Two regime transitions to pseudo-homogeneous and heterogeneous bubble flow for various liquid viscosities

The gas hold-up variation and regime transition were investigated with different liquid viscosities ranging from 1.0 mPa s to 31.5 mPa s using a 0.15-m-in-diameter bubble column. In contrast to common observations, the gas hold-up graph with the superficial gas velocity could be categorized into three flow regimes: homogeneous, pseudo-homogeneous and heterogeneous flow regimes. The formation of large bubbles caused a transition from the homogeneous to the pseudo-homogenous flow regime, in which large bubbles rose vertically without oscillatory turbulence. According to the results from the dynamic gas disengagement (DGD) technique, large bubbles began to form at the transition superficial gas velocity to the pseudo-homogeneous flow regime. The transition to a heterogeneous flow regime was initiated by the turbulent movement of large bubbles. The transition superficial velocities to pseudo-homogeneous and heterogeneous flow regimes, u_t1 and u_t2, decreased with increasing liquid viscosity below a critical viscosity and converged to a certain value above that viscosity. However, the correlations from the literatures could not make a reasonable estimation of the transition superficial velocities because they did not consider the possible transition to a pseudo-homogeneous flow regime. Therefore, the two transition points should be predicted separately.     

Effect of gas expansion on the velocity of individual Taylor bubbles rising in vertical columns with water: Experimental studies at atmospheric pressure and under vacuum

This study was designed to determine the effect of gas expansion on the velocity of Taylor bubbles rising individually in a vertical column of water. This experimental study was conducted at atmospheric pressure or under vacuum (33.3 and ) using three different acrylic columns with internal diameters of 0.022, 0.032, and 0.052 m, and more than 4.0 m high. A non-intrusive optical method was used to measure velocity and length of Taylor bubbles at five different locations along the columns. The operating conditions used correspond to inertial controlled regime.In experiments performed under vacuum, there is considerable gas expansion during the rise of Taylor bubbles, particularly when they approach the liquid free surface where the pressure drop (due to the hydrostatic pressure) is of the order of magnitude of the absolute pressure. The liquid ahead of the bubble is displaced upward by an amount proportional to the gas expansion resulting in increased bubble velocity. The calculated Reynolds number suggests a laminar regime in the liquid ahead of the bubble. However, the experimentally determined velocity coefficient C for each column was much smaller than 2, which would be expected for laminar flow. The value of C obtained ranges from 1.13±0.09, for the narrowest column, to 1.40±0.24, for the widest column. This suggests that a fully developed laminar flow in the liquid ahead of the bubble is never achieved due to continuous bubble expansion at a variable rate, regardless of column height.The velocity coefficient C can be used to calculate the contribution of liquid motion to bubble velocity. Subtracting this contribution from the measured bubble velocity defines a constant value which is nearly identical to the bubble rise velocity measured in the same column operated as a constant volume system (two ends closed) where gas expansion is absent.     

Flow patterns in the wake of a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids: An experimental study

The flow in the wake and near-wake regions of individual Taylor bubbles rising through stagnant and co-current vertical columns of Newtonian liquids was studied, employing simultaneously particle image velocimetry (PIV) and pulsed shadowgraphy techniques (PST). Experiments were made with water and aqueous glycerol solutions covering a wide range of viscosities , in an acrylic column of 32 mm ID.Different wake structures (laminar, transitional and turbulent) are identified, in both stagnant and co-current flow conditions. In stagnant liquids, the wake flow pattern is only dependent on the dimensionless group N_f. The different types of wakes obtained are in accordance with the critical N_f numbers proposed in previous works. For co-current flow conditions, the flow patterns in the wake depend on the Reynolds number based on the relative (to the bubble) average velocity of the upward liquid flow, the laminar-transitional and transitional-turbulent limits being for the first time experimentally determined.The wake flow patterns are quantified by means of instantaneous and average flow fields. Values for the wake length and wake volume are also presented and compare well with correlations found in literature. Study of the flow in the near-wake zone enabled determination of the distance needed to recover the undisturbed liquid velocity profile.The detailed study of the flow in the wake and near-wake regions is an important contribution to better understanding the interaction and coalescence mechanisms between Taylor bubbles.The data reported are relevant to the validation of numerical simulation codes in the vertical slug flow regime.     

