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.

Effects of processing parameters on microstructure of semi-solid slurry of AZ91D magnesium alloy prepared by gas bubbling

The semi-solid slurry of AZ91 D magnesium alloy was prepared by gas bubbling process.The effect of processing parameters,including gas flow rate,cooling rate and stirring end temperature,on microstructure of AZ91 D semi-solid slurry was investigated.With increasing the gas flow rate from 0 to 5 L/min,the average size of primary α-Mg particles decreases from 119.1 to77.2μm and the average shape factor increases continuously from 0.1 to 0.596.The formation of non-dendritic primary α-Mg particles during gas bubbling is the result of combined effects of dendrite fragmentation and copious nucleation.With increasing the cooling rate from 3.6 to 14.6℃/min,the average particle size of primary α-Mg phase decreases from 105.0 to 68.1μm while the average shape factor peaks at 9.1℃/min.Both high and low cooling rates can induce dendritic growth of primary α-Mg particles.Changing the stirring end temperature from 590 to 595℃ has little effect on the average size and shape factor of primary α-Mg particles in AZ91 D semi-solid slurry.The insensitivity of semi-solid microstructures to the stirring end temperature is attributed to the sufficient quantity of primary particles formed in the melt.

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.

A pilot-scale jet bubbling reactor for wet flue gas desulfurization with pyrolusite

MnO2 in pyrolusite can react with SO2 in flue gas and obtain by-product MnSO4· H2O. A pilot scale jet bubbling reactor was applied in this work. Different factors affecting both SO2 absorption efficiency and Mn2^＋ extraction rate have been investigated, these factors include temperature of inlet gas flue, ration of liquid/solid mass flow rate（ L/S）, pyrolusite grade, and SO2 concentration in the inlet flue gas. In the meantime, the procedure of purification of absorption liquid was also discussed. Experiment results indicated that the increase of temperature from 30 to 70 K caused the increase of SO2 absorption efficiency from 81.4% to 91.2%. And when SO2 concentration in the inlet flue gas increased from 500 to 3000 ppm, SO2 absorption efficiency and Mn2^＋ extraction rate decreased from 98.1% to 82.2% and from 82.8% to 61.7%, respectively. The content of MnO2 in pyrolusite had a neglectable effect on SO2, absorption efficiency. Low L/S was good for both removal of SO2 and Mn2^＋ extraction. The absorption liquid was filtrated and purified to remove Si, Mg, Ca, Fe, Al and heavy metals, last product MnSO4· H2O was obtained which quality could reach China GB1622-86, the industry grade standards.

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.

Experimental determination of gas holdup and volumetric mass transfer coefficient in a jet bubbling reactor

The hydrodynamics and mass transfer characteristics of a lab-scale jet bubbling reactor(JBR)including the gas holdup,volumetric mass transfer coefficient and specific interfacial area were assessed experimentally investigating the influence of temperature,pH and superficial gas velocity.The reactor diameter and height were 11 and 30 cm,respectively.It was equipped with a single sparger,operating at atmospheric pressure,20 and 40℃,and two pH values of 3 and 6.The height of the liquid was 23 cm,while the superficial gas velocity changed within 0.010-0.040 m·s^(-1)range.Experiments were conducted with pure oxygen as the gas phase and saturated lime solution as the liquid phase.The liquid-side volumetric mass transfer coefficient was determined under unsteady-state oxygen absorption in a saturated lime solution.The gas holdup was calculated based on the liquid height change,while the specific interfacial area was obtained by a physical method based on the bubble size distribution(BSD)in different superficial gas velocities.The results indicated that at the same temperature but different pH,the gas holdup variation was negligible,while the liquid-side volumetric mass transfer coefficient at the pH value of 6 was higher than that at the pH=3.At a constant pH but different temperatures,the gas holdup and the liquid-side volumetric mass transfer coefficients at 40℃were higher than that of the same at 20℃.A reasonable and appropriate estimation of the liquid-side volumetric mass transfer coefficient(kla)in a pilot-scale JBR was provided which can be applied to the design and scale-up of JBRs.

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.

