Immersed boundary method (IBM) based direct numerical simulation of open‐cell solid foams: Hydrodynamics

A sharp interface implicit immersed boundary method is developed and used for direct numerical simulations of the flow through open‐cell solid foams with a cellular structure. The complex solid structure of the foam is resolved on a non‐boundary fitted Cartesian computational‐grid. A single representative unit cell of the foam is considered in a periodic domain, and its geometry is approximated based on the structural packing of a tetrakaidecahedron. Simulations are performed for a wide range of porosities (0.638–0.962) and Reynolds numbers (0–500). Flow is enforced by applying a constant body force (momentum source) for three different flow directions along the {100}, {110}, and {111} lattice‐vectors. The drag force on the foam is calculated and a non‐dimensional drag/pressure drop correlation is proposed that fits the entire data set with an average deviation of 5.6%. Moreover, the accurate numerical simulations have helped to elucidate the detailed fluid‐solid interaction in complex porous media. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 1152–1173, 2017     

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016     

Filtered and heterogeneity‐based subgrid modifications for gas–solid drag and solid stresses in bubbling fluidized beds

Two different approaches to constitutive relations for filtered two‐fluid models (TFM) of gas–solid flows are deduced. The first model (Model A) is derived using systematically filtered results obtained from a highly resolved simulation of a bubbling fluidized bed. The second model (Model B) stems from the assumption of the formation of subgrid heterogeneities inside the suspension phase of fluidized beds. These approaches for the unresolved terms appearing in the filtered TFM are, then, substantiated by the corresponding filtered data. Furthermore, the presented models are verified in the case of the bubbling fluidized bed used to generate the fine grid data. The numerical results obtained on coarse grids demonstrate that the computed bed hydrodynamics is in fairly good agreement with the highly resolved simulation. The results further show that the contribution from the unresolved frictional stresses is required to correctly predict the bubble rise velocity using coarse grids. © 2013 American Institute of Chemical Engineers AIChE J, 60: 839–854, 2014     

Numerical investigation of gas mixing in gas‐solid fluidized beds

Gas mixing in a tall narrow fluidized bed operated in the slugging fluidization regime is simulated with the aid of computational fluid dynamics. In the first part, a parametric study is conducted to investigate the influence of various parameters on the gas mixing. Among the parameters studied, the specularity coefficient for the partial‐slip solid‐phase wall boundary condition had the most significant effect on gas mixing. It was found that the solid‐phase wall boundary condition needs to be specified with great care when gas mixing is modeled, with free slip, partial slip and no‐slip wall boundary conditions giving substantial differences in the extent of gas back mixing. Axial and radial tracer concentration profiles for different operating conditions are generally in good agreement with experimental data from the literature. Detailed analyses of tracer back mixing are carried out in the second part. Two parameters, the tracer backflow fraction and overall gas backflow fraction, in addition to axial profiles of cross‐sectional averaged tracer concentrations, are evaluated for different flow conditions. Qualitative trends are consistent with reported experimental findings. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Transient multi gas—solid reactions in a bubbling fluidized bed

A “multimodel” for gas‐solid reactions in a reacting particle has been applied to a bubbling fluidized bed reactor. The particle is tracked and bed and particle variables are determined continuously. The conservation equations of mass and heat with auxiliary relations are solved in an accelerating particle, which may rise or fall. The effects of bulk pressure, velocity and temperature, and particle diameter are studied. Heat and mass transfer coefficients may fluctuate up to 75% and 148% respectively. Doubling the pressure changes h_c by 75% and k_c by ?45%. Increase in pellet diameter reduces both h_c and k_c.     

Borescopy in pressurized gas‐solid fluidized beds

A borescopic technique was used for finding the effect of pressure on the hydrodynamics of gas‐solid fluidized beds. The results showed that solids radial distribution may become more or less uniform with increasing pressure depending on the superficial gas velocity. Moreover, it is found that the solids volume fraction of the emulsion phase may decrease at relatively high pressures, only in the central region of the bed. Additionally, it is observed that with increasing pressure the bubble size generally decreased in the central regions and increased near the wall regions. This trend was more complicated at low excess gas velocities. The number of bubbles increased for the central regions and near the walls for all the performed experiments. However, this parameter showed a different trend at other radial positions. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 3303–3311, 2018     

Filtration model for polydisperse aerosols in gas‐solid flow using granule‐resolved direct numerical simulation

An analytical framework for calculating the filtration efficiency of polydisperse aerosols in a granular bed is developed for cases where inertial impaction and interception are the principal filtration mechanisms. This framework is used to develop a model for the polydisperse single‐collector efficiency from monodisperse single‐collector efficiency correlations. Conceptually, the polydisperse model is developed by transforming the probability density of particle radius into a probability density of particle Stokes number that is then used to weight the monodisperse single‐collector efficiency at a given Stokes number. An extension of this polydisperse filtration concept results in an analytical solution for the axial variation of polydisperse particle flux in a random three‐dimensional granule configuration. In order to verify the analytical results for polydisperse particle filtration, a granule‐resolved direct numerical simulation approach is coupled with Lagrangian particle tracking to simulate filtration of polydisperse aerosols in a granular bed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3594–3606, 2015     

