On the liquid turbulence energy spectra in two-phase bubbly flow in a large diameter vertical pipe

The liquid turbulence structure of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. A dual optical probe was used to measure the bubble characteristics, while the liquid turbulence was measured using hot-film anemometry. Experiments were performed at two liquid superficial velocities of 0.2 and 0.68 m/s for gas superficial velocities in the range of 0–0.18 m/s, corresponding to an area averaged void fraction up to 13.6%. In general, there is an increase in the liquid turbulence energy when the bubbles are introduced into the liquid flow. The increase in the energy mainly occurs over a range of length scales that are on the order of the bubble diameter. A suppression of the turbulence was observed close to the wall at very low void fraction flows. Initially, the suppression occurs in the low wave number range and then extends to higher wave numbers as the suppression is increased.     

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.     

On the use of area-averaged void fraction and local bubble chord length entropies as two-phase flow regime indicators

In this work, the use of the area-averaged void fraction and bubble chord length entropies is introduced as flow regime indicators in two-phase flow systems. The entropy provides quantitative information about the disorder in the area-averaged void fraction or bubble chord length distributions. The CPDF (cumulative probability distribution function) of void fractions and bubble chord lengths obtained by means of impedance meters and conductivity probes are used to calculate both entropies. Entropy values for 242 flow conditions in upward two-phase flows in 25.4 and 50.8-mm pipes have been calculated. The measured conditions cover ranges from 0.13 to 5 m/s in the superficial liquid velocity j _f and ranges from 0.01 to 25 m/s in the superficial gas velocity j _g. The physical meaning of both entropies has been interpreted using the visual flow regime map information. The area-averaged void fraction and bubble chord length entropies capability as flow regime indicators have been checked with other statistical parameters and also with different input signals durations. The area-averaged void fraction and the bubble chord length entropies provide better or at least similar results than those obtained with other indicators that include more than one parameter. The entropy is capable to reduce the relevant information of the flow regimes in only one significant and useful parameter. In addition, the entropy computation time is shorter than the majority of the other indicators. The use of one parameter as input also represents faster predictions.     

Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe

The bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. The bubble characteristics were measured using a dual optical probe, while the liquid-phase turbulence was measured using hot-film anemometry. Measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. At low void fraction flow, the radial void fraction distribution showed a wall peak which changed to a core peak profile as the void fraction was increased. The liquid average velocity and the turbulence intensities were less uniform in the core region of the pipe as the void fraction profile changed from a wall to a core peak. In general, there is an increase in the turbulence intensities when the bubbles are introduced into the flow. However, a turbulence suppression was observed close to the wall at high liquid superficial velocities for low void fractions up to about 1.6%. The net radial interfacial force on the bubbles was estimated from the momentum equations using the measured profiles. The radial migration of the bubbles in the core region of the pipe, which determines the shape of the void profile, was related to the balance between the turbulent dispersion and the lift forces. The ratio between these forces was characterized by a dimensionless group that includes the area averaged Eötvös number, slip ratio, and the ratio between the apparent added kinetic energy to the actual kinetic energy of the liquid. A non-dimensional map based on this dimensionless group and the force ratio is proposed to distinguish the conditions under which a wall or core peak void profile occurs in bubbly flows.     

Bubble dynamics and interactions with a pair of micro pillars in tandem

This study investigates flow patterns and bubble dynamics of two-phase flow around two 100 μm diameter circular pillars in tandem, which were entrenched inside a horizontal micro channel. Bubble velocity, trajectory, size, and void fraction were measured using a high speed camera and analyzed using a particle tracking velocimetry method. A range of gas and liquid superficial velocities were tested, resulting in different bubbly flow patterns, which were consistent with previous studies. These flow patterns were altered as they interacted with the pillars. Depending on the relative transverse location of bubbles to the pillars, and through bubble–bubble interaction, the flow sometimes returned to its original state. It was also determined that the pillars altered both the bubble trajectory and void fraction, especially in the pillars region.     