Multi-fluid simulation of turbulent bubbly pipe flows

Radial distributions of void fraction α_G, bubble aspect ratio E, phasic velocities V_G and V_L and turbulent kinetic energy k in bubbly pipe flows are measured using an image processing method and a laser Doppler velocimetry. Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows. The experimental results indicate that aspect ratio of bubbles in the near wall region takes a higher value than that of free rising bubbles due to the presence of wall, and that the change in the aspect ratio induces decrease in relative velocity between bubbles and liquid in the near wall region. Drag coefficient C_D of a bubble in a bubbly pipe flow tends to increase with magnitude of shear flow, and the effect of shear flow on C_D is estimated by the correlation proposed by Legendre and Magnaudet (1998). Comparison between the simulated and the measured results indicate that the effects of bubble shape and shear flow on drag force acting on bubbles should be taken into account for accurate predictions of bubbly pipe flows. The turbulence models proposed by Lopez de Bertodano et al. (1994) and by Hosokawa and Tomiyama (2004a) give good predictions for turbulence modification caused by bubbles.     

Flow in the nose region and annular film around a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids

The flow in the nose region and in the annular film around individual Taylor bubbles rising through stagnant and co-current vertical columns of liquid were studied, employing particle image velocimetry (PIV) and pulsed shadowgraphy techniques (PST) at the same time. The combined techniques enabled simultaneous determination of the bubble shape and the velocity profiles in the liquid film. Experiments were performed with water and aqueous glycerol solutions in a wide range of viscosities , in an acrylic column of 32 mm ID.Values for the distance ahead of the nose in which the flow is disturbed by the presence of the bubble are presented for the conditions studied. The bubble shapes in the nose region are compared with Dumitrescu's shape for potential flow. The velocity profiles show that after the nose region the liquid begins to accelerate downwards, and at a certain distance from the bubble nose the velocity profile and the liquid film thickness stabilise. The liquid film acquires characteristics of a free-falling film. Values of the developing length and film thickness are reported for the experimental conditions studied. Average velocity profiles in the fully developed film are also presented. A critical Reynolds number of around 80 (based on the mean absolute velocity in the liquid film and on the film thickness) is reported for the transition from laminar to turbulent regime. Shear stress profiles (in the fully developed film) are also provided.The data reported are relevant for the validation of numerical codes in slug flow.     

Modeling pressure losses for Newtonian and non-Newtonian laminar and turbulent flow in long square edged orifices

A lack of experimental data and predictive models prompted the determination of loss characteristics of four sharp square-edged orifices for laminar to turbulent flow regime (1 ≤ Re ≤ 100,000). Novel experimental data for β ratios of 0.36, 0.4, 0.5 and 0.7 obtained with Newtonian and non-Newtonian fluids and an empirical correlation for predicting pressure losses through long square edged orifice plates is presented. For turbulent flow, new experimental results compared well with existing predictive models, thus validating the experimental results. Comparison of existing correlations as well as the new correlation shows that, although with some shortcomings, good progress is made toward a design correlation that spans a wide range of laminar to turbulent flow conditions for long orifices.     

