Computational study of bubble coalescence/break-up behaviors and bubble size distribution in a 3-D pressurized bubbling gas-solid fluidized bed of Geldart A particles

A computational study was carried out on bubble dynamic behaviors and bubble size distributions in a pressurized lab-scale gas-solid fluidized bed of Geldart A particles.High-resolution 3-D numerical simulations were performed using the two-fluid model based on the kinetic theory of granular flow.A finegrid,which is in the range of 3–4 particle diameters,was utilized in order to capture bubble structures explicitly without breaking down the continuum assumption for the solid phase.A novel bubble tracking scheme was developed in combination with a 3-D detection and tracking algorithm(MS3 DATA)and applied to detect the bubble statistics,such as bubble size,location in each time frame and relative position between two adjacent time frames,from numerical simulations.The spatial coordinates and corresponding void fraction data were sampled at 100 Hz for data analyzing.The bubble coalescence/break-up frequencies and the daughter bubble size distribution were evaluated by using the new bubble tracking algorithm.The results showed that the bubble size distributed non-uniformly over cross-sections in the bed.The equilibrium bubble diameter due to bubble break-up and coalescence dynamics can be obtained,and the bubble rise velocity follows Davidson’s correlation closely.Good agreements were obtained between the computed results and that predicted by using the bubble break-up model proposed in our previous work.The computational bubble tracking method showed the potential of analyzing bubble motions and the coalescence and break-up characteristics based on time series data sets of void fraction maps obtained numerically and experimentally.

Inversion method of bubble size distribution based on acoustic nonlinear coefficient measurement

Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium.The bubbles show highly nonlinear properties under finite amplitude acoustic excitation,so the acoustic fields from bubble population are easily observed at the second harmonics as well as at the fundamental frequency,which shows that the nonlinear coefficient increases obviously.The inversion method of bubble size distribution based on nonlinear acoustic effects can peel off the influence of complex environment and obtain the size distribution coefficient information of bubbles more accurately.The previous nonlinear inversion methods of bubble size distribution are mostly based on the nonlinear scattering cross-section characteristics of bubbles.However,the stability of inversion is not high enough.In this paper,we introduce a new acoustic inversion method for bubble size distribution,which is based on the nonlinear coefficients of bubble medium.Compared with other inversion methods based on linear or nonlinear scattering cross section,the inversion method based on nonlinear coefficients of bubble medium proposed in this paper shows good robustness in both simulation and experiment.

Numerical Simulation of Sub-cooled Cavitating Flow by Using Bubble Size Distribution

A new cavitating model by using bubble size distribution based on mass of bubbles is proposed. Liquid phase is treated with Eulerian framework as a mixture containing minute cavitating bubbles. Vapor phase consists of various sizes of minute vapor bubbles, which is distributed to classes based on their mass. The change of bubble number density for each class was solved by considering the change of bubble mass due to phase change as well as generation of new bubbles due to heterogeneous nucleation. In this method the mass of bubbles is treated as an independent variable, in other word, a new coordinate, and dependant variables are solved in Eulerian framework for spatial coordinates and bubble-mass coordinate. The present method is applied to a cavitating flow in a convergent-divergent nozzle, and the two-phase flow with bubble size distribution and phase change was successfully predicted.

Nano-microbubble flotation of fine and ultrafine chalcopyrite particles

As is well known to mineral processing scientists and engineers, fine and ultrafine particles are difficult to float mainly due to the low bubble-particle collision efficiencies. Though many efforts have been made to improve flotation performance of fine and ultrafine particles, there is still much more to be done. In this paper, the effects of nano-microbubbles （nanobuhbles and microbubbles） on the flotation of fine （-38 ＋ 14.36 μm） and ultrafine （-14.36 ＋ 5μm） chalcopyrite particles were investigated in a laboratory scale Denver flotation cell. Nano-microbubbles were generated using a specially-designed nano- microbubble generator based on the cavitation phenomenon in Venturi tubes. In order to better under- stand the mechanisms of nano-microbubble enhanced froth flotation of fine and ultrafine chalcopyrite particles, the nano-microbubble size distribution, stability and the effect of frother concentration on nano- bubble size were also studied by a laser diffraction method. Comparative flotation tests were performed in the presence and absence of nano-microbubbles to evaluate their impact on the fine and ultrafine chalcopyrite particle flotation recovery. According to the results, the mean size of nano-microbubbles increased over time, and decreased with increase of frother concentration. The laboratory-scale flotation test results indicated that flotation recovery of chalcopyrite fine and ultrafine particles increased by approximately 16-21% in the presence of nano-microbubbles, depending on operating conditions of the process. The presence of nano-microbubbles increased the recovery of ultrafine particles （-14.36 ＋ 5 μm） more than that of fine particles （-38 ＋ 14.36 μm）. Another major advantage is that the use of nano-microbubbles reduced the collector and frother consumptions by up to 75% and 50%, respectively.

