Gas entrainment by a liquid film falling around a stationary Taylor bubble in a vertical tube

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a 0.1 m diameter vertical tube is studied experimentally with the purpose of validating a model formulated in an earlier phase of our research. According to this model for a fixed liquid velocity the gas entrainment should be proportional to the waviness of the film (its intermittency) and the wave height and inversely proportional to the film thickness. For Taylor bubble lengths ranging from 1D to 15D these film parameters have been measured with a Laser Induced Fluorescence technique. The gas entrainment has been determined from the net gas flux into the liquid column underneath the Taylor bubble by using data on gas re-coalescence into the rear of the Taylor bubble. These data are available for lengths ranging from 4.5D to 9D. The model results with the measured film characteristics compare well with the observed gas entrainment. The fact that the net gas flux becomes constant for long Taylor bubbles, whereas the wave height still increases, warrants further study.     

Experimental investigation of single helium bubbles rising in FLiNaK molten salt

An experimental investigation of single helium bubbles rising in a stagnant molten fluoride salt mixture was conducted in a 25.4 mm quartz tube at 600 °C and atmospheric pressure. The fluoride salt chosen for this research was the eutectic mixture of LiF-NaF-KF (46.5–11.5–42%), also known as FLiNaK. The images obtained using a high-speed camera were processed to estimate the bubble size, rising velocity, trajectory and shape. The shape of the bubble showed typical characteristics of wobbling bubble corresponding to published classifications. The trajectory of the rising bubble showed complex path oscillations and combinations of rectilinear, zig-zag and helical motion. The projected area-equivalent diameter and experimental terminal velocity varied from 5.26 to 6.23 mm and 232.35–259.57 mm/s, respectively. Several important dimensionless numbers were calculated and reported based on the experimental results, which are closely related to the phenomena involving a gas bubble rising in liquid. The measured terminal velocity was compared with the predictions of existing correlations that include the dimensionless numbers and showed reasonable agreement. The Particle Image Velocimetry (PIV) technique was applied to complement the experimental data set with high-fidelity measurements of the velocity field of the liquid molten salt surrounding the bubble. The paper presents a unique set of PIV and two-phase experimental data capturing the behavior of rising helium bubbles in molten FLiNaK and its surrounding flow field.     

Investigation of surfactant effect on the bubble shape and mass transfer in a milli-channel using high-resolution microfocus X-ray imaging

In this paper we present an experimental study on the influence of surface active agents (surfactants) on Taylor bubble flow in a vertical millimeter-size channel. Moreover we give a short review on the subject and previous investigations. We investigated the shape and dissolution rate of individual elongated carbon dioxide Taylor bubbles, which were hydraulically fixed in a downward flow of water. Bubble shape and dissolution rate was determined from microfocus X-ray radiographs. From the shrinking rate we calculated the liquid side mass transfer coefficient.The results show that the presence of surfactants causes a change of the bubble shape and leads to a slight increase of the liquid film thickness around the bubble and as a result the elongation of contaminated bubbles. In addition, the comparison of clean and contaminated bubbles indicate that presence of surfactant has a more significant impact on the dissolution rate of small bubbles. Furthermore, applying different concentrations of surfactant reveals that in our case, where surface coverage ratio of surfactant on the bubbles is high, increase of contamination does not have a noticeable influence on the mass transfer coefficient of bubbles.     

Ellipsoidal model of the rise of a Taylor bubble in a round tube

The rise velocity of long gas bubbles (Taylor bubbles) in round tubes is modeled by an ovary ellipsoidal cap bubble rising in an irrotational flow of a viscous liquid. The analysis leads to an expression for the rise velocity which depends on the aspect ratio of the model ellipsoid and the Reynolds and Eötvös numbers. The aspect ratio of the best ellipsoid is selected to give the same rise velocity as the Taylor bubble at given values of the Eötvös and Reynolds numbers. The analysis leads to a prediction of the shape of the ovary ellipsoid which rises with same velocity as the Taylor bubble.     

