Quantitative assessment of fine‐grid kinetic‐theory‐based predictions of mean‐slip in unbounded fluidization

The quantitative ability of a kinetic‐theory‐based, two‐fluid model is demonstrated in a clustering (unstable) gas‐solid system via highly resolved simulations. Unlike previous works, this assessment is validated against ideal computational fluid dynamics‐discrete element method data to minimize sources of discrepancy. Overall, good agreement in mean‐slip velocities is observed with relative errors less than 20% over a mean solids concentration range of 0.02–0.25. Local concentration gradient distributions are also studied, showing a distinct shift toward higher gradients at higher mean solids concentrations which is proposed as the bottleneck in obtaining grid‐independence rather than the cluster length scale. © 2015 American Institute of Chemical Engineers AIChE J, 62: 11–17, 2016     

Verification of filtered two‐fluid models for gas‐particle flows in risers

The effect of solid boundaries on the closure relationships for filtered two‐fluid models for riser flows was probed by filtering the results obtained through highly resolved kinetic theory‐based two‐fluid model simulations. The closures for the filtered drag coefficient and particle phase stress depended not only on particle volume fraction and the filter length but also on the distance from the wall. The wall corrections to the filtered closures are nearly independent of the filter length and particle volume fraction. Simulations of filtered model equations yielded grid length independent solutions when the grid length is ～half the filter length or smaller. Coarse statistical results obtained by solving the filtered models with different filter lengths were the same and corresponded to those from highly resolved simulations of the kinetic theory model, which was used to construct the filtered models, thus verifying the fidelity of the filtered modeling approach. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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     

Co‐current descending two‐phase flows in inclined packed beds: Experiments versus simulations

The effect of inclination angle of a packed bed on its corresponding gas–liquid flow segregation and liquid saturation spatial distribution was measured in co‐current descending gas–liquid flows for varying inclinations and fluid velocities, and simulated using a two‐phase Eulerian computational fluid dynamics framework (CFD) adapted from trickle‐bed vertical configuration and based on the porous media concept. The model predictions were validated with our own experimental data obtained using electrical capacitance tomography. This preliminary attempt to forecast the hydrodynamics in inclined packed bed geometries recommends for the formulation of appropriate drag force closures which should be integrated in the CFD model for improved quantitative estimation.     

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     

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     

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     

Discussion on the pressure drop calculation for oil‐water separated flow using a one dimensional two‐fluid model

The purpose of this work is to seek the key factors influencing the pressure drop calculation for oil‐water separated flow using a one dimensional two‐fluid model. Closure relations published for the two‐fluid model such as interface configuration, wall, and interfacial shear stress correlations are summarized. Interface configurations are established by numerically solving the Young‐Laplace equation, correlated with the Bond number, contact angle, and water holdup. Results show that the interface transforms from concave to convex with the enlargement of the contact angle and becomes flat as the Bond number increases. For the pressure drop calculation, a limited difference of predicted accuracy between the curve and flat interface is found. Discussions of both the wall and interfacial friction factor correlation on the pressure drop calculation are performed. In contrast to the effect of the interfacial friction factor, the correlation of the wall friction factor is found to have more contributions. We validate the prediction accuracy of different wall frictions factors using eight groups of published experiment results, and one correlation is recommended and being further extended.     

Validation study on spatially averaged two‐fluid model for gas–solid flows: I. A priori analysis of wall bounded flows

In our prior study (Schneiderbauer, AIChE J, 2017;63(8):3544–3562), we presented a spatially averaged two‐fluid model, where closure models for the unresolved terms were derived. These closures require constitutive relations for the turbulent kinetic energies (TKEs) of the gas and solids phase as well as for the sub‐filter variance of the solids volume fraction (VVF). In this study, we have performed highly resolved TFM simulations of a set of three‐dimensional wall dominated periodic channels. An a priori analysis shows that these closures are able to correctly predict the wall profiles of the sub‐grid drag modification, the TKEs, the turbulent viscosities and the VVF without requiring special wall corrections. Solely the mixing lengths, which is required by the closures, has to be adapted in the vicinity of wall similar to single‐phase turbulence; in particular, the minimum of the filter size and the distance to the wall should be used. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1591–1605, 2018     

Volume‐of‐fluid‐based model for multiphase flow in high‐pressure trickle‐bed reactor: Optimization of numerical parameters

Aiming to understand the effect of various parameters such as liquid velocity, surface tension, and wetting phenomena, a Volume‐of‐Fluid (VOF) model was developed to simulate the multiphase flow in high‐pressure trickle‐bed reactor (TBR). As the accuracy of the simulation is largely dependent on mesh density, different mesh sizes were compared for the hydrodynamic validation of the multiphase flow model. Several model solution parameters comprising different time steps, convergence criteria and discretization schemes were examined to establish model parametric independency results. High‐order differencing schemes were found to agree better with the experimental data from the literature given that its formulation includes inherently the minimization of artificial numerical dissipation. The optimum values for the numerical solution parameters were then used to evaluate the hydrodynamic predictions at high‐pressure demonstrating the significant influence of the gas flow rate mainly on liquid holdup rather than on two‐phase pressure drop and exhibiting hysteresis in both hydrodynamic parameters. Afterwards, the VOF model was applied to evaluate successive radial planes of liquid volume fraction at different packed bed cross‐sections. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Gas dispersion in air‐lift reactors: Contribution of the turbulent part of the added mass force

