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.     

Characterisation of gas-liquid two-phase flow in minichannels with co-flowing fluid injection inside the channel,part II: gas bubble and liquid slug lengths,film thickness,and void fraction within Taylor flow

Current research proofs the potential of apparatuses containing minichannel flow structures to intensify gas-liquid-solid contacting processes. The excellent heat and mass transfer in these devices as well as a sharp RTD mainly result from the Taylor flow regime. A proper design of corresponding contactors requires precise information on the provided interfacial areas. However, the characterisation of gas-liquid Taylor flow with industrially relevant fluids at elevated pressure and created by capillary injection devices gained little attention so far.This work analyses adiabatic gas-liquid Taylor flow in a square minichannel of 1.0 mm hydraulic diameter using water, water-glycerol, or water-ethanol mixtures as liquid phase and hydrogen or nitrogen as gas phase to cover a broad range of material parameters. In the mixing zone located within the flow channel, gas was injected into the co-flowing liquid by so-called capillary injectors with variable inner diameter (0.184, 0.317, 0.490 mm).Two different bubble forming mechanisms were identified leading to a complex interaction between physical properties of the fluids, geometrical parameters and the observed gas bubble and liquid slug lengths. According to the Pi-theorem, these lengths were affected by 6 dimensionless groups, namely (u_G,s/ u_L,s), Re_L, We_L, (d_In,CI/ d_h), (d_Ou,CI / d_h), and Θ^*. Based on more than 370 experimental data, novel correlations to predict gas bubble and liquid slug lengths were developed.     

Oscillation and breakup of a bubble under forced vibration

Coupled shape oscillations and translational motion of an incompressible gas bubble in a vibrating liquid container is studied numerically. The bubble oscillation characteristics are mapped based on the bubble Bond number (Bo) and the ratio of the vibration amplitude of the container to the bubble diameter (A/D). At small Bo and A/D, the bubble oscillation is found to be linear with small amplitudes, and at large Bo and A/D, it is nonlinear and chaotic. This chaotic bubble oscillation is similar to those observed in two coupled nonlinear systems, here being the gas inside the bubble and its surrounding liquid. Further increases in the forcing, results in the bubble breakup due to large liquid inertia.     

Experimental study of the falling film of liquid around a Taylor bubble

The present work reports an experimental study of the falling liquid film around single Taylor bubbles rising in vertical tubes filled with stagnant liquids by using a pulse-echo ultrasonic technique. The experiments were carried out in acrylic tubes 2.0  m long, with inner diameters of 0.019, 0.024 and 0.034  m, with five water-glycerin mixtures, corresponding to inverse viscosity number ranging from 15 to 22422. The rising bubble and the falling liquid film were measured by using ultrasonic transducers located at the one side of the tube. The velocity and profile of the Taylor bubble, and the development length and equilibrium thickness of the falling liquid film around the bubble were obtained by the ultrasonic signals processing. Based on the experimental results of the present study, several correlations available to estimate the equilibrium thicknesses of liquid films falling around Taylor bubbles were evaluated and new correlations were proposed to estimate the dimensionless equilibrium film thickness and the film development length respectively.     

Measurement of liquid film thickness in a micro parallel channel with interferometer and laser focus displacement meter

In the present study, liquid film thicknesses in parallel channels with heights of H = 0.1, 0.3 and 0.5 mm are measured with two different optical methods, i.e., interferometer and laser focus displacement meter. Ethanol is used as a working fluid. Liquid film thicknesses obtained from two optical methods agree very well. At low capillary numbers, dimensionless liquid film thickness is in accordance with Taylor’s law. However, as capillary number increases, dimensionless liquid film thickness becomes larger than Taylor’s law for larger channel heights. It is attributed to the dominant inertial effect at high capillary numbers. Using channel height H for dimensionless liquid film thickness δ₀/H and hydraulic diameter D_h = 2H as the characteristic length for Reynolds and Weber numbers, liquid film thickness in a parallel channel can be predicted well by the circular tube correlation previously proposed by the authors. This is because curvature differences between bubble nose and flat film region are identical in circular tubes and parallel channels.     

