Taylor Bubble Research Articles

Bubble formation in viscous fluids by a microfluidic flow-focusing junction: a computational study

A three-dimensional (3D) numerical study of bubble formation process in viscous fluids in a microfluidic flow-focusing junction is carried out in the present study. The numerical approach is first validated by the experimental data and shows a very good agreement, and a reciprocal relationship can be derived between the normalized bubble length and liquid fraction. Afterwards, the numerical approach is further applied to study bubble formation in fluids with different viscosities ranging from 5.6 to 400 mPa s, and the viscosity ratio of liquid phase to gas phase (μl/μg) is up to 2.2 × 104. Two different interpolation treatments including the Geo-Reconstruction method and the CICSAM are implemented when dealing with the situation for high viscosity, and the results are compared with the experimental data, indicating a better performance of the Geo-Reconstruction method. The numerical results of the bubble shapes are also compared with the experimental visualization results, showing good agreements. The evolution of the gas tip is further investigated quantitatively, and the liquid film is found to play a very important role in affecting the velocity of the gas tip. Finally, the hydrodynamic behaviors of the Taylor bubble formed in the junction including velocity and pressure distributions are studied in detail, and the contribution of pressure drop within the channel is also discussed.

Reconstruction of Taylor Bubbles in Slug Flow Using a Direct-Image Multielectrode Conductance Sensor

Gas-liquid two-phase flows are widely encountered in industrial processes. To realize the dynamic detection of gas-liquid slug flows, a direct-image multi-electrode conductance sensor (DMCS) is optimized using the finite element method to access high measurement sensitivity. Through carrying out an experiment of vertical gas-liquid two-phase flows, the gas-liquid interfaces in slug flows are detected by the DMCS and compared to the results from a planar laser-induced fluorescence (PLIF) system. The interfaces detected by the DMCS and the PLIF system indicate a good agreement. By selecting an optimal threshold, the liquid film thicknesses around Taylor bubbles (TBs) are derived, and the asymmetry of circumferential film thickness distribution is investigated. Besides, the local cross-correlation velocities at circumferential pipe wall are measured by the DMCS. Finally, the TBs in slug flows are reconstructed based on the thickness and the velocity of the TBs. The reconstructed TBs allow for a clear indication of gas-liquid slug flow structures.

Experimental study of the flow structure around Taylor bubbles in the presence of dispersed bubbles

This work presents an experimental study focusing on the interactions between the dispersed and Taylor bubbles in a slug flow pattern. In order to better investigate these interactions, a quasi-real slug flow was studied, where a single Taylor bubble is injected in a bubbly flow background stream, under controlled and repeatable conditions, controlling the bubbly flow superficial gas and liquid velocity, and also the Taylor bubble length. In this way, ensemble averaged results can be obtained over several Taylor bubbles. The flow was analyzed through the laser diode photocell, high-speed camera imaging and PIV techniques. Results revealed that the terminal Taylor bubble velocity is affected by the gas volume fraction of the bubbly background flow. Ensemble average velocity profiles are presented for Taylor bubble nose and tail regions. Since the experimental apparatus used in the present work allowed a large number of instantaneous PIV acquisitions, the turbulent statistics around the Taylor bubble can also be calculated. These experimental results can be used for the implementation and validation of multidimensional CFD models for flows with different interface length scales.

Slug flow development study in a horizontal pipe using particle image velocimetry

The development of slug flow along a horizontal pipe was quantitatively investigated through particle image velocimetry. Quantitative information is essential to understand the hydraulic behavior of the slug flow and is a reference for numerical simulations. The flow in the horizontal pipe of 11.5 m length and 0.051 m diameter was maintained in a fully turbulent condition with 0.41 m/s gas superficial velocity and 0.50 m/s liquid superficial velocity. PIV measurement was carried out at three locations along the pipe, and a sophisticated ensemble averaging technique was applied to obtain the statistical flow properties. Morphological analysis revealed the unsteadiness of Taylor bubble and variation of bubble population in the slug region. From the velocity information, the similarity of velocity fields in the slug body and tail is found. In addition, the occurrence of local maximum velocity and an increase of the mixing eddy length in the slug nose were observed. Moreover, a modified 1D mixture model to predict the slug translational velocity was proposed based on the local maximum velocity in the slug tail. We believe this study clearly shows the strength of PIV method to improve the understanding of physics in the slug flow.