Void fraction,bubble velocity and bubble size in two-phase flow

Experiments were performed in atmosphereic vertical air-water flows, for void fractions between 0.25 and 0.75 (cross-sectional averages) and superficial liquid velocities of 1.3, 1.7 and 2.1 m/s. Local values of void fraction and bubble velocity as well as the bubble diameter were measured by means of a resistivity probe technique. Reliable values were obtained for the local void fraction over the entire range $\text{0 ≤ α ≤ 1}$. The void fraction profiles appeared to have a local maximum at the pipe center, local maxima close to the wall were obviously absent. The resistivity probes are shown to measure the velocity of the interface between the conducting and nonconducting phases, which equals the gas velocity only for low void fractions. The measured data for void fraction and bubble velocity were correlated by means of power law distribution functions, with exponents given by a function of the cross-sectionally averaged void fraction. The Sauter mean diameters for the bubble size spectra found, agree reasonably well with diameters predicted by a theoretical model based on the energy dissipation in the flow.     

Prediction of mono-disperse gas–liquid turbulent flow in a vertical pipe

A two-fluid model in the Eulerian–Eulerian framework has been implemented for the prediction of gas volume fraction, mean phasic velocities, and the liquid phase turbulence properties for gas–liquid upward flow in a vertical pipe. The governing two-fluid transport equations are discretized using the finite volume method and a low Reynolds number $k-\varepsilon$ model is used to predict the turbulence field for the continuous liquid phase. In the present analysis, a fully developed one-dimensional flow is considered where the gas volume fraction profile is predicted using the radial force balance for the bubble phase. The current study investigates: (1) the turbulence modulation terms which represent the effect of bubbles on the liquid phase turbulence in the k–ε transport equations; (2) the role of the bubble induced turbulent viscosity compared to turbulence generated by shear; and (3) the effect of bubble size on the radial forces which results in either a center-peak or a wall-peak in the gas volume fraction profiles. The results obtained from the current simulation are generally in good agreement with the experimental data, and somewhat improved over the predictions of some previous numerical studies.     

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.     

Void fraction and pressure waves in a transient horizontal slug flow

The void fraction and the pressure waves in an air–water mixture flowing in the slug regime are experimentally investigated in a horizontal line. The test section is made of a transparent Plexiglas pipe with 26 mm ID and 26.24 m long, operating at ambient temperature and pressure. The flow induced transients are made by quickly changing the air or the water inlet velocity. The test grid has four operational points. This choice allows one to create expansion and compression waves due to the changes to the gas or to the liquid. Each experimental run is repeated 100 times to extract an ensemble average capable of filtering out the intrinsic flow intermittence and disclosing the void fraction and pressure waves’ features. The slug flow properties such as the bubble nose translational velocity, the lengths of liquid film underneath the bubble and the liquid slug are also measured. The objective of the work is two-fold: access the main characteristics of the void fraction and pressure waves and disclose the mechanics of the transient slug flow as described through the changes of the slug flow properties.     

Effect of bubble size on void fraction fluctuations in dispersed bubble flows

It is known that bubble size affects seriously the average void fraction in bubbly flows where buoyant velocities vary considerably with bubble size. On the contrary, there is no systematic literature report about bubble size effects on the intensity and frequency of void fraction fluctuations around the average void fraction. This work aims to provide such information. An electrical impedance technique is employed along with non-intrusive ring electrodes to register void fraction fluctuations down to 10⁻⁵. Bubble size fluctuations are estimated from high resolution optical images. Experiments are conducted in co-current upward dispersed bubble flow inside a 21 mm tube with average bubble size between ∼50 and ∼700 μm. Water and blood simulant are used as test liquids with velocity from ∼3 to ∼30 cm s⁻¹. The above resemble conditions of Decompression Sickness (DCS) in the bloodstream of human vena cava. It is found that the intensity and frequency of void fraction fluctuations vary appreciably with bubble size at constant gas and liquid flow rates. Moreover, these variations are not random but scale with bubble size. As a first step to quantify this effect, an empirical expression is derived that relates average bubble size to the ratio standard deviation/average value of void fraction.     

