Prediction of pressure fluctuations and minimum fluidization velocity of binary mixtures of geldart group b particles in bubbling fluidized beds

A simple method was proposed to find the pressure fluctuations of binary systems of Geldart Group B particles under bubbling fluidized bed conditions. The pressure fluctuations of binary systems could be predicted from the pressure fluctuations of the individual particles component which comprised the binary systems for completely mixed and partially mixed systems. The predicted pressure fluctuations could be used to calculate the minimum fluidization velocity of the binary systems. The predicted and experimental values of pressure fluctuations and the minimum fluidization velocity of binary systems were in fairly good agreement.     

气固搅拌流化床压力脉动的小波分析

在内径188 mm、静床高400 mm的搅拌流化床中,采用Geldart D类颗粒为实验物料,通过小波分析研究了不同气速和搅拌桨转速下搅拌流化床的压力脉动行为.实验发现,搅拌桨的转动作用促使在普通流化床中不易散式流态化的D类颗粒形成了散式流态化.随着气速的增加,第1尺度的小波能量特征值在某一个气速范围内发生急剧变化,进而提出了将该气速范围的下限和上限分别定义为临界鼓泡速度和充分鼓泡速度的判据.随搅拌转速的增加,散式流态化的气速操作范围线性增加.在鼓泡流态化状态下,气速是流化床气泡行为的主导因素,搅拌桨转速的增加对气泡产生的频率无明显影响但可使气泡的直径变小.     

气-固微型流化床压降特性及最小流化速度的实验研究

在内径3～20 mm的4个气-固微型流化床中,分别考察了A类和B类两种类型颗粒的流化特性,同时研究了床几何结构、操作条件、物相性质等各因素对其最小流化速度的影响.结果 表明,气-固微型流化床中的床层压降特性与颗粒类型密切相关,不同的流动状态下两种类型颗粒的流动特性存在显著地差异.在固定床阶段,与B类颗粒相比,A类颗粒与...     

Effect of cohesive powders on pressure fluctuation characteristics of a binary gas-solid fluidized bed

The effect of cohesive particles on the pressure fluctuations was experimentally investigated in a binary gas-solid fluidized bed. The pressure fluctuation signals were measured by differential pressure sensors under conditions of various weight percentages of cohesive particles. The cohesive particles increased the fixed bed pressure drop per unit height and decreased the minimum fluidization velocity. The Wen & Yu equation well predicts the minimum fluidization velocity of the binary system. The addition of cohesive particles slightly decreased the bubble size in bubbling flow regime when the cohesive particles and the coarse particles mixed well, while the bubble size greatly decreased when the cohesive particles agglomerated on the bed surface. The time series of pressure fluctuations was analyzed by using the methods of time domain, frequency domain and wavelet transformation. The normalized standard deviation of pressure fluctuations decreased with increasing weight percentages of cohesive particles. A wide bandwidth frequency of 0 to 1Hz got narrower with a single peak around 0.6Hz with an increase in proportion of the cohesive particles. The meso-energy and micro-energy of pressure fluctuations were decreasing with increasing cohesive particles proportions, which indicated that adding cohesive particles could reduce the energy dissipation of bubble and particle fluctuations.     

CFD simulation of gas-solid bubbling fluidized bed containing FCC particles

The hydrodynamics of a bubbling gas-solid fluidized bed of 57.4 μm FCC particles was simulated by using a state-of-the-art two-fluid model integrating the kinetic theory of granular flow for particulate phase stresses. The overestimation of the bed expansion was resolved by using a suitable scale factor in the drag model as suggested by McKeen and Pugsley (T.R. McKeen, T.S. Pugsley, Powder Technol., 129, 139 (2003)). This study showed that the method was appropriate in simulation of a gas-solid fluidized bed of Geldart A particles at high gas velocities (0.3 to 0.61 m/s). The reduction of computational time especially for simulation of large-scale systems was achieved. The time-averaged local voidage was compared with the experimental data and the trend of varying several parameters on the hydrodynamic of the bed was investigated. The simulation results showed both qualitative and quantitative agreement with the literature.     

磷矿颗粒流态化特性的实验研究

在高1 m、内径42mm的流化床中,对粒径54-600 μm、密度2 252-2 665 kg/m3的磷矿颗粒的流态化特性进行实验研究.实验结果表明:磷矿颗粒粒径和密度对磷矿颗粒流态化行为有较大影响,床层膨胀比随着磷矿颗粒粒径的增大而逐渐减小.当磷矿颗粒属于Geldart B类颗粒时,流化较好;而当颗粒平均粒径为82 ...     

