Investigation of the kinetics of breakup of gas bubbles in liquid metals with digital simulation method

The method of digital system simulation can be effectively used to quantify the complex multiphase interactions within a gas injection process. Process simulation results yield a better understanding and a better aimed engineering of gas dispersion techniques in metallurgical processes. In this paper the breakup phenomenon of gas bubbles in stagnant liquids is simulated and the dependencies between breakup of bubbles and various parameters of a gas dispersion process such as operative parameters, system parameters and mass transfer rates are investigated. The bubble diameter after breakup is almost independent of the nozzle diameter and gas flow rate. The frequency of bubble breakup and critical bubble size depend on the rate of mass transfer into the bubble. An almost constant rising velocity is achieved only in those cases investigated where mass transfer and bubble breakup are considered. In all other cases no stationary rising velocity is obtained. The interplay between bubble size, rising velocity and the inertia of the surrounding liquid and the influence of mass transfer and breakup are investigated. Simulation results reveal that the behaviour of an ascending bubble is strongly influenced by the mass transfer rate, i. e. by the composition of the melt. Verification of the simulation results with empirical equations from literature shows a very good agreement in all dispersion systems investigated.     

Estimating the Oil Droplet Size Distributions in Deepwater Oil Spills

Oil released in a deepwater blowout breaks up into droplets. Hence, the time it takes for oil to reach the water surface, its location, and the size of the surface slick at a given time, are all affected by oil droplet sizes. Information on oil surfacing time, its location, and slick size are essential for emergency spill response as well as contingency planning. Despite the importance of the oil droplet size on oil fate in many oil spill problems, our ability to estimate oil droplet sizes has been poor. In this paper, methods are developed for a deepwater oil spill model to estimate the oil droplet size distribution generated due to an accidental release. Models for estimating oil droplet size distribution generated by a deepwater release are developed based on the maximum entropy formalism. The quality of results depends on the constraint equations used. The paper shows results using only the mass balance and specific surface area as constraint equations. The latter case showed markedly improved results. Model results for droplet size distribution are compared with limited experimental data.     

Computer simulation on the hydrodynamics of gas injection process in liquid steel

It is shown that with the aid of digital simulation methods complex multiphase interrelated systems, such as gas-injection process can be analysed. Interdependencies can be revealed and quantitative evaluation of characteristic system quantities are provided. The method of digital system simulation is a very convenient tool for process analysis or system engineering. Results of the computer-aided process simulations (Caps) yield a better understanding of complex phenomena and better aimed engineering of gas dispersion techniques in metallurgical processes. A particular interest of this investigation is to reveal the effect of mass-transfer rate on the hydrodynamic behaviour of a gas-injection process. The combined effects of total flow rate of injected gas and mass-transfer rate on the system quantities such as mixing power, induced liquid flow rate, holdup, interfacial area and volumetric mass transfer coefficient are evaluated under steady state conditions of the investigated systems and illustrated in simulation plots. The liquid velocity has a minor effect on bubble size at some distance from the orifice but controls the location of bubble breakup. The frequency of bubble breakup and final bubble size depends on the intensity of mass transfer. Mixing power due to gas bubbles and circulation velocity of the steel bath increase appreaciably if there is a chance of bath reactions producing more gas. The integral mean values of mixing power, induced velocity of liquid and holdup in plume, specific interfacial area and volumetric mass-transfer coefficient increase with increasing total flow rate of injected gas and intensity of mass transfer.     

Modeling Total Dissolved Gas Concentration Downstream of Spillways

Dams are often operated to facilitate downstream juvenile anadromous fish migration over the spillways, but such operation can cause high dissolved concentrations of oxygen and nitrogen that can be harmful to fish. The concentration of total dissolved gas (TDG) in the flow changes with distance downstream of the spillway crest and depends on the geometric configuration of the spillway and on hydraulic and operating conditions. A model is presented that simulates the physical processes of gas transfer with the goal of having an accurate and more widely applicable TDG model for plunging spillway discharges. Bubble transfer is dominant in the stilling basin, while water surface transfer is dominant downstream. Sensitivity analyses suggest which physical processes are important for accurate total dissolved gas predictions. Instantaneous bubble coalescence and breakup based upon local turbulence conditions is an appropriate assumption. Vertical bubble profiles do not need to be simulated in this type of model. Water surface roughness provides a significant increase to surface transfer. Tailwater depth is important to downstream TDG concentrations. Finally, a 10% difference in air entrained at the plunge point causes relatively minor differences in TDG of 1.4 and 3.1% at low and high discharges, respectively.     

