Evolution Of Bubble Size Distribution Research Articles

NNumerical investigation of bubble interaction mechanisms in gas-liquid bubbly flows: Harmonisation of bubble breakup and coalescence effects

Numerical investigation of the dynamics of gas-liquid bubbly flow has been performed by using the population balance approach. Using the homogeneous MUSIG model coupled with the two-fluid model, the evolution of bubble size distribution in vertical pipes has been simulated with appropriate consideration of bubble interaction mechanisms. In particular, the study focuses on harmonising the imbalance often associated with breakup and coalescence rates by performing extensive numerical investigations for the examination and comparison of different model formulations to harmonise the coalescence calibration factor of Prince and Blanch (1990) model. To avoid the fine-tuning procedure of selecting calibration factors to harmonise the breakup and coalescence effects, a breakup calibration factor of 1.0 (default setting in ANSYS CFX) was used and three different expressions area-averaged and included as the coalescence calibration factor for the model of Prince and Blanch (1990) modelled using CFX Expression Language (CEL). The performance of the three different “cases” (modifications) has been investigated, compared with each other and validated against the experimental data reported by Monrós et al. (2013). In general, the comparison has shown that all the “cases” yielded satisfactory results when the numerical results were compared with five primitive experimental parameters, namely: gas volume fraction, interfacial area concentration, Sauter mean bubble diameter, gas velocity and liquid velocity. The encouraging results obtained clearly show the capability of the “cases” modelled in capturing the evolution of the bubble sizes. The agreement with the gas volume fraction profiles indicates a level of confidence in the interfacial force models used. Similarly, the agreement seen with the interfacial area concentration indicates that the “cases” modelled for the birth and death processes are reasonably adequate to describe the bubble dynamics. Overall, the comparison shows that the model labelled as “case 2” presented the best results in most of the experimental conditions simulated.

Evolution of bubble size distribution, number density, and shape in semi‐batch vertical gas–liquid Taylor vortex flow

AbstractBubble size distribution and bubble ellipticity were measured as a function of axial position in a vertically oriented semi‐batch gas–liquid Taylor vortex reactor with varying gas flow rate and inner cylinder rotation speed producing axial Reynolds numbers in the range 23.8–119 and azimuthal Reynolds numbers up to 4.2 × 104. The mean bubble size increases monotonically with axial distance from the bottom of the reactor at the location of gas injection. The functional form of the growth of the mean bubble size with axial position depends upon the azimuthal Reynolds number. Specifically, when the azimuthal Reynolds number is less than 1.3 × 104, the mean bubble size increases linearly with axial distance from the bubble injection point. In contrast, for azimuthal Reynolds numbers greater than this critical value, the mean bubble size increases with axial distance in a sigmoidal manner.

Update to the MUSIG model in ANSYS CFX for reliable modelling of bubble coalescence and breakup

The MUSIG (Multiple Size Group) model in the commercial CFD code ANSYS CFX is a population balance approach for describing binary bubble coalescence and breakup events. It is widely used in the simulation of poly-dispersed bubbly flows. The purpose of this work is to identify the internal inconsistencies in the discrete method that is applied for the solution of the population balance equation in MUSIG, and to propose an internally consistent one for discretising the source and sink terms that result from bubble coalescence and breakup. The new formulation is superior to the existing ones in preserving both mass and number density of bubbles, allowing arbitrary discretisation schemes and is free of costly numerical integrations. The numerical results on the evolution of bubble size distributions in bubbly flows reveal that the inconsistency in the original MUSIG regarding bubble breakup is non-negligible for both academic and practical cases. The discussion on the effect of internal inconsistency as well as updates to the model presented in this work are necessary and important for calibration of bubble coalescence and breakup models using the MUSIG approach.

Bubble Size Distribution in Foaming of Liquid Aluminum and the Role of Coarsening and Coalescence

Evolution of bubble size distribution in liquid aluminum foam prepared by dissociation of TiH2 particles is studied by rapidly cooling samples during foam expansion and carrying out metallographic analysis of the solidified foam. Further, diameters of bubbles growing directly on TiH2 particles are calculated to arrive at volume expansion and bubble size distribution. The cells in the solidified foam are orders of magnitude coarser and fewer than those predicted by the “pure growth” based model at all stages of foam expansion. If bubble coarsening was accounted for, the calculated bubble sizes are less than, but the same order of magnitude as the experimentally observed cell sizes. The remaining discrepancy of cell size (and population) can be explained based on bubble coalescence, strongly supported by observations on early stages of foaming.

