Applicability of Markov chain-based stochastic model for bubbling fluidized beds

A Markov chain-based stochastic model （MCM） is developed to simulate the movement of particles in a 2D bubbling fluidized bed （BFB）. The state spaces are determined by the discretized physical cells of the bed, and the transition probability matrix is directly calculated by the results of a discrete element method （DEM） simulation. The Markov property of the BFB is discussed by the comparison results calculated from both static and dynamic transition probability matrices. The static matrix is calculated based on the Markov chain while the dynamic matrix is calculated based on the memory property of the particle movement. Results show that the difference in the trends of particle movement between the static and dynamic matrix calculation is very small. Besides, the particle mixing curves of the MCM and DEM have the same trend and similar numerical values, and the details show the time averaged characteristic of the MCM and also expose its shortcoming in describing the instantaneous particle dynamics in the BFB.

CFD simulation of bubbling and collapsing characteristics in a gas-solid fluidized bed

Computational Fluid Dynamics （CFD） has become an alternative method to experiments for understanding the fluid dynamics of multiphase flow. A two-fluid model, which contains additional terms in both the gas- and solid-phase momentum equations, is used to investigate the fluidization quality in a fluidized bed. A case study for quartz sand with a density of 2,660 kg/m^3 and a diameter of 500 μm, whose physical property is similar to a new kind of catalyst for producing clean fuels through the residue fluid catalytic cracking process, is simulated in a two-dimensional fluidized bed with 0.57 m width and 1.00 m height. Transient bubbling and collapsing characteristics are numerically investigated in the platform of CFX 4.4 by integrating user-defined Fortran subroutines. The results show that the fluidization and collapse process is in fair agreement with the classical theory of Geldart B classification, but the collapse time is affected by bubbles at the interface between the dense phase and freeboard.

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.

Comparative analysis on gas–solid drag models in MFIX-DEM simulations of bubbling fluidized bed

In this study,the open-source software MFIX-DEM simulations of a bubbling fluidized bed(BFB)are applied to assess nine drag models according to experimental and direct numerical simulation(DNS)results.The influence of superficial gas velocity on gas–solid flow is also examined.The results show that according to the distribution of time-averaged particle axial velocity in y direction,except for Wen–Yu and Tenneti–Garg–Subramaniam(TGS),other drag models are consistent with the experimental and DNS results.For the TGS drag model,the layer-by-layer movement of particles is observed,which indicates the particle velocity is not correctly predicted.The time domain and frequency domain analysis results of pressure drop of each drag model are similar.It is recommended to use the drag model derived from DNS or fine grid computational fluid dynamics–discrete element method(CFD-DEM)data first for CFD-DEM simulations.For the investigated BFB,the superficial gas velocity less than 0.9 m·s^(-1) should be adopted to obtain normal hydrodynamics.

A Theoretical Model for the Size Prediction of Single Bubbles Formed under Liquid Cross-flow

The size of initial bubbles is an important factor to the developed bubble size distribution in a gas-liquid contactor. A liquid cross-flow over a sparger can produce smaller bubbles, and hereby enhance the performance of contactor. A one stage model by balancing the forces acting on a growing bubble was developed to describe the formation of the bubble from an orifice exposed to liquid cross-flow. The prediction with this model agrees with the experimental data available in the literatures, and show that orifice size strongly affects the bubble size. It is showed that the shear-lift force, inertia force, surface tension force and buoyancy force are major forces, and a simplified mathematical model was developed, and the detachment bubble diameter can be predicted with accuracy of <±21%.

Numerical simulation and experimental verification of bubble size distribution in an air dense medium fluidized bed

Bubble size distribution is the basic apparent performance and obvious characteristics in the air dense medium fluidized bed (ADMFB). The approaches of numerical simulation and experimental verification were combined to conduct the further research on the bubble generation and movement behavior. The results show that ADMFB could display favorable expanded characteristics after steady fluidization. With different particle size distributions of magnetite powder as medium solids, we selected an appropriate prediction model for the mean bubble diameter in ADMFB. The comparison results indicate that the mean bubble diameters along the bed heights are 35 mm < D b < 66 mm and 40 mm < D b < 69 mm with the magnetite powder of 0.3 mm+0.15mm and 0.15mm+0.074mm, respectively. The prediction model provides good agreements with the experimental and simulation data. Based on the optimal operating gas velocity distribution, the mixture of magnetite powder and <1mm fine coal as medium solids were utilized to carry out the separation experiment on 6-50mm raw coal. The results show that an optimal separation density d P of 1.73g/cm 3 with a probable error E of 0.07g/cm 3 and a recovery efficiency of 99.97% is achieved, which indicates good separation performance by applying ADMFB.