Mathematical modeling of gas-liquid mass transfer rate in bubble columns operated in the heterogeneous regime

In this paper, a multi-scale approach is followed to study gas-liquid mass transfer in bubble columns. First, a single bubble of equivalent diameter d is considered. Its morphology and its gas to liquid relative velocity are related to the bubble diameter through the use of known correlations. Then, the gas-liquid mass transfer between the bubble and the surrounding liquid is studied theoretically. An equation describing the transport of the transferred species in the viscous boundary layer around the bubble is solved. In a second step, a bubble column of 6-10 m height is studied experimentally. The gas phase in the column is characterized experimentally by means of a gammametric technique. Finally, the two studies are linked, yielding a 1D mathematical model able to predict the gas-liquid mass transfer rate in a bubble column operated in the heterogeneous regime.     

The influence of electrolytes on gas hold-up and regime transition in bubble columns

Experiments were conducted in a 0.12-m-in-diameter bubble column to investigate the effect of electrolytes on gas hold-up (ε) and on the regime transition point in bubble columns. Air was used as the dispersed phase and aqueous solutions of three different salts (NaCl, Na₂SO₄ and NaI), as well as double-distilled water, were utilised as the continuous phase, varying the gas superficial velocity (u_G) in the range 0-0.26 m/s. The ε×u_G curves were a function of both the chemical nature and the concentration of the electrolytes. However, similar ε×u_G profiles were obtained regardless of the electrolyte for a given ratio between the concentration in the solution and the critical concentration of the electrolyte for bubble coalescence. This ratio therefore presents itself as a promising modelling parameter to account for the chemical nature of electrolytes. The gas hold-up data were employed to compute the regime transition point according to two different methods, evidencing its non-linear dependence on the concentration of electrolytes in the liquid.     

An experimental study of air-water Taylor flow and mass transfer inside square microchannels

Flow and mass transfer properties under air-water Taylor flow have been investigated in two square microchannels with hydraulic diameters of 400 and 200 μm. Experimental data on Taylor bubble velocity, pressure drop and liquid side volumetric mass transfer coefficient (k_La) have been presented. It was shown that the measured Taylor bubble velocity in square microchannels could be well interpreted based upon an approximate measurement of the liquid film profile therein. Then, the obtained two-phase frictional pressure drop values in both microchannels were found to be significantly higher than the predictions of the correlation proposed by Kreutzer et al. [2005b. Inertial and interfacial effects on pressure drop of Taylor flow in capillaries. A.I.Ch.E. Journal 51, 2428-2440] when the liquid slug was very short, which can be explained by the inadequacy of their correlation to describe the excess pressure drop caused by the strong inner circulation in such short liquid slugs. An appropriate modification has been made to this correlation in order to improve its applicability in microchannels. Finally, the experimental (k_La) values in the microchannel with hydraulic diameter of 400 μm were found to be in poor agreement with those predicted by the existing correlations proposed for capillaries with diameters of several millimeters. The observed deviation was mainly due to the fact that mass transfer experiments in this microchannel actually corresponded to the case of short film contact time and rather poor mixing between the liquid film and the liquid slug, which was not in accordance with mass transfer assumptions associated with these correlations. A new empirical correlation has been proposed to describe mass transfer data in this microchannel.     

Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows

Closure laws are needed for the qualification of CFD codes for two-phase flows. In case of bubbly and slug flow, forces acting on the bubbles usually model the momentum transfer between the phases. Several models for such forces can be found in Literature. They show, that these forces depend on the liquid flow field as well as on the size and the shape of the bubbles. A validation of consistent sets of bubble force models for poly-disperse flows is given, basing on a detailed experimental database for vertical pipe flows, which contains data on the radial distribution of bubbles of different size as well as local bubble size distributions. A one-dimensional (1D) solver provides velocity profiles and bubble distributions in radial direction. It considers a large number of bubble size classes and is used for the comparison with the experiments. The simplified model was checked against the results of full 3D simulations done by the commercial code CFX-5.7 for simplified monodisperse cases. The effects of the number of bubbles classes as well as the effect of the lateral extension of the bubbles were analyzed. For the validation of bubble force models measured bubble size distributions were taken as an input for the calculation. On basis of the assumption of an equilibrium of the lateral bubble forces, radial volume fraction profiles were calculated separately for each bubble class. In the result of the validation of different models for the bubble forces, a set of Tomiyama lift and wall force, deformation force and Favre averaged turbulent dispersion force was found to provide the best agreement with the experimental data. Some discrepancies remain at high liquid superficial velocities.     