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.     

Bubbly-to-cap bubbly flow transition in a long-26 m vertical large diameter pipe at low liquid flow rate

The concurrent upward two-phase flow of air and water in a long vertical large diameter pipe with an inner diameter (D) of 200 mm and a height (z) of 26 m (z/D = 130) was investigated experimentally at low superficial liquid velocities from 0.05009 to 0.3121 m/s and the superficial gas velocities from 0.01779 to 0.5069 m/s. The resultant void fractions range from 0.03579 to 0.4059. According to the observations using a high speed video camera, the flow regimes of bubbly, developing cap bubbly and fully-developed cap bubbly flows prevailed in the flows. The developing cap bubbly flow appeared as a flow regime transition from bubbly to fully-developed cap bubble flow in the vertical large diameter pipe. The developing cap bubbly flow changes gradually and lasts for a long time period and a wide axial region in the flow direction, in contrast to a sudden transition from bubbly to slug flows in a small diameter pipe. The analysis in this study showed that the flow regime transition depends not only on the void fraction but also on the axial distance in the flow and the pipe diameter. The axial flow development brings about the transition to happen in a lower void fraction flow and the increase of pipe diameter causes the transition to happen in a higher void fraction flow. The measured void fraction showed an N-shaped axial changing manner that the void fraction increases monotonously with axial position in the bubbly flow, decreases non-monotonously with axial position in the developing cap bubbly flow, and increases monotonously again with axial position in the fully-developed cap bubbly flow. The temporary void fraction decrease phenomenon in the transition region from bubbly to cap bubbly flow can be attributed to the formation of medium to large cap bubbles and their gradual growth into the maximum size of cap bubble and/or cluster of large cap bubbles in the developing cap bubbly flow. In order to predict the N-shaped axial void fraction changing behaviors in the flow regime transition from bubbly to cap bubbly flow, the existing 12 drift flux correlation sets for large diameter pipes are reviewed and their predictabilities are studied against the present experimental data. Although some drift flux correlation sets, such as those of Clark and Flemmer (1986) and Hibiki and Ishii (2003), can predict the present experimental data with reasonable average relative deviations, no drift flux correlation set for distribution parameter and drift velocity can give a reliable prediction for the observed N-shaped axial void fraction changing behaviors in the region from bubbly to cap bubbly flow in a vertical large diameter pipe.     

Numerical modeling and experimental investigation of gas–liquid slug formation in a microchannel T-junction

Gas–liquid two-phase flow in a microfluidic T-junction with nearly square microchannels of 113 μm hydraulic diameter was investigated experimentally and numerically. Air and water superficial velocities were 0.018–0.791 m/s and 0.042–0.757 m/s, respectively. Three-dimensional modeling was performed with computational fluid dynamics (CFD) software FLUENT and the volume of fluid (VOF) model. Slug flow (snapping/breaking/jetting) and stratified flow were observed experimentally. Numerically predicted void fraction followed a linear relationship with the homogeneous void fraction, while experimental values depended on the superficial velocity ratio U_G/U_L. Higher experimental velocity slip caused by gas inlet pressure build-up and oscillation caused deviation from numerical predictions. Velocity slip was found to depend on the cross-sectional area coverage of the gas slug, the formation of a liquid film and the presence of liquid at the channel corners. Numerical modeling was found to require improvement to treat the contact angle and contact line slip, and could benefit from the use of a dynamic boundary condition to simulate the compressible gas phase inlet reservoir.     

