A stochastic model of bubble distribution in gas–solid fluidized beds

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.

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.

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.

Impact of a Mobile Void within a Charge Distribution on the Electric Field

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.

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.

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.

Numerical analysis of residence time distribution of solids in a bubbling fluidized bed based on the modified structure-based drag model

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.

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.

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.