Flow structure of gas-liquid two-phase flow in an annulus

The flow structure of gas-liquid two-phase flow in vertical annulus channel has been investigated. The inner and outer diameters of the annular channel were 19.1 and 38.1 mm, respectively. The total height of the test section was 4.37 m. Nineteen inlet flow conditions were selected, which cover bubbly, cap-slug, and churn-turbulent flows. The local flow parameters, such as void fraction, interfacial area concentration (IAC), and bubble interface velocity, were measured at nine radial positions within the gap of the annulus at z/D_h=230 of the test section. The flow regimes of the flow conditions, which were based on visual observations, were compared with several flow regime maps. In addition, the local measurements were used to calculate distribution parameter, C₀ in drift-flux model, and area-averaged IAC. A new correlation of C₀ was proposed based on the experimentally obtained C₀ values. This correlation was tested in the drift-flux model successfully along with Ishii's drift velocity correlations. The area-averaged IAC values were compared with the most widely used models. The advantages and drawbacks of these models were highlighted.     

水平管内气液段塞流液塞长度发展规律的实验和模拟研究

In petroleum industry, the slug flow is a fre-quently encountered flow regime in multiphase flowpipeline. For pipeline designers, the liquid slug lengthdistribution is important for the proper design ofdownstream facilities, such as slug catcher and sepa-ration system. However, for its transient and unsteadynature, it is a great challenge for engineers to correctlypredict the flow parameters of slug flow, especiallythe maximum liquid slug length. The unit cell model for slug flow in horizontal…     

Hydrodynamic characteristics of gas-liquid slug flow in a downward inclined pipe

Gas-liquid slug flow in a downward inclined pipe was studied experimentally by employing a wire-mesh sensor that enables quantitative measurements of the cross-sectional void fraction distribution. Processing of the wire-mesh sensor data was applied to carry out a statistical analysis of characteristic parameters of downward slug flow, such as bubble and liquid slug length distributions, as well as to determine the ensemble-averaged shapes of the bubble nose, liquid film and bubble tail. It was found that the pipe inclination affects mainly the bubble length, while variation in the gas flow rate affects both bubble and slug length. The bubble nose shape is more sensitive to the flow conditions than the bubble tail. The 3D structure of an elongated bubble in downward slug flow was reconstructed from the wire-mesh sensor data.     

Liquid re-circulation in turbulent vertical pipe flow behind a cylindrical bluff body and a ventilated cavity attached to a sparger