Behavior of Oil and Gas from Deepwater Blowouts

This paper presents a detailed analysis of different deepwater blowout scenarios using the Clarkson deepwater oil and gas model (CDOG). In CDOG, hydrate formation, hydrate decomposition, gas dissolution, nonideal behavior of gas, and possible gas separation from the main plume due to strong cross-currents, are integrated with the jet/plume hydrodynamics and thermodynamics. CDOG takes into account unsteady-state three-dimensional variation of ambient currents and density stratification. Detailed comparisons between CDOG simulations and deepspill field experiments have been published. The model is used to simulate 30 deepwater blowout scenarios based on realistic cases and the results are analyzed in this paper. The scenarios demonstrate the differences in plume behavior due to different ambient conditions, different types of gas, possible hydrate formation, and variations in gas-to-oil ratio. Some key findings of these analyses follow. Oil droplet sizes affect the oil surfacing time significantly. For oil-only blowouts, the ambient conditions do not affect the oil surfacing time significantly, but the location and the size of the slick are affected. For oil and gas mixes, the surfacing time is not sensitive to the type of gas in the mix, but is somewhat dependent on the ambient conditions. In none of the cases simulated here, did free gas reach the water surface. While changing the release temperature had only an insignificant effect on the model results, changing oil type or gas-to-oil ratio did affect the model results. The analyses are useful to engineers/scientists and administrators.     

CFD-PBM simulation of bubble coalescence and breakup in top blown-rotary agitated reactor

Gas-liquid flow and bubble coalescence and breakup behavior were studied in a top blown-rotary agitated reactor for steelmaking.Several important models of bubb...     

Buoyant Velocity of Spherical and Nonspherical Bubbles∕Droplets

An integrated formulation is presented to calculate the buoyant velocity of bubbles∕droplets of various sizes. The bubble∕droplet shape can be a sphere, ellipsoid, or a spherical-cap. This formulation can be applied to solids, liquids, or gases. The comparison of the calculated results with experimental data shows a good match and that the formulation presented is better than the Stokes law and Reynolds law combination when dealing with bubbles∕droplets in a wider range of sizes. This work was developed in connection with oil and gas spill models that have buoyant oil, gas, or gas hydrates, although they can also be applied to other hydraulic engineering problems.     

Bubble Formation through Reaction at Liquid‐Liquid Interfaces

Slag foaming is an important phenomenon in steelmaking processes with both beneficial as well as negative effects. The present work is part of the wider project on the modelling of slag foaming, with special reference to dynamic conditions. Since bubble formation is the first step to foam formation, the present work was carried out in an attempt to simulate the bubble formation in slag/metal reactions in steelmaking processes by water‐modelling experiments. The bubble formation due to the gas produced through chemical reaction at the interface between oleic acid and sodium bicarbonate solution was systematically monitored. The chemical reaction rate was varied by varying the concentration of sodium bicarbonate. The bubbles were observed to be generated in the heavier aqueous phase just below the water‐oil interface. The bubbles penetrated the interface and escaped through the oil phase. The rate of the reaction was estimated from the volume of the gas that passed the water/oil interface. It was observed that the bubble formation and bubble growth mechanism were influenced by the reaction rate while the bubble size seemed to be unaffected by the reaction rate.     

