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.     

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.     

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.     

Convective and diffusive surfactant transfer in multiphase liquid systems

Laser interferometry was used to investigate diffusive and convective mass transfer in a multicomponent fluid mixture with a liquid–liquid or liquid–gas interface. For this purpose, an immobile gas bubble or insoluble fluid droplet, having the shape of a short cylinder with a free lateral surface, was inserted into a thin liquid layer. In the case of non-uniform distribution of the dissolved surfactant component, the Marangoni convection near the drop/bubble was initiated by the surface tension inhomogeneities, depending on the surfactant concentration. The applied experimental techniques allowed us to study the structure and evolution of the convective flows and concentration fields in a liquid layer, which due to its small thickness were nearly two-dimensional. Making use of both the vertical and horizontal orientation of the liquid layer, we investigated the mass transfer process at different levels of the interaction between gravity and capillary forces. During the experiments, we detected new solutocapillary phenomena, which were found to be caused by oscillatory regimes of solutal convection occurring around air bubbles and chlorobenzene drops in heterogeneous aqueous solutions of alcohol with a vertical surfactant concentration gradient. The role of the oscillatory instability in the processes of drop saturation by the surfactant from its water solution and an inverse process of surfactant extraction from the drop into the surrounding homogeneous fluid (water) was determined. A reasonable explanation for the driving mechanisms of the discovered effects has been proposed.     

A novel numerical scheme for the investigation of surface tension effects on growth and collapse stages of cavitation bubbles

In the present study the effects of surface tension on the growth and collapse stages of cavitation bubbles are studied individually for both spherical and nonspherical bubbles. The Gilmore equation is used to simulate the spherical bubble dynamics by considering mass diffusion and heat transfer. For the collapse stage near a rigid boundary, the Navier–Stokes and energy equations are used to simulate the flow domain, and the VOF method is adopted to track the interface between the gas and the liquid phases. Simulations are divided into two cases. In the first case, the collapse stage alone is considered in both spherical and nonspherical situations with different conditions of bubble radius and surface tension. According to the results, surface tension has no significant effects on the flow pattern and collapse rate. In the second case, both the growth and collapse stages of bubbles with different initial radii and surface tensions are considered. In this case surface tension affects the growth stage considerably and, as a result, the jet velocity and collapse time decrease with increasing surface tension coefficient. This effect is more significant for bubbles with smaller radii.     

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.     

Effect of orifice shape on bubble formation mechanism

The effect of orifice shape on the mechanism of bubble formation in gas–liquid two-phase flow is investigated experimentally with three different orifice geometries regarding a circle, a square, and a triangle with same cross-sectional areas. The liquid and gas phases are purified water at 20 °C and air at room temperature, respectively. Gas is injected at the rate of 50–1200 mlph into a stagnant pool of liquid in distances of 5, 10, and 15 cm below the liquid surface. The position, velocity, and acceleration of bubbles are measured at bubbles’ centers of mass (CM) and the effects of these parameters on the bubble volume are investigated. Moreover, the forces acting on a bubble are balanced and the effects of geometry and gas flow rate on each force are presented. In addition, the changes of the acting forces versus time are plotted and discussed for a specific condition. Results show the bubbles formed with the square and circular orifice cross-sectional areas have the most and least volumes at detachment, respectively.     

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.     