Numerical investigation for the suitable choice of bubble diameter correlation for EMMS/bubbling drag model

Mesoscale bubbles exist inherently in bubbling fluidized beds and hence should be considered in the constitutive modeling of the drag force.The energy minimization multiscale bubbling(EMMS/bubbling)drag model takes the effects of mesoscale structures(i.e.,bubbles)into the modeling of drag coefficient and thus improves the coarse-grid simulation of bubbling and turbulent fluidized beds.However,its dependence on the bubble diameter correlation has not been thoroughly investigated.The hydrodynamic disparity between homogeneous and heterogeneous fluidization is accounted for by the heterogeneity index,H_(d),which can be affected by choice of bubble diameter correlation.How this choice of bubble diameter correlation influences the model prediction calls for further fundamental research.This article incorporated seven different bubble diameter correlations into EMMS/bubbling drag model and studied their effects on H_(d).The performance of these correlations has been compared with the correlation used previously by EMMS/bubbling drag model.We found that some of the correlations predicted lower Hd by order of a magnitude than the correlation used by the original EMMS/bubbling drag.Based on such analysis,we proposed a modification in the EMMS drag model for bubbling and turbulent fluidized beds.A computational fluid dynamics(CFD)simulation using two-fluid model with the modified EMMS/bubbling drag model was performed for two bubbling and one turbulent fluidized beds.Voidage distribution,time averaged solid concentration and axial solid concentration profiles were studied and compared with the previous version of the EMMS/bubbling drag model and experimental data.We found that the right choice of bubble diameter correlations can significantly improve the results for CFD simulations.

A model for predicting bubble rise velocity in a pulsed gas solid fluidized bed

Bed stability, and especially the bed density distribution, is affected by the behavior of bubbles in a gas solid fluidized bed. Bubble rise velocity in a pulsed gas-solid fluidized bed was studied using photographic and computational fluid dynamics methods. The variation in bubble rise velocity was investigated as a function of the periodic pulsed air flow. A predictive model of bubble rise velocity was derived: ub=ψ(Ut+Up-Umf)+kp(gdb)(1/2). The software of Origin was used to fit the empirical coefficients to give ψ = 0.4807 and kp = 0.1305. Experimental verification of the simulations shows that the regular change in bubble rise velocity is accurately described by the model. The correlation coefficient was 0.9905 for the simulations and 0.9706 for the experiments.

Effect of bubbles addition on teetered bed separation

To improve the separation efficiency of a conventional Teetered Bed Separator(TBS) in beneficiation of fine coal with a wide size range,an Aeration TBS(A-TBS) was proposed in this investigation.The bubbles were introduced to A-TBS by a self-priming micro-bubble generator.This study theoretically analyzed the effect of bubbles on the difference in hindered settling terminal velocity between different density particles,investigated the impact of superficial water velocity(V_(SW)) and superficial gas velocity(V_(Sg)) on bed fluidization,and compared the performance of the TBS and A-TBS in treating 1-0.25 mm size fraction particles.The results show that the expansion degree of fluidized bed which was formed by different size particles or has different initial height,is increased by the introduction of bubbles.Compared with the TBS,at the same level of clean coal ash content,the A-TBS shows an increase in the combustible recovery of clean coal,ash content of tailings,and practical separation density by 5.26%,6.56%,and 0.088 g/cm3 respectively,while it shows a decrease in the probable error(E_p) and V_(SW) by 0.031 and 3.51 mm/s,respectively.The addition of bubbles at a proper amount not only improves the separation performance of TBS,but also reduces the upward water velocity.

Multi-scale and multi-fractal analysis of pressure fluctuation in slurry bubble column bed reactor

The Daubechies second order wavelet was applied to decompose pressure fluctuation signals with the gas flux varying from 0.18 to 0.90 m3/h and the solid mass fraction from 0 to 20% and scales 1?9 detail signals and the 9th scale approximation signals. The pressure signals were studied by multi-scale and R/S analysis method. Hurst analysis method was applied to analyze multi-fractal characteristics of different scale signals. The results show that the characteristics of mono-fractal under scale 1 and scale 2, and bi-fractal under scale 3?9 are effective in deducing the hydrodynamics in slurry bubbling flow system. The measured pressure signals are decomposed to micro-scale signals, meso-scale signals and macro-scale signals. Micro-scale and macro-scale signals are of mono-fractal characteristics, and meso-scale signals are of bi-fractal characteristics. By analyzing energy distribution of different scale signals,it is shown that pressure fluctuations mainly reflects meso-scale interaction between the particles and the bubble.

