Two sample applications of a classical isoperimetric problem of the calculus of variations to fluid mechanical problems in fluidization and spouting

This paper is devoted to outlining precisely the basic mathematics of a classical isoperimetric problem of the calculus of variations and showing how significant fluid mechanical problems in fluidization and spouting can be addressed using this approach.     

Complementarity of CFD, experimentation and reactor models for solving challenging fluidization problems

Experimentalists, numerical modellers and reactor modellers need to work together, not only just for validation of numerical codes, but also to shed fundamental light on each other＇s problems and underlying assumptions. Several examples are given, Experimental gas axial dispersion data provide a means of choosing the most appropriate boundary condition （no slip, partial slip or full slip） for particles at the wall of fluidized beds. CFD simulations help to identify how close ＂two-dimensional＂ experimental columns are to being truly two-dimensional and to representing three-dimensional columns. CFD also can be used to provide a more rational means of establishing assumptions needed in the modelling of two-phase fluidized bed reactors, for example how to deal with cases where there is a change in molar flow （and hence volumetric flow） as a result of chemical reactions.     

Modeling and scale analysis of gaseous fuel reactors in chemical looping combustion systems

This work investigates the scale-up of chemical looping combustion (CLC), a next-generation technology for carbon capture and storage, to the industrial scale. The study focused on the bottom bed of the unit, which was considered to be the critical region during scale-up due to the large solids inventory in this zone combined with relatively inefficient gas–solids contact. Two CLC reactors of vastly different sizes (bench and utility scale) were studied to discern their difference related to scale-up via a one-dimensional model. This model considered kinetics that varied with the degree of oxidation and population distribution of the oxygen carriers, the mixing of which accounts for both convective and dispersive transport. The model was validated against bench scale data, and was used to evaluate the performance of a 1000 MW_th CLC fuel reactor using either syngas or methane as fuels. Sensitivity analyses were also carried out with this model to determine the effects of several parameters on fuel conversion, including solids circulation, oxygen carrier reactivity, bed height, and maximum bubble size. The results show that the mass transfer of gas from bubbles to the emulsion phase represents a significant limiting factor for fuel conversion in the bottom bed of a utility scale fuel reactor.     

5.12汶川大地震诱发大型崩滑灾害动力特征初探

对乙炔氧气混合气体中爆轰波与激波的正面对撞现象的实验研究是以高速摄影获 取两波对撞的x-t纹影图,以烟迹板记录对撞中的爆轰胞格图案,并基于激波 理论和经典CJ爆轰理论求解了两波对撞的稳态解并探寻其规律. 研究发现透射波系包括一道激波和爆轰波, 以及紧随爆轰波后的稀疏波区,这一结果对应于一维理论分析中的CJ解. 透射波系基本不受 初始压强影响;初始温度也只成比例地改变流场整体速度,温度越高,速度越快;对波系起 实质影响作用的是入射激波强度,激波越强,则整个透射流场呈现偏向激波的趋势;理论分 析还指出,稀疏波区的出现不可避免,当激波强度趋于声波稀疏波区趋于消失,激波越强则 疏波区趋于扩大. 两波对撞存在一个有限的转变阶段,透射爆轰首先减缓,接着迅速迸发为 过驱爆轰,然后再逐渐平衡为CJ爆轰. 对于强不稳定的燃气,对撞后爆轰波在空间上的发展 极不均衡,一些区域发生火焰面与诱导激波的严重脱离,随后的火焰面失稳发展为诱导激波 区内的爆轰波,实验观察到了这种爆轰在烟迹板上留下的极为精细的迹线.     

CFD simulation of gas–solid flow with a cluster structure-dependent drag coefficient model in circulating fluidized beds

To model the effect of clusters on hydrodynamics of gas and particles phases in risers, the interfacial drag coefficient is taken into account in computational fluid dynamic simulations by means of a two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are described by the multi-scale resolution approach. The model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) in the full range of Reynolds number. The model of CSD drag coefficient is then incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. The distributions of volume fraction and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature.     