Intermittent slug flow identification and characterization from pressure signature

Despite of its occurrence in several industrial applications, it remains an open issue to accurately predict the behavior of multiphase flow. More specifically, when direct observation of the flow is not possible, which typically occurs in the petroleum industry, indirect methods of identifying main features of the flow are necessary. In this paper, we propose a method for the determination of some important parameters in two-phase gas–liquid flow, the velocity in situ of the Taylor Bubble, using differential pressure measurements. This is done through the analysis of the time and frequency signature of a normalized signal and its coupling with void fraction waves. A phase difference estimator based on the cross-spectra between differential pressure signals is proposed. It is experimentally shown that there is a region of the spectrum where the differential pressure signals and the void fraction kinematic waves are coupled. Besides, a relation between the differential pressure signals and the void fraction wave is established, allowing to discuss the underlying physics of the two-phase flow and then determining the Taylor bubble velocity. In this paper, results are shown for intermittent slug flow only, but the proposed approach can potentially be extended to different flow patterns. The presented results show that the use of differential pressure measurements related to void fraction waves have the potential of becoming a methodology applicable by the industry as a tool to identify and characterize flow patterns.

Approach and breakup of Taylor bubble and Taylor drop in a Hele-Shaw cell

The collision dynamics of a Taylor drop and a Taylor bubble is investigated in an immiscible surrounding liquid. The interaction of both the fluidic entities is studied using experiments and simulation in a vertically aligned Hele-Shaw cell. The steady rise of the bubble and fall of the drop are followed by a deceleration regime where their velocity has decreased due to the pressure imposed by the leading interfaces, indicated by the change in the curvature of their tip. Subsequently, the rapid outward expansion of the bubble has caused the swelling of the tip of the drop. The drop swell has then grown exponentially similar to Rayleigh–Taylor instability and resulted in a split of the bubble into two volumes.

Scale-dependent Rayleigh–Taylor dynamics with variable acceleration by group theory approach

Rayleigh–Taylor instability (RTI) has critical importance for a broad range of plasma processes, from supernovae to fusion. In most instances, RTI is driven by variable acceleration, whereas the bulk of existing studies have considered only constant and impulsive acceleration. This work focuses on RTI driven by acceleration with a power-law time-dependence. We review the existing theoretical approaches, apply the group theory approach to solve this long-standing problem, and yield the unified framework for the scale-dependent dynamics of Rayleigh–Taylor (RT) bubbles and RT spikes. For the early-time linear dynamics, we provide the dependence of RTI evolution on the acceleration parameters and the initial conditions. For the late-time nonlinear dynamics, we find a continuous family of asymptotic solutions, directly link the interface velocity to the interface morphology and the interfacial shear, derive solutions for the regular bubbles and for the singular spikes, and study the stability of these solutions. The properties of special nonlinear solutions in the RT family are scrupulously described, including the critical, Taylor, Layzer-drag, and Atwood solutions. It is shown that the fastest Atwood bubble is regular and stable, and the fastest Atwood spike is singular and unstable. The essentially multi-scale and interfacial character of RT dynamics is demonstrated. The former can be understood by viewing the RT coherent structure of bubbles and spikes as a standing wave with the growing amplitude. The latter implies that RT flow has effectively no motion of the fluids away from the interface and has intense motion of the fluids near the interface, with shear-driven vortical structures appearing at the interface. Our theory agrees with available observations and elaborates extensive benchmarks for future research and for better understanding of RT driven phenomena in plasmas.

Thermal diffusion response to gas–liquid slug flow and its application in measurement

A novel on-line, contactless and nearly non-intrusive measurement method based on thermal diffusion is proposed for gas–liquid slug flow in this paper. Temperature fluctuations of a pipe wall heated at a constant heat flux are induced by Taylor bubbles and liquid slugs due to their different heat exchange capacities. The slug flow characteristics, including velocity, length, and frequency, in the vertical pipe, can be obtained through temperature fluctuation detection. Correlations between wall temperature fluctuations and slug flow characteristics are developed. Through experimental tests on air–water slug flow in a 25 mm diameter pipe at the atmospheric pressure of 1 bar and room temperature of approximately 20 °C, the average relative errors in average velocity for the Taylor bubbles and liquid slugs are 1.84% and 2.28% with maximum values of 4.67% and 5.79%, respectively. The average relative errors in average length are 4.65% and 3.68% with maximum values of 12.75% and 10.48%, respectively, under the conditions of 0.16–0.65 m/s of gas superficial velocity, 0.22–0.49 m/s of liquid velocity, and 0.34–2.96 of gas–liquid ratio.