Eulerian–Lagrangian simulation of bubble coalescence in bubbly flow using the spring-dashpot model

The Eulerian–Lagrangian simulation of bubbly flow has the advantage of tracking the motion of bubbles in continuous fluid, and hence the position and velocity of each bubble could be accurately acquired. Previous simulation usually used the hard-sphere model for bubble–bubble interactions, assuming that bubbles are rigid spheres and the collisions between bubbles are instantaneous. The bubble contact time during collision processes is not directly taken into account in the collision model. However, the contact time is physically a prerequisite for bubbles to coalesce, and should be long enough for liquid film drainage. In this work we applied the spring-dashpot model to model the bubble collisions and the bubble contact time, and then integrated the spring-dashpot model with the film drainage model for coalescence and a bubble breakage model. The bubble contact time is therefore accurately recorded during the collisions. We investigated the performance of the spring-dashpot model and the effect of the normal stiffness coefficient on bubble coalescence in the simulation.The results indicate that the spring-dashpot model together with the bubble coalescence and breakage model could reasonably reproduce the two-phase flow field, bubble coalescence and bubble size distribution. The influence of normal stiffness coefficient on simulation is also discussed.

Hydrodynamics features of dispersed bubbles in the ventilated wake flow of a cylinder

An experimental study was conducted to investigate the 2 D bubbly flow downstream of a cylinder. Sparsely distributed bubbles were produced using the ventilation method. The carrier flow was measured using the particle image velocimetry(PIV) technique. The shadow imaging technique was used to capture instantaneous bubbly flow images. An image-processing code was compiled to identify bubbles in acquired image, calculate the bubble equivalent diameter and the bubble velocity. The effects of Reynolds number and the flow rate of the injected air were considered. The result indicates that the carrier flow is featured by distinct flow structures and the wake region is suppressed as the upstream velocity increases. Regarding the bubbles trapped in the wake flow, the number of small bubbles increases with the upstream velocity. On the whole, the bubble velocity is slightly lower than that of the carrier flow. The consistency between small bubbles and the carrier flow is high in terms of velocity magnitude, which is justified near the wake edge. The difference between the bubble velocity and the carrier flow velocity is remarkable near the wake centerline. For certain Reynolds number, with the increase in the air flow rate, the bubble equivalent diameter increases and the bubble void fraction is elevated.

Bubble performance of a novel dissolved air flotation(DAF) unit

ES-DAF, a novel DAF with low cost, high reliability and easy controllability, was studied. Without a costly air saturator, ES-DAF consists of an ejector and a static mixer between the pressure side and suction side of the recycle rotary pump. The bubble size distribution in this novel unit was studied in detail by using a newly developed CCD imagination through a microscope. Compared with M-DAF under the same saturation pressure, ES-DAF can produce smaller bubble size and higher bubble volume concentration, especially in lower pressure. In addition, the bubble size decreases with the increase of reflux ratio or decrease of superficial air-water ratio. These results suggested that smaller bubbles will be formed when the initial number of nucleation sites increases by enhancing the turbulence intensity in the saturation system.

