On the basis of the Langevin equation and the Fokker-Planck equation, a stochastic model of bubble distribution in a gas-solid fluidized bed was developed. A fluidized bed with a cross section of 0.3 m×0.02 m and...On the basis of the Langevin equation and the Fokker-Planck equation, a stochastic model of bubble distribution in a gas-solid fluidized bed was developed. A fluidized bed with a cross section of 0.3 m×0.02 m and a height of 0.8 m was used to investigate the bubble distribution with the photographic method. Two distributors were used with orifice diameters of 3 and 6 mm and opening ratios of 6.4% and 6.8%, respectively. The particles were color glass beads with diameters of O.3, 0.5 and 0.8 mm （Geldart group B particles）. The model predictions are reasonable in accordance with the experiment data. The research results indicated that the distribution of bubble concentration was affected by the particle diameter, the fluidizing velocity, and the distributor style. The fluctuation extension of the distribution of bubble concentration narrowed as the particle diameter, fluidizing velocity and opening ratio of the distributor increased. For a given distributor and given particles the distribution was relatively steady along the bed height as the fluidizing velocity changed.展开更多
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 ...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.展开更多
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 ...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.展开更多
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 b...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%.展开更多
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 ...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.展开更多
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 sim...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.展开更多
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 particl...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.展开更多
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...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.展开更多
The electric field of a 3D spherical uniform charge distribution embodying a spherical mobile void at an exterior point is calculated. The size of the void and its path is arbitrary. Specifically, three different traj...The electric field of a 3D spherical uniform charge distribution embodying a spherical mobile void at an exterior point is calculated. The size of the void and its path is arbitrary. Specifically, three different trajectories are analyzed. The movement of the void impacts the electric field so that the field becomes time-dependent. In terms of the chosen path and the size of the bubble, we evaluate the time-dependent electric field. The time profile of the field is calculated. Because of the computational challenges, the most of calculation is carried out utilizing a Computer Algebra System (CAS), specifically Mathematica [1]. This project makes the CAS an essential tool not only for calculating the field but for animating the features of the mobile void. An atlas of the study cases is included.展开更多
Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow ch...Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow characteristics including interfacial forces,void fraction distribution,and interfacial area transport.Throughout the flow progression,the BSD changes along the channel due to variations in pressure and interactions among bubbles.Accurately predicting the evolution of BSD can enhance the modeling of two-phase flow.This study presents a novel BSD evolution(BSDE) model,where the governing equation for the probability density function is formulated by considering the conservation of bubbles within a onedimensional control volume in the channel.The downstream BSD is predicted based on the upstream BSD and the effects of pressure variations and bubble interactions along the channel.To account for the multiscale nature of the two-phase flow,the bubbles are categorized into small groups(G_(1)) and large groups(G_(2)).Six distinct source term distributions for intra/inter bubble interactions have been developed.Each source term accounts for the distributions of consumed and generated bubbles,ensuring the conservation of bubble volume through constraints on model coefficients.The model has been tested on a tight-lattice rod bundle using experimental data,with deviations of less than 5% and 15% for G_(1)and G_(2) flow,respectively.Since the model development is independent of specific geometry,the framework of the BSDE model can also be effectively applied to channels of varying shapes.展开更多
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...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.展开更多
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 dispersi...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.展开更多
The bending moment acting on the overhung shaft of a gas-sparged vessel stirred by a Rushton turbine,as one of the results of fluid and structure interactions in stirred vessels,was measured using a moment sensor equi...The bending moment acting on the overhung shaft of a gas-sparged vessel stirred by a Rushton turbine,as one of the results of fluid and structure interactions in stirred vessels,was measured using a moment sensor equipped with digital telemetry.An analysis of the shaft bending moment amplitude shows that the amplitude distribution of the bending moment,which indicates the elasticity nature of shaft material against bending deformation,follows the Weibull distribution.The trends of amplitude mean,standard deviation and peak deviation characteristics manifest an "S" shape versus gas flow.The "S" trend of the relative mean bending moment over gas flow rate,depending on the flow regime in gas-liquid stirred vessels,resulted from the competition among the nonuniformity of bubbly flow around the impeller,the formation of gas cavities behind the blades,and the gas direct impact on the impeller when gas is introduced.A further analysis of the bending moment power spectral density shows that the rather low frequency and speed frequency are evident.The low-frequency contribution to bending moment fluctuation peaks in the complete dispersion regime.展开更多