Fluidization and bubbling behavior of potash particles in a deep fluidized bed

Most existing models for predicting bubble size and bubble frequency have been developed for freely bubbling fluidized beds. Accurate prediction of bubbling behavior in deep fluidized beds, however, has been a challenge due to the higher degree of bubble coalescence and break up, high probability of the slugging regime, partial fluidization, and chaotic behavior in the bubbling regime. In this work, the bubbling and fluidization behavior of potash particles was investigated in a deep fluidized bed employing a twin-plane electrical capacitance tomography (ECT) system. Solid volume fraction, average bubble velocity, average bubble diameter, and bubble frequency in both bubbling and slugging regimes were measured at two different bed height ratios (H/D = 3.5 and H/D = 3.78). This work is the first to illustrate a sequential view of bubbles at different superficial gas velocities in a fluidized bed. The results show that both the bubble diameter and rising velocity increased with increasing the superficial gas velocity for the two bed heights, with larger values observed in the deeper bed compared to the shallower one. Predicted values for bubble diameter, bubble rise velocity and bubble frequency from different models are compared with the experimental data obtained from the ECT system in this work. Good agreement has been achieved between the values predicted by the previous models and the experimental data for the bubble diameter and bubble rise velocity with an average absolute deviation of 16% and 15% for the bed height of 49 cm and 13% and 8% for the bed height of 53 cm, respectively.     

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.     

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.     

Full-scale two-phase flow measurements on Athena research vessel

Measurements of gas volume fraction, bubble velocity, chord length and bubble size distributions were performed on the research vessel Athena II operating in Saint Andrew Bay in the gulf coast near Panama City, FL. Double tipped sapphire optical local phase-detection probes were used to acquire indicator functions downstream of the breaking bow wave, behind the masker and at the stern. These indicator functions were also taken at different depths, operating speeds and headings respect to the waves. The data processing includes the computation of velocity of individual bubbles and chord lengths, resulting in chord length distributions. These chord length distributions are used to obtain bubble size distributions using a novel procedure described in detail herein. Uncertainty analysis is performed for gas volume fraction, average bubble velocity and chord length. The results indicate that air entrainment increases with ship speed and sailing against the waves at all positions. The bow wave exhibits unsteady breaking that creates bubble clouds, which were characterized and identified by signal processing. At the stern a very strong dependence of bubble size with depth was found, with evidence that small bubbles (smaller than 500 μm) are transported through the bottom of the hull and reach the transom. The roller present at the transom, the associated strong unsteadiness and bubble entrainment are well captured, as indicated by the stern results, showing the frothy nature of the upper layer.     

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.     

Counter-current gas–liquid flow in a vertical narrow channel—Liquid film characteristics and flooding phenomena

Results are reported of an experimental investigation of gas–liquid counter-current flow in a vertical rectangular channel with 10 mm gap, at rather short distances from liquid entry. Flooding experiments are carried out using air and various liquids (i.e., water, 1.5% and 2.5% aqueous butanol solutions) at liquid Reynolds numbers Re_L < 350. Visual observations and fast recordings suggest that the onset of flooding at low Re_L (<250) is associated with liquid entrainment from isolated waves, whereas “local bridging” is dominant at the higher Re_L examined in this study. Significant reduction of flooding velocities is observed with decreasing interfacial tension, as expected. Instantaneous film thickness measurements show that under conditions approaching flooding, a sharp increase of the mean film thickness, of mean wave amplitude and of the corresponding RMS values takes place. Film thickness power spectra provide evidence that by increasing gas flow the wave structure is significantly affected; e.g., the dominant wave frequency is drastically reduced. These data are complemented by similar statistical information from instantaneous wall shear stress measurements made with an electrochemical technique. Power spectra of film thickness and of shear stress display similarities indicative of the strong effect of waves on wall stress; additional evidence of the drastic changes in the liquid flow field near the wall due to the imposed gas flow, even at conditions below flooding, is provided by the RMS values of the wall stress. A simple model is presented for predicting the mean film thickness and mean wall shear stress under counter-current gas–liquid flow, below critical flooding velocities.     

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.     