The turbulent flow field (Re=60024) in the wake of a cylindrical bluff body in a 0.105 m internal diameter pipe with an area blockage ratio of 82% in turbulent single-phase flow was studied using laser Doppler velocimetry (LDV). The results for the time-averaged velocity showed a toroidal vortex below the bluff body. The axial location below the bluff body where both the time-averaged radial and axial velocity components were zero (eye of the vortex) was found at approximately 0.72D. The end of the re-circulation region as defined by a stagnation point on the centreline of the pipe was found at an axial location below the bluff body of approximately 1.3D. These two locations did not change when altering the liquid superficial velocity confirming that the geometry (i.e., size) of the toroidal vortex is not dependent on the superficial liquid velocity or the speed of the vortex.Similar measurements using LDV were taken in the wake of a ventilated cavity in a vertical 0.105 m internal diameter pipe, with an area blockage ratio of 80%. The flow beneath the cavity was turbulent two-phase bubbly flow and the liquid-only flow ahead of the cavity was turbulent (Re=45618). The cavity was attached to a (central) sparger, which is a scale-up of the design used by Bacon (1995). The average gas void fraction in the wake of the cavity was 7%. The results for the time-averaged velocity confirmed the formation of a toroidal vortex remarkably similar to the vortex formed below the bluff body. The eye of the vortex and the end of the re-circulation region were found at an axial location below the ventilated cavity of 0.78 and 1.35D, respectively, i.e., almost identical to the results for the bluff body.The LDV results of the cylindrical bluff body and the ventilated cavity were compared with the fully predictive model of the velocity distribution in the vortex proposed by Thorpe et al. (2001) and good agreement was found in both cases. The model also agreed well with the data of van Hout et al. (2002) for a Taylor bubble rising in stagnant liquid in a 0.025 m internal diameter pipe. The CFX simulations of Thorpe et al. (2001) carried out for a 0.050 m internal diameter pipe, agreed well with the experimental data of the cylindrical bluff body, the ventilated cavity and the data obtained by van Hout et al. (2002) when correlating the results in the appropriate dimensionless form. Our analysis showed that the maximum axial re-circulation velocity in the centre of the vortex ring was directly proportional to the mean velocity in the annulus at the base of the cylindrical bluff body, the ventilated cavity or the Taylor bubble. The proportionality constant for all cases was found to be approximately 0.38 confirming the value proposed by Thorpe et al. (2001).     

Hydrodynamic properties of coal in turbulent fluidized beds

Hydrodynamic properties in turbulent fluidized beds of three different sizes of coal (d _p = 0.507, 0.987, 1.147 mm) have been determined from the pressure fluctuations in a 0.1 m-ID × 3.0 m high Plexiglas column. The transition velocity from the slugging to turbulent flow regimes can be determined from the statistical analysis of pressure fluctuations such as mean amplitude, standard deviation and skewness, the pressure wave velocity, and the bed expansion with gas velocity. The bed expansion in the slugging and turbulent flow regimes cannot be estimated from the two-phase theory. The voids rise velocity and the bed expansion ratio (H/H _mf ) in the turbulent flow regime have been correlated with the relevant dimensionless and operating parameters The ransition velocity to the turbulent flow regime has been determined based on the slug breakdown caused by the inertial force of an upflowing maximum stable slug which overcomes the gravitational force induced by solid refluxing as:      

Evolution of hydrodynamic and statistical parameters of gas-liquid slug flow along inclined pipes

The development of slug flow along two long inclined pipes (2-90° from the horizontal) with internal diameters of 0.024 and was measured by three optical fiber probes. The probes were located in a measurement module at axial distances of between the fiber tips. To measure the evolution of slug flow, the module was placed at different positions along the pipe. Instantaneous elongated bubble velocities and corresponding elongated bubble and liquid slug lengths were determined by processing the optical probe signals. The evolution of the liquid slug and elongated bubble length distributions along the pipes is characterized by a gradual growth of the mean and mode values. The growth rate decreases with decreasing inclination. Mean elongated bubble lengths have a minimum at about 60°, while mean liquid slug lengths decrease slowly with decreasing inclination angle. The coalescence rate, defined as the decrease in the ensemble size, becomes almost negligible at x/D>60, independent of pipe diameter, flow rates and inclination angle. The slug frequency has a maximum at about 60° inclination.     

Effect of solids on homogeneous-heterogeneous flow regime transition in bubble columns

Experiments were conducted to study the effect of the presence of the solid phase on the homogeneous-heterogeneous flow regime transition in a bubble column 0.14 m diameter. Air, distilled water and calcium alginate beads (2.1 mm, ) at concentrations c=0-30% (vol.) were the phases. The basic data were the voidage-gas flow rate dependences. The critical point, where the homogeneous regime loses stability and the transition begins, was evaluated by the drift flux model. The critical values of voidage and gas flow rate were the quantitative measures of the homogeneous regime stability. These were plotted against the solid phase concentration. It was found, that both the voidage and the critical values increased with the solid content at low solid loading, approx. c=0-3%, and decreased at higher loading, c>3%. The homogeneous regime was thus first stabilized and then destabilized. To explain this dual effect, possible physical mechanisms of the solid phase influence on the uniform bubble bed were discussed.     

