The role of scale resolution versus inter-particle cohesive forces in two-fluid modeling of bubbling fluidization of Geldart A particles

Coarse grid simulations of Geldart A particles in bubbling fluidized beds using standard two-fluid (TF) models, where the constitutive laws are based on the homogeneity of sub-grid scale structures, have been demonstrated to be unsuccessful due to the existence of significant sub-grid scale heterogeneous structures. However, a definite consensus on the fundamental origin of the failure is still lacking. Some claim that the existence of significant inter-particle cohesive forces results in the sub-grid scale heterogeneous structures which takes the form of agglomerates or clusters; others claim that the inter-particle cohesive forces are not the dominant factor, and that the poor performance of TF models is primarily due to the fact that the grid sizes and the time step used in previous studies are too coarse to fully resolve the bubbling structure. To this end, a short overview is firstly presented to discuss the role of scale resolution and inter-particle cohesive force in two-fluid modeling of Geldart A particles; We then qualitatively explain, using a state-of-the-art discrete particle method, why the methods based on the existence of aggregates or clusters work quite well, although the sub-grid scale structure is not properly identified, that is, the sub-grid scale structure takes the form of a bubble-emulsion phase.     

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.     

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.     

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。     

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.     

Numerical Simulation of Particle Segregation in Bubbling Gas‐Fluidized Beds

A multi‐fluid Eulerian model incorporating the kinetic theory of granular flow is used for the simulation of bubbling fluidized beds containing a binary mixture of Geldart B particles at low gas velocities. The cases of density, size and combined density/size segregation are investigated using computational fluid dynamic simulations. Various expressions for the drag force are evaluated for predicting different segregations. The simulation results show that summation of the particle‐particle drag force, i.e., the “hindrance effect” term, and the Stokes drag of particles, which is modified based on the Wen‐Yu drag model can be used for accurate simulation of a binary mixture of particles differing in size, density, or both. Bed expansion and dimensionless axial segregation profiles of CFD results are compared with the experimental data and good agreement is found.     

Coarse grid simulation of bed expansion characteristics of industrial-scale gas–solid bubbling fluidized beds

Two-fluid modeling of the hydrodynamics of industrial-scale gas-fluidized beds proves a long-standing challenge for both engineers and scientists. In this study, we suggest a simple method to modify currently available drag correlations to allow for the effect of unresolved sub-grid scale structures, by assuming that the particles inside each computational cell are presented in the form of a two-phase structure. This method would thus make it possible to simulate the hydrodynamics of industrial-scale bubbling fluidized beds of Geldart B and D particles with a coarse computational mesh. It is shown that with the proposed modification of the drag force correlation, the experimentally measured bed expansion characteristics of industrial-scale bubbling fluidized beds can be reasonably predicted at acceptable computational cost. Also the simulation result for the macroscopic solid circulation pattern is in qualitative agreement with the experimental data.     

Investigation of Drying Geldart D and B Particles in Different Fluidization Regimes

Drying of nylon (Geldart D) and expanded polystyrene (Geldart B) particles in fixed and fluidized beds were studied experimentally and theoretically. Fluidized bed dryers are sometimes operated at velocities beyond bubbling fluidization to mitigate against de‐fluidization of surface wet particles. It was found that theoretical analysis using three different drying methods could predict the constant‐drying rate at such velocities and also across the entire fluidization regimes (fixed bed, bubbling, slugging and turbulent fluidization) as long as the bed remains completely fluidized. Results also showed that the theoretical predictions were accurate beyond previously reported velocity limits in a laboratory scale dryer. During bubbling fluidization, the cross flow factor method was used effectively to predict the influence of bubble phase on drying rates. In the falling‐rate period, it is demonstrated that the drying behaviour of nylon at different gas velocities can be characterised by a single normalized drying curve.     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

Flow of gas and particles in a bubbling fluidized bed with a filtered two-fluid model

Numerical simulations of gas-particles flow in a bubble fluidized bed with two large eddy simulations of gas and solid phases are presented. For gas phase and solid phase, the sub-grid scale model for the viscosity is based on the Smagorinsky form. The sub-grid model for the particle pressure proposed by Igci et al. (2008) is modified by replacing the minimum fluidization velocity. The collisional interaction of particles is considered by the kinetic theory of granular flow. Flow behavior of gas and particles is performed by means of these two sub-grid scale models. The subgrid closure for the particle phase viscosity and pressure led to a qualitative change in the simulation results. Predictions are compared with experimental data measured by Yuu et al. (2000) and Taghipour et al. (2005) in the bubbling fluidized beds. The distributions of concentration and velocity of particles are predicted in the bubbling fluidized bed. The predicted filtered particle phase pressure increases and the filtered particle phase viscosity decreases with the increase of particle concentration. The qualitative importance of the model constant c_s of particles is demonstrated.     

A numerical study of fluidization behavior of Geldart A particles using a discrete particle model

This paper reports on a numerical study of fluidization behavior of Geldart A particles by use of a 2D soft-sphere discrete particle model (DPM). Some typical features, including the homogeneous expansion, gross particle circulation in the absence of bubbles, and fast bubbles, can be clearly displayed if the interparticle van der Waals forces are relatively weak. An anisotropy of the velocity fluctuation of particles is found in both the homogeneous fluidization regime and the bubbling regime. The homogeneous fluidization is shown to represent a transition phase resulting from the competition of three kinds of basic interactions: the fluid-particle interaction, the particle-particle collisions (and particle-wall collisions) and the interparticle van der Waals forces. In the bubbling regime, however, the effect of the interparticle van der Waals forces vanishes and the fluid-particle interaction becomes the dominant factor determining the fluidization behavior of Geldart A particles. This is also evidenced by the comparisons of the particulate pressure with other theoretical and experimental results.     