Effect of bed size on hydrodynamics in 3‐D gas–solid fluidized beds

It is well known that hydrodynamics observed in large scale gas–solid fluidized beds are different from those observed in smaller scale beds. In this article, an efficient two‐fluid model based on kinetic theory of granular flow is applied, with the goal to highlight and investigate hydrodynamics differences between three‐dimensional fluidized beds of diameter 0.10, 0.15, 0.30, 0.60, and 1.0 m, focusing on the bubble and solids flow characteristics in the bubbling regime. Results for the 0.30 m diameter bed are compared with experimental results from the literature. The bubble size evolution closely follows a correlation proposed by Werther for small beds, and a correlation proposed by Darton for sufficiently large beds. The bubble size increases as the bed diameter is increased from 0.10 to 0.30 m, and remains approximately constant for bed diameters from 0.30 to 1.0 m. Concurrently, an increase in bubble rise velocity is observed, with a much high bubble rise velocity in the largest bed of diameter 1.0 m due to gulf stream circulations. The dynamics in shallow and deep beds is predicted to be different, with marked differences in bubble size and solids circulation patterns. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1492–1506, 2015     

Fluid‐particle drag in inertial polydisperse gas–solid suspensions

In this article, we extend the low Reynolds number fluid‐particle drag relation proposed by Yin and Sundaresan for polydisperse systems to include the effect of moderate fluid inertia. The proposed model captures the fluid‐particle drag results obtained from lattice‐Boltzmann simulations of bidisperse and ternary suspensions at particle mixture Reynolds numbers ranging from 0 ≤ Re_mix ≤ 40, over a particle volume fraction range of 0.2 ≤ ? ≤ 0.4, volume fraction ratios of 1 ≤ ?_i/?_j ≤ 3, and particle diameter ratios of 1 ≤ d_i/d_j ≤ 2.5. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Particle entrainment from gas‐solid fluidized beds: Conductive vs. dielectric fines

Conductive and non‐conductive fine powders were entrained by air at atmospheric temperature and pressure in a fluidization column of diameter 0.15 m made of stainless steel. Under equivalent operating conditions, entrainment of the conductive particles was markedly higher than for non‐conductive species. This finding cannot be explained by hydrodynamic factors. Examining the electrostatic interaction between touching particles reveals that dominance of the inter‐particle attractive forces hinders independent motion of non‐conductive particles in the freeboard. In addition, because of non‐uniform distribution of the electrical charges over the surface of dielectric particles, they are subject to stronger electrostatic forces than for particles made of conductive materials. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1194–1202, 2017     

Experimental investigation of electrostatic effect on particle motions in gas‐solid fluidized beds

The excess accumulation of charges in the fluidized bed has a severe impact on hydrodynamics. Due to lack of effective experimental methods, electrostatic effects on hydrodynamics have mostly been studied using numerical simulation. By injecting a trace of liquid antistatic agents into a fluidized bed, charges were controlled and electrostatic influences on particle motions were investigated. The average particle–wall impact angles are acquired by developing multiscale wavelet decomposition of acoustic emission signals. The impact angles are significantly influenced by both charge levels and gas velocities. If the electric force is reduced and/or fluid drag is increased, friction dominates the particle–wall interactions. Under a larger gas velocity where fluid drag dominates, charges elimination causes no significant variation in particle impact angles, but particle velocities increase as well as at lower gas velocities. In addition, existence of electrostatic charges influences the ranges of bubble growing zone and jet impacting zone. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3628–3638, 2015     

Link between bubbling and segregation patterns in gas‐fluidized beds with continuous size distributions

Experiments involving a bubbling, gas‐fluidized bed with Gaussian and lognormal particle‐size distributions (PSDs) of Geldart Group B particles have been carried out, with a focus on bubble measurements. Previous work in the same systems indicated the degree of axial species segregation varies non‐monotonically with respect to the width of lognormal distributions. Given the widely accepted view of bubbles as “mixing agents,” the initial expectation was that bubble characteristics would be similarly non‐monotonic. Surprisingly, results show that measured bubble parameters (frequency, velocity, and chord length) increase monotonically with increasing width for all PSDs investigated. Closer inspection reveals a bubble‐less bottom region for the segregated systems, despite the bed being fully fluidized. More specifically, results indicate that, the larger the bubble‐less layer is, the more segregated the system becomes. The direct comparison between bubbling and segregation patterns performed provides a more complete physical picture of the link between the two phenomena. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Axial segregation in bubbling gas‐fluidized beds with Gaussian and lognormal distributions of Geldart Group B particles