Mass transfer from a pulsating drop

The primary difficulty in solving the problem of mass transport through an isolated drop (or bubble) moving in a fluid medium at high Reynolds numbers lies in the extreme complexity of the hydrodynamic pattern of the phenomenon. For sufficiently high velocities a separation of the external flow will occur in the rear portion of the drops and bubbles, which leads to the appearance of a turbulent wake and a sharp increase of the hydrodynamic resistance. Beginning with those dimensions for which the resistance force acting per unit surface of the drop or bubble from the external medium becomes greater than the capillary pressure, the surface of the drops and bubbles begins to deform and pulsate. The local variations of the surface tension, resulting either from the process of convective diffusion or from adsorption of surface-active substances, have a large effect on the hydrodynamics of drops and bubbles (particularly on the deformation of their surface) [1, 2], The presence of vortical, and possibly even turbulent, motion within the drops and bubbles may, under certain conditions [1], lead to their fractionation.Naturally, at the present time such complex hydrodynamics cannot be described by exact quantitative relations. Several authors have attempted to solve this problem approximately within the framework of certain assumptions. In particular [3–6], a theory was developed for the boundary layer on the surface of spherical and ellipsoidal gaseous bubbles moving in a liquid, studies were made [7, 8] of the hydrodynamics of drops located in a gas flow and the conditions were found for which fractionation of such drops takes place. Of considerable practical interest is the development of the theory of mass transfer in pulsating drops and bubbles and finding in explicit form the dependence of the mass transfer coefficients on the hydrodynamic characteristics of these systems. Until this relationship is established, every theory which ignores the effect of hydrodynamics on the mass transfer rate from an individual drop or bubble cannot be considered in any way well-founded. This relates particularly to the theories [9, 10] which consider mass transfer in systems with concentrated streams of drops and bubbles. The present paper is devoted to the study of mass transport through the surface of an isolated drop in an irrotational gas or liquid stream for large Peclet numbers P.In conclusion the authors wish to thank V. G. Levich for his helpful discussions.     

Explosive boiling of water in parallel micro-channels

The objective of this study is to visualize the flow pattern and to measure heat transfer coefficient during explosive boiling of water in parallel triangular micro-channels. Tests were performed in the range of inlet Reynolds number 25–60, mass flux 95–340 kg/m²s, and heat flux 80–330 kW/m².The flow visualization showed that the behavior of long vapor bubbles, occurring in a micro-channel at low Reynolds numbers, was not similar to annular flow with interposed intermitted slugs of liquid between two long vapor trains. This process may be regarded as explosive boiling with periodic wetting and dryout.In the presence of two-phase liquid–vapor flow in the micro-channel, there are pressure drop oscillations, which increase with increasing vapor quality.This study shows strong dependence of the heat transfer coefficient on the vapor quality. The time when liquid wets the heated surface decreases with increasing heat flux. Dryout occurs immediately after venting of the elongated bubble.     

Experimental study on near wall transport characteristics of slug flow in a vertical pipe

In this work, the wall shear stress and the mass transfer coefficient of the gas–liquid two-phase upward slug flow in a vertical pipe are investigated experimentally, using limiting diffusion current probes and digital high-speed video system. In experiments, the instantaneous and averaged characteristics of wall shear stress and mass transfer coefficient are concerned. The experimental results are compared with the numerical results in previous paper of the authors. Both experiment and numerical simulation show that the superficial gas and liquid velocities have an obvious influence on the instantaneous characteristics of the two profiles. The mass transfer coefficient has characteristics similar to the wall shear stress. The instantaneous wall shear stress and mass transfer coefficient profiles have the periodicity of slug flow. The averaged wall shear stress and mass transfer coefficient increase with increased superficial gas velocity. However, there is inconsistency in the variation trends of the averaged wall shear stress and mass transfer coefficient with superficial liquid velocity between experimental result and numerical simulation result, which can be attributed to the difference in flow condition. Moreover, the Taylor bubble length is also another impacting factor. The experimental and numerical results all shows that the product scale can not be damaged directly by the flow movement of slug flow. In fact, the alternative forces and fluctuations with high frequency acting on the pipe wall due to slug flow is the main cause for the slug flow enhanced CO₂ corrosion process.     

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.     

The interaction of background ocean air bubbles with a surface ship

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.     

Model of gas absorption in gas-liquid plug flow with first-order and zero-order chemical reaction

A model of mass transfer during gas absorption in gas-liquid plug flow accompanied by irreversible chemical reaction of the first order and zero order is suggested. The expressions for coefficients of mass transfer during chemical absorption from a single Taylor bubble are derived in the approximation of the thin concentration boundary layer in a liquid phase. Under the assumptions of a perfect liquid mixing in liquid plugs recurrent relations for the dissolved gas concentrations in the n-th liquid plug and mass fluxes from the n-th Taylor bubble are derived. The total mass fluxes in gas-liquid plug flow during chemical absorption are determined. In the limiting case of absorption without chemical reaction the derived formulas recover the expressions for mass transfer during physical absorption in gas-liquid plug flow. Theoretical results are compared with available experimental data.     

