Particle‐resolved direct numerical simulation of gas–solid dynamics in experimental fluidized beds

Particle‐resolved direct numerical simulations (PR‐DNS) of a simplified experimental shallow fluidized bed and a laboratory bubbling fluidized bed are performed by using immersed boundary method coupled with a soft‐sphere model. Detailed information on gas flow and individual particles’ motion are obtained and analyzed to study the gas–solid dynamics. For the shallow bed, the successful predictions of particle coherent oscillation and bed expansion and contraction indicate all scales of motion in the flow are well captured by the PD‐DNS. For the bubbling bed, the PR‐DNS predicted time averaged particle velocities show a better agreement with experimental measurements than those of the computational fluid dynamics coupled with discrete element models (CFD‐DEM), which further validates the predictive capability of the developed PR‐DNS. Analysis of the PR‐DNS drag force shows that the prevailing CFD‐DEM drag correlations underestimate the particle drag force in fluidized beds. The particle mobility effect on drag correlation needs further investigation. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1917–1932, 2016     

Hydrodynamic characterisation of liquid–solid two–phase fluidised beds: Vibration signature and pressure fluctuations analyses

Hydrodynamic behaviour of a two–phase liquid–solid fluidised bed was investigated over a wide range of liquid velocities by means of simultaneous vibration and pressure fluctuations analyses. The liquid velocities were set in a way that covered two most important hydrodynamic events in the bed, namely minimum fluidisation and circulating‐solid regime. To prevent solids from being carried out of the bed, the maximum liquid velocity was kept lower than the terminal velocity of solids. Statistical analysis on the vibration signatures of bed shell proved to be a strong representative for minimum fluidisation characterisation and solid regime change. The minimum fluidisation velocity can be obtained from the intersection of two linear parts in the standard deviation of vibration fluctuation signals. Moreover, the kurtosis of vibration signals could predict the minimum fluidisation and approximate solid regime transition successfully. Meanwhile, statistical parameters, such as standard deviation, skewness, and kurtosis as well as newly‐introduced parameters, namely the energy and average cycle frequency of pressure signals, determined both of minimum fluidisation condition and circulating‐solid flow regime. © 2011 Canadian Society for Chemical Engineering     

Comparison of the impact of flow pulsations on the performance of various liquid–gas injectors in a gas–solid fluidised bed

This article shows that spray nozzles pulsations can greatly improve the distribution of the sprayed liquid on fluidised bed particles, as characterised by a Nozzle Performance Index (NPI). Appropriate pulsations increased the NPI by nearly 100% under several operating conditions. This article compares four pulsating, gas atomised nozzles under various operating conditions. The performance of each nozzle was evaluated by measuring the electric conductance of a bed of silica sand particles fluidised by air, subsequent to liquid injection. Three sets of experiments were conducted to investigate the effect of operating conditions on the performance of the four gas atomised nozzles. The first set determined the effect of the liquid flowrate, the second set measured the effect of a restriction orifice on the atomisation gas line and the third set studied the effect of the atomisation air to liquid ratio. Artificial nozzle spray pulsations were found to have similar beneficial effects with the different types of gas‐atomised nozzles. © 2011 Canadian Society for Chemical Engineering     

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     

Novel phenomenological discrete bubble model of freely bubbling dense gas–solid fluidized beds: Application to two‐dimensional beds

A phenomenological discrete bubble model has been developed for freely bubbling dense gas–solid fluidized beds and validated for a pseudo‐two‐dimensional fluidized bed. In this model, bubbles are treated as distinct elements and their trajectories are tracked by integrating Newton's equation of motion. The effect of bubble–bubble interactions was taken into account via a modification of the bubble velocity. The emulsion phase velocity was obtained as a superposition of the motion induced by individual bubbles, taking into account bubble–bubble interaction. This novel model predicts the bubble size evolution and the pattern of emulsion phase circulation satisfactorily. Moreover, the effects of the superficial gas velocity, bubble–bubble interactions, initial bubble diameter, and the bed aspect ratio have been carefully investigated. The simulation results indicate that bubble–bubble interactions have profound influence on both the bubble and emulsion phase characteristics. Furthermore, this novel model may become a valuable tool in the design and optimization of fluidized‐bed reactors. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Filtered two‐fluid models of fluidized gas‐particle flows: New constitutive relations