Evolution of bubble size distribution from gas blowout in shallow water

AbstractGas is often emanated from the sea bed during a subsea oil and gas blowout. The size of a gas bubble changes due to gas dissolution in the ambient water and expansion as a result of a decrease in water pressure during the rise. It is important to understand the fate and transport of gas bubbles for the purpose of environmental and safety concerns. In this paper, we used the numerical model, VDROP‐J to simulate gas formation in jet/plume upon release, and dissolution and expansion while bubble rising during a relatively shallow subsea gas blowout. The model predictions were an excellent match to the experimental data. Then a gas dissolution and expansion module was included in the VDROP‐J model to predict the fate and transport of methane bubbles rising due to a blowout through a 0.10 m vertical orifice. The numerical results indicated that gas bubbles would increase the mixing energy in released jets, especially at small distances and large distances from the orifice. This means that models that predict the bubble size distribution (BSD) should account for this additional mixing energy. It was also found that only bubbles of certain sizes would reach the water surfaces; small bubbles dissolve fast in the water column, while the size of the large bubbles decreases. This resulted in a BSD that was bimodal near the orifice, and then became unimodal.

Foam stabilisation using surfactant exfoliated graphene

Liquid–air foams have been stabilised using a suspension of graphene particles at very low particle loadings. The suspension was prepared through the liquid phase exfoliation of graphite in the presence of the non-ionic tri-block surfactant, Pluronic® F108. The graphene particles possess an extremely high aspect ratio, with lateral dimensions of between 0.1 and 1.3μm as evidenced by TEM imaging. The particles were shown to exhibit a number of other properties known to favour stabilisation of foam structures. Particle surface activity was confirmed through surface tension measurements, suggesting the particles favour adsorption at the air–water interface. The evolution of bubble size distributions over time indicated the presence of particles yielded improvements to foam stability due to a reduction in disproportionation. Foam stability measurements showed a non-linear relationship between foam half-life and graphene concentration, indicative of the rate at which particles adsorb at bubble surfaces. The wettability of the graphene particles was altered upon addition of alkali metal chlorides, with the stability of the foams being enhanced according to the series Na+>Li+>K+>Cs+. This effect is indicative of the relative hydration capacity of each salt with respect to the surfactant, which is adsorbed along the graphene plane as a result of the exfoliation process. Thus, surfactant exfoliated graphene particles exhibit a number of different features that demonstrate efficient application of high-aspect ratio particles in the customisation and enhancement of foams.

Comparative Analysis of Coalescence and Breakage Kernels in Vertical Gas‐Liquid Flow

The evolution of bubble size distribution is an important consideration in vertical gas‐liquid flow, especially in determining the appropriate mass, momentum, and heat transfer between two phases. In order to adequately capture the distribution and to account for its effect on the local hydrodynamics, which generally represents the dominant flow characteristic in such a practical system, a numerical assessment has been performed to understand the six widely adopted different bubble coalescence and bubble breakage kernels. Three different breakage kernels have been selected where each kernel considers a different shape of the daughter size distribution of the bubbles, such as the U‐shape, bell‐shape, and M‐shape. These are combined with different coalescence kernels. The bubble size distribution, void fraction, interfacial area concentration, and gas velocity profiles are compared against the experimental data. Numerical results reveal that the effect on the two‐phase flow structure is mainly due to the application of the different breakage kernels. Moreover, the predicted results also show that the bell‐shape daughter size distribution favours equal breakage of bubbles, which could lead to the over‐prediction of large bubbles. A more sophisticated model for handling bubble induced turbulence should nonetheless be applied in future investigations of vertical gas‐liquid flow.