The determination of bubble size distribution is a prerequisite for the study of gas-liquid two-phase flow characteristics in electrolytic cells.Here the departure diameter of hydrogen bubbles and oxygen bubbles and t...The determination of bubble size distribution is a prerequisite for the study of gas-liquid two-phase flow characteristics in electrolytic cells.Here the departure diameter of hydrogen bubbles and oxygen bubbles and their detachment process from a nickel wire electrode during water electrolysis are studied using high-speed photography.The results show that in industrial alkaline environment,the departure diameters of most hydrogen bubbles and oxygen bubbles are generally smaller than 60μm and 250μm with the current density ranges from 0.15 to 0.35A/cm^(2).The adhesion force of hydrogen bubbles on a nickel wire is found to be so weak that they can separate with a tiny size.The diameters of oxygen bubbles conform to normal distribution,and its distribution range widens with the increase of current density.The theoretical analysis show that the comprehensive conversion rate of current-to-bubble is unexpectedly low especially at low current densities,which may be attributed to the loss of gas components caused by bubble detachment mode.The majority of oxygen bubbles detach by a sudden bounce after coalescence,which may bring strong disturbance to the concentration boundary layer.This also indicates the coalescence-induced bubble departure mode may occupy a dominant position in the electrolyzers.展开更多
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 aid...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.展开更多
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 a...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.展开更多
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, wh...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.展开更多
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 ess...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.展开更多
The residence time distribution （RTD） of solids and the fluidized structure of a bubbling fluidized bed were investigated numerically using computational fluid dynamics simulations coupled with the modified structur...The residence time distribution （RTD） of solids and the fluidized structure of a bubbling fluidized bed were investigated numerically using computational fluid dynamics simulations coupled with the modified structure-based drag model. A general comparison of the simulated results with theoretical values shows reasonable agreement. As the mean residence time is increased, the RTD initial peak intensity decreases and the RTD curve tail extends farther. Numerous small peaks on the RTD curve are induced by the back- mixing and aggregation of particles, which attests to the non-uniform flow structure of the bubbling fluidized bed. The low value of t50 results in poor contact between phases, and the complete exit age of the overflow particles is much longer for back-mixed solids and those caught in dead regions. The formation of a gulf-stream flow and back-mixing for solids induces an even wider spread of RTD.展开更多
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 prevail...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.展开更多
文摘On the basis of the Langevin equation and the Fokker-Planck equation, a stochastic model of bubble distribution in a gas-solid fluidized bed was developed. A fluidized bed with a cross section of 0.3 m×0.02 m and a height of 0.8 m was used to investigate the bubble distribution with the photographic method. Two distributors were used with orifice diameters of 3 and 6 mm and opening ratios of 6.4% and 6.8%, respectively. The particles were color glass beads with diameters of O.3, 0.5 and 0.8 mm （Geldart group B particles）. The model predictions are reasonable in accordance with the experiment data. The research results indicated that the distribution of bubble concentration was affected by the particle diameter, the fluidizing velocity, and the distributor style. The fluctuation extension of the distribution of bubble concentration narrowed as the particle diameter, fluidizing velocity and opening ratio of the distributor increased. For a given distributor and given particles the distribution was relatively steady along the bed height as the fluidizing velocity changed.
基金supported by the National Natural Science Foundation of China(21908062)。
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.11674074 and 61701133).
文摘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.
基金West Virginia State Coal and Energy Research Bureau(WVCERB)the Department of Mining Engineering,West Virginia University
文摘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%.
基金the Tarbiat Modares University (TMU), the Iran Mineral Processing Research Center (IMPRC) and the IMIDRO for the technical assistance and financial support
文摘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.
基金the National Natural Science Foundation of China(Grant No.91434121)Ministry of Science and Technology of China(Grant No.2013BAC12B01)+1 种基金State Key Laboratory of Multiphase complex systems(Grant No.MPCS-2015-A-03)Chinese Academy of Sciences(Grant No.XDA07080301)
文摘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.
基金Supported by the National Natural Science Foundation of China(51676087)
文摘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.
文摘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.
文摘The electric field of a 3D spherical uniform charge distribution embodying a spherical mobile void at an exterior point is calculated. The size of the void and its path is arbitrary. Specifically, three different trajectories are analyzed. The movement of the void impacts the electric field so that the field becomes time-dependent. In terms of the chosen path and the size of the bubble, we evaluate the time-dependent electric field. The time profile of the field is calculated. Because of the computational challenges, the most of calculation is carried out utilizing a Computer Algebra System (CAS), specifically Mathematica [1]. This project makes the CAS an essential tool not only for calculating the field but for animating the features of the mobile void. An atlas of the study cases is included.
