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.     

Rising behavior of single bubble in infinite stagnant non-Newtonian liquids

This work is an experimental study of the rising behavior of single air bubbles in infinite stagnant non-Newtonian liquids. Aqueous solutions of carboxymethyl cellulose (CMC) are selected to study the effect of rheological properties. The high speed photography is employed to record the bubble motion in CMC solutions. The bubble size, rising trajectory, bubble shape and velocities are determined by digital image processing technique. As expected, the rheological properties have great influence on the rising behavior of single bubble. In the less concentrated CMC solutions, the bubble rising process can be divided into three stages according to spatial evolution of bubble shape. The deformation changes the trajectories of rising bubbles and bubble hydrodynamics. As the solution concentration increases, the transitional stage gradually disappears. In the most concentrated CMC solution, the first continuous shape flattening stage is directly followed by a rising process with bubble shape basically constant, the rectilinear path and constant rising velocity. Dimensional analysis is performed to formulate a general dimensionless correlation for the deformation and motion of bubbles in infinite liquids by considering the rheological properties.     

The effect of viscoelasticity on a rising gas bubble

This paper investigates the role of viscoelasticity on the dynamics of rising gas bubbles. The dynamics of bubbles rising in a viscoelastic liquid are characterised by three phenomena: the trailing edge cusp, negative wake, and the rise velocity jump discontinuity. There is much debate in the literature over the cause of the jump discontinuity, which is observed once the bubble exceeds a certain critical volume. In this paper, the employment of some choice modelling assumptions allows insights into the mechanisms of the jump discontinuity which cannot be ascertained experimentally. The ambient fluid is assumed incompressible and the flow irrotational, with viscoelastic effects included through the stress balance on the bubble surface. The governing equations are solved using the boundary element method. Some Newtonian predictions are discussed before investigating the role of viscoelasticity. The model predicts the trademark cusp at the trailing end of a rising bubble to a high resolution. However, the irrotational assumption precludes the prediction of the negative wake. The corresponding absence of the jump discontinuity supports the hypothesis that the negative wake is primarily responsible for the jump discontinuity, as mooted in previous studies.     

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.     

Drag reduction in the turbulent pipe flow of polymers

The paper concerns an experimental study of the fully developed turbulent pipe flow of several different aqueous polymer solutions: 0.25%, 0.3% and 0.4% carboxymethylcellulose (CMC), 0.2% xanthan gum (XG), a 0.09%/0.09% CMC/XG blend, 0.125% and 0.2% polyacrylamide (PAA). The flow data include friction factor vs. Reynolds number, mean velocity and near-wall shear rate distributions, and axial velocity fluctuation intensity u′ at a fixed radial location as a laminar/turbulent transition indicator. For each fluid we also include measurements of shear viscosity, first normal-stress difference and extensional viscosity. At high shear rates we find that the degree of viscoelasticity increases with concentration (0.3% CMC is an exception) for a given polymer, and in the sequence XG, CMC/XG, CMC, PAA, whilst at low shear rates the ranking changes to CMC, CMC/XG, XG, PAA. The extensional viscosity ranking is XG/CMC, XG, CMC, PAA at high strain rates and the same as that for the viscoelasticity at low shear rates. We find that the observed drag-reduction behaviour is consistent for most part with the viscoelastic and extensional-viscosity behaviour at the low shear and strain rates typical of those occurring in the outer zone of the buffer region.Although laminar/turbulent transition is practically indiscernible from the friction factor vs. Reynolds number plots, particularly for PAA and XG, the u′ level provides a very clear indicator and it is found that the transition delay follows much the same trend with elasticity/extensional viscosity as the drag reduction.     

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.     

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.     

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     

The minimum in-line coalescence height of bubbles in non-Newtonian fluid

The minimum in-line coalescence height of bubbles generated from a submerged nozzle was investigated experimentally in shear thinning non-Newtonian fluid at lower Reynolds number (2∼60). Carboxymethyl cellulose sodium (CMC) aqueous solution and carbon dioxide were used as the liquid phase and the gas phase, respectively. The process of the formation, movement and in-line coalescence of bubbles was visualized and recorded by a high-speed digital camera. The influences of bubble size, bubble generation frequency and liquid property on the minimum in-line coalescence height of bubbles were investigated by changing nozzle diameter, gas flow rate and the mass concentration of CMC aqueous solutions. For a given liquid, the generating frequency and size of bubbles increased but the minimum coalescence height of in-line bubbles decreased when the nozzle diameter and gas flow rate were increased. When the nozzle diameter and gas flow rate were fixed, the shear-thinning effect of CMC aqueous solution became stronger with increasing CMC mass concentration, which led to the increase in both the terminal rise velocity and average acceleration of the trailing bubble, consequently, the minimum in-line coalescence height of bubbles decreased. An empirical correlation for estimating the minimum in-line bubble coalescence height was proposed, the calculating values accords well with experimental data with a mean relative deviation only 7.6%.     

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 study of single bubble motion in a liquid metal column exposed to a DC magnetic field

The motion of single Argon bubbles rising in the eutectic alloy GaInSn under the influence of a DC longitudinal magnetic field (parallel to the direction of bubble motion) was examined. The magnetic field strength was varied up to 0.3 T corresponding to a magnetic interaction parameter N (which measures the ratio of electromagnetic forces to inertial forces) slightly greater than 1. The liquid metal was at rest in a cylindrical container. Bubble and liquid velocities were measured using ultrasound Doppler velocimetry (UDV). The measured bubble terminal velocity showed oscillations indicating a zigzag movement of ellipsoidal bubbles. For small bubbles (d_e ⩽ 4.6 mm) an increase of the drag coefficient with increasing magnetic interaction parameter N was observed, whereas for larger bubbles (d_e ⩾ 5.4 mm) the application of the magnetic field reduces the drag coefficient. The measurements revealed a distinct electromagnetic damping of the bubble induced liquid velocity leading to more rectilinear bubble trajectories when the magnetic field is applied. Moreover, significant modifications of the bubble wake structure were observed. Raising of the magnetic field strength caused an enlargement of the eddies in the wake. The Strouhal number decreases with increasing magnetic interaction parameter N.     