Flow around individual Taylor bubbles rising in stagnant polyacrylamide (PAA) solutions

The flow around single Taylor bubbles rising in stagnant non-Newtonian solutions of polyacrylamide (PAA) polymer was studied using a technique employing simultaneous particle image velocimetry (PIV) and shadowgraphy. Solutions with different weight percentages of polymer, varying from 0.01 to 0.80 wt.%, were used to cover a wide range of flow regimes. The rheological fluid properties and pipe dimension yielded Reynolds numbers between 2 and 1160, and Deborah numbers up to 115. The shape of the bubbles rising in the different solutions was compared and quantified by fitting correlations. The flow around the nose of the bubbles was found to be similar for all conditions studied. Velocity profiles were measured and analysed in the liquid film around the bubbles. A comparison of bubble wake flow patterns was made. For the 0.10 and 0.20 wt.% PAA solutions, long wakes with a recirculation region were observed. Below the wakes, a flow of stretched liquid was found. Negative wakes were also observed for the more concentrated solutions.     

Interaction between Taylor bubbles rising in stagnant non-Newtonian fluids

The interaction between Taylor bubbles rising in stagnant non-Newtonian solutions was studied. Aqueous solutions of carboxymethylcellulose (CMC) and polyacrylamide (PAA) polymers were used to study the effect of different rheological properties: shear viscosity and viscoelasticity. The solutions studied covered a range of Reynolds numbers between 10 and 714, and Deborah numbers up to 14. The study was performed with pairs of Taylor bubbles rising in a vertical column (0.032 m internal diameter) filled with stagnant liquid. The velocities of the leading and trailing bubbles were measured by sets of laser diodes/photocells placed along the column. The velocity of the trailing bubble was analysed together with the liquid velocity profile in the wake of a single rising bubble (Particle Image Velocimetry data obtained from the literature). For the less concentrated CMC solutions, with moderate shear viscosity and low viscoelasticity, the interaction between Taylor bubbles was similar to that found in Newtonian fluids. For the most concentrated CMC solution, which has high shear viscosity and moderate viscoelasticity, a negative wake forms behind the Taylor bubbles, inhibiting coalescence since the bubbles maintain a minimum distance of about 1D between them. For the PAA solutions, with moderate shear viscosity but higher viscoelasticity than the CMC solutions, longer wake lengths are seen, which are responsible for trailing bubble acceleration at greater distances from the leading bubble. Also in the PAA solutions, the long time needed for the fluid to recover its initial shear viscosity after the passage of the first bubble makes the fluid less resistant to the trailing bubble flow. Hence, the trailing bubble can travel at a higher velocity than the leading bubble, even at distances above 90D.     

Measurement of the liquid film thickness in micro tube slug flow

Slug flow is one of the representative flow regimes of two-phase flow in micro tubes. It is well known that the thin liquid film formed between the tube wall and the vapor bubble plays an important role in micro tube heat transfer. In the present study, experiments are carried out to clarify the effects of parameters that affect the formation of the thin liquid film in micro tube two-phase flow. Laser focus displacement meter is used to measure the thickness of the thin liquid film. Air, ethanol, water and FC-40 are used as working fluids. Circular tubes with five different diameters, D = 0.3, 0.5, 0.7, 1.0 and 1.3 mm, are used. It is confirmed that the liquid film thickness is determined only by capillary number and the effect of inertia force is negligible at small capillary numbers. However, the effect of inertia force cannot be neglected as capillary number increases. At relatively high capillary numbers, liquid film thickness takes a minimum value against Reynolds number. The effects of bubble length, liquid slug length and gravity on the liquid film thickness are also investigated. Experimental correlation for the initial liquid film thickness based on capillary number, Reynolds number and Weber number is proposed.     