Why the two-fluid model fails to predict the bed expansion characteristics of Geldart A particles in gas-fluidized beds: A tentative answer

It is well known that two-fluid models (TFMs) can successfully predict the hydrodynamics of Geldart B and D particles. However, up to now, TFM have failed to accurately describe the hydrodynamics of Geldart A particles inside bubbling gas-fluidized beds: Researchers have reported that bed expansions are over-predicted by as much as 70%. In this work we show—for the first time—that TFM can predict the correct bed expansion, without any artificial modifications, provided that a sufficiently fine grid size and small time step is used. This suggests that the previously reported failure of TFM is mainly due to the lack of scale resolution, and that from a modeling point of view there is no fundamental difference between Geldart A particles and Geldart B and D particles.     

Tomographic imaging of a conical fluidized bed of dry pharmaceutical granule

Hydrodynamics in a conical fluidized bed were studied using electrical capacitance tomography (ECT) for a bimodal and mono-disperse particle size distribution (PSD) of dry pharmaceutical granule. The bimodal PSD exhibited a continuous distribution with modes at 168 and 1288 μm and contained approximately 46% Geldart A, 32% Geldart B and 22% Geldart D particles by mass. The mono-disperse PSD had a mean particle size of 237 μm and contained approximately 71% Geldart A, 27% Geldart B, and 2% Geldart C particles by mass. The granule particle density was 830 kg/m³. Experiments were conducted at a static bed height of 0.16 m for gas superficial velocities ranging from 0.25 to 2.50 m/s for the mono-disperse PSD, and from 0.50 to 3.00 m/s for the bimodal PSD. These gas velocities covered both the bubbling and turbulent fluidization regimes. An ‘M’-shaped time-averaged radial voidage profile appeared upon transition from bubbling to turbulent fluidization. The ‘M’-shaped voidage profile was characterized by a dense region near the wall of the fluidized bed with decreasing solids concentration towards the centre. An increased solids concentration was observed in the middle of the bed. Frame-by-frame analysis of the images showed two predominant bubble types: spherical bubbles with particle penetration in the nose which created a core of particles that extended into, but not through, the bubble; and spherical bubbles. Penetrated bubbles, responsible for the ‘M’ profile, were a precursor to bubble splitting; which became increasingly prevalent in the turbulent regime.     

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.     

Improvement of the Uniformity of Radial Solids Concentration Profiles in Circulating Fluidized‐Bed Risers

In order to enhance the uniformity of the radial solids distribution and thereby the performance of industrial circulating fluidized‐bed (CFB) risers, an approach by using the air jet from the riser circumference is proposed. The Eulerian‐Eulerian computational fluid dynamics (CFD) model with the kinetic theory of granular flow is adopted to simulate the gas‐solids two‐phase flow in a CFB riser with fluid catalytic cracking (FCC) particles. The numerical results indicate that by employing the circumferential air jet approach under appropriate jet velocities, the maximum solids concentration in the near‐wall region can be greatly reduced, the entrance region can be shortened, and the uniformity of the flow structure can be significantly improved.     

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.     

CFD modeling and validation of the turbulent fluidized bed of FCC particles

An experimental and computational study is presented on the hydrodynamic characteristics of FCC particles in a turbulent fluidized bed. Based on the Eulerian/Eulerian model, a computational fluid dynamics (CFD) model incorporating a modified gas‐solid drag model has been presented, and the model parameters are examined by using a commercial CFD software package (FLUENT 6.2.16). Relative to other drag models, the modified one gives a reasonable hydrodynamic prediction in comparison with experimental data. The hydrodynamics show more sensitive to the coefficient of restitution than to the flow models and kinetics theories. Experimental and numerical results indicate that there exist two different coexisting regions in the turbulent fluidized bed: a bottom dense, bubbling region and a dilute, dispersed flow region. At low‐gas velocity, solid‐volume fractions show high near the wall region, and low in the center of the bed. Increasing gas velocity aggravates the turbulent disorder in the turbulent fluidized bed, resulting in an irregularity of the radial particle concentration profile. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

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.     

3‐D full‐loop simulation of an industrial‐scale circulating fluidized‐bed boiler

Three‐dimensional (3‐D) simulations using an Eulerian multiphase model were employed to explore flow behaviors in a full‐loop industrial‐scale CFB boiler with and without fluidized‐bed heat exchanger (FBHE), where three solids phases were employed to roughly represent the polydisperse behavior of particles. First, a simulation of the boiler without FBHE is implemented to evaluate drag models, in terms of pressure profiles, mixing behaviors, radial velocity profiles, etc. Compared to the conventional model, the simulation using the energy‐minimization multiscale (EMMS) model successfully predicts the pressure profile of the furnace. Then, such method is used to simulate the boiler with FBHE. The simulation shows that solid inventory in the furnace is underpredicted and reduced with an increase of the valve opening, probably due to the underevaluated drag for FBHE flows. It is suggested to improve EMMS model which is now based on a single set of operating parameters to match with the full‐loop system. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1108–1117, 2013