Modeling of particle transport and combustion phenomena in a large-scale circulating fluidized bed boiler using a hybrid Euler-Lagrange approach

The constantly developing fiuidized combustion technology has become competitive with a conventional pulverized coal （PC） combustion. Circulating fluidized bed （CFB） boilers can be a good alternative to PC boilers due to their robustness and lower sensitivity to the fuel quality. However, appropriate engineering tools that can be used to model and optimize the construction and operating parameters of a CFB boiler still require development. This paper presents the application of a relatively novel hybrid Euler-Lagrange approach to model the dense gas-solid flow combined with a combustion process in a large-scale indus- trial CFB boiler. In this work, this complex flow has been resolved by applying the ANSYS FLUENT 14.0 commercial computational fluid dynamics （CFD） code. To accurately resolve the multiphase flow, the original CFD code has been extended by additional user-defined functions. These functions were used to control the boiler mass load, particle recirculation process （simplified boiler geometry）, and interphase hydrodynamic properties. This work was split into two parts. In the first part, which is referred to as pseudo combustion, the combustion process was not directly simulated. Instead, the effect of the chemi- cal reactions was simulated by modifying the density of the continuous phase so that it corresponded to the mean temperature and composition of the flue gases, In this stage, the particle transport was simu- lated using the standard Euler-Euler and novel hybrid Euler-Lagrange approaches, The obtained results were compared against measured data, and both models were compared to each other. In the second part, the numerical model was enhanced by including the chemistry and physics of combustion. To the best of the authors＇ knowledge, the use of the hybrid Euler-Lagrange approach to model combustion is a new engineering application of this model, In this work, the combustion process was modeled for air-fuel combustion. The simulation results were compared with experimental data.     

Determination of hydrodynamic behavior of gas–solid fluidized beds using statistical analysis of acoustic emissions

In the processes involving the movement of solid particles, acoustic emissions are caused by particle friction, collision and fluid turbulence. Particle behavior can therefore be monitored and characterized by assessing the acoustic emission signals. Herein, extensive measurements were carried out by microphone at different superficial gas velocities with different particle sizes. Acoustic emission signals were processed using statistical analysis from which the minimum fluidization velocity was determined from the variation of standard deviation, skewness and kurtosis of acoustic emission signals against superficial gas velocity. Initial minimum fluidization velocity, corresponding to onset of fluidization of finer particles in the solids mixture, at which isolated bubbles occur, was also detected by this method. It was shown that the acoustic emission measurement is highly feasible as a practical method for monitoring the hydrodynamics of gas–solid fluidized beds.     

Time-series analysis of pressure fluctuations in gas–solid fluidized beds – A review

This work reviews methods for time-series analysis for characterization of the dynamics of gas–solid fluidized beds from in-bed pressure measurements for different fluidization regimes. The paper covers analysis in time domain, frequency domain, and in state space. It is a follow-up and an update of a similar review paper written a decade ago. We use the same pressure time-series as used by Johnsson et al. (2000). The paper updates the previous review and includes additional methods for time-series analysis, which have been proposed to investigate dynamics of gas–solid fluidized beds. Results and underlying assumptions of the methods are discussed.     

Effect of coefficient of restitution in Euler-Euler CFD simulation of fluidized-bed hydrodynamics

Collision between particles plays an important role in determining the hydrodynamic characteristics of gas-solid flow in a fluidized bed.In the present work,earlier work(Loha,Chattopadhyay. Chatterjee,2013) was extended to study the effect of the elasticity of particle collision on the hydrodynamic behavior of a bubbling fluidized bed filled with 530-μm particles.The Eulerian-Eulerian two-fluid model was used to simulate the hydrodynamics of the bubbling fluidized bed.where the solid-phase properties were calculated by applying the kinetic theory of granular flow.To investigate the effect of the elasticity of particle collision,different values of the coefficient of restitution were applied in the simulation and their effects were studied in detail.Simulations were performed for two different solid-phase wall boundary conditions.No bubble formation was observed for perfectly elastic collision.The bubble formation started as soon as the coefficient of restitution was set below 1.0,and the space occupied by bubbles in the bed increased with a decrease in the coefficient of restitution.Simulation results were also compared with experimental data available in the literature,and good agreement was found for coefficients of restitution of 0.95 and 0.99.     

A new drag model for TFM simulation of gas-solid bubbling fluidized beds with Geldart-B particles

In this work, a new drag model for TFM simulation in gas-solid bubbling fluidized beds was proposed, and a set of equations was derived to determine the meso-scale structural parameters to calculate the drag characteristics of Geldart-B particles under low gas velocities. In the new model, the meso-scale structure was characterized while accounting for the bubble and meso-scale structure effects on the drag coefficient. The Fluent software, incorporating the new drag model, was used to simulate the fluidization behavior. Experiments were performed in a Plexiglas cylindrical fluidized bed consisting of quartz sand as the solid phase and ambient air as the gas phase. Comparisons based on the solids hold-up inside the fluidized bed at different superficial gas velocities, were made between the 2D Cartesian simulations, and the experimental data, showing that the results of the new drag model reached much better agreement with exoerimental data than those of the Gidasoow dra~ model did.