Fluidization of Group B particles with a rotating distributor

A novel rotating distributor fluidized bed is presented. The distributor is a rotating perforated plate, with 1% open-area ratio. This work evaluates the performance of this new design, considering pressure drop, Δp, and quality of fluidization. Bed fluidization was easily achieved with the proposed device, improving the solid mixing and the quality of fluidization.In order to examine the effect of the rotational speed of the distributor plate on the hydrodynamic behavior of the bed, minimum fluidization velocity, U_mf, and pressure fluctuations were analyzed. Experiments were conducted in the bubbling free regime in a 0.19 m i.d. fluidized bed, operating with Group B particles according to Geldart's classification. The pressure drop across the bed and the standard deviation of pressure fluctuations, σ_p, were used to find the minimum fluidization velocity, U_mf. A decrease in U_mf is observed when the rotational speed increases and a rise in the measured pressure drop was also found. Frequency analysis of pressure fluctuations shows that fluidization can be controlled by the adjustable rotational speed, at several excess gas velocities.Measurements with several initial static bed heights were taken, in order to analyze the influence of the initial bed mass inventory, over the effect of the distributor rotation on the bed hydrodynamics.     

SHANNON ENTROPY ANALYSIS OF DYNAMIC BEHAVIOR OF GELDART GROUP B AND GELDART GROUP D PARTICLES IN A FLUIDIZED BED

Pressure fluctuations resulting from the nonuniform flow behavior of solid particles in a fluidized bed (0.06 m ID × 5.0 m in height) were analyzed using the Shannon entropy analysis method. Particles representing Geldart group B and group D types were employed in the experiments. Results show that with the increase of the superficial gas velocity, transitions between bubbling fluidization, turbulent fluidization, and fast fluidization were effectively detected based on the Shannon entropy of pressure fluctuations in the bed. Meanwhile, a higher static bed height resulted in a larger value of Shannon entropy due to the wall effect of smaller diameter column and the greater resistance to bubble formation affected by the increased weight of the bed. Comparison of the particle types indicated that despite the different details of their behavior, the overall trends were similar.     

导流筒分布器位置对环隙气升式气固环流反应器流体力学性能的影响

环流反应器的研究绝大多数都局限于气液、气液固系统,涉及气固环流反应器的研究较为稀少,且大多针对气升式气固环流反应器和喷动床。本文研究了一种处理A类粒子的环隙气升式气固环流反应器,考察了操作条件和导流筒分布器位置对床层密度分布、环流速度和质量流率的影响。发现将分布器位置下移后可以有效地改善区域的流化质量、减小滑移区,床层密度沿径向的分布得到了明显改善,颗粒环流质量流率有了明显提高;进气位置以上r/R<0.367的床层得到了良好的流化,但是0.367相似文献   

Statistical and deterministic chaos analysis of pressure fluctuations in a fluidized bed of polymer powders

The absolute and differential pressure fluctuations in gas-solid fluidized beds have been analyzed by statistical and deterministic chaos methods. Linear low-density polyethylene (LLDPE) particles with a mean diameter of 1.23 mm were used as a fluidizing material. The statistical methods are composed of the mean, standard deviation, skewness and kurtosis, and the deterministic methods are composed of autocorrelation, mutual information function, pseudo-phase space and correlation dimension. The minimum slug velocity of LLDPE particles is found to be 0.34 m/s by using the statistical and deterministic methods. As slugs appear and grow with increasing gas velocity, pressure fluctuations in the fluidized bed of LLDPE are oscillated and more periodic. This paper is dedicated to Professor Dong Sup Doh on the occasion of his retirement from Korea University.     

鼓泡流态化向湍动流态化过渡的判别

通过对流化床床层压力脉动信号的计算机在线分析,对气-固密相流化床中鼓泡流态化向湍动流态化的转变过程进行了研究.在较大范围内考察了颗粒重度、颗粒尺寸和床层结构条件对这一流型转变的影响.给出了鼓泡流化向湍动流化转变速度U_c的计算式:U_c/(gd_ρ)~(1/2)=[k(D_f/d_ρ)·((ρ_ρ-ρ_f)/ρ_f)]~n并察明Geldart的颗粒分类方法亦可反映床层流型转变的特征,从而赋予了Geldart颗粒分类方法以新的内涵.     