An investigation on near wall transport characteristics in an adiabatic upward gas–liquid two-phase slug flow

The near-wall transport characteristics, inclusive of mass transfer coefficient and wall shear stress, which have a great effect on gas–liquid two-phase flow induced internal corrosion of low alloy pipelines in vertical upward oil and gas mixing transport, have been both mechanistically and experimentally investigated in this paper. Based on the analyses on the hydrodynamic characteristics of an upward slug unit, the mass transfer in the near wall can be divided into four zones, Taylor bubble nose zone, falling liquid film zone, Taylor bubble wake zone and the remaining liquid slug zone; the wall shear stress can be divided into two zones, the positive wall shear stress zone associated with the falling liquid film and the negative wall shear stress zone associated with the liquid slug. Based on the conventional mass transfer and wall shear stress characteristics formulas of single phase liquid full-pipe turbulent flow, corrected normalized mass transfer coefficient formula and wall shear stress formula are proposed. The calculated results are in good agreement with the experimental data. The shear stress and the mass transfer coefficient in the near wall zone are increased with the increase of superficial gas velocity and decreased with the increase of superficial liquid velocity. The mass transfer coefficients in the falling liquid film zone and the wake zone of leading Taylor bubble are lager than those in the Taylor bubble nose zone and the remaining liquid slug zone, and the wall shear stress associated falling liquid film is larger than that associated the liquid slug. The mass transfer coefficient is within 10⁻³ m/s, and the wall shear stress below 10³ Pa. It can be concluded that the alternate wall shear stress due to upward gas–liquid slug flow is considered to be the major cause of the corrosion production film fatigue cracking.     

On the interaction of Taylor bubbles rising in two-phase co-current slug flow in vertical columns: turbulent wakes

An experimental study on the interaction between Taylor bubbles rising through a co-current flowing liquid in a vertical tube with 32 mm of internal diameter is reported. The flow pattern in the bubble's wake was turbulent and the flow regime in the liquid slug was either turbulent or laminar. When the flow regime in the liquid slug is turbulent (i) the minimum distance between bubbles above which there is no interaction is 5D-6D; (ii) the bubble's rising velocity is in excellent agreement with the Nicklin relation; (iii) the experimental values of the bubble length compare well with theoretical predictions (Barnea 1990); (iv) the distance between consecutive bubbles varied from 13D to 16D and is insensitive to the liquid Reynolds number. When the flow regime in the liquid slug is laminar (i) the wake length is about 5D-6D; (ii) the minimum distance between bubbles above which there is no interaction is higher than 25D; (iii) the bubble's rising velocity is significantly smaller than theoretical predictions. These results were explained in the light of the findings of Pinto et al. (1998) on coalescence of two Taylor bubbles rising through a co-current liquid. Received: 2 February 2000 / Accepted: 15 March 2001     

Hydrodynamic and mass transfer characteristics of slug flow in a vertical pipe with and without dispersed small bubbles

In this work, we present a numerical study to investigate the hydrodynamic characteristics of slug flow and the mechanism of slug flow induced CO₂ corrosion with and without dispersed small bubbles. The simulations are performed using the coupled model put forward by the authors in previous paper, which can deal with the multiphase flow with the gas–liquid interfaces of different length scales. A quasi slug flow, where two hypotheses are imposed, is built to approximate real slug flow. In the region ahead of the Taylor bubble and the liquid film region, the presence of dispersed small bubbles has less impacts on velocity field, because there are no non-regular intensive disturbance forces or centrifugal forces breaking the balance of the liquid and the dispersed small bubbles. In the liquid slug region, the strong centrifugal forces generated by the recirculation below the Taylor bubble lead to the effect of heterogeneity, which makes the profile of the radial liquid velocity component sharper with higher volume fraction of dispersed small bubbles. The volume fraction has a maximum value in the range of r/R = 0.5–0.6. Meanwhile, it is usually higher than 0.35, which means that larger dispersed bubbles can be formed by coalescences in this region. These calculated results are in good agreement with experimental results. The wall shear stress and the mass transfer coefficient with dispersed small bubbles are higher than those without dispersed small bubbles due to enhanced fluctuations. For short Taylor bubble length, the average mass transfer coefficient is increased when the gas or liquid superficial velocity is increased. However, there may be an inflection point at low mixture superficial velocities. For the slug with dispersed small bubbles, the product scales still cannot be damaged directly despite higher wall shear stress. In fact, the alternate wall shear stress and the pressure fluctuations perpendicular to the pipe wall with high frequency are the main cause for breaking the product scales.     