进气方向对文丘里微气泡发生器气泡直径的影响

文丘里微气泡发生装置常采用自吸式进气的方式,在工程应用中可能存在微气泡通量不足的问题。采用压缩空气进气,并通过照相法重点考察了错流、逆流和并流3种进气方向对文丘里管微气泡发生器生成气泡直径的影响。结果表明：喉管处液速超过4.72 m/s时所产生的湍流剪切场才能将进入的气泡破碎成~200 μm级别的微气泡;添加3-戊醇能够稳定生成的微气泡,抑制生成的气泡在从文丘里管到测试槽表面逸出过程中的聚并和破碎过程,从而使测试槽中不同位置处气泡直径能保持生成时的微气泡的直径;3种进气方向中,错流进气因气泡进入后更贴近壁面流动,所生成气泡直径最大;而并流进气气泡脱离时间更短,使得生成气泡尺寸最小。在相同条件下,并流进气生成的微气泡比表面积最大,约是错流进气的3倍,最有利于气液传质。     

Plume characteristics and liquid circulation in gas injection through a porous plug

Various forms of plumes have been identified following the injection of air at different rates through a porous plug into water contained in a ladle-shaped vessel. Discrete bubbles form at the plug and rise uniformly through the column of liquid at gas flow rates up to 14 cm³/s cm² of plug surface; at higher flow rates, groups of bubbles increasingly coalesce into larger gas pockets, and beyond about 40 cm³/s cm², the gas globes are large enough to cover the entire plug surface before detachment and gradual disintegration as they rise through the body of liquid. The gas fraction, as well as bubble frequency, bubble velocity, and bubble size, have been measured in the various dispersion regimes by means of an electroresistivity probe. The radial distributions of gas fraction and bubble frequency are approximately bell-shaped about the axis of flow, and the reduced values are close to Gaussian functions of the reduced radial distance from the axis. The gas fraction along the axis has been correlated to the reduced height of the plume; it increases with decreasing distance above the plug and with increasing gas flow rate. The axial bubble frequency shows a decrease in the vicinity of the plug with the onset of bubble coalescence, but the values of the frequencies at all gas injection rates converge to about 12 s⁻¹ toward the surface of the bath. The mean bubble velocity increases with increasing flow rate but drops once coalescence is fully established. Conversely, there is a sudden increase in the mean bubble diameter with the onset of coalescence. The axial and radial components of the velocity of the liquid surrounding the plume have been measured by means of a Laser-Doppler Velocimeter (LDV), and the results show that the circulation patterns are identical, irrespective of the dispersion regime. The axial flow which is upward in the vicinity of the plume decreases in magnitude with increasing radial distance, ultimately reversing to an in-creasing downward flow beyond a certain distance from the plug axis. Similarly, the radial flow which is outward from the plume near the liquid surface decreases steadily with depth and eventually reverses to an inward flow at a depth independent of the gas injection rate. The profiles of the axial velocities are almost sigmoidal, except in the coalescence regime, where the effect of turbulence is profound at the upper liquid layers. The radial liquid velocities are generally small relative to the axial components, only about one-fifth as large, considering the maximum average values.     

Development and Application of Oil Spill Model for Singapore Coastal Waters

This paper presents the development and application of a three-dimensional oil spill model for predicting the movement and fate of an oil slick in the coastal waters of Singapore. In the model, the oil slick is divided into a number of small elements or grids for simulating of the oil processes of spreading, advection, turbulent diffusion, evaporation, dissolution, vertical dispersion, shoreline deposition and adsorption by sediment. This model is capable of predicting the horizontal movement of surface oil slick, the mass balance of oil spill and the oil particle concentration distribution in water body. Satellite images and field observations of oil slicks on the surface in the Singapore Straits, and measurements of the vertical concentration of oil particles in flume are used to validate the newly developed model. Compared with the observations, the numerical results of the oil spill model show good conformity.     

Numerical simulation of froth formation in aerated slurry coupled with population balance modelling

A computational fluid dynamic (CFD) model has been developed to incorporate pulp and froth zones into one model. In the present research, froth was considered as a separate phase comprised of a mixture of gas, liquid and solids. Considering the froth phase as a separate phase, allowed the incorporation of pulp and froth zones into one model by tracking the formation and destruction of the froth phase due to mass exchange between the pulp and froth. Bubble break-up and coalescence were taken into account in the pulp zone, by employing user functions, written using FORTRAN. The effect of bubble coalescence process due to ?lm rupture was considered in the froth phase. The variation in the concentration of attached particles due to attachment and detachment processes were also taken into account. The CFD model predicted the height of froth layer, the concentration of different bubble sizes in both pulp and froth zones, and finally the multiphase ?ow phenomena in the slurry column. Froth height was found to increase with the increase of gas flow rate while increasing solid concentration decreased froth height.     

