开发的相场晶格玻尔兹曼方法被用于研究。这种方法通过将保守的 Allen-Cahn 方程与 Navier-Stokes 流体动力学耦合来解决两相流动行为。本文在与泰勒气泡流动相关的三个基本领域做出了贡献。首先，该模型用于确定无量纲参数（Eotvos 和 Morton 数）与气泡上升速度（Froude 数）之间的关系。目前不存在考虑流体特性的环形管中泰勒气泡上升的替代模型。相反，关系通常仅包括外管和内管的直径。这项研究涵盖了 10 到 700 之间的 Eotvos 数和 10-6 到 100 之间的莫顿数。因此，建议的相关性适用于该参数范围内的同心环形管道。对该范围之外的参数的相关性进行了评估；然而，这并不是调查的主要范围。在此之后，引入了管道倾斜的影响以及对测量的上升速度的影响。提出了倾斜角和上升速度之间的相关性，并根据可用的有限实验数据对其性能进行了量化。最后，对高保真数值结果进行了分析，以提供对与环形泰勒气泡相关的物理机制及其形成的形状的关键见解。为了扩展这项工作，未来对管道偏心影响的研究，