New constitutive relations for filtered two‐fluid models (TFM) of gas‐particle flows are obtained by systematically filtering results generated through highly resolved simulations of a kinetic theory‐based TFM. It was found in our earlier studies that the residual correlations appearing in the filtered TFM equations depended principally on the filter size and filtered particle volume fraction. Closer inspection of a large amount of computational data gathered in this study reveals an additional, systematic dependence of the correction to the drag coefficient on the filtered slip velocity, which serves as a marker for the extent of subfilter‐scale inhomogeneity. Furthermore, the residual correlations for the momentum fluxes in the gas and particle phases arising from the subfilter‐scale fluctuations are found to be modeled nicely using constitutive relations of the form used in large‐eddy simulations of single‐phase turbulent flows. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3265–3275, 2013     

A second‐order moment method applied to gas–solid risers

Second‐order moment method of particles is proposed on the basis of the kinetic theory of granular flow. Closure equations for the third‐order velocity moments are presented to account for the increase of the probability of collisions of particles on the basis of the elementary kinetic theory and order of magnitude analysis. The boundary conditions for the set of equations describing flow of particles are proposed with the consideration of the momentum exchange by collisions between the wall and the particles. The distributions of velocity, concentration and moments of particles are predicted. Simulated results are compared with experimental data measured by Tartan and Gidaspow and Bhusarapu et al. in risers, and Tsuji et al. in a vertical pipe. The effects of the closure equations for the third‐order velocity moments and the fluid‐particle velocity correlation tensor on flow behavior of particles are analyzed. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Validation study on spatially averaged two‐fluid model for gas‐solid flows: II. Application to risers and fluidized beds

In our prior study (Schneiderbauer, AIChE J. 2017;63(8):3544–3562), a spatially averaged two‐fluid model (SA‐TFM) was presented, where closure models for the unresolved terms were derived. These closures require constitutive relations for the turbulent kinetic energies of the gas and solids phase as well as for the subfilter variance of the solids volume fraction. We had ascertained that the filtered model do yield nearly the same time‐averaged macroscale flow behavior in bubbling fluidized beds as the underlying kinetic‐theory‐based two‐fluid model, thus verifying the SA‐TFM model approach. In the present study, a set of 3D computational simulations for validation of the SA‐TFM against the experimental data on riser flow and bubbling fluidized beds is performed. Finally, the SA‐TFM predictions are in fairly good agreement with experimental data in the case of Geldart A and B particles even though using very coarse grids. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1606–1617, 2018     

Hydrodynamics of gas–liquid flow in micropacked beds: Pressure drop,liquid holdup,and two‐phase model

Hydrodynamics of gas–liquid two‐phase flow in micropacked beds are studied with a new experimental setup. The pressure drop, residence time distribution, and liquid holdup are measured with gas and liquid flow rates varying from 4 to 14 sccm and 0.1 to 1 mL/min, respectively. Key parameters are identified to control the experimentally observed hydrodynamics, including transient start‐up procedure, gas and liquid superficial velocities, particle and packed bed diameters, and physical properties of the liquids. Contrary to conventional large packed beds, our results demonstrate that in these microsystems, capillary forces have a large effect on pressure drop and liquid holdup, while gravity can be neglected. A mathematical model describes the hydrodynamics in the micropacked beds by considering the contribution of capillary forces, and its predictions are in good agreement with experimental data. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4694–4704, 2017     

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     

A spatially‐averaged two‐fluid model for dense large‐scale gas‐solid flows

We present a spatially‐averaged two‐fluid model (SA‐TFM), which is derived from ensemble averaging the kinetic‐theory based TFM equations. The residual correlation for the gas‐solid drag, which appears due to averaging, is derived by employing a series expansion to the microscopic drag coefficient, while the Reynolds‐stress‐like contributions are closed similar to the Boussinesq‐approximation. The subsequent averaging of the linearized drag force reveals that averaged interphase momentum exchange is a function of the turbulent kinetic energies of both, the gas and solid phase, and the variance of the solids volume fraction. Closure models for these quantities are derived from first principles. The results show that these new constitutive relations show fairly good agreement with the fine grid data obtained for a wide range of particle properties. Finally, the SA‐TFM model is applied to the coarse grid simulation of a bubbling fluidized bed revealing excellent agreement with the reference fine grid solution. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3544–3562, 2017     

Investigation of gas–solid bubbling fluidized beds using ECT with a modified Tikhonov regularization technique

Electrical capacitance tomography (ECT) provides a non‐intrusive means to visualize cross‐sectional material distribution of gas–solid bubbling fluidized beds. Successful application of ECT strongly depends on the image reconstruction algorithm used. For on‐line measurements of bubbling fluidized beds, employing an algorithm that can produce high‐quality images without extensive computation is necessary. Using the conventional Tikhonov regularization algorithm, image quality in the central area is basically satisfied but suffers from artifacts in the near‐wall region. To solve this problem, a similar division operation learned from linear back projection was introduced to modify the conventional Tikhonov algorithm. Both numerical simulations and experiments were performed to evaluate the modified technique. The results indicate that the artifacts can be effectively removed and the reconstructed image quality is similar to Landweber method with dozens of iterations. Furthermore, the modified Tikhonov technique shows high accuracy when obtaining important hydrodynamic parameters in gas–solid bubbling fluidized beds. © 2017 American Institute of Chemical Engineers AIChE J, 63: 29–41, 2018     