Polymorph and morphology of CaCO_3 in relation to precipitation conditions in a bubbling system

Simulating the typical carbonation step in a mineral CO_2 sequestration, precipitated calcium carbonate(PCC) was prepared by bubbling CO_2 gas into a rich Ca solution. These carbonation reactions were conducted at three p H ranges, namely 10.0–9.0, 9.0–8.0, and 8.0–7.0, in which temperature and CO_2 flow rate are additional experimental variables. The PCC obtained in experiments was examined by Fourier transform infrared spectroscopy(FTIR)and X-ray diffraction(XRD). It was found that supersaturation determined by p H value and flow rate of CO_2 has significant influence on polymorph of PCC. Vaterite was preferably formed at high supersaturation, while dissolution of metastable vaterite and crystallization of calcite occurred at low supersaturation. High temperature is a critical factor for the formation of aragonite. At 70 °C, vaterite, calcite and aragonite were observed to coexist in PCC because transformation from vaterite to aragonite via calcite occurred at this temperature. Scanning electron microscopy(SEM) technology was performed on prepared PCC, and various morphologies consistent with polymorphs were observed.

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.

Validation of Dimensionless Parameters for Distinguishing between Homogeneous and Bubbling Fluidizations

The difference between homogeneous and bubbling fluidization behaviors has been studied for the past 70 years, where several researchers have reported on the influence of interparticle forces in fluidization. Although interparticle forces such as van der Waals forces are evident in a real system, these forces are not the determinant in homogeneous fluidization, which can be simulated without any interparticle forces. In our previous study, the difference in fundamental mechanisms of the two fluidization states was analytically determined with a dimensionless gravity term, comprising the Reynolds number, Archimedes number, and density ratio. Nevertheless, some researchers insist that interparticle forces are dominant and a hydrodynamic force is not dominant. In this study, a dimensional analysis was applied to obtain a dominant parameter for distinguishing two fluidizations. Furthermore, some parameters were examined by comparing the experimental data in previous studies. The results indicated that hydrodynamic force is the dominant factor and the dimensionless gravity term is the dominant parameter in differentiating the two fluidized states.

Bubbling to Jetting Transition during Argon Injection in Molten Steel

Bubbling to Jetting Transition is of the outmost importance in metallurgical processes given that the flow regime influences the refining rates, the refractory erosion, and the blockage of injection nozzles. Bubbling to jetting transition during subsonic bottom injection of argon in molten steel is studied here. The effect of the molten steel height, the injection velocity, the nozzle diameter, and the molten steel viscosity on the jet height and the bubbling to jetting transition is numerically analyzed using Computational Fluid Dynamics. Five subsonic argon injection velocities are considered: 5, 25, 50, 100 and 150 m/s. Three values of the metal height are taken into account, namely 1.5 m, 2 m and 2.5 m. Besides, three values of the nozzle diameters are considered: 0.001 m, 0.005 m and 0.01 m. Finally, three values of the molten steel viscosity are supposed: 0.0067, 0.1 and 1 kg/(m·s). It is observed that for the argon-molten steel system, the bubbling to jetting transition occurs for an injection velocity less than 25 m/s and that for the range of viscosities considered, the molten steel viscosity does not exert significant influence on the jet height and the bubbling to jetting transition. Due to the jet instability at subsonic velocities, a second transition, namely jetting to bubbling, is appreciated.

An Analysis on the Partial Bubbling in the Macroeconomic

The factors influencing the economy contain the disequilibrium in the actual economy and the price bubbling in the fictitious economy. These factors can transform to each other, so cannot be divided distinctly. The individuals will always have overmuch optimism on the profit of all kinds of investment, and this kind of conduct can induce the partial bubbling in the economy. If we cannot release the partial bubbling in time, it can accumulate and transform to the bubbling economy.

Bubbling Threat

The shift of China’s monetary policy stance from "moderately loose" to "prudent" in 2011 indicates curbing inflation and asset bubbles have become the Central Government’s top priority. But is China’s bubble problem short-term or long-term? Is it only monetary or related to economic structure? Is it the cause of China’s economic imbalance or the result? And what kind of deep-rooted problems in the macro economy does it reflect? All these questions call for deep thought,said Zhang Monan,a

Lance Design for Argon Bubbling in Molten Steel

Three lance designs for argon bubbling in molten steel are presented. Bottom bubbling is considered too. Geometries considered are straight-shaped, T-shaped, and disk-shaped. The bubbling behavior of these lances is analyzed using Computational Fluid Dynamics, so transient three dimensional, isothermal, two-phase, numerical simulations were carried out. Using the numerical results, the bubble distribution and the open eye area are analyzed for the considered lance geometries. The plume volume is calculated from the open eye area and the lance immersion depth using geometrical considerations. Among the three lance designs considered, disk-shaped lance has the bigger plume volume and the smaller mixing time. As the injection lance is deeper immersed, the power stirring is increased and the mixing time is decreased.