Theoretical prediction of flow regime transition in bubble columns by the population balance model

Theoretical prediction of flow regime transition in bubble columns was studied based on the bubble size distribution by the population balance model (PBM). Models for bubble coalescence and breakup due to different mechanisms, including coalescence due to turbulent eddies, coalescence due to different bubble rise velocities, coalescence due to bubble wake entrainment, breakup due to eddy collision and breakup due to large bubble instability, were proposed. Simulation results showed that at relatively low superficial gas velocities, bubble coalescence and breakup were relatively weak and the bubble size was small and had a narrow distribution; with an increase in the superficial gas velocity, large bubbles began to form due to bubble coalescence, resulting in a much wider bubble size distribution. The regime transition was predicted to occur when the volume fraction of small bubbles sharply decreased. The predicted transition superficial gas velocity was about 4 cm/s for the air-water system, in accordance with the values obtained from experimental approaches.     

Analytical and numerical evaluation of two-fluid model solutions for laminar fully developed bubbly two-phase flows

An analysis of the two-fluid model in the case of vertical fully developed laminar bubbly flows is conducted. Firstly the phase distribution in the central region of the pipe (where wall effects vanish) is considered. From the model equations an intrinsic length scale L is deduced such that the scaled system reduces to a single equation without parameters. With the aid of this equation some generic properties of the solutions of the model for pipes with diameter greater than about 20L (the usual case, since L is of the order of the bubble radius) are found. We prove that in all physically meaningful solutions an (almost) exact compensation of the applied pressure gradient with the hydrostatic force occurs (with ρ_eff the effective density and the gravity). This compensation implies flat void fraction and velocity profiles in the central region not affected by the wall, even when no turbulence effects are accounted for.We then turn to consider the complete problem with a numerical approach, with the effect of the wall dealt via wall forces. The previous mathematical results are confirmed and the near-wall phase distributions and velocity profiles are found. With the numerical code it is also possible to investigate the regime in which the pressure gradient is greater than the weight of the pure liquid, in which case a region of strictly zero void fraction develops surrounding the axis of the pipe (in upward flow of bubbles).Finally, the same code is used to study the effect of reducing the gravity. As decreases, so does the relative velocity between the phases, making the lift force increasingly dominant. This produces, in upward bubbly flows, narrower and sharper void fraction peaks that also appear closer to the wall.     

RADIAL DISPERSION AND BUBBLE CHARACTERISTICS IN THREE-PHASE FLUIDIZED BEDS

The effects of gas and liquid velocities, liquid viscosity and particle size on the radial dispersion coefficient of liquid phase (D_r) and the bubble properties in three-phase fluidized beds have been determined. A new flow regime map based on the drift flux theory in three-phase fluidized beds has been proposed.

In three-phase fluidized beds, D, increases with increasing gas velocity in the bubble coalescing and in the slug flow regimes, but it decreases in the bubble disintegrating regime. The coefficient exhibits a maximum value in the bed of small particles with increasing liquid velocity at lower gas velocities. However, it increases with increasing liquid velocity at higher gas velocities. In two and three-phase fluidized beds of larger particles (6,8 mm), D_r exhibits a maximum value with an increase in liquid viscosity at lower gas velocities, but it increases at higher gas velocities. The mean bubble chord length and its rising velocity increase with increasing gas velocity and liquid viscosity. However, the bubble chord length decreases with an increase in liquid velocity and it exhibits a maximum value with increasing particle size in the bed. The radial dispersion coefficients in the bubble coalescing and disintegrating regimes of three-phase fluidized beds in terms of the Peclet number in the present and previous studies have been well represented by the correlations based on the concept of isotropic turbulence theory.