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.     

Effects of bubble size on heat transfer enhancement by sub-millimeter bubbles for laminar natural convection along a vertical plate

Injection of sub-millimeter bubbles is considered a promising technique for enhancing natural convection heat transfer for liquids. So far, we have experimentally investigated heat transfer characteristics of laminar natural convection flows with sub-millimeter bubbles. However, the effects of the bubble size on the heat transfer have not yet been understood. The purpose of this study is to clarify the effects of the bubble size on the heat transfer enhancement for the laminar natural convection of water along a vertical heated plate with uniform heat flux. Temperature and velocity measurements, in which thermocouples and a particle tracking velocimetry technique are, respectively used, are conducted to investigate heat transfer and flow characteristics for different bubble sizes. Moreover, two-dimensional numerical simulations are performed to comprehensively understand the effects of bubble injection on the flow near the heated plate. The result shows that the ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection ranges from 1.3 to 2.2. The result also shows that for a constant bubble flow rate, the heat transfer coefficient ratio increases with a decrease in the mean bubble diameter. It is expected from our estimation based on both experimental data and simulation results that this increase results from an increase in the advection effect due to bubbles.     

DISCRETE MODELLING OF TWO-DIMENSIONAL LIQUID FOAMS

Liquid foam is a dense random packing of gas or liquid bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to the investigation of the spatial structure and physical properties of foams, and the situation becomes even more complicated as the fluid flows. To solve these problems, a discrete model of two-dimensional liquid foams on the bubble scale is proposed in this work. The bubble surface is represented with finite number of nodes, and the liquid within Plateau borders is discretized into lattice particles. The gas in bubbles is treated as ideal gas at constant temperatures. This model is tested by choosing an arbitrary shape bubble as the initial condition. This then automatically evolves into a circular shape, which indicates that the surface energy minimum routine is obeyed without calling external controlling conditions. Without inserting liquid particle among the bubble channels, periodic ordered and disordered dry foams are both simulated, and the fine foam structures are developed. Wet foams are also simulated by inserting fluid among bubble channels. The calculated coordination number, as a function of liquid fractions, agrees well with the standard values.     

Bubble growth in saturated pool boiling in water and surfactant solution

The presence of surfactant additives in water was found to enhance the boiling heat transfer significantly. The objective of the present investigation is to compare the bubble growth in water to that of a surfactant solution with negligible environmental impact. The study was conducted at two values of heat fluxes to clarify the effect of the heat flux on the dynamics of bubble nucleation. The bubble growth under condition of pool boiling in water and non-ionic surfactant solution was studied using high speed video technique. The bubble generation was studied on a horizontal flat surface; and the natural roughness of the surface was used to produce the bubbles.     

Study on heat transfer performance of spray cooling: model and analysis

In consideration of droplet–film impaction, film formation, film motion, bubble boiling (both wall nucleation bubbles and secondary nucleation bubbles), droplet–bubble interaction, bulk air convection and radiation, a model to predict the heat and mass transfer in spray cooling was presented in this paper. The droplet–film impaction was modeled based on an empirical correlation related with droplet Weber number. The film formation, film motion, bubble growth, and bubble motion were modeled based on dynamics fundamentals. The model was validated by the experimental results provided in this paper, and a favorable comparison was demonstrated with a deviation below 10%. The film thickness, film velocity, and non-uniform surface temperature distribution were obtained numerically, and then analyzed. A parameters sensitivity analysis was made to obtain the influence of spray angle, surface heat flux density, and spray flow rate on the surface temperature distribution, respectively. It can be concluded that the heat transfer induced by droplet–film impaction and film-surface convection is dominant in spray cooling under conditions that the heated surface is not superheated. However, the effect of boiling bubbles increases rapidly while the heated surface becomes superheated.     

Dynamics of bubble rising in the presence of surfactants

The results of experimental studies and theoretical analysis of the dynamics of a spherical bubble rising in a liquid with surfactants are presented for a wide range of Reynolds numbers. A refined empirical dependence for the bubble drag coefficient in the steady-state regime at Re < 1 is obtained. The influence of surfactants on the bubble shape and rising velocity in the transient regime is analyzed.