颗粒旋转对鼓泡流化床内气固两相流动特性影响的数值模拟

运用考虑颗粒自旋转流动对颗粒碰撞能量交换和耗散影响的颗粒动理学方法,建立鼓泡流化床气固两相Euler-Euler双流体模型,数值模拟流化床内气体颗粒两相流动特性。分析表明,颗粒平动温度与旋转温度之比是法向和切向颗粒弹性恢复系数和摩擦系数的函数。与不考虑颗粒旋转效应计算结果相比,考虑颗粒旋转效应后床内较容易形成气泡,颗粒自旋转运动将导致床内非均匀结构更明显。并且床层平均空隙率和床层膨胀高度增加,床中心区域颗粒轴向速度提高,床内颗粒平动温度下降。考虑颗粒旋转效应后预测的颗粒轴向速度和颗粒脉动速度与文献实验结果基本吻合。考虑颗粒旋转效应后获得的气泡直径更接近于前人经验关联式。     

Bubble dynamics in a 3‐D gas–solid fluidized bed using ultrafast electron beam X‐ray tomography and two‐fluid model

Bubble characteristics in a three‐dimension gas‐fluidized bed (FB) have been measured using noninvasive ultrafast electron beam X‐ray tomography. The measurements are compared with predictions by a two‐fluid model (TFM) based on kinetic theory of granular flow. The effect of bed material (glass, alumina, and low linear density polyethylene (LLDPE), d_p ～1 mm), inlet gas velocity, and initial particle bed height on the bubble behavior is investigated in a cylindrical column of 0.1‐m diameter. The bubble rise velocity is determined by cross correlation of images from dual horizontal planes. The bubble characteristics depend highly upon the particle collisional properties. The bubble sizes obtained from experiments and simulations show good agreement. The LLDPE particles show high gas hold‐up and higher bubble rise velocity than predicted on basis of literature correlations. The bed expansion is relatively high for LLDPE particles. The X‐ray tomography and TFM results provide in‐depth understanding of bubble behavior in FBs containing different granular material types. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1632–1644, 2014     

Numerical study of cluster and particle rebound effects in a circulating fluidised bed

Gas-particle flows in a vertical two-dimensional configuration appropriate for circulating fluidised bed applications were investigated numerically. In the computational study presented herein the motion of particles was calculated based on a Lagrangian approach and particles were assumed to interact through binary, instantaneous, non-frontal, inelastic collisions including friction. The model for the interstitial gas phase is based on the Navier-Stokes equations for two-phase flows. The numerical study of cluster structures has been validated with experimental results from literature in a previous investigation. Numerical experiments were performed in order to study the effects of different cluster and particle rebound characteristics on the gas-particle flow behaviour.Firstly, we investigated the hard sphere collision model and its effect on gas-particle flow behaviour. The coefficient of restitution in an impact depends not only on the material properties of the colliding objects, but also on their relative impact velocity. We compared the effect of a variable restitution coefficient, dependent on the relative impact velocity, with the classical approach, which supposes the coefficient of restitution to be constant and independent of the relative impact velocity.Secondly, we studied the effects of different cluster properties on the gas-particle flow behaviour. Opposing clustering effects have been observed for different particle concentrations: within a range of low concentrations, groups of particles fall faster than individual particles due to cluster formation, and within a well-defined higher concentration range, return flow predominates and hindered settling characterises the suspension. We propose herein a drag law, which takes into account both opposing effects and have compared the resulting flow behaviour with that predicted by a classical drag law, which takes into account only the hindered settling effect.     

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.     

The impacts of standard wall function and drag model on the turbulent modelling of gas–particle flow in a circulating fluidised bed riser

A transient turbulence model was applied to simulate the gas–particle system in a circulating fluidised bed riser. The k–epsilon turbulent equations coupled with the fluctuating energy equation were used to simulate the gas–particle system in a riser. The simulation results were validated by the experimental data of a CFB system. A grid study was implemented to examine the impact of grid discretisation. A comparison between the conventional drag models and the EMMS model was also conducted. Other factors, like the restitution coefficient particle to particle, was also found to have a significant impact on the turbulence model. © 2013 Canadian Society for Chemical Engineering