Pressure wave breakdown of a gas film in a liquid-filled slit

In [1–4] the results of investigating the breakdown of gas bubbles by medium-intensity pressure waves are presented and various bubble breakdown mechanisms are proposed. It is shown that breakdown may occur as a result of the formation of a cumulative jet on the boundary of the bubble or as a result of instability due to the relative motion of the bubble in the wave. In [5] experimental data on the pressure wave breakdown of a gas film in a liquid on a solid wall are reported. It is shown that at wave amplitudes p/p₀1 a liquid jet is formed at the edge of the gas film. The jet, traveling along the wall, strips off the film and carries it into the surrounding liquid. Below we investigate the pressure wave behavior of a gas film in a liquid-filled slit.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 175–178, September–October, 1992.     

Experimental study on axial development of liquid film in vertical upward annular two-phase flow

Accurate measurements of the interfacial wave structure of upward annular two-phase flow in a vertical pipe were performed using a laser focus displacement meter (LFD). The purpose of this study was to clarify the effectiveness of the LFD for obtaining detailed information on the interfacial displacement of a liquid film in annular two-phase flow and to investigate the effect of axial distance from the air–water inlet on the phenomena. Adiabatic upward annular air–water flow experiments were conducted using a 3 m long, 11 mm ID pipe. Measurements of interfacial waves were conducted at 21 axial locations, spaced 110 mm apart in the pipe. The axial distances from the inlet (z) normalized by the pipe diameter (D) varied over z/D = 50–250. Data were collected for predetermined gas and liquid flow conditions and for Reynolds numbers ranging from Re_G = 31,800 to 98,300 for the gas phase and Re_L = 1050 to 9430 for the liquid phase. Using the LFD, we obtained such local properties as the minimum thickness, maximum thickness, and passing frequency of the waves. The maximum film thickness and passing frequency of disturbance waves decreased gradually, with some oscillations, as flow developed. The flow development, i.e., decreasing film thickness and passing frequency, persisted until the end of the pipe, which means that the flow might never reach the fully developed state. The minimum film thickness decreased with flow development and with increasing gas flow rate. These results are discussed, taking into account the buffer layer calculated from Karman’s three-layer model. A correlation is proposed between the minimum film thickness obtained in relation to the interfacial shear stress and the Reynolds number of the liquid.     

Analysis of the characteristic lengths in the bubble and slug flow regimes generated in a capillary T-junction

We present an analysis of the geometry of the continuous and disperse phases in the bubble and slug flow regimes in air–water mixtures generated in a capillary T-junction of 1  mm internal diameter. Bubble size dispersion is very low in the considered flow patterns. The concept of unit cell is used to identify two characteristic lengths of the two-phase flow, namely, the unit cell length and the bubble length. The relationship between these lengths and the gas and liquid superficial velocities, gas mean velocity, bubble generation frequency and volume average void fraction is analysed. We conclude that in the considered configuration the unit cell and bubble lengths can be predicted either by the ratio of the gas–liquid superficial velocities or the volume average void fraction.     

Co-current flow effects on a rising Taylor bubble

The effects of co-current flows on a rising Taylor bubble are systematically investigated by a front tracking method coupled with a finite difference scheme based on a projection approach. Both the upward (the co-current flows the same direction as the buoyancy force) and the downward (the co-current moves in the opposite direction of the buoyancy force) co-currents are examined. It is found that the upward co-current tends to elongate the bubble, while the downward co-current makes the bubble fatter and shorter. For large N_f (the inverse viscosity number), the upward co-current also elongates the skirted tail and makes the tail oscillate, while the downward co-current shortens the tail and even changes a dimpled bottom to a round shape. The upward co-current promotes the separation at the tail, while the downward co-current suppresses the separation. The terminal velocity of the Taylor bubble rising in a moving flow is a linear combination of the mean velocity (U_C) of the co-current and the terminal velocity (U₀) of the bubble rising in the stagnant liquid, and the constant is around 2 which agrees with the literature. The wake length is linearly proportional to the velocity ratio (U_C/U₀). The co-currents affect the distribution of the wall shear stresses near the bubble, but not the maximum.     