TWO-AREA MODEL FOR BUBBLE DISTRIBUTION IN A TURBULENT FLUIDIZED BED OF FINE PARTICLES

The flow behavior of gas and solid was investigated in FCC simulator of φ710×4000/φ870×11000mm.The axial and radial distributions were detected with matrix fiber-opticprobes.It was found that the distribution of bubble diameter in the turbulent region of the fluidizedbed of fine particles was different from the results reported for lab-scale experiments.Radially therewere three areas,i.e.,the central(r/R=0-0.4),the intermittent or stable(r/R=0.4-0.8)and thenear wall(r/R=0.8-1.0)areas respectively.It was noticed that bubbles were almost non-existing atthe near wall area.Hence,according to the coalescence and splitting theory of bubbles,a two-areamodel of bubble diameter distribution was proposed and a dimensionless parameter(γ_M)regarded asan index for’quality’of fluidization was deduced.

AN EXPERIMENTAL RESEARCH ON BUBBLE PROPERTIES OF MAGNETIC FLUIDIZED BEDS BY MAGNETIC INDUCTIVE METHOD

In view of the fact that the existing methods of measuring bubble propertiesare difficult to be realized in magnetic fluidized beds,a new method,the magnetic induc-tive method,has been developed.With the help of this method the bubble properties inmagnetic fluidized beds were studied successfully,which concerned mainly with the influ-ence of magnetic intensity,single jet gas flow rate and main fluidizing gas flow rate onbubble frequency,velocity volume and coalescence or splitting.

The motion mechanism and characteristic of bubble in a pseudo-2D tapered fluidized bed

The different carbon nanotube(CNT)particles(^(@)A and^(@)V)were bed materials in the pseudo-2D tapered fluidized bed(TFB)with/without a distributor.A detailed investigation of the motion mechanism of bubbles was carried out.The high-speed photography and image analysis techniques were used to study bubble characteristic and mixing behavior in the tapered angle of TFB without a distributor.The fractal analysis method was used to analyze the degree of particles movement.Results showed that an S-shaped motion trajectory of bubbles was captured in the bed of^(@)V particles.The population of observational bubbles in the bed of^(@)V particles was more than that of^(@)A particles,and the bubble size was smaller in the bed of^(@)V particles than that of^(@)A particles.The motion mechanism of bubbles had been shown to be related to bed materials and initial bed height in terms of analysis and comparison of bubble diameter,bubble aspect ratio and bubble shape factor.Importantly,compared to the TFB with a distributor,the TFB without a distributor had been proved to be beneficial to the CNT fluidization according to the study of bubble characteristic and the degree of the particle movement.Additionally,it was found that the mixing behavior of^(@)V particles was better than^(@)A particles in the tapered angle of TFB without a distributor.

Numerical simulation on the fluidized bed gasification and CaO dechlorination of refuse derived fuel

A three-dimensional numerical model verified by previous experimental data is developed to simulate the fluidized bed gasification of refuse derived fuel （RDF）. The CaO dechlorination model obtained by the thermal gravity analysis （TGA） is coupled to investigate the process of CaO dechlorination. An Eulerian-Eulerian method is adopted to simulate the gas-solid flow and self-developed chemical reaction modules are used to simulate chemical reactions. Flow patterns, gasification results and dechlorination efficiency are obtained by numerical simulation. Meanwhile, simulations are performed to evaluate the effects of Ca/Cl molar ratio and temperature on dechlorination efficiency. The simulation results show that the presence of bubbles in the gasifier lowers the CaO dechlorination efficiency. Increasing the Ca/Cl molar ratio can enhance the dechlorination efficiency. However, with the temperature increasing, the dechlorination efficiency increases initially and then decreases. The optimal Ca/Cl molar ratio is in the range of 3. 0 to 3. 5 and the optimal temperature is 923K.

Fluidization characteristics of magnetic particles and determination of stable fluidization zone in magnetically fluidized bed

To determine and calculate the stable fluidization zone in a magnetically fluidized bed, the fluidization characteristics of magnetic particles are investigated. Four kinds of magnetic particles with different average diameters, ranging from 231 to 512 μm, are fluidized in the presence of magnetic fields with specified values of the intensity in the range of zero to 7330 A/m, and the particle fluidization curves are plotted. For marking the stable fluidization zone in the curves, the minimum bubbling velocities of particles are measured by the pressure-drop fluctuation. Based on the fluidization curves, the influences of the average particle diameter and magnetic field intensity on the zone are analyzed and discussed. A correlation to determine the stable fluidization zone is derived from the experimental data, using three dimensionless numbers, i. e., the ratio of magnetic potential to gravity potential, the Reynolds number and the Archimedes number. Compared with available data reported, it is shown that the correlation is more simplified to predict relative parameters for the bed operating in the state of stable fluidization under reasonable conditions.