A population balance treatment of bubble size evolution in free draining foams

Evolving size distributions of bubbles in a foam undergoing simultaneous drainage, coalescence and ripening. • Experimental bubble size distribution evolution in a draining foam. • The distributions follow a log-normal shape with evolving parameters. • Inverse population balance problem for coalescence and/or ripening rates. Modeling foam drainage is an important step in understanding foam stability properties. There is a two way coupling between foam drainage dynamics and bubble size evolution. The bubble size evolution is determined in the general case by two processes: ripening and coalescence. The ripening problem modeling is relatively easy and it has been extensively studied. The coalescence problem is very complex and its modeling attempts are limited. The most sophisticated studies are based on the statistics of bubble films leading to the evolution of the average bubble size. Here an alternative approach to indirect modeling of the coalescence process is attempted. Experimental results of the evolution of bubble size distribution in free draining foams are registered. Then the so called inverse population balance approach is invoked to estimate the coalescence and ripening rates leading to the experimental bubble size evolution. Several surfactant concentrations are employed to yield foams of varying stability. It is shown that the experimental bubble size distributions can be adequately described in all cases by a log-normal distribution. This simplifies vastly the inverse problem solution since approximate methods can now be used for the solution of the population balance equation.

Evolution of bubble size distribution in particle stabilised bubble dispersions: Competition between particle adsorption and dissolution kinetics

It is shown that in systems containing bubbles stabilised by nanoparticles, the time scales for the dissolution of small microbubbles can be comparable with those involving the transport and adsorption of the stabilising nanoparticles onto the surface of the bubbles. We have studied the evolution of model bubble size distribution functions in the light of this effect and also the competition between different sized bubbles for the finite number of available particles. It is found that for dispersions moderately rich in nanoparticles, the width of the final distribution function can become broader than the initial one, whereas for cases deficient in particles the reverse is observed. For each given bubble size, there exists a particle to bubble concentration ratio above which the final size of a bubble of this radius is no longer affected by the presence of other bubbles. In a system deficient in particles, this can still hold true for bubbles in the lower end of the size distribution range, but not the ones at the upper end. By considering simple cases consisting of just two bubbles sizes, we show that the degree of shrinkage of the bigger bubbles is significantly increased in the presence of a small amount of gas in the form of smaller bubbles. In contrast, the final bubble size of the smaller bubbles is found to be largely insensitive to the amount of gas included within larger bubbles. The implications of these results for the final fraction of retained gas, in these types of particle stabilised bubble systems, are also discussed.

Baseline closure model for dispersed bubbly flow: Bubble coalescence and breakup

A set of closures for two-fluid modelling of adiabatic bubbly flows has been defined as baseline model, which provides a common basis for further improvement and development. It includes closures for bubble forces, bubble-induced turbulence as well as bubble coalescence and breakup. In this work, the baseline model is implemented in the commercial code ANSYS CFX 14.5 and applied to the case of adiabatic upward vertical pipe flows. Special attention is paid to the performance of the newly proposed coalescence and breakup model. The comparison with measurements shows that the baseline model is able to capture the evolution of bubble size distribution, gas volume fraction and velocity profiles along the pipe over a wide range of flow conditions.

Modeling of bubble size distribution in isothermal gas–liquid flows: Numerical assessment of population balance approaches

Gas–liquid flows are commonly encountered in many industrial flow systems. In many cases, the evolution of bubble size distribution is a crucial factor governing the momentum, heat and mass transfer between phases within the system. Aiming to evaluate the capability of existing models, numerical assessment of three different population balance approaches – direct quadrature method of moments (DQMOM), average bubble number density (ABND) model and homogeneous MUlti-SIze-Group (MUSIG) models – is presented in this paper. Model predictions were validated against experimental measurements from medium and large scale bubble columns where bubble sizes within the system were found to be dominant by coalescence and break-up mechanism, respectively. In result of the bubble size change, transitions of phase distribution from wall peak to core peak profile were also found in both experiments. In general, predictions of the three models were in satisfactory agreement with experiment measurements clearly demonstrating its applicability for large scale practical systems. Encouraging results have also been obtained in capturing the evolution of bubble size distribution. Nevertheless, noticeable errors were also found in predictions of the MUSIG and DQMOM model indicating some potential deficiencies of the model. To evaluate the numerical efficiency of the three models, computational requirements of each model were also compared.