Developing a Web-Based System for Large-Scale Environmental Hydraulics Problems with Application to Oil Spill Modeling

Oil spill models are used for decision making during emergencies, contingency planning, and risk assessment. Many of these oil spill models are desktop based. A typical desktop model system is served by an input and output interface to communicate with the user. In a desktop model system, all components reside in the user’s computer. The development of a Web-based model system (Web-CDOG) for large-scale environmental hydraulics problems with an application to oil spill modeling is presented in this paper. The Web-CDOG provides a number of advantages and features that are not available through a desktop system. It helps users to access the model, improves user-developer communication, gives the user access to distributed data, restricts some user access to data (e.g., direct transfer of data from third party sites to the model system without allowing user access), classifies users with different levels of accessibility, and allows multiple users to access the same data. Other examples where a similar Web-based system could be useful include modeling sediment plumes and deepwater oil well blowouts.     

Investigation into the Total Dissolved Gas Dynamics of Wells Dam Using a Two-Phase Flow Model

Bubbles entrained by spilled water at hydroelectric projects increase the concentration of total dissolved gas (TDG), which may lead to gas bubble disease in fish. In this paper, the TDG dynamics downstream of Wells Dam are investigated using a two-phase flow model that accounts for the effect of the bubbles on the flow field. The TDG is calculated with a transport equation in which the source is the bubble/liquid mass transfer, a function of the gas volume fraction and bubble size. The model uses anisotropic turbulence modeling and includes attenuation of normal fluctuation at the free surface to capture the flow field and TDG mixing. The model is validated using velocity and TDG field data. Simulations under two plant operational configurations are performed to gain a better understanding of the effect of spill operations on the production, transport, and mixing of TDG. Model results indicate that concentrated spill releases create surface jets that result in the lowest TDG concentration downstream. On the other hand, spreading the spill release, with moderate flow through each gate, produces the highest TDG values downstream as a result of more air available for dissolution and smaller degasification at the free surface.     

Critical fluid-flow phenomenon in a gas-stirred ladle

Measurement of the velocities of bubbles and liquid with a two-element electroresistivity probe and laser-Doppler velocimeter, respectively, during bottom injection of air into a water bath, has confirmed the existence of a critical gas-injection rate. Above the critical flow rate, the change of axial bubble velocity in the air jet, and of liquid velocity with increasing volume flow rate, diminishes markedly. The existence of the critical flow rate is explicable from high-speed motion pictures of the vertical gas jets, which reveal four zones of gas dispersion axially distributed above the orifice: primary bubble at the orifice, free bubble, plume consisting of disintegrated bubbles, and spout at the bath surface. With increasing gas-injection rate, the free-bubble zone expands such that the point of bubble disintegration rises closer to the bath surface. Above the critical flow rate, the free bubbles rise with minimal breakup and erupt from the bath surface with maximum energy discharge. The combined Kelvin-Helmholtz, Rayleigh-Taylor instability theory has been applied to analyze the bubble breakup in the bath and the critical gas-injection rate in a gas-stirred ladle. The criterion for the critical diameter of bubble breakup has been found to depend primarily on the surface tension and density of the liquid. In the analysis, the propagation time of a disturbance on a bubble surface at the “most unstable” wave number has been compared with the bubble rising time in the bath in order to determine the critical gas-flow rate. The predicted critical values are in close agreement with the measured results. M. ZHOU formerly was Post Doctoral Fellow with the Centre for Metallurgical Process Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4 J.K. BRIMACOMBE holds the Alcan Chair in Materials Process Engineering     

Detailed Modeling of Gas Flow in Liquid Steel: Bubble Size Distribution and Voidage Calculation