The interrelation between void fraction fluctuations and flow patterns in two-phase flow

A fast response, linearized X-ray void measurement system has been used to obtain statistical measurements in normally fluctuating air-water flow in a rectangular channel. It is demonstrated that the probability density function (PDF) of the fluctuations in void fraction may be used as an objective and quantitative flow pattern discriminator for the three dominant patterns of bubbly, slug, and annular flow. This concept is applied to data over the range of 0.0 to 37 m/sec mixture velocities to show that slug flow is simply a transitional, periodic time combination of bubbly and annular flows. Film thicknesses calculated from the PDF data are similar in magnitude in both slug and annular flows. Calculation of slug length and residence time ratios along with bubble lengths in slug flow are also readily obtainable from the statistical measurements. Spectral density measurements showed bubbly flow to be stochastic while slug and annular flows showed periodicities correlatable in terms of the liquid volume flux.     

Development of co-current air–water flow in a vertical pipe

Measurements of the cross-sectional distribution of the gas fraction and bubble size distributions were conducted in a vertical pipe with an inner diameter of 51.2 mm and a length of about 3 m for air/water bubbly and slug flow regimes. The use of a wire-mesh sensor obtained a high resolution of the gas fraction data in space as well as in time. From this data, time averaged values for the two-dimensional gas fraction profiles were decomposed into a large number of bubble size classes. This allowed the extraction of the radial gas fraction profiles for a given range of bubble sizes as well as data for local bubble size distributions. The structure of the flow can be characterized by such data. The measurements were performed for up to 10 different inlet lengths and for about 100 combinations of gas and liquid volume flow rates. The data is very useful for the development and validation of meso-scale models to account for the forces acting on a bubble in a shear liquid flow and models for bubble coalescence and break-up. Such models are necessary for the validation of CFD codes for the simulation of bubbly flows.     

Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column

A new approach for simulating the formation of a froth layer in a slurry bubble column is proposed. Froth is considered a separate phase, comprised of a mixture of gas, liquid, and solid. The simulation was carried out using commercial flow simulation software (FIRE v2014) for particle sizes of 60–150 μm at solid concentrations of 0–40 vol%, and superficial gas velocities of 0.02–0.034 m/s in a slurry bubble column with a hydraulic diameter of 0.2 m and height of 1.2 m. Modelling calculations were conducted using a Eulerian–Eulerian multiphase approach with k–ε turbulence. The population balance equations for bubble breakup, bubble coalescence rate, and the interfacial exchange of mass and momentum were included in the computational fluid dynamics code by writing subroutines in Fortran to track the number density of different bubble sizes. Flow structure, radial gas holdup, and Sauter mean bubble diameter distributions at different column heights were predicted in the pulp zone, while froth volume fraction and density were predicted in the froth zone. The model was validated using available experimental data, and the predicted and experimental results showed reasonable agreement. To demonstrate the effect of increasing solid concentration on the coalescence rate, a solid-effect multiplier in the coalescence efficiency equation was used. The solid-effect multiplier decreased with increasing slurry concentration, causing an increase in bubble coalescence efficiency. A slight decrease in the coalescence efficiency was also observed owing to increasing particle size, which led to a decrease in Sauter mean bubble diameter. The froth volume fraction increased with solid concentration. These results provide an improved understanding of the dynamics of slurry bubble reactors in the presence of hydrophilic particles.     

The structure of bubbly flow through venturis

The phase structure of vertical air-water mixture flows through venturis were investigated using area contraction ratios of 3.16 and 7.11 and with variations in angles of convergence and divergence. The flow conditions were predominantly of the bubbly type and covered a range of gas volume fraction at the throat between 0.2 and 0.6 for average mixture velocities of up 32 m/s. Resistivity probe signals indicating void fluctuations were analyzed to yield local void fraction, bubble velocity, bubble detection rate and probability density function of bubble sizes in the flow. Velocity ratios were also obtained to provide information on the overall behaviour of the two concurrent phases. The resistivity probe was shown to give reliable results for bubble flows in a wide range of speeds indicating velocity ratios up to 1.7 in the venturi throat. All flows tended toward a stable and well-mixed bubbly pattern downstream of the venturi exit following a sufficient length. The void and velocity profiles here always appeared to be characterized by a local maximum in the pipe centre, the local maximum close to the wall of some of the inlet flows being eliminated. Bubble coalescence was noted in the convergent passage whilst significant bubble fragmentation in the divergent passage was observed from the results.     