Bubbling, gas‐fluidized bed experiments involving Geldart Group B particles with continuous‐size distributions have been carried out. Sand of various widths of Gaussian or lognormal distributions were completely fluidized, then axial concentration profiles were obtained from frozen‐bed sectioning. Similar to previous works on binary systems, results show that mean particle diameter decreases with increasing bed height, and that wider Gaussian distributions show increased segregation extents. Surprisingly, however, lognormal distributions exhibit a nonmonotonic segregation trend with respect to distribution widths. In addition, the shape of the local‐size distribution is largely preserved with respect to that of the overall distribution. These findings on the nature of local‐size distribution provide experimental confirmation of previous results for granular and gas‐solid simulations. Lastly, an interesting observation is that although monodisperse Geldart Group D particles cannot be completely fluidized, their presence in lognormal distributions investigated still results in complete fluidization of all particles. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Clusters identification and characterization in a gas–solid fluidized bed by the wavelet analysis

The local solid flow structure of the bubbling fluidized bed of sand particles was investigated in order to identify and characterize the clusters. Extensive experiments were carried out using an optical fibre probe, measuring the velocity and the diameter of clusters. Under all operating conditions, ascending and descending clusters co‐existed at all measurement locations. The locus of the inversion point at which the directions of cluster motion changed was determined. The velocity of the ascending clusters was a function of both superficial gas velocity and the radial and axial position. With increasing superficial gas velocity, both the velocity and the diameter of ascending clusters decreased near the wall. However, the velocity of descending clusters depended mainly on superficial gas velocity and the largest clusters existed closer to the wall. The results of this study help to explain cluster hydrodynamics in fluidized beds.     

Experimental and numerical research for fluidization behaviors in a gas–solid acoustic fluidized bed

The effects of sound assistance on fluidization behaviors were systematically investigated in a gas–solid acoustic fluidized bed. A model modified from Syamlal–O'Brien drag model was established. The original solid momentum equation was developed and an acoustic model was also proposed. The radial particle volume fraction, axial root‐mean‐square of bed pressure drop, granular temperature, and particle velocity in gas–solid acoustic fluidized bed were simulated using computational fluid dynamics (CFD) code Fluent 6.2. The results showed that radial particle volume fraction increased using modified drag model compared with that using the original one. Radial particle volume fraction was revealed as a parabolic concentration profile. Axial particle volume fraction decreased with the increasing bed height. The granular temperature increased with increasing sound pressure level. It showed that simulation values using CFD code Fluent 6.2 were in agreement with the experimental data. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Investigation into the hydrodynamics of gas–solid fluidized beds using particle image velocimetry coupled with digital image analysis

The hydrodynamics of a freely bubbling, pseudo 2‐D fluidized bed has been investigated experimentally for different bed aspect ratios at different superficial gas velocities by using Particle Image Velocimetry (PIV) combined with Digital Image Analysis (DIA). Coupling of both non‐invasive measuring techniques allows us to obtain information on both the bubble behaviour and emulsion phase circulation patterns simultaneously. In particular, the combination of DIA with PIV allows to correct for the influence of particle raining through the roof of the bubbles on the time‐averaged emulsion phase velocity profiles.     

不等粒径流化床的软球模拟

基于颗粒轨道模型,提出了粒径分别服从均匀分布与正态分布的软球方法,其中流体运动用Navier-Stokes方程描述,颗粒运动服从牛顿第二定理.模拟了不等粒径流化床中的气泡和节涌现象,并分别研究了表观气速、颗粒刚度系数、粒径分布不同时,固相颗粒的速度分布规律.其研究结果表明：分布板结构和表观气速对气泡行为有一定影响,随表观气速的增加,气泡形成、上升、破裂的速度加快;并且刚度系数越大,颗粒轴向速度随时间衰减越快;宽粒径分布的颗粒轴向速度大于窄粒径分布的颗粒轴向速度.     

Comparative analysis of subgrid drag modifications for dense gas‐particle flows in bubbling fluidized beds

Many subgrid drag modifications have been put forth to account for the effect of small unresolved scales on the resolved mesoscales in dense gas‐particle flows. These subgrid drag modifications significantly differ in terms of their dependencies on the void fraction and the particle slip velocity. We, therefore, compare the hydrodynamics of a three‐dimensional bubbling fluidized bed computed on a coarse grid using the drag correlations of the groups of (i) EMMS, (ii) Kuipers, (iii) Sundaresan, (iv) Simonin, and the homogenous drag law of (v) Wen and Yu with fine grid simulations for two different superficial gas velocities. Furthermore, we present an (vi) alternative approach, which distinguishes between resolved and unresolved particle clusters revealing a grid and slip velocity dependent heterogeneity index. Numerical results are analyzed with respect to the time‐averaged solids volume fraction and its standard deviation, gas and solid flow patterns, bubble size, number density, and rise velocities. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4077–4099, 2013