On the rise characteristics of Taylor bubbles in annular piping

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.

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

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 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.

On the dynamics of Richtmyer–Meshkov bubbles in unstable three-dimensional interfacial coherent structures with time-dependent acceleration

Richtmyer–Meshkov instability (RMI) plays an important role in many areas of science and engineering, from supernovae and fusion to scramjets and nano-fabrication. Classical RMI is induced by a steady shock and impulsive acceleration, whereas in realistic environments, the acceleration is usually variable. We focus on RMI induced by acceleration with power-law time-dependence and apply group theory to study the dynamics of regular bubbles. For early time linear dynamics, we find the dependence of the growth rate on the initial conditions and show that it is independent of the acceleration parameters. For late-time nonlinear dynamics, we consider regular asymptotic solutions, find a continuous family of such solutions, including their curvature, velocity, Fourier amplitudes, and interfacial shear, and study their stability. For each solution, the interface dynamics is directly linked to the interfacial shear. The non-equilibrium velocity field has intense fluid motion near the interface and effectively no motion in the bulk. The quasi-invariance of the fastest stable solution suggests that the dynamics of nonlinear RM bubbles is characterized by two macroscopic length scales: the wavelength and the amplitude, in agreement with observations. The properties of a number of special solutions are outlined. These are the flat Atwood bubble, the curved Taylor bubble, the minimum shear bubble, the convergence limit bubble, and the critical bubble. We elaborate new theory benchmarks for future experiments and simulations.

Gas-liquid hydrodynamics and mass transfer in microreactors under ultrasonic oscillation

Integration of microreactors with ultrasound is a promising way to intensify gas-liquid mass transfer. The present study locally visualized and characterized the O2 mass transfer around Taylor bubbles flowing in a square microchannel reactor under ultrasonic oscillation. The effect of acoustic field on the gas-liquid hydrodynamics and mass transfer were investigated. A reciprocating phenomenon of the bubble contraction and expansion was observed, and the evolution of bubble length was found to be a periodic harmonic process. It was also revealed that the cavitation microstreaming generated by the bubble surface oscillation, as well as the periodic bubble length variation, could strongly modify and twist the recirculation loops in the liquid slug, thus intensify the mass transfer. As the bubble surface oscillation during the bubble formation was not as fierce as during the bubble flowing, the enhancement factors of mass transfer by the ultrasonic oscillation range from 1.04 to 1.85 for the formation and from 1.27 to 3.17 for the flowing stage. Semi-empirical equations were established to predict the overall mass transfer coefficient in terms of the acoustic power density and Reynolds number.

Prediction model and energy dissipation analysis of Taylor bubble rise velocity in yield stress fluid

In this study, a velocity field model around a Taylor bubble is established after the analysis of the disturbed region around the bubble. The model combines the continuity and yield stress fluid constitutive equations. Based on this velocity field model, an energy dissipation model for the work accomplished by each resistance of bubbles is proposed. In addition, based on an analysis of energy conservation, a new model for predicting the velocity of a Taylor bubble in a yield stress fluid is presented. The experiments of Taylor bubble through Carbopol solution migration in 50 and 60 mm diameter tubes were carried out. Results show that the yield stress has considerable influence on the rise speed of the bubble, improving the anti-disturbance ability of the fluid and further stabilizing the tail of the bubble. Combined with experimental data, the bubble velocity prediction model is verified, and the error value of the calculation result is found to be less than 6%. An energy analysis of the Taylor bubble rising process shows that the volume of the bubble increases, the proportion of work done by inertial force and surface tension decreases, and that done by viscosity force and yield stress increases. The work done by surface tension has little effect on the rise speed of bubbles, which can be ignored. The Taylor bubble velocity changes slightly with the volume, as the bubble volume increases, and the buoyancy work is consumed by the viscous and inertial forces in the film region.