Four-way coupled Eulerian–Lagrangian Direct Numerical Simulations in a vertical laminar channel flow

Direct Numerical Simulations of a laminar two-phase flow into a vertical channel are investigated. An Eulerian–Lagrangian approach allows tracking each bubble position with a four-way coupling strategy, i.e. taking into account bubble-fluid and bubble-bubble interactions. The flow configuration has been chosen to highlight the buoyancy effects due to significant values of void fraction (high numbers of bubbles); hence the bubbles collisions and wall effects are the critical parameters to ensure the dispersion of the bubble plume. The DNS approach is self-consistent and does not rely on closure relations or empirical correlations for describing the collective bubble dynamics. It is found that the DNS predicts well the behavior of the bubble plume and its back effect on the liquid phase when compared with a mixture model and experimental data. The elastic nature of collisions, the sensitivity of the mean and RMS values of velocities and void fraction to the mesh quality are explored.     

One-dimensional interfacial area transport of vertical upward bubbly flow in narrow rectangular channel

The design and safety analysis for miniature heat exchangers, the cooling system of high performance microelectronics, research nuclear reactors, fusion reactors and the cooling system of the spallation neutron source targets requires the knowledge of the gas–liquid two-phase flow in a narrow rectangular channel. In this study, flow measurements of vertical upward air–water flows in a narrow rectangular channel with the gap of 0.993 mm and the width of 40.0 mm were performed at seven axial locations by using the imaging processing technique. The local frictional pressure loss gradients were also measured by a differential pressure cell. In the experiment, the superficial liquid velocity and the void fraction ranged from 0.214 m/s to 2.08 m/s and from 3.92% to 42.6%, respectively. The developing two-phase flow was characterized by the significant axial changes of the local flow parameters due to the bubble coalescence and breakup in the tested flow conditions. The existing two-phase frictional multiplier correlations such as Chisholm, 1967, Mishima et al., 1993 and Lee and Lee (2001) were verified to give a good prediction for the measured two-phase frictional multiplier. The predictions of the drift-flux model with the rectangular channel distribution parameter correlation of Ishii (1977) and several existing drift velocity correlations of Ishii, 1977, Hibiki and Ishii, 2003 and Jones and Zuber (1979) agreed well with the measured void fractions and gas velocities. The interfacial area concentration (IAC) model of Hibiki and Ishii (2002) was modified by taking the channel width as the system length scale and the modified IAC model could predict the IAC and Sauter mean diameter acceptably.     

Fiber-optic probe measurements of void fraction and bubble size distributions beneath breaking waves

Experiments were performed to determine the accuracy of single-tip fiber-optic probes for making simultaneous measurements of the void fraction and bubble size distributions under breaking waves. Tests in a vertical bubble column showed that the normalized RMS error in the void fraction measurements was ∼10%. The relationship between bubble rise time and bubble velocity was investigated in a unidirectional flow cell. Similar to previous studies the rise time and bubble velocity were found to be related by a power law equation. The probes can provide mean bubble velocities accurate to ±10% when a minimum of ∼15 individual bubble velocities are averaged. The fiber-optic probes were deployed beneath a plunging breaking wave in a laboratory wave channel. The slope and shape of the bubble cord length size distribution measured with the probes was found to agree closely with the size distribution measured from digital video recordings. The probes were then positioned in the splash-up zone of a plunging breaker and the resulting cord length distribution had a shape and slope that was in agreement with previous measurements. These results demonstrate that single-tip fiber optic probes can provide accurate simultaneous measurements of the void fraction and bubble sizes inside the dense bubble clouds entrained by breaking waves.