基金supported by the National Natural Science Foundation of China (12322510 and 12275174)the Shanghai Rising-Star Program (22QA1404500)+1 种基金the Science and Technology Commission of Shanghai Municipality (24DZ3100300)the Lingchuang Project of China National Nuclear Corporation
文摘Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow characteristics including interfacial forces,void fraction distribution,and interfacial area transport.Throughout the flow progression,the BSD changes along the channel due to variations in pressure and interactions among bubbles.Accurately predicting the evolution of BSD can enhance the modeling of two-phase flow.This study presents a novel BSD evolution(BSDE) model,where the governing equation for the probability density function is formulated by considering the conservation of bubbles within a onedimensional control volume in the channel.The downstream BSD is predicted based on the upstream BSD and the effects of pressure variations and bubble interactions along the channel.To account for the multiscale nature of the two-phase flow,the bubbles are categorized into small groups(G_(1)) and large groups(G_(2)).Six distinct source term distributions for intra/inter bubble interactions have been developed.Each source term accounts for the distributions of consumed and generated bubbles,ensuring the conservation of bubble volume through constraints on model coefficients.The model has been tested on a tight-lattice rod bundle using experimental data,with deviations of less than 5% and 15% for G_(1)and G_(2) flow,respectively.Since the model development is independent of specific geometry,the framework of the BSDE model can also be effectively applied to channels of varying shapes.
文摘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.
基金Project(2012BAB14B05)supported by National Key Technology Research and Development Program of the Ministry of Science and Technology of China
文摘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.
文摘The bending moment acting on the overhung shaft of a gas-sparged vessel stirred by a Rushton turbine,as one of the results of fluid and structure interactions in stirred vessels,was measured using a moment sensor equipped with digital telemetry.An analysis of the shaft bending moment amplitude shows that the amplitude distribution of the bending moment,which indicates the elasticity nature of shaft material against bending deformation,follows the Weibull distribution.The trends of amplitude mean,standard deviation and peak deviation characteristics manifest an "S" shape versus gas flow.The "S" trend of the relative mean bending moment over gas flow rate,depending on the flow regime in gas-liquid stirred vessels,resulted from the competition among the nonuniformity of bubbly flow around the impeller,the formation of gas cavities behind the blades,and the gas direct impact on the impeller when gas is introduced.A further analysis of the bending moment power spectral density shows that the rather low frequency and speed frequency are evident.The low-frequency contribution to bending moment fluctuation peaks in the complete dispersion regime.
基金support by the National Key R&D Program of China(2022YFB4202201)Ordos-Tsinghua Innovative&Collaborative Research Program in Carbon Neutrality,Science and Technology Department of Jiangsu Province under Grand BE2022040Support Plan for Young Excellent Talents of the Department of Energy and Power Engineering,Tsinghua University.
文摘The determination of bubble size distribution is a prerequisite for the study of gas-liquid two-phase flow characteristics in electrolytic cells.Here the departure diameter of hydrogen bubbles and oxygen bubbles and their detachment process from a nickel wire electrode during water electrolysis are studied using high-speed photography.The results show that in industrial alkaline environment,the departure diameters of most hydrogen bubbles and oxygen bubbles are generally smaller than 60μm and 250μm with the current density ranges from 0.15 to 0.35A/cm^(2).The adhesion force of hydrogen bubbles on a nickel wire is found to be so weak that they can separate with a tiny size.The diameters of oxygen bubbles conform to normal distribution,and its distribution range widens with the increase of current density.The theoretical analysis show that the comprehensive conversion rate of current-to-bubble is unexpectedly low especially at low current densities,which may be attributed to the loss of gas components caused by bubble detachment mode.The majority of oxygen bubbles detach by a sudden bounce after coalescence,which may bring strong disturbance to the concentration boundary layer.This also indicates the coalescence-induced bubble departure mode may occupy a dominant position in the electrolyzers.
文摘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.
文摘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.
文摘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.
基金gratefully acknowledged the financial supports by the National Natural Science Foundation of China(Grant No.20606021)Foundation for the Author of National Excellent Doctoral Dissertation of China(No.200757)the State Key Development Program for Basic Research Project of China(Grant No.2007CB714302).
文摘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.
文摘The residence time distribution （RTD） of solids and the fluidized structure of a bubbling fluidized bed were investigated numerically using computational fluid dynamics simulations coupled with the modified structure-based drag model. A general comparison of the simulated results with theoretical values shows reasonable agreement. As the mean residence time is increased, the RTD initial peak intensity decreases and the RTD curve tail extends farther. Numerous small peaks on the RTD curve are induced by the back- mixing and aggregation of particles, which attests to the non-uniform flow structure of the bubbling fluidized bed. The low value of t50 results in poor contact between phases, and the complete exit age of the overflow particles is much longer for back-mixed solids and those caught in dead regions. The formation of a gulf-stream flow and back-mixing for solids induces an even wider spread of RTD.
文摘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.
