Development of closure relations for the motion of Taylor bubbles in vertical and inclined annular pipes using high-fidelity numerical modeling

Abstract

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 (Eötvös 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 Eötvös numbers between 10 and 700 and Morton numbers between 10 −6 and 10 0 . 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.

Analysis of Taylor bubble dynamics via high-fidelity numerical modelling

“…However, understanding of their behaviour in annular sections is still limited. This piping configuration has increased in importance in, for example, the realisation of unconventional extraction techniques currently employed to maintain supply of natural gas as well as with the design of modern heat exchangers [4].…”

“…This approach was feasible due to the body of research available on tubular pipe flows, however, this does not exist for the annular analogue. To avoid the cost of conducting experimental studies over wide parameter ranges, numerical methods have emerged as an established approach for developing such closure models [4,9], and provide the basis for this study.…”

“…More recently, the volume of fluid and level-set methods have emerged as arguably the most popular approaches to solve the governing multiphase equations. For a more detailed review on the computational analysis of Taylor bubbles, the interested reader is pointed towards the earlier work of Mitchell and Leonardi [4].…”

“…It is only very recent that computational multi-fluid dynamics has been applied to study Taylor bubbles in annular conduits [4,12,13]. Rohilla and Das [12] coupled a level set-volume of fluid approach to capture the interface evolution, focusing on the dynamics as a bubble progressed from a tubular pipe into an annular conduit.…”

“…Rohilla and Das [12] coupled a level set-volume of fluid approach to capture the interface evolution, focusing on the dynamics as a bubble progressed from a tubular pipe into an annular conduit. Mitchell and Leonardi [4,13] provide the basis for this paper, and applied a coupled phase-field lattice Boltzmann approach to characterise the behaviour of Taylor bubbles in various fluids and flow conditions. The remainder of this paper starts by presenting the governing dynamics for a multiphase flow as well as the numerical methods applied to resolve them.…”