bubble-based EMMS／PFB模型的建立及在加压流化床浓相段的应用

基于多尺度分解和能量消耗分析方法,结合压力下锥形分布板射流床气泡直径关联式,建立了一个适于加压流化床(PFB)的能量最小多尺度模型——bubble-based EMMS/PFB模型。应用此模型模拟一个二维加压射流床,分析了操作压力、位置高度、空隙率及剩余速度对非均匀因子的影响。通过模拟结果与实验数据的对比,发现该模型相比于Gidaspow模型,能够更准确地模拟加压射流床内颗粒浓度的分布状态及颗粒靠近壁面处的速度变化;将这种曳力模型应用到流化床浓相段的模拟,预测了床内颗粒浓度瞬时分布及沿轴向的时均值分布、颗粒的速度分布等流动行为,使流化床浓相段的气固流动行为可视化,对流化床的设计、放大有一定的指导作用。

基于含晕气泡曳力模型的鼓泡床流化行为分析

气固鼓泡流态化系统具有非平衡、非线性的多尺度特征。为研究含晕鼓泡床内复杂流动行为,利用含晕气泡多尺度曳力模型对三维鼓泡床反应器开展数值模拟,获得不同位置颗粒速度与体积分数的变化规律。对颗粒体积分数时间波动序列进行小波变换,分析轴向和径向位置颗粒脉动和气泡波动的变化。结果表明:基于含晕气泡的多尺度曳力模型能够较好地预测床内流动状态,床内整体呈现颗粒在中心上升而沿壁面下落的环-核流动形式;与颗粒速度波动相比,颗粒体积分数的波动频率更高且更加难以分辨;小波分析获得的颗粒相和气泡相的波动强度沿床高增加,但随着靠近壁面逐渐减弱;A类颗粒鼓泡床内气泡更强烈的破碎与聚并行为,使径向气泡分布较为均匀,能量分率径向差异较小;入口流速的增大增强了颗粒径向分布的非均匀性,且增大了颗粒相和气泡相波动信号的能量分率。

Hydrodynamics and OCM reaction performance in a bubbling fluidized bed reactor and a riser reactor

The reasonable reactor design is of great importance for increasing the C_(2) yield(C2H4 and C2H6)of the oxidative coupling of methane(OCM),and the OCM reactor should remove the heat released in reactions quickly and efficiently and minimize the consecutive reaction of ethylene to carbon oxides.The fluidized bed reactor is characterized by excellent heat transfer,superior mass transport,and large handling capacity,while fewer studies focused on large-scale fluidized bed reactors for the OCM reaction.Therefore,large cold-model experiments and computational fluid dynamics simulations were conducted to investigate hydrodynamics and the OCM reaction performance in a large-scale bubbling fluidized bed(BFB)and a large-scale riser.In the BFB reactor,consecutive reactions of ethylene are acute because of the strong gas back-mixing,high solids holdup,and non-uniform solids distribution.While the consecutive reactions of ethylene are negligible due to the plug flow structure and low solids holdup in the riser reactor.Further,both reactors can achieve isothermal operation for the OCM process.The C_(2) selectivity of 45.4% and C_(2) yield of 21.1% are obtained in the riser reactor,increasing by 20.3% and 5.8% individually than that in the BFB reactor.This study provides useful information and reference to the OCM reactor designandcommercialization.

Characterization of Pressure Signals in Fluidized Beds Loaded with Large Particles Using Wigner Distribution Analysis: Feasibility of Diagnosis of Agglomeration

An experimental verification is reported on the early predicting index of agglomeration in bubbling fluidized bed. Coarse quartz sand, which has the same density but larger diameter than the bed material, was used to simulate the initial agglomerated particle. Wigner distribution was used to analyze the pressure fuctuation of the tested bed, and the average amplitude of local domain frequency （LDF） and local peak weighted average frequency （LPWA） under different operating conditions were measured and compared. The results showed that the LDF is sensitive to the agglomeration phenomena and had quick response to the incipient agglomeration in fluidized beds. It can be concluded from the results that these two parameters could be taken as the characteristic indexes to the agglomeration in fuidized beds.

Effect of Gas Distributor Structure on Fluidization Characteristics in a Gas-Solid Fluidized Bed

In the present paper,the experimental method and computational fluid dynamics(CFD)method were used to investigate the effect of gas distributors with different orifice sizes and orifice pitches on fluidization characteristics in a gas-solid fluidized bed.The Euler-Euler two fluid model(TFM)approach based on the kinetic theory of granular flow(KTGF)and the standard k-epsilon turbulence model was employed in the numerical simulation by using ANSYS Fluent 15.0.The results showed that the orifice size and the orifice pitch of gas distributor had a significant influence on the flow characteristics in the gas-solid fluidized bed.With a decreasing orifice size and orifice pitch of gas distributor having the same opening area,the distributor pressure drop,the initial bubble size,and the height of dead zone just above the distributor were decreased,and the bed pressure drop was increased more than that of the larger orifice size and orifice pitch of distributors,the distribution of solid volume fraction was also more homogeneous for the smaller orifice size.