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.     

Transition of plug to slug flow and associated fluid dynamics

Transition of plug to slug flow is associated with bubble detachment from elongated bubble tail or bubble entrainment inside the liquid slug. The mechanism responsible for this transition was earlier identified by Ruder and Hanratty (1990) and Fagundes Netto et al. (1999) based on the shape of the hydraulic jump observed at elongated bubble tail region. The transition mechanism reported by Ruder and Hanratty (1990) and Fagundes Netto et al. (1999) was only based on their flow visualization study. Plug to slug transition and associated dynamics of bubble detachment from the elongated bubble is analysed in the present paper using flow visualization and local velocity measurements. Experiments are reported for 13 different inlet flow conditions of air and water phases. Images of plug/slug flow structures are captured at a rate of 4000 FPS using FASTCAM Photron camera and the local values of axial liquid velocity are measured using LDV system synchronised with a 3D automated traverse system. LDV measurement of local liquid velocity in the liquid slug and liquid film establishes the reason for detachment of bubbles from the slug bubble tail.     

Elongated bubble shape in inclined air-water slug flow

The shape of elongated bubbles in upward inclined air-water slug flow was studied experimentally by quantitative measurements of the cross sectional distribution of the phases within the pipe, using a wire mesh sensor. Ensemble-averaged shapes of elongated bubbles were determined for a wide range of gas and liquid flow rates, as well as for different pipe inclination angles. The elongated bubble nose can be characterized by an annular domain where liquid is present above the gas. The effect of gas and liquid flow rates, as well as of the pipe inclination angle on the bubble shape (front and tail) is studied. A simplified theoretical model is proposed to determine the bubble front shape. The model predictions compare favorably with the experimental results.     

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.     

Transition mechanism from bubble flow to slug flow in a riser

An experiment was performed to examine the mechanism of flow pattern transition from bubble flow to slug flow in a riser. The flow was measured by a double resistivity probe system, and photographs of the flow were taken using strobe lights. The negative diffusion distance of bubbles was estimated using a voidage wave equation and compared with the interbubble distance. The flow pattern transition from bubble flow to slug flow occurred when the diffusion distance was larger than the interbubble distance. Conversely, when the diffusion distance was smaller than the interbubble distance, the bubble flow was sustained. Therefore, it is found that the negative diffusion caused by the instability of the voidage wave brings about the flow pattern transition.     

Experimental investigation of horizontal air–water bubbly-to-plug and bubbly-to-slug transition flows in a 3.81 cm ID pipe

The present study seeks to investigate horizontal bubbly-to-plug and bubbly-to-slug transition flows. The two-phase flow structures and transition mechanisms in these transition flows are studied based on experimental database established using the local four-sensor conductivity probe in a 3.81 cm inner diameter pipe. While slug flow needs to be distinguished from plug flow due to the presence of large number of small bubbles (and thus, large interfacial area concentration), both differences and similarities are observed in the evolution of interfacial structures in bubbly-to-plug and bubbly-to-slug transitions. The bubbly-to-plug transition is studied by decreasing the liquid flow rate at a fixed gas flow rate. It is found that as the liquid flow rate is lowered, bubbles pack near the top wall of the pipe due to the diminished role of turbulent mixing. As the flow rate is lowered further, bubbles begin to coalesce and form the large bubbles characteristic of plug flow. Bubble size increases while bubble velocity decreases as liquid flow rate decreases, and the profile of the bubble velocity changes its shape due to the changing interfacial structure. The bubbly-to-slug transition is investigated by increasing the gas flow rate at a fixed liquid flow rate. In this transition, gas phase becomes more uniformly distributed throughout the cross-section due to the formation of large bubbles and the increasing bubble-induced turbulence. The size of small bubbles decreases while bubble velocity increases as gas flow rate increases. The distributions of bubble size and bubble velocity become more symmetric in this transition. While differences are observed in these two transitions, similarities are also noticed. As bubbly-to-plug or bubbly-to-slug transition occurs, the formation of large elongated bubbles is observed not in the uppermost region of bubble layer, but in a lower region. At the beginning of transitions, relative differences in phase velocities near the top of the pipe cross-section to those near the pipe center become larger for both gas and liquid phases, because more densely packed bubbles introduce more resistance to both phases.     

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     

Elongated bubbles in microchannels. Part II: Experimental study and modeling of bubble collisions

The collision of elongated bubbles has been studied along adiabatic glass microchannels of 509 and 790 μm internal diameters for refrigerant R-134a. The slug flow regime obtained here comes from the nucleation process inside a micro-evaporator located upstream. Using an optical measurement technique based on two lasers and two photodiodes, it was possible to determine the vapor bubble length distributions at the exit of the micro-evaporator and 70 mm downstream and thus characterize both diabatic and adiabatic bubble collisions. The database includes 412 coupled sets of distributions involving thousands of bubbles. Half of the database has been obtained under diabatic conditions and the second half under adiabatic conditions.     