Optimization of cavitation venturi tube design for pico and nano bubbles generation

Hydrodynamic cavitaion venturi tube technique is used for pico and nano bubble generations in coal column flotation. In order to determine the optimal design of hydrodynamic cavitation venture tube for pico and nano bubble generation, a four-factor three-level Central Composite Design of Experimental was conducted for investigating four important design parameters of cavitation venturi tube governing the median size and the volume of pico and nano bubbles. The test results showed that maximum volume of pico and nano bubbles, 65–75%, and minimum mean pico and nano bubble size,150–240 nm, were achieved at the medium ratio of the diameter of outlet of the venturi-tube and diameter of throat(3–4), medium outlet angle(11–13°), high inlet angle(26–27°) and high ratio of the length of the throat and the diameter of throat(2.3–3). Study the effects of the producing pico and nano bubbles on fine coal flotation was performed in a 5 cm diameter 260 cm height flotation column. The optimal percentage of pico and nano bubbles was about 70%, which produced maximum combustible material recovery of 86% with clean coal ash content of 11.7%.

Experiences in using gas dispersion measurements to evaluate metallurgical performance of scavenger cleaner and recleaner circuit at Vale's Thompson Mill

The performance of a flotation circuit is largely the result of the operator's response to visual clues. This includes manipulation of the gas input and how it is distributed to cells in a bank. A new gas dispersion technology was presented which was conducted to perform characterization tests in Outokumpu 30 m3 and 50 m3 flotation cells installed at Thompson Vale's concentrator, and subsequent data analysis. The experimental program was designed to establish "as-found" baseline conditions for each cell of the two-parallel banks in the scavenger-cleaner and recleaner circuit, to select and characterize one typical cell in the two banks with either different frother concentrations or different air flow rates, and establish what variables can be manipulated in future characterization work. A three-parameter model was developed in order to link the bubble size and frother concentration. This relationship can be used to correlate gas dispersion change to improved metallurgical performance.

Measurement and Prediction of Interfacial Area on a DistiIlation Tray

In this paper the modern electron optical equipment is used to translate the clear image of speed moving bubbles in bubbling liquid on a sieve tray into the digital information stored in computer, and the computer aided image processing technique is utilized to measure the bubble size distributions and interfacial areas under various operating conditions. And the dynamic behavior of bubbles in turbulent liquid is analyzed theoretically; the mechanism of bubble deformation and breakage is explored on the basis of Kolmogoroff′s isotropic turbulence hypothesis; the mathematical model for predicting the gas liquid interfacial area is proposed. The comparison between the simulated results and the experimental data shows that the model is higher in accuracy, simple in form and convenient in use.

Numerical investigation of gas bubble behavior in tapered fluidized beds

In this article, the behavior of gas bubbles in tapered fluidized beds is investigated with the use of a two- fluid model incorporating kinetic theory of granular flow. The effects of various parameters such as apex angle, particle size, and particle density on the size distribution and the rise velocity of gas bubbles were examined. In addition, the simulation results for the bubble fraction and axial velocity of gas bubbles were compared with experimental data reported in the literature and good agreement was observed. As the apex angle was increased, the fraction of gas bubbles with large sizes increased and the fraction of bubbles with small sizes decreased. As the particle size increased, the fraction of gas bubbles with large diameters decreased; however, the fraction of bubbles with medium diameters increased. The obtained results clearly indicate that an increased solid density increased the bubble rise velocity up to a specified height and reduced the velocity at larger heights, in tapered fluidized beds.

Simulation of bubble column reactors using CFD coupled with a population balance model

Bubble columns are widely used in chemical and biochemical processes due to their excellent mass and heat transfer characteristics and simple construction.However,their fundamental hydrodynamic behaviors,which are essential for reactor scale-up and design,are still not fully understood.To develop design tools for engineering purposes,much research has been carried out in the area of computationalfluid dynamics(CFD)modeling and simulation of gas-liquidflows.Due to the importance of the bubble behavior,the bubble size distribution must be considered in the CFD models.The population balance model(PBM)is an effective approach to predict the bubble size distribution,and great efforts have been made in recent years to couple the PBM into CFD simulations.This article gives a selective review of the modeling and simulation of bubble column reactors using CFD coupled with PBM.Bubble breakup and coalescence models due to different mechanisms are discussed.It is shown that the CFD-PBM coupled model with proper bubble breakup and coalescence models and interphase force formulations has the ability of predicting the complex hydrodynamics in differentflow regimes and,thus,provides a unified description of both the homo-geneous and heterogeneous regimes.Further study is needed to improve the models of bubble coalescence and breakup,turbulence modification in high gas holdup,and interphase forces of bubble swarms.