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.     

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.     

Pressure-oscillation defoaming for viscoelastic fluid

The enhancement of bubble rising velocity was experimentally investigated by mechanically applying an oscillating pressure to a single small air bubble (e.g., 1 mm³) in a viscoelastic fluid. For shear-thinning fluids, the cyclic change in bubble diameter induced by the oscillating pressure generates a continuous strong local flow near the bubble surface. Consequently, the apparent liquid viscosity is reduced and the bubble rising velocity increases by 400 times or more compared to the case without oscillating pressure. However, for a Newtonian fluid, almost no effect was observed with oscillating pressure. Time-series data of the longitudinal and horizontal bubble diameters were obtained experimentally using a stroboscope and a video system, and these data were used to estimate the local shear rate and the local shear viscosity. The increase in bubble rising velocity estimated from the shear viscosity behavior agreed well with the experimental data. Additionally, a periodic change in the bubble shape from a sphere at the maximum bubble size to a cusped shape at the minimum bubble size was observed under strong oscillatory pressure.     

On the interaction between two consecutive elongated bubbles in a vertical pipe

The motion of elongated air bubbles in a vertical pipe filled with water is studied quantitatively using video imaging of the flow and subsequent digital image processing of the recorded sequence of images. Experiments are carried out to determine the influence of the separation distance between two consecutive bubbles (liquid slug length) upon the behavior of the trailing bubble in vertical slug flow. The details of the trailing bubble acceleration and merging process are observed and the instantaneous parameters of the trailing bubble, such as its shape, velocity, acceleration, etc., are measured as a function of the separation distance. The leading bubble is found to be unaffected by the trailing elongated bubble.     

Air transport in chute flows

The air bubble rise velocity in still water depends mainly on the bubble size and is basically influenced by buoyancy, viscosity and surface tension. In high-speed flows the number of forces acting on air bubbles increases with turbulence, non-hydrostatic pressure gradient, shear forces, bubble clouds and free-surface entrainment. Air bubbles in these flows are used for cavitation protection of hydraulic structures such as chutes, spillways and bottom outlets. Here, air is normally added by means of aerators upstream of regions where the cavitation number falls below a critical value mainly to reduce the sonic velocity of the fluid and cushion the cavitation bubble collapse process. The distance between successive aerators depends basically on the bubble rise velocity. Until today, the bubble rise velocity in high-speed flows was not thoroughly investigated because of limited laboratory instrumentation. The present project focused on the streamwise development of air concentrations in high-speed flows along a 14 m long model chute. The bubble rise velocity was indirectly derived from the air detrainment gradient of the air concentration contour lines downstream of an aeration device. It accounts for the main hydraulic parameters chute slope, Froude number and air concentration. It is demonstrated that the bubble rise velocity in high-speed flow and stagnant water differ significantly due to fracturing processes, turbulence, and the ambient air concentration.     

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.     

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.     

Terminal velocity of a Taylor drop in a vertical pipe

A scaling analysis based on the field equations for two phases and the jump conditions at the interface is carried out to deduce a balance of forces acting on a Taylor drop rising through stagnant liquid in a vertical pipe. The force balance is utilized to deduce a functional form of an empirical correlation of terminal velocity of the Taylor drop. Undetermined coefficients in the correlation are evaluated by making use of available correlations for two limiting cases, i.e. extremely high and low Reynolds number Taylor bubbles in large pipes. Terminal velocity data obtained by interface tracking simulations are also used to determine the coefficients. The proposed correlation expresses the Froude number Fr as a function of the drop Reynolds number Re_D, the Eötvös number Eo_D and the viscosity ratio μ^*. Comparisons between the correlation, simulations and experimental data confirm that the proposed correlation is applicable to Taylor drops under various conditions, i.e., 0.002 < Re_D < 4960, 4.8 < Eo_D < 228, 0 ? μ^* ? 70, 1 < N < 14700, −12 < log M < 4, and d/D < 1.6, where N is the inverse viscosity number, M the Morton number, d the sphere-volume equivalent drop diameter and D the pipe diameter.     

Interaction between two consecutive axisymmetric Taylor drops flowing in a heavier liquid in a vertical tube

A study regarding the interaction between two consecutive Taylor drops flowing in a heavier liquid in a vertical tube is reported. Under certain conditions, due to the wake of the leading drop, the trailing drop accelerates, leading to coalescence of the two drops. This study was developed using a numerical model based in the Volume of Fluid method in an axisymmetric geometry. The simulations reported in the present work had to fulfill two conditions: axisymmetry (due to the numerical model) and a high enough drop Reynolds number (which is related to the disturbances in the wake of an isolated drop, and thus to the tendency to drop interaction). Relevant dimensionless numbers are used to assess the effect of the acting forces. Detailed flow patterns and drop shapes are provided. Furthermore, the approaching velocity acquired by the trailing drop is analyzed and velocity profiles between the leading and the trailing drop are also reported. In general, the trailing drop shows an accelerating region, followed by a deceleration near the leading drop. The increase of Eotvos number promotes higher accelerations, while the increase in Morton number and viscosity ratio has the opposite effect. By comparison to literature gas-liquid studies, it was also found that interfacial forces promote the shape stability of the drops.