Spatial distribution of void fraction within a liquid slug and some other related slug parameters

The structure of vertical upward slug flow in a pipe is studied. The distribution of the phases in the Taylor bubble zone and the liquid slug zone is investigated by simultaneous measurements with two optical fiber probes. In the Taylor bubble zone the shape of the Taylor bubble and the distribution of the bubble length is reported. In the liquid slug region, the distribution of the void fraction is obtained over a dense grid in both the axial and radial directions. These experimental results shed some light on the hydrodynamics of the two-phase slug flow, in particular regarding the production of the dispersed bubbles and their distribution along the liquid slug.     

Experimental study on hydrodynamic characteristics of upward gas–liquid slug flow

To clarify the impacts of the hydrodynamic boundary layer and the diffusion boundary layer in the near wall zone on gas–liquid two-phase flow induced corrosion in pipelines, the hydrodynamic characteristics of fully developed gas–liquid slug flow in an upward tube are investigated with limiting diffusion current probes, conductivity probes and digital high-speed video system. The Taylor bubble and the falling liquid film characteristics are studied, the effects of various factors are examined, and the experimental results are compared with the data and models available in literature. The length of Taylor bubble, the local void fraction of the slug unit and the liquid slug, the shear stress and mass transfer coefficient in the near wall zone, are all increased with the increase of superficial gas velocity and decreased with the increase of superficial liquid velocity, whereas the length of liquid slug and the liquid slug frequency are changed contrarily. The alternate wall shear stress due to upward gas–liquid slug flow is considered to be one of the major causes for the corrosion production film fatigue cracking. A normalized formula for mass transfer coefficient is obtained based on the experimental data.     

Simultaneous PIV and pulsed shadow technique in slug flow: a solution for optical problems

A recent technique of simultaneous particle image velocimetry (PIV) and pulsed shadow technique (PST) measurements, using only one black and white CCD camera, is successfully applied to the study of slug flow. The experimental facility and the operating principle are described. The technique is applied to study the liquid flow pattern around individual Taylor bubbles rising in an aqueous solution of glycerol with a dynamic viscosity of 113×10^–3 Pa s. With this technique the optical perturbations found in PIV measurements at the bubble interface are completely solved in the nose and in annular liquid film regions as well as in the rear of the bubble for cases in which the bottom is flat. However, for Taylor bubbles with concave oblate bottoms, some optical distortions appear and are discussed. The measurements achieved a spatial resolution of 0.0022 tube diameters. The results reported show high precision and are in agreement with theoretical and experimental published data.Symbols D internal column diameter (m) - g acceleration due to gravity (m s^–2) - l _w wake length (m) - Q _v liquid volumetric flow rate (m³ s^–1) - r radial position (m) - r * radial position of the wake boundary (m) - R internal column radius (m) - U _s Taylor bubble velocity (m s^–1) - u _z axial component of the velocity (m s^–1) - u _r radial component of the velocity (m s^–1) - z distance from the Taylor bubble nose (m) - Z * distance from the Taylor bubble nose for which the annular liquid film stabilizes (m) Dimensionless groups Re Reynolds number ( ) - N _f inverse viscosity number ( ) Greek letters liquid film thickness (m) - liquid kinematic viscosity (m² s^–1) - liquid dynamic viscosity (Pa s) - liquid density (kg m^–3)     

垂直上升管内油—气—水三相弹状流压力降的研究

给出一种垂直上升油－气－水三相弹状流压力降的计算模型。该模型考虑弹状流中Ｔａｙｌｏｒ气泡周围下降液膜的变化历程。通过油－气－水弹状流的实验研究发现，该模型的数值模拟结果与低压工况下的实验值符合得较好。本模型是计算垂直油－气－水三相弹状流中液相的连续相为水相时的压力降的有效方法。     

Dynamics of a Taylor bubble in steady and pulsatile co-current flow of Newtonian and shear-thinning liquids in a vertical tube