Impeding effect of air bubbles on normal grain growth of ice

Normal grain growth experiments were performed using polycrystalline ice samples with and without air bubbles. The bubble-free polycrystalline ice was prepared by a special sample preparation technique that employed a phase change method. The ice samples with air bubbles were prepared from a mixture of ice powder and pure distilled water using conventional methods. The temperature dependencies of the rate of grain growth were measured in artificial polycrystalline ice samples with and without air bubbles. The average grain growth exponent n of the ice with bubbles was much greater than the theoretical value of 2, while that of bubble-free ice was close to 2. The activation energy for the grain boundary migration of bubble-free ice was 110–120 kJ mol−1, whereas that of the ice with bubbles was between 40 and 70 kJ mol−1. The observation of the microscopic images of samples and analyses of the evolution of bubble size distribution and location during grain growth revealed that small air bubbles are caught and swept by moving grain boundaries and a coalescence of bubbles occurs. This indicates that the slow grain boundary migration of ice with bubbles is controlled by the migration of air bubbles dragged by grain boundary migration.

Development of a generalized coalescence and breakup closure for the inhomogeneous MUSIG model

In the present study we propose new coalescence and breakup closures for the inhomogeneous MUltiple bubble Size Group (MUSIG) model. The major purpose is to consider bubble coalescence and breakup due to different mechanisms in turbulent gas–liquid mixtures and to develop a generally applicable constitutive model for CFD applications. For bubble coalescence the new model includes coalescence due to turbulence, laminar shear, wake-entrainment and eddy-capture. Bubble breakup mechanisms encompass turbulent fluctuation, laminar shear and interfacial slip velocity. The new model was implemented in the commercial CFD software (CFX-12.0) and applied to the case of turbulent air–water mixtures in a large vertical pipe (DN 200). Simulation results for the evolution of bubble size distributions were compared to the standard closure model of Luo and Svendsen (1996) and Prince and Blanch (1990) as well as the experimental data of TOPFLOW test facility. Better prediction is accomplished by the proposed new model.

Numerical simulation of bubble size distribution of aluminium foams in liquid state

A mathematical model for predicting the evolution of bubble size distribution in Al foams is presented, which takes into account effects of both the coarsening due to gas diffusion between bubbles and the liquid drainage. A bubble size distribution equation and a one-dimensional drainage equation are solved coupledly by a finite difference approach. Comparison with experimental results from the literature shows a general agreement. The model predictions indicate that the bubble size increases exponentially with time that is in good agreement with MacPherson's theory. Furthermore, computational results reveal that bubble size distributions are dependent strongly on the drainage behaviour, the Henry constant, gas diffusivity and surface tension of the Al foam in liquid state.

Evolution of bubble size distribution in baked foods

A model to predict the bubble size distribution in baked foods and the oven rise during baking process is presented, and the effect of changing various model parameters on the model output is studied. The model incorporates a population balance equation for the formation and expansion of bubbles coupled with reaction kinetics and heat and mass transfer equations. Nucleation and growth of bubbles occur because of production of carbon dioxide in the dough due to decomposition of baking soda, which is assumed to follow a first-order kinetics. The results are compared to experimental bubble size distributions in bread samples, obtained using confocal laser scanning microscopy. The sensitivity of the results to different parameters has been analyzed. The model provides a framework to predict the dynamic evolution of the foam structure, which is an important characteristic in defining the quality of baked foods.

Evolution of the structure of a gas–liquid two-phase flow in a large vertical pipe

The evolution of the structure of a gas–liquid flow in a large vertical pipe of 195 mm inner diameter was investigated at the TOPFLOW test facility in Rossendorf. Wire-mesh sensors were used to measure sequences of two-dimensional distributions of local instantaneous gas fraction within the complete pipe cross-section. The sensors own a resolution of 3 mm at a frequency of 2500 Hz. Superficial velocities were varied in a range covering flow regimes from bubbly to churn-turbulent flow. The distance between the gas injection and the sensor position was changed using a so-called variable gas injection system. It consists of six gas injection units, each equipped with three rings of injection orifices in the pipe wall (orifice diameter: 1 and 4 mm), which are fed from ring chambers. The gas flow towards these distributor chambers is individually controlled by valves. Measured bubble-size resolved radial gas fraction profiles reveal differences in the lateral migration of bubbles of different size starting from the injection at the wall. The evolution of bubble-size distributions allows to study bubble coalescence and break-up. The influence of the physical properties of the fluid was studied by comparing cold air–water experiments with steam–water tests at 65 bar.