Practical validation of the two-fluid model applied to dense gas-solid flows in fluidized beds

This paper discusses the simulation of bubbling gas-solid flows by using the Eulerian two-fluid approach. Predictions of particle motion, bed expansion, bubble size and bubble velocity in bubbling beds containing Geldart B particles are compared with experimental results and correlations found in the literature. In addition, gas mixing in a bed of Geldart A particles is investigated.An in-house code has been developed based on the finite-volume method and the time-splitting approach using a staggered grid arrangement. The velocities in both phases are obtained by solving the 2D Reynolds-averaged Navier/Stokes equations using a partial elimination algorithm (PEA) and a coupled solver. The k-ε turbulence model is used to describe the turbulent quantities in the continuous phase.In general, the model predictions are in good agreement with experimental data found in the literature. Most important observations are: the level of the restitution coefficient was found to be crucial in order to obtain successful results from 2D axisymmetric simulations of a system containing Geldart B particles. Bubble size and bubble rise velocities are not as sensitive to the restitution coefficient. The turbulence model is of outmost importance concerning gas mixing in a fluidized bed of Geldart A particles.From these numerical analyzes an optimized granular flow two-fluid model can be designed for the purpose of simulating reactive systems in fluidized bed reactors.     

CFD study of the minimum bubbling velocity of Geldart A particles in gas-fluidized beds

The minimum bubbling velocity, which demarcates the homogeneous and heterogeneous fluidization regimes, plays a pivotal role in gas fluidization of Geldart A particles. We systematically study the effect of gas and particle properties on the minimum bubbling velocity of Geldart A particles in gas-fluidized beds using both Eulerian–Eulerian and Eulerian–Lagrangian models. We find that the minimum bubbling velocities as obtained from the simulations are in reasonable agreement with the well-known experimental correlation of Abrahamsen and Geldart (Powder Technology, 1980, 26: 35–46). To our best knowledge, this is the first time that the minimum bubbling velocity is correctly predicted by Eulerian–Eulerian models, without using an artificial ad-hoc modification of the gas–solid interaction force. Furthermore, we have performed a systematic investigation into the effect of the specific method that is used for determining minimum bubbling velocity. Our simulations show that the minimum bubbling velocity that would be obtained from the simulated bed contraction is larger than the one obtained from visual observation, which in its turn exceeds the one obtained from sudden change of standard deviation of pressure drop. We find that the abrupt change of the granular temperature with increasing superficial gas velocity may be a more suitable indicator for identifying the onset of heterogeneous fluidization.     

Investigation of Hydrodynamics of High‐Temperature Fluidized Beds by Pressure Fluctuations

Hydrodynamics of a gas‐solid fluidized bed at elevated temperatures was investigated by analyzing pressure fluctuations in time and frequency domains. Sand particles were fluidized with air at various bed temperatures. At a constant gas velocity, the standard deviation, power spectrum density function, and wide‐band energy of pressure fluctuations reach a maximum at 300 °C. Increasing the temperature to this value causes larger bubble sizes and after the bubbles reach their maximum size, they break into smaller bubbles. The Archimedes number decreases with higher temperature and the type of fluidization becomes closer to that of Geldart A boundary at this maximum temperature. Based on estimation of the drag force acting on the emulsion phase, it was concluded that 300 °C was a transition temperature at which the drag force reaches a minimum due to a significant change of interparticle and hydrodynamic forces.     

The role of contact stresses and wall friction on fluidization

Fluidization and defluidization experiments, where we increased the gas superficial velocity in small increments and then decreased it, were performed in tubes of different diameters to probe the role of wall friction on pressure drop and bed height. Such experiments, covering the regimes of packed bed, stable bed expansion and bubbling bed, were carried out for several different particles. The compressive yield strength of the particle assemblies at various volume fractions was determined by measuring the height of fully defluidized beds at various mass loading levels. The systematic effect of the tube diameter on pressure drop and bed height hysteresis could be rationalized in terms of a one-dimensional model that accounted for the effect of wall friction and path-dependent contact stresses in the particle phase. Bubbling seemed to set in when the yield stress in the particle assembly could be overcome by the inherent fluctuations. Our experiments, which focused primarily on gas velocities below the minimum bubbling conditions, did not reveal any dramatic change across the Geldart A-B boundary. This is consistent with the original observation by Geldart (Powder Technol. 7 (1973) 285). The distinct difference between beds of group A and B particles in the gently bubbling regime reported by Cody et al. (Powder Technol. 87 (1996) 211) is thus likely to be due to changes in the dynamics of the bubbles, as we observed no striking difference between these beds at gas velocities below minimum bubbling conditions.     

声场高温流化床流化特性

在内径50 mm、高1000 mm的声场高温鼓泡流化床中,研究Geldart A, B两类颗粒的流化特性,考察了床层温度、声波频率及声压级对流化床最小流化速度的影响. 结果表明,引入声场后,颗粒的最小流化速度随温度升高而下降;固定温度及频率,最小流化速度随声压级增大而减小;固定声压级与温度,颗粒最小流化速度随声波频率增大先减小后增大,存在一个最佳频率范围. 对床内压力波动信号进行分析,得出声场影响高温流化床流化质量的判据：当声压大于110 dB、频率在100~200 Hz范围内时压力波动偏差与最小流化速度值最小.     