A computational analysis is carried out to ascertain the effects of steady and pulsatile co-current flow, on the dynamics of an air bubble rising in a vertical tube containing water or a solution of Carboxymethylcellulose (CMC) in water. The mass fraction (m_f) of CMC in the solution is varied in the range 0.1% ⩽ m_f ⩽ 1% to accommodate zero-shear dynamic viscosities in the range 0.009–2.99 Pa-s. It was found that the transient and time-averaged velocities of Taylor bubbles are independent of the bubble size under both steady as well as pulsatile co-current flows. The lengths of the Taylor bubbles under the Newtonian conditions are found to be consistently greater than the corresponding shear-thinning non-Newtonian conditions for any given zero-shear dynamic viscosity of the liquid. In contrast to observations in stagnant liquid columns, an increase in the dynamic viscosity of the liquid (under Newtonian conditions) results in a concomitant increase in the bubble velocity, for any given co-current liquid velocity. In shear-thinning liquids, the change in the bubble velocity with an increase in m_f is found to be relatively greater at higher co-current liquid velocities. During pulsatile shear-thinning flows, distinct ripples are observed to occur on the bubble surface at higher values of m_f, the locations of which remain stationary with reference to the tube for any given pulsatile flow frequency, while the bubble propagated upwards. In such a pulsatile shear-thinning flow, a localised increase in dynamic viscosity is accompanied near each ripple, which results in a localised re-circulation region inside the bubble, unlike a single re-circulation region that occurs in Newtonian liquids, or shear-thinning liquids with low values of m_f. It is also seen that as compared to frequency, the amplitude of pulsatile flow has a greater influence on the oscillating characteristics of the rising Taylor bubble. The amplitude of oscillation in the bubble velocity increases with an increase in the CMC mass fraction, for any given value of pulsatile flow amplitude.     

Characterization of plunging liquid jets: A combined experimental and numerical investigation

This paper presents a combined experimental and numerical study of the flow characteristics of round vertical liquid jets plunging into a cylindrical liquid bath. The main objective of the experimental work consists in determining the plunging jet flow patterns, entrained air bubble sizes and the influence of the jet velocity and variations of jet falling lengths on the jet penetration depth. The instability of the jet influenced by the jet velocity and falling length is also probed. On the numerical side, two different approaches were used, namely the mixture model approach and interface-tracking approach using the level-set technique with the standard two-equation turbulence model. The numerical results are contrasted with the experimental data. Good agreements were found between experiments and the two modelling approaches on the jet penetration depth and entraining flow characteristics, with interface tracking rendering better predictions. However, visible differences are observed as to the jet instability, free surface deformation and subsequent air bubble entrainment, where interface tracking is seen to be more accurate. The CFD results support the notion that the jet with the higher flow rate thus more susceptible to surface instabilities, entrains more bubbles, reflecting in turn a smaller penetration depth as a result of momentum diffusion due to bubble concentration and generated fluctuations. The liquid average velocity field and air concentration under tank water surface were compared to existing semi-analytical correlations. Noticeable differences were revealed as to the maximum velocity at the jet centreline and associated bubble concentration. The mixture model predicts a higher velocity than the level-set and the theory at the early stage of jet penetration, due to a higher concentration of air that cannot rise to the surface and remain trapped around the jet head. The location of the maximum air content and the peak value of air holdup are also predicted differently.     

Effect of gas expansion on the velocity of a Taylor bubble: PIV measurements

The effect of gas expansion on the velocity of a Taylor bubble was studied experimentally. The velocity field in the liquid ahead of a Taylor bubble was measured by particle image velocimetry (PIV), and the bubble velocity was measured with two pairs of laser diodes and photocells. The experiments were done in a 7.0 m long vertical tube with a 32 mm internal diameter. Solutions of carboxymethylcellulose (CMC) polymer with weight percentages between 0.01% and 0.1% were used. The expansion of slug gas induces an increase in the bubble velocity and a corresponding displacement of the liquid ahead of the bubble. The velocity of the bubble increases by an amount equal to the maximum velocity in the liquid displaced. For the solutions studied, the induced velocity profile was parabolic and the bubble velocity increase was equal to the liquid velocity at the tube axis, i.e., twice the mean velocity in the liquid displaced. The corrected velocity obtained by subtracting the velocity increase from the value of the bubble velocity is independent of the bubble length.     