Theoretical analysis on the atomization characteristics of liquid nitrogen jets

Atomization with cryogenic fluids is complicated due to the combined effects of both the mechanical breakup and thermodynamic flashing. However, the weight of the two effects on the atomization has not been determined yet. This paper proposes a hybrid mathematical model to evaluate the weight of the thermodynamic effect and aerodynamic effect. The entire process of jet spray breakup, including the primary breakup and secondary atomization, is described in the model. A linear stability analysis is carried out using the dispersion equations for the primary breakup. In the secondary atomization, the Taylor analogy breakup and bubble micro-explosion models are employed to study aerodynamic and thermodynamic effects on the atomization, respectively. The homogeneous nucleation is implemented in the bubble micro-explosion models. A criterion is obtained which can be evaluated to predict the dominant effect. Accordingly, the influence of factors such as ambient pressure and other physical parameters on the atomization process is analyzed. The results reveal that, under low ambient pressure, thermodynamic flashing is stronger. Besides, the mechanical action is restrained when the surface tension is increased.

Study of intermittent flow characteristics experimentally and numerically in a horizontal pipeline

The gas-liquid intermittent flow regime is the dominant flow pattern, which significantly occurs in the oil and gas industries. The intermittent flow is challenging in the hydrocarbon transportation systems and separators operation. The present investigation aims to comprehend the behavior of intermittent flow characteristics using experimental and numerical methods simultaneously. Superficial velocities of water and air were set in ranges of (0.18–0.84 m/s) and (1.22–4.9 m/s), respectively. The research was conducted in a horizontal pipe with a diameter of 44 mm and 147D long to study slug frequency, slug length, translational slug velocity, pressure drops, as well as slug's initiation location using static pressure data and high-speed camera tools. In this regard, the volume of fluid (VoF) method and SST k-ω model were also applied to specify film thickness, maximum Taylor bubble velocity, and to grasp behaviors of the flow field in more detail. The results revealed that liquid superficial velocity has more effects on slug frequencies than gas superficial velocity. On the other hand, slug initiation location, as well as slug fully developed length, is affected by the gas superficial velocity more than liquid superficial velocity. Moreover, both the gas and liquid superficial velocities have the same effects on translational slug velocities. The obtained experimental results were also employed to define a distinctive inlet boundary condition in the numerical simulation, which leads to a 65 percent reduction in the computational domain.

Gas-liquid mass transfer around Taylor bubbles flowing in a long, in-plane, spiral-shaped milli-reactor

Gas–liquid mass transfer was investigated around Taylor bubbles flowing in a long, in-plane, spiral-shaped milli-reactor involving various configurations. Using a colorimetric technique and image post-treatment, the variation of the equivalent O2 concentration inside the liquid slugs was measured. The coloration positions, corresponding to 99% of the maximum concentration reached in the liquid slug, changed significantly under various operating conditions. Overall volumetric mass transfer coefficients were evaluated on the basis of these coloration positions, without considering the hydrodynamics change. The intensification factor of two configurations was found to be proportional to the increase in Dean number. Considering the changes in pressure drop, bubble length and velocity, the axial variation of cumulated mass flux could be measured. It decreased along tube and finally tended towards a constant value. A scaling law for the Sherwood number was proposed by introducing a normalized time, dimensionless liquid slug length, and the Péclet and Dean numbers.

LES of Turbulent Co-current Taylor Bubble Flow

Turbulent co-current Taylor bubble flow was modeled with LES alongside the VOF interface tracking solver. The method is first validated in the context of single phase turbulent pipe flow and three distinct laminar Taylor bubble flow cases. The turbulent co-current Taylor bubble flow is simulated using a moving frame of reference which is attached to the bubble, allowing for a straight-forward time averaging and Dirichlet-type flow recycling inlet boundary condition. In contrast to periodic inlet and outlet boundary conditions, the Dirichlet one assures that small bubbles which are lost by the Taylor bubble are removed from the computation once they leave the domain, therewith not interfering with the nose of the Taylor bubble. The transient loss of small bubbles which is observed in our simulations implies that the problem is inherently unsteady. We therefore present an averaging strategy which consists of combined time, space and ensemble averaging. This strategy allows systematic comparison of results across different computational meshes. The results show that the approach captures distinct features of turbulent co-current Taylor bubble flow well, in the sense that good agreement is observed with experimental data from literature in terms of the toroidal vortex flow field in the wake of the Taylor bubble. Agreement with measured velocity fluctuation profiles in the wake of the Taylor bubble is less pronounced, and is discussed in the paper. Nevertheless, the simulation approach of co-current Taylor bubble flow proposed in this paper may serve as a tool that will provide deeper insights in two-phase turbulent flow for future research.