Multi-scale analysis on particle-phase stresses of coarse particles in bubbling fluidized beds

Despite the restless efforts devoted to the hydrodynamics of bubbling fluidized beds, the particle-phase stress, which is one of the critical issues in modeling bubbling fluidized beds by the Eulerian approach, is not well understood. To address this problem, a mathematical model is developed to describe the kinetic properties of coarse particles, such as granular temperature and granular pressure, based on a multi-scale analysis of particle velocity fluctuation. Contributions from both high-frequency particle-scale fluctuations and low-frequency bubble-induced fluctuations are considered. It is proven to agree well with experimental data available up to date from bubbling fluidized beds for Geldart B and D particles.     

A second-order moment method of dense gas-solid flow for bubbling fluidization

A gas-solid two-fluid model with the second-order moment method is presented to close the set of equations applied to fluidization. With the kinetic theory of granular flow, transport equations for the velocity moments are derived for the particle phase. Closure equations for the third-order moments of velocity and for the fluid-particle velocity correlation are presented. The former is based on a modified model with the contribution of the increase of the binary collision probability, and the latter uses an algebraic model proposed by Koch and Sangani [1999. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. Journal of Fluid Mechanics 400, 229-263]. Boundary conditions for the set of equations describing flow of particles proposed by Strumendo and Canu [2002. Method of moments for the dilute granular flow of inelastic spheres. Physical Review E 66, 041304/1-041304/20] are modified with the consideration of the momentum exchange by collisions between the wall and particles. Flow behavior of gas and particles is performed by means of gas-solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized bed. Predictions are compared with experimental data measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168]. in the bubbling fluidized beds. The simulated second-order moment in the vertical direction is 1.1-2.5 [Muller, C.R., Holland, D.J., Sedeman, A.J., Scott, S.A., Dennis, J.S., Gladden, L.F., 2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and 1.1-4.0 [Yuu, S., Umekage, T., Johno, Y., 2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168] times larger than that in the lateral direction because of higher velocity fluctuations for particles in the bubble fluidized bed. The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. [2004. Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 Flour-Daniel lecture. Powder Technology 148, 123-141.] are computed from the simulated hydrodynamic velocities. The predictions are in agreement with experimental second-order moments measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and fluctuating velocity of particles measured by Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168].     

Determination of minimum fluidization velocity by pressure fluctuation measurement

Using the standard deviation of pressure fluctuations to find the minimum fluidization velocity, U_mf, avoids the need to de-fluidize the bed so U_mf, can be found for operational bubbling fluidized beds without disrupting the process provided only that the superficial velocity may be altered and that the bed remains in the bubbling fluidized state. This investigation has concentrated on two distinct aspects of the pressure fluctuation method for U_mf determination: (1) the minimum number of pressure measurements required to obtain reliable estimates of standard deviation has been identified as about 10000 and (2) pressure fluctuation measurements in the plenum below the gas distributor are suitable for U_mf determination so the problems of pressure probe clogging and erosion by bed particles may be avoided.     

一个基于双流体理论预测三维流化床内流动特性的数学模型(Ⅰ)气固体系散式或鼓泡流态化特性

将考虑拟平衡状态下颗粒与流体相互作用的附加力添加到基于双流体理论动量方程的数学模型中,用于Geldart A类物料散式流态化和B类物料鼓泡/床层塌落特性的三维数值模拟。该模型主要特点是将表征颗粒离散属性的特征长度视为颗粒直径的同一数量级且只需曳力系数一个关联式来封闭控制方程。在商业软件CFX4.4平台上,通过增加用户自定义子程序模拟了长0.2 m、宽0.2 m和高0.5 m流化床内瞬态流动特性。为了检验数学模型的实用性和数值模拟的可靠性,首先考察了两种A类物料在表观气速为u_mf和1.5u_mf下的散式流态化特性,结果展示出床层均匀膨胀的固有属性。随后,考察了扰动对A类物料在网格尺度上的局部空隙率和固体速度分布以及在设备尺度上床层压降的影响,探索了B类物料在网格尺度上鼓泡和床层塌落以及在设备尺度上鼓泡过程中床层压降和塌落过程中平均床层高度和相界面标准偏差的动态特性。上述模拟结果与经典的Geldart理论、前人的实验或模拟结果相吻合,说明该模型可以用来预报三维气固流化床内A类物料散式流态化和B类物料鼓泡及塌落的时空特性。