Motion of bubbles in a fluidized bed

The steady-state motion of a bubble (a cavity free from suspended particles and occupied solely by the liquid phase) in a fluidized bed of uniform concentration is considered. The change in the shape of the bubble which takes place as it rises through the fluidized bed is established; the rising velocity is determined for both large and small bubbles. The basic parameter characterizing the shape of a large bubble in either a fluidized bed or a homogeneous liquid is calculated. This, in particular, enables the well-known Taylor problem of a large drop or bubble in an unlimited medium to be solved.     

Forced convective flow and heat transfer of upward cocurrent air–water slug flow in vertical plain and swirl tubes

This experimental study comparatively examined the two-phase flow structures, pressured drops and heat transfer performances for the cocurrent air–water slug flows in the vertical tubes with and without the spiky twisted tape insert. The two-phase flow structures in the plain and swirl tubes were imaged using the computerized high frame-rate videography with the Taylor bubble velocity measured. Superficial liquid Reynolds number (Re_L) and air-to-water mass flow ratio (AW), which were respectively in the ranges of 4000–10000 and 0.003–0.02 were selected as the controlling parameters to specify the flow condition and derive the heat transfer correlations. Tube-wise averaged void fraction and Taylor bubble velocity were well correlated by the modified drift flux models for both plain and swirl tubes at the slug flow condition. A set of selected data obtained from the plain and swirl tubes was comparatively examined to highlight the impacts of the spiky twisted tape on the air–water interfacial structure and the pressure drop and heat transfer performances. Empirical heat transfer correlations that permitted the evaluation of individual and interdependent Re_L and AW impacts on heat transfer in the developed flow regions of the plain and swirl tubes at the slug flow condition were derived.     

Vertical stability of bubble chain: Multiscale approach

Linear stability is investigated of a uniform chain of equal spherical gas bubbles rising vertically in unbounded stagnant liquid at Reynolds number Re = 50–200 and bubble spacing s > 2.6 bubble radii. The equilibrium bubble positions are questioned for their stability with respect to small displacements in the vertical direction, parallel to the chain motion. The transverse displacements are not considered, and the chain is assumed to be laterally stable. The bubbles are subjected to three kinds of forces: buoyant, viscous, inviscid. The viscous and inviscid forces have both pairwise (local) and distant (nonlocal) components. The pairwise forces are expressed by the leading-order formulas known from the literature. The distant forces are expressed as a linear superposition of the pairwise forces taken over several farther neighbours. The stability problem is addressed on three different length scales corresponding to: discrete chain (microscale), continuous chain (mesoscale), bubbly chain flow (macroscale). The relevant governing equations are derived for each scale. The microscale equations are a set of ODE’s, the Newton force laws for the individual discrete bubbles. The mesoscale equation is a PDE for bubbles continuously distributed along a line, obtained by taking the continuum limit of the microscale equations. The macroscale equations are two PDEs, the mass and momentum conservation equations, for an ensemble of noninteracting mesoscale chains rising in parallel. This transparent two-step process (micro → meso → macro) is an alternative to the usual one-step averaging, in obtaining the macroscale equations from microscale information. Here, the scale-up methodology is demonstrated for 1D motion of bubbles, but it can be used for behaviour of 2D and 3D lattices of bubbles, drops, and solids.It is found that the uniform equilibrium spacing results from a balance between the attractive and repulsive forces. On all three length scales, the equilibrium is stabilized by the viscous drag force, and destabilized by the viscous shielding force (shielding instability). The inviscid forces are stability neutral and generate conservative oscillations and concentration waves. The stability region in the parameter plane s − Re is determined for each length scale. The stable region is relatively small on the microscale, larger on the mesoscale, and shrinks to zero on the macroscale where the bubbly chain flow is inherently unstable.The shielding instability is expected to occur typically in intermediate Re flows where the vertical bubble interactions dominate over the horizontal interactions. This new kind of instability is studied here in a great detail, likely for the first time. Its relation to the elasticity properties of bubbly suspension on different length scales is discussed too. The shielding force takes the form of a negative bulk modulus of elasticity of the bubbly mixture.