Rayleigh-Taylor growth measurements of three-dimensional modulations in a nonlinear regime

An understanding of the nonlinear evolution of Rayleigh-Taylor (RT) instability is essential in inertial confinement fusion and astrophysics. The nonlinear RT growth of three–dimensional (3-D) broadband nonuniformities was measured near saturation levels using x-ray radiography in planar foils accelerated by laser light. The initial 3-D target modulations were seeded by laser nonuniformities and subsequently amplified by the RT instability. The measured modulation Fourier spectra and nonlinear growth velocities are in excellent agreement with those predicted by Haan's model [S. Haan, Phys. Rev. A 39, 5812 (1989)]. These spectra and growth velocities are insensitive to initial conditions. In a real-space analysis, the bubble merger was quantified by a self-similar evolution of bubble size distributions, in agreement with the Alon–Oron–Shvarts theoretical predictions [D. Oron et al. Phys. Plasmas 8, 2883 (2001)].

Bubble Size Distributions for Dispersed Air – Water Flows in a 100 mm Horizontal Pipeline

AbstractThe bubble size distributions of air dispersed in water flowing in a 100 mm horizontal pipeline were studied. Size distributions were obtained with a high‐speed digital camera at axial positions 0.5, 15.3 and 42.3 m from the air injection point. Air was injected into the pipeline through a narrow tube extending into the pipe, perpendicular to the pipe axis. The effects of average water velocity, air concentration, and injection nozzle diameter on the evolution of bubble size distribution with axial pipe position were studied. For the lowest air concentration of 0.07%, equilibrium bubble size distributions were dependent only on water velocity. Nozzle injection diameter did not affect the downstream bubble size distributions at air concentrations of 0.07% and 0.3%. Levich's break‐up theory was found to over‐predict the experimental dmax for each test condition.

Direct-contact evaporation in the homogeneous and heterogeneous bubbling regimes. Part I: experimental analysis

Using the air–water system, transient experimental measurements of liquid temperature, bubbling height, evaporation rate, gas hold-up and bubble size distributions in a direct-contact evaporator were performed for four gas superficial velocities including operation in both homogeneous and heterogeneous bubbling regimes. Perforated and porous plates were used as spargers. Significant effects of both the sparger and the gas flow rate upon the equipment performance were verified and systematically analysed, revealing some rather interesting features of transient non-isothermal bubbling, such as temporal evolution of bubble size distributions and gas hold-up values.

Dynamics of gas–liquid flow in a rectangular bubble column: experiments and single/multi-group CFD simulations

Several flow processes influence overall dynamics of gas–liquid flow and hence mixing and transport processes in bubble columns. In the present work, we have experimentally as well as computationally studied the effect of gas velocity, sparger design and coalescence suppressing additives on dynamics of gas–liquid flow in a rectangular bubble column. Wall pressure fluctuations were measured to characterize the low frequency oscillations of the meandering bubble plume. Bubble size distribution measurements were carried out using high-speed digital camera. Dispersed gas–liquid flow in bubble column was modelled using Eulerian–Eulerian approach. Bubble population was represented in the model with a single group or multiple groups. Bubble coalescence and break-up processes were included in the multi-group simulations via a suitable population balance framework. Effect of superficial gas velocity and sparger configurations was studied using single-group simulations. Model predictions were verified by comparison with the experimental data. Role of bubble size in determining plume oscillation period was studied. Multi-group simulations were carried out to examine evolution of bubble size distribution. An attempt is made to understand the relationship between local and global (over all the dispersion volume) bubble size distribution. The models and results reported here would be useful to develop and to extend the applications of multi-group CFD models.