Although the role of gas purging in liquid steel systems is well recognized, it has yet to be adequately analyzed. One key aspect of this process is the prediction of gas voidage in the bath, which has been studied in great detail beginning with water modeling in the early days and using advanced multiphase models more recently. Still, there are significant unresolved issues with gas purging systems. When gas is introduced through a nozzle at high flow rate, a jet may form which is undesirable. The break‐up of this jet into bubbles is a separate topic of research. The more common practice in the steel industry is to use porous plugs for gas injection. Gas entry through a porous plug can be characterized by the stretched bubble regime, and the laws of coalescence and fragmentation used to analyze bubble column reactors are generally applicable. Calculation of the bubble size distribution is important for two reasons. First, the voidage distribution in the bath is significantly modified by the injection system and flow rates used, primarily due to changes in flow regime and bubble dynamics (collision, break‐up, coalescence). Second, the voidage distribution directly determines the buoyancy, that influences the physical mixing process, and the specific‐area‐density, that influences surface reactions (for example, decarburization, desulfurization and nitrogen pick‐up). In this paper, a numerical study is presented that combines a bubble dynamics model with an Eulerian multiphase model. The results of the simulation are compared with the experimental data from Anagbo and Brimacombe (1990). Relevant discussion and reviews will be presented to distinguish the differences of this detailed bubble dynamics model with the uniform bubble diameter approximations reported in various recent studies.     

Emulsions in Metallurgical and Chemical Processes

A review of the metallurgical and chemical literature involving foams and emulsions is presented. Experimental techniques for the measurement of drop sizes in such systems are reviewed, and the basic mechanisms of drop breakup and coalescence are discussed, along with an analysis of the pertinent mass-transfer processes. A detailed discussion on a number of industrial processes using foams and emulsions is also presented.     

The impact of bubble dynamics on the flow in plumes of ladle water models

Bubbly plumes are widely encountered in metallurgical processes when gas is injected into liquid metals for refining purposes. Based on the experimental findings from a water model ladle, this phenomenon was simulated with a mathematical model, paying special attention to the dynamics of the bubbles in the plume. In the model, the liquid flow field is first calculated in an Eulerian frame with an estimated distribution of the void fraction. The trajectories of bubbles are then computed in a Lagrangian manner using the estimated flow field, experimentally measured information on bubble drag coefficients, lateral migration due to lateral lift forces, and variation in bubble size due to breakup. Turbulence in the two-phase zone is modeled with a modifiedk-ε model with extra source terms to account for the second phase. The computed void fraction and turbulent liquid flow field distributions are in good agreement with experimental measurements.     

Physical modeling of gas/liquid mass transfer in a gas stirred ladle

The absorption of gas through the plume eye and of an injected gas in a steelmaking ladle process was investigated, using a physical model of CO₂ absorption into a NaOH solution. The results show that the inert gas escaping through the plume eye is ineffective in protecting the bath from the atmosphere, and placing an oil layer (simulated slag) decreases the absorption rate significantly. Increasing the flow rate of the inert gas not only exposes more of the liquid surface to the CO₂ atmosphere, but also increases the mass transfer coefficient at the surface. The overall mass transfer between an injected CO₂ gas and NaOH solution includes the mass transfer through the surface of the bath as well as the mass transfer in the bubble dispersion zone. The difference between the mass transfer in the bubble dispersion zone and the overall mass transfer was found to be significant for relatively low gas flow rates. The mass transfer coefficient of CO₂ in the bubble dispersion zone was estimated using available information regarding the bubble size and velocity. Mass transfer coefficient estimated for the constant bubble frequency regime shows a dependence on gas flow rate. However, if a constant characteristic size of bubbles is assumed as an alternative approach, the mass transfer coefficient is independent of the gas flow rate.     

Effect of Foaming Temperature on Bubble Size Distribution of Liquid Aluminium Foam: Modeling and Experimental Studies

The present study examines the effect of foaming temperature on the final foam expansion and the bubble size distribution of liquid aluminium foam through mathematical modeling and validation experiments. The model calculates the rate of hydrogen release from the foaming agent (TiH₂) particles, super saturation of the melt, nucleation and growth of bubbles and finally, evaluates the evolving bubble size distribution using a population balance approach. The model does not consider bubble coalescence and breakage and uses only solute diffusion for bubble growth. The simulation is performed for two conditions; firstly, for pure temperature effects and secondly, for temperature and TiH₂ quantity combined effects. Upon comparison of simulation results with the experiments, following important observations are made; firstly, the predicted total number of bubbles is found to be one order of magnitude higher than the experiments while the predicted average size is one order of magnitude lower. Secondly, the spread of the predicted distributions is observed to be much narrower. These discrepancies are considered to be due to bubble coalescence and coarsening which are not modeled and shown to be strongly influenced by the foaming temperature.