Effects of hydrophilic particles on bubbly flow in slurry bubble column

To investigate the effects of hydrophilic particles on slurry bubble flows in a bubble column, distributions of the local gas holdup and the bubble frequency are measured using an electric conductivity probe. Particles are made of silica and their diameter is 100 μm. The particle volumetric concentration C_S is varied from 0 to 0.40. The measured data imply that the presence of particles promotes bubble coalescence. The film drainage time for two coalescing bubbles in a quasi two-dimensional bubble flow in a small vessel is also measured to quantitatively evaluate the particle effect on coalescence. A particle-effect multiplier is introduced into a coalescence efficiency model by taking into account the data of film drainage time and is implemented into a multi-fluid model. The main conclusions obtained are as follows: (1) the local gas holdup and bubble frequency in slurry bubble flows decrease with increasing the particle concentration, (2) the hydrophilic particles enhance bubble coalescence and the enhancement saturates at C_S ≃ 0.45, (3) the particle effect on coalescence is well accounted for by introducing the particle-effect multiplier to the film drainage time, and (4) the multi-fluid model can give good predictions for the distribution of the local gas holdup in the slurry bubble column.     

Comment on “Correlation of entrainment for annular flow in horizontal pipes”, by Pan,L., Hanratty,T.J., Int. J. Multiphase flow, 28(3), (2002), pp. 385–408

The above referenced paper, published in International Journal of Multiphase Flow (Pan and Hanratty, 2002), proposed an entrainment fraction correlation for annular flow in horizontal pipes. The entrainment fraction in annular flow is defined as the ratio of the mass flow rate of the liquid droplets in the gas to the total mass flow of liquid, F_E = W_LE/W_L. The proposed correlation was verified with experimental data for liquids with viscosities close to that of water. The proposed entrainment fraction correlation includes another correlation for the critical film flow rate, W_F,cr to estimate a maximum entrainment fraction F_E,max. It is shown that the critical film flow rate correlation can result in negative maximum entrainment fraction values, for low liquid flow rates.     

Air concentration and bubble characteristics downstream of a chute aerator

Chute aerators separate the flow of water from the bottom of a chute, and air bubbles generated in the cavity zone must go through the impact zone as they travel downstream. In this study, the air concentration and air bubble characteristics along the chute were investigated systematically by a series of model tests that eliminated the effect of the upper aeration region. It was found that the large amount of air entrained in the cavity zone was only partially entrained into the final flow. Based on the lower air discharge properties, the chute downstream of the aerator was partitioned into four reasonable zones: the cavity zone (0 < x < L), the impact zone (L ≤ x ≤ L_m), the equilibrium zone (L_m ≤ x ≤ L_D), and the far zone (x > L_D). The details of the bubble chord length and bubble frequency distributions in each zone were measured. In the cavity zone, the bubble frequency distribution was related to the air concentration by a parabolic law. In the impact zone, the air concentration decreased sharply while the bubble frequency decreased to a lesser extent. Due to the turbulent fluctuation effect, the probability of smaller bubbles increased while the probability of larger bubbles decreased as they progressed down the chute. In the equilibrium zone, the bubble frequency decreased slightly. At the cross section, the range of probability of bubble chord lengths tended to increase from the bottom to the upper surface. The distributions of the mean chord lengths followed approximately a power low distribution. A formula was provided to predict the maximum air bubble frequency in the impact and equilibrium zones.     

Crown behavior and bubble entrainment during a drop impact on a liquid film

Physical and mathematical models are established to simulate a single liquid drop impinging onto a liquid film using the coupled level set and volume of fluid method. The crown liquid sheet after impact is obtained, which coincides well with the experimental results in literatures. Influence of Weber number, Reynolds number and the dimensionless film thickness on the crown diameter and height is discussed quantitatively. Results indicate that the crown diameter is independent of the two non-dimensional numbers, while it can be increased by reducing the dimensionless film thickness. The crown height increases with the increasing of Weber number, but Reynolds number has small effect on it. Mechanism of the jet formation process is revealed by analyzing pressure distribution and velocity field in the liquid. It is found that both pressure difference in the neck region and velocity discontinuity can greatly affect the jet formation. Besides, the bubble entrainment phenomenon during a liquid drop impact on a liquid film is successfully captured with this numerical method. It is found that the increase in both impact Weber number and the drop diameter contributes to the emerging of bubble rings.