Planar dynamics of inclined curved flexible riser carrying slug liquid–gas flows

Flexible risers transporting hydrocarbon liquid–gas flows may be subject to internal dynamic fluctuations of multiphase densities, velocities and pressure changes. Previous studies have mostly focused on single-phase flows in oscillating pipes or multiphase flows in static pipes whereas understanding of multiphase flow effects on oscillating pipes with variable curvatures is still lacking. The present study aims to numerically investigate fundamental planar dynamics of a long flexible catenary riser carrying slug liquid–gas flows and to analyse the mechanical effects of slug flow characteristics including the slug unit length, translational velocity and fluctuation frequencies leading to resonances. A two-dimensional continuum model, describing the coupled horizontal and vertical motions of an inclined flexible/extensible curved riser subject to the space–time varying fluid weights, flow centrifugal momenta and Coriolis effects, is presented. Steady slug flows are considered and modelled by accounting for the mass–momentum balances of liquid–gas phases within an idealized slug unit cell comprising the slug liquid (containing small gas bubbles) and elongated gas bubble (interfacing with the liquid film) parts. A nonlinear hydrodynamic film profile is described, depending on the pipe diameter, inclination, liquid–gas phase properties, superficial velocities and empirical correlations. These enable the approximation of phase fractions, local velocities and pressure variations which are employed as the time-varying, distributed parameters leading to the slug flow-induced vibration (SIV) of catenary riser. Several key SIV features are numerically investigated, highlighting the slug flow-induced transient drifts due to the travelling masses, amplified mean displacements due to the combined slug weights and flow momenta, extensibility or tension changes due to a reconfiguration of pipe equilibrium, oscillation amplitudes and resonant frequencies. Single- and multi-modal patterns of riser dynamic profiles are determined, enabling the evaluation of associated bending/axial stresses. Parametric studies reveal the individual effect of the slug unit length and the translational velocity on SIV response regardless of the slug characteristic frequency being a function of these two parameters. This key observation is practically useful for the identification of critical maximum response.     

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.     

Large scale structure in gas-liquid mixture flows

Relatively slow variation in mixture void fraction in gas-liquid mixture flows are indicated by low pass filter averaging. The slow void fluctuations are found to have a regular characteristic frequency or scale in the churn flow regime or near the boundary with the dispersed bubble flow regime. These regular disturbances develop inherently in a vertical pipe flow in strength and in size and are not due to the method of flow mixing. There was no evidence of distinctive gas slugs in the flow, and the structures were identified as large clouds of bubbles which moved faster than the average velocity, growing in size and strength as they moved with the flow. The magnitude of the voidage fluctuations in the churn flow regime was on average 57% of the value for a slug flow. The large scale bubble clouds convect coherently over relatively long distances at up to 1.45 times the mean mixture flow velocity at a gas volume flow fraction of 0.4. In the bubble flow regime, the slow voidage variations were more random in scale and were only approx. 10% of the slug flow (maximum possible) value. However, even in the bubble flow regime, the disturbances convected coherently over relatively long distances at a velocity of approx. 1.1 times the mean mixture velocity.     

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%.     

Slug and bubble flows in a flat sheet ultrafiltration module: Experiments and numerical simulation

In this paper, the effect of gas bubbling including slug and bubble flows on enhancing shear force in an ultrafiltration (UF) process in a flat sheet module is investigated experimentally by image processing and numerically using the OpenFOAM software. In order to study characteristics of bubbles in the slug and bubble flows, the flat sheet module is analyzed by a video system facilitated with a high speed camera. The experimental results show that the average diameter of the slug flow is much larger than that of the bubble flow. The permeate flux for the slug and bubble flows is increased by 78% and 30%, respectively, compared to the case with no gas bubbling. The numerical results are shown to be in good agreement with those of the measurements both qualitatively and quantitatively. The results of simulations also demonstrate that although both flow patterns increase the shear stress by increasing the velocity gradient and/or vorticity, the shear stress induced by the slug flow is considerably larger. Therefore, the slug flow with a higher induced shear stress is more effective on the enhancement of the permeate flux in a UF process.     

Flow regime transition criteria for two-phase flow in a vertical annulus

In this work, a new flow regime transition model is proposed for two-phase flows in a vertical annulus. Following previous works, the flow regimes considered are bubbly (B), slug (S) or cap-slug (CS), churn (C) and annular (A). The B to CS transition is modeled using the maximum bubble package criteria of small bubbles. The S to C transition takes place for small annulus perimeter flow channels and it is assumed to occur when the mean void fraction over the entire region exceeds that over the slug–bubble section. If the annulus perimeter is larger that the distorted bubble limit the cap-slug flow regime will be considered since in these conditions it is not possible to distinguish between cap and partial-slug bubbles. The CS to C transition is modeled using the maximum bubble package criteria. However, this transition considers the coalescence of cap and spherical bubbles in order to take into account the flow channel geometry. Finally, the C to A transition is modeled assuming two different mechanisms, (a) flow reversal in the liquid film section along large bubbles; (b) destruction on liquid slugs or large waves by entrainment or deformation. In the S to C and C to A flow regime transitions the annulus flow channel is considered as a rectangular flow channel with no side walls. In all the modeled transitions the drift-flux model is used to obtain the final correlations. The final equations for every flow regime transition are easy to be implemented in computational codes and not experimental input is needed. The prediction accuracy of the newly developed model has been checked against air–water as well as boiling flow regime maps. In all the cases, the new developed model shows better predicting capabilities than the existing correlations most used in literature.     