Experimental study of single Taylor bubbles rising in vertical and slightly deviated circular tubes

This paper reports an experimental study of single Taylor bubbles rising in stagnant water-glycerin mixtures inside slightly deviated cylindrical tubes. The inclination angles studied were 0°, 2.5°, 5°, 7.5°, 10° and 15° from the vertical. The rise bubble velocity and the shape of the bubbles at two vertical orthogonal planes that intersect at the tube axis were measured by using a pulse-echo ultrasonic technique. Thus, the liquid films draining at the top, bottom and lateral sides of the bubbles were observed. The experimental results indicated that for all liquid mixtures studied, the bubble velocity increased when the inclination angle was increased, and that the bubble velocity was independent of the bubble length. The influence of liquid properties and of tube diameter on the bubble movement and shape were evaluated for deviated angles ranging from 0° to 15°. Different correlations to predict the drift velocity of Taylor bubbles rising in inclined tubes were tested for this particular range of inclination.

Exploring Two-Phase Flow Regime Transition Mechanisms Using High-Resolution Virtual Experiments

Recent advancements in computing power allow utilization of state-of-the-art direct numerical simulations (DNSs), coupled with interface tracking techniques, to perform fully resolved simulations of complex two-phase flows, such as flow regime transitions. Studying the highly resolved temporal and spatial information produced from these virtual experiments can advance our understanding of the phenomenon and inform coarser models. With these improved models, better predictions of flow regime behavior and location in boiling water reactors can be made. The presented research uses the PHASTA code, which employs the level set method for interface tracking, to examine the mechanisms of flow regime transition, specifically the slug-to-bubbly and slug-to–churn-turbulent regime transitions. The DNS was validated using theoretical and experimental work found in open literature. Different geometries, including pipes and minichannels, were explored in order to improve the fundamental understanding of the complex flow phenomenon. Using advanced analysis techniques, the transient flow properties were analyzed at resolutions not available to other methods. The numerical data analysis allows for calculation of both time and spatially averaged properties as well as local instantaneous properties. Possible mechanisms for the transition are discussed. Examples include liquid kinetic energy/surface tension energy balance and interfacial shear forces in the liquid film. It is also noted that the transition out of slug flow can take at least two pathways: interfacial wave-induced instability development in the Taylor bubble, leading to its disintegration, or strong bubble shearing at the tail of the bubble.

Isolated Taylor Bubbles in Co-Current with Shear Thinning CMC Solutions in Microchannels—A Numerical Study

Slug flow is a multiphase flow pattern characterized by the occurrence of long gas bubbles (Taylor bubbles) separated by liquid slugs. This multiphase flow regime is present in many and diversified natural and industrial processes, at macro and microscales, such as in eruption of volcanic magmas, oil recovery from pre-salt regions, micro heat exchangers, and small-sized refrigerating systems. Previous studies in the literature have been mostly focused on tubular gas bubbles flowing in Newtonian liquids. In this work, results from several numerical simulations of tubular gas bubbles flowing in a shear thinning liquid in microchannels are reported. To simulate the shear thinning behavior, carboxymethylcellulose (CMC) solutions with different concentrations were considered. The results are compared with data from bubbles flowing in Newtonian liquids in identical geometric and dynamic conditions. The numerical work was carried out in computational fluid dynamics (CFD) package Ansys Fluent (release 16.2.0) employing the volume of fluid (VOF) methodology to track the volume fraction of each phase and the continuum surface force (CSF) model to insert the surface tension effects. The flow patterns, the viscosity distribution in the liquid, the liquid film thickness between the bubble and the wall, and the bubbles shape are analyzed for a wide range of shear rates. In general, the flow patterns are similar to those in Newtonian liquids, but in the film, where a high viscosity region is observed, the thickness is smaller. Bubble velocities are smaller for the non-Newtonian cases.