Micro-flow structure at regime transition from bubbling to turbulent fluidization in a fluidized bed

Gas-solid fluidized beds have found extensive utilization in frontline manufacturing,in particular as low-velocity beds.The fluidization status,the bubbling or turbulent flow regime and the transition in between,determine the system performance in practical applications.Though the convoluted hydrodynamics are quantitively evaluated through numerous data-processing methodologies,none of them alone can reflect all the critical information to identify the transition from the bubbling to the turbulent regime.Accordingly,this study was to exploit a coupling data processing methodology,in the combination of standard deviation,power spectrum density,probability density function,wavelet transform,and wavelet multiresolution method,to jointly explain the micro-flow structure at the regime transition from bubbling to turbulent fluidization.The transient differential pressure fluctuation was measured for the evaluation in a fluidized bed(0.267 m i.d.×2.5 m height)with FCC catalysts(d_(p)=65μm,ρ_(p)=1780kg/m^(3))at different superficial gas velocities(0.02–1.4 m/s).The results show that the onset of turbulent fluidization starts earlier in the top section of the bed than in the bottom section.The wavelet decomposition displays that the fluctuation of differential pressure mainly concentrates on the sub-signals with an intermediate frequency band.These sub-signals could be synthesized into three types of scales(micro-scale,meso-scale,and macro-scale),representing the multi-scale hydrodynamics in the fluidized bed.The micro-scale signal has the characteristic information of bubbling fluidization,and the characteristic information of turbulent fluidization is mainly represented by the meso-scale signal.This work provides a systematic comprehension of fluidization status assessment and serves as an impetus for more coupling analysis in this sector.

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.

A model for predicting the segregation directions of binary Geldart B particle mixtures in bubbling fluidized beds

In gas fluidization processes involving different types of particles,the mixing or segregation behavior of the solid mixture is crucial to the overall outcome of the process.This study develops a model to predict the segregation directions of binary mixtures of Geldart B particles with density and size differences in bubbling fluidized beds.The proposed model was established by combining the particle segregation model,a previous particle segregation model,with a derived bed voidage equation of the bubbling fluidization based on the two-phase theory.The model was then analyzed with different function graphs of the model equations under various conditions.The results indicated that an increase in gas velocity or volume fraction of larger particles would strengthen size segregation,causing the larger and less dense components to descend.To validate the model,42 sets of data collected from 6 independent literature sources were compared with the predictions of the model.When the gas velocities were below 3.2 times the minimum gas velocity,the predictions were consistent with experimental results.This study has shed new light on the mechanisms of particle segregation in binary fluidized systems and provides a theoretical foundation for designing and manipulating gas-solid fluidized reactors.

Fluidization and bubbling behavior of potash particles in a deep fluidized bed

Most existing models for predicting bubble size and bubble frequency have been developed for freely bubbling fluidized beds.Accurate prediction of bubbling behavior in deep fluidized beds,however,has been a challenge due to the higher degree of bubble coalescence and break up,high probability of the slugging regime,partial fluidization,and chaotic behavior in the bubbling regime.In this work,the bubbling and fluidization behavior of potash particles was investigated in a deep fluidized bed employing a twin-plane electrical capacitance tomography(ECT)system.Solid volume fraction,average bubble velocity,average bubble diameter,and bubble frequency in both bubbling and slugging regimes were measured at two different bed height ratios(H/D=3.5 and H/D=3.78).This work is the first to illustrate a sequential view of bubbles at different superficial gas velocities in a fluidized bed.The results show that both the bubble diameter and rising velocity increased with increasing the superficial gas velocity for the two bed heights,with larger values observed in the deeper bed compared to the shallower one.Predicted values for bubble diameter,bubble rise velocity and bubble frequency from different models are compared with the experimental data obtained from the ECT system in this work.Good agreement has been achieved between the values predicted by the previous models and the experimental data for the bubble diameter and bubble rise velocity with an average absolute deviation of 16%and 15%for the bed height of 49 cm and 13%and 8%for the bed height of 53 cm,respectively.

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.

Bubbling solutions of fourth order mean field equations on S^(4)

In this paper,we first establish the existence of blow-up solutions with two antipodal points of the fourth order mean field equations on S^(4).Moreover,we construct non-axially symmetric solutions with blow-up points at the vertices of regular configurations,i.e.,equilateral triangles on a great circle,regular tetrahedrons,cubes,octahedrons,icosahedrons and dodecahedrons.The bubbling rates of these blow-up solutions rely on various bubbling configurations.