Measurement of multiple gas-bubble velocities in gas–liquid flows using hot-film anemometry

A dual-probe hot-film anemometry technique has been developed to measure multiple gas-bubble velocities corresponding to different gas-bubble size groups in air–water flows. A data reduction scheme using wavelet analysis combined with a phase-detection technique is used to discriminate the hot-film anemometer output signals into signals corresponding to different bubble size groups. The phase and bubble size discrimination is based on the magnitude and time derivative of the signal, and the streamwise length of the gas bubbles. A cross-correlation between the discriminated signals from the two probes yields an average time difference of arrival of the gas bubbles at the two sensor locations. The velocities are estimated from the distance between the sensors and the time difference of arrival. The mean bubble size is estimated from the chord length distribution. Measurements performed in vertical-up air–water slug flow show the technique to be a viable method for obtaining bubble velocity and size information. The velocity measurements from the hot-film anemometry are corroborated using a high-speed quantitative flow visualization system. Received: 22 December 1999/Accepted: 8 May 2001     

Characterization of the interaction of two oscillating bubbles near a thin elastic membrane

Oscillating bubbles appear in the bodily fluid during many medical treatments, for example in Extracorporeal Shockwave Lithotripsy. We report a systematic study on the complex interaction between two such bubbles and an elastic membrane, which could be a biological membrane in the human body. We have grouped our analysis into similarly sized bubbles, and differently sized bubbles. All bubbles are created at the same time. For the similarly sized bubbles, it can be broadly characterized as the splitting up of two bubbles in vertical direction perpendicular to (vertical split) and at an angle to (oblique split) the membrane surface, jetting towards each other and bubble coalescence. For the two differently sized bubbles, there is the jetting towards or away from the large bubble for the small bubble and the ??catapult?? effect observed. The two bubbles dynamics depend on the relative bubble sizes, the distance from the membrane, and the inter-bubble distance.     

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.     

Review on vertical gas–liquid slug flow

Vertical slug flow is characterized by the rise of long bullet-shaped gas bubbles with a diameter almost matching that of the tube - Taylor bubbles. Liquid slugs separate consecutive Taylor bubbles, which may interact and coalesce if the distance between them is small. Slug flow has numerous industrial applications, being also observed on physiological and geological systems. In spite of the contribution of the development of non-intrusive experimental techniques to a deeper understanding of slug flow features, the complexity of this flow pattern requires the combined use of numerical approaches to overcome some of the optical problems reported in experimental methods, and other limitations related to the flow aperiodic behavior.The need to systematize the large amount of data published on the subject and to understand the limitations of the techniques employed constitutes the motivation for this review. In the present work, literature on vertical gas–liquid slug flow, with Newtonian fluids, from 1943 to 2015, covering theoretical, experimental and numerical approaches, is reviewed. Focus is given to single and trains of Taylor bubbles rising through stagnant and co-current liquids.It should be emphasized, however, that further research still needs to be conducted in some particular areas, namely the hydrodynamics of the liquid film surrounding the Taylor bubbles, the interaction between consecutive bubbles, and a more detailed approach to the flow of Taylor bubbles through co-current liquids.     

Mass transfer during gas absorption in a vertical gas-liquid slug flow with small bubbles in liquid plugs

A model is developed for the analysis of mass transfer during isothermal absorption in a vertical gas-liquid slug flow at large Reynolds numbers with liquid plugs containing small bubbles. Simple formulas for mass flux from the N-th unit cell of gas-liquid slug flow and for total mass flux from N unit cells are derived. In the limiting case the derived formulas for mass transfer during gas absorption in a slug flow with liquid plugs containing small bubbles recover the derived expressions for mass transfer in slug flow without small bubbles in the liquid plugs. Using the developed model recommendations concerning the design of the absorber operating in a slug flow regime are suggested. Received on 28 July 1997     

Holdup of the liquid slug in two phase intermittent flow

A physical model for the prediction of gas holdup in liquid slugs in horizontal and vertical two phase pipe slug flow is presented. This model can also be used to yield the transition between elonganted bubbles and slug flow within the intermittent flow pattern. In addition a previously published model for predicting the stable slug length in vertical upward slug flow (Taitel et al. 1980) is extended here for the case of horizontal slug flow.