BUBBLE CHARACTERISTICS IN A TWO-DIMENSIONAL VERTICALLY VIBRO-FLUIDIZED BED

Measurement of bubble size and local average bubble rise velocity was carried out in a vertically sinusoidal vibre-fluidized bed. Glass beads of Geldart group B particles were fluidized at different gas velocities, while the bed was vibrated at different frequencies and amplitudes to study their effects on the bubble behavior. This is compared with the case of no vibration in a two-dimensional bed and it is concluded that with vibration the local average bubble size dbav, decreases significantly, especially at minimum bubbling velocity. The average bubble size increases slightly with increasing vibration frequency and amplitude. The local average bubble rise velocity is higher than that with no vibration, though with increasing vibration frequency and amplitude, it does not change significantly.

The pseudo-homogeneous flow regime in large-scale bubble columns:experimental benchmark and computational fluid dynamics modeling

A precise prediction of the fluid dynamics in bubble columns is of fundamental importance to correctly design“industrial-scale”reactors.It is known that the fluid dynamics in bubble columns is related to the prevailing bubble size distribution existing in the systems.In this respect,multiphase computational fluid dynamic simulations,in the Eulerian multi-fluid framework,are able to predict the local bubble size distributions and,thus,the global fluid dynamics from the fluid flow conditions and by applying modeling closured.In particular,in in“industrial-scale”reactors,owing to the large gas sparger openings,the“pseudo-homogeneous”flow regimedcharacterized by a wide spectrum of bubble sizesdis typically observed.Unfortunately,reliable predictions of the“pseudo-homogeneous”flow regime are limited up to now:one important drawback concerns the selection of appropriate models for the coalescence and break-up.A set of closure relations was collected at the Helmholtz-Zentrum Dresden-Rossendorf that represents the best available knowledge.Recently,the authors have extended the validation of this set of closure relations to the“pseudo-homogeneous”flow regime,by comparing the numerical predictions to a comprehensive experimental dataset(gas holdup,bubble size distributions and local flow measurements).Unfortunately,the previous study suffers from some limitations;in particular,in the previous experimental dataset,the bubble size distributions concerned only one axial position and a detailed characterization of the gas sparger was missing.This study contributes to the existing discussion and proposed a step ahead in the study of the“pseudo-homogenous”flow regime.To this end,we propose an experimental study,to improve the comprehensive dataset previously obtained.The novel datasetdobtained for two gas velocitiesdconcerns bubble size distributions at different axial and radial positions and a precise characterization of the gas sparger.The comprehensive bubble size distribution dataset may serve as basis to improve the coalescence and break-up closures;conversely,the precise characterization of the gas sparger served as an improved input to the numerical simulations.The numerical results,with two different lift force implementations,have been compared with the whole dataset and have been critically analyzed.Reasons for the discrepancies between the numerical results and the experimental data have been identified and may serve as basis for future studies.

Eulerian simulations of bubbling and jetting regimes in a fluidized bed

The mode of gas-injection is known to influence the local bubbling and jetting behavior in gas-solid fluidized beds.The resultant bubbling behavior influences the mixing and distribution of the gas and solid phases,which in turn can influence heat and mass transfer,and reaction performance in large-scale gas-solid fluidized beds.In the present work,we simulated unary gas-solid flow of particles differing in density,fluidized using uniform and two-jet distributors at different UG.The predictions are validated using the measured local gas-phase area fraction fluctuations,bubble size distribution,and bubble rise velocity.The effect of the models used for calculation of gas-solid drag(βgs),solids frictional pressure(Psf),and specularity coefficient(φ)on the bubbling characteristics under dense and dilute flow con-ditions are analysed.Under dense bed condition(UG=1.1 Umf),an increase in the Psf and φ led to an increase in solids viscosity,which in turn led to a decrease in the bubble rise velocity and size.In the case of the two-jet distributor,an increase in βgs predicted merging of the larger jets and formation of larger bubbles.Further,to predict the different jetting regimes(isolated jets,breakage/merging of jets,and generation of larger bubbles)at different UG correctly,we show that different βgs models are required.Whereas,in the case of gas-solid flows comprised of particles of different density fluidized with the uniform distributor,a single βgs model predicted the bubbling characteristics reasonably well with measurements.