Gas dispersion in an airlift reactor focusing on the closure law on turbulent contribution of added mass is presented. A data bank for bubbly flow in an airlift reactor is presented. The liquid velocity is measured by hot film anemometry and gas fraction and velocity are measured with an optical probe. The sensitivity of numerical simulations of gas dispersion to the modeling of turbulent contribution of added mass is shown. Without the turbulent contribution, the bubbles move toward the region where the turbulence is high and the pressure is low. When the turbulent contribution is introduced, the bubble migration towards the low pressure region is counter‐balanced and the void fraction profile is significantly modified. The modeling of the turbulent contribution of added mass is expressed in terms of the turbulent correlations in the gas phase, u_Gi^′u_Gj^′ , that can be related to the Reynolds stress in the liquid phase, u_i^′u_j^′ . © 2011 American Institute of Chemical Engineers AIChE J, 2011     

CFD analysis of two‐phase turbulent flow in internal airlift reactors

The hydrodynamic performance of three internal airlift reactor configurations was studied by the Eulerian–Eulerian k–ε model for a two‐phase turbulent flow. Comparative evaluation of different drag and lift force coefficient models in terms of liquid velocity in the riser and downcomer and gas holdup in the riser was highlighted. Drag correlations as a function of Eötvös number performed better results in comparison to the drag expressions related to Reynolds number. However, the drag correlation as a function of both Reynolds and Eötvös numbers fitted well with experimental results for the riser gas holdup and downcomer liquid velocity in configurations I and II. Positive lift coefficients increase the liquid velocity and decrease the riser gas holdup, while opposite results were obtained for negative values. By studying the effects of bubble size and their shape, the smaller bubbles provide a lower liquid velocity and a gas holdup. The effects of bubble‐induced turbulence and other non‐drag closure models such as turbulent dispersion and added mass forces were analysed. The gas velocity and gas holdup distributions, liquid velocity in the riser and downcomer, vectors of velocity magnitude and streamlines for liquid phase, the dynamics of gas holdup distribution and turbulent viscosity at different superficial gas velocities for different reactor configurations were computed. The effects of various geometrical parameters such as the draft tube clearance and the ratio of the riser to the downcomer cross‐sectional area on liquid velocities in the riser and the downcomer, the gas velocity and the gas holdup were explored. © 2011 Canadian Society for Chemical Engineering     

Modeling gas‐particle two‐phase flows with complex and moving boundaries using DEM‐CFD with an immersed boundary method

An immersed boundary method (IBM) has been developed and incorporated into the coupled discrete element method and computational fluid dynamics (DEM‐CFD) approach to model particulate systems consisting of a compressible gas and solid particles with complex and/or moving boundaries. The IBM is used to deal with the interaction between gas and complex and moving boundaries by using simple rectangular grids to discretize the fluid field. The developed method has been applied to simulate some typical powder handling processes (e.g., gas fluidization with an immersed tube, segregation in a vertically vibrated bed, and pneumatic conveying). Good agreement is achieved between the present simulation results and the experimental ones reported in the literature. It has been demonstrated that the capacity of DEM‐CFD is enhanced with the incorporation of IBM, which can be used to simulate a wide range of problems that could not be handled with the conventional DEM‐CFD method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1075–1087, 2013     

A two‐zone model for fluid catalytic cracking riser with multiple feed injectors

Developments in modeling of the fluid catalytic cracking (FCC) process have progressed along two lines. One emphasizes composition‐based kinetic models based on molecular characterization of feedstocks and reaction products. The other relies on computational fluid dynamics. The aim is to develop an FCC model that strikes a balance between the two approaches. Specifically, we present an FCC riser model consisting of an entrance‐zone and a fully developed zone. The former has four overlapping, fan‐shaped oil sprays. The model predicts the plant data of Derouin et al. and reveals an inherent two‐zone character of the FCC riser. Inside the entrance zone, cracking intensity is highest and changes rapidly, resulting in a steep rise in oil conversion. Outside the entrance zone, cracking intensity is low and varies slowly, leading to a sluggish increase in conversion. The two‐zone model provides a computationally efficient modeling approach for FCC online control, optimization, and molecular management. © 2014 American Institute of Chemical Engineers AIChE J, 61: 610–619, 2015     

Computational investigation of the mechanisms of particle separation and “fish‐hook” phenomenon in hydrocyclones

The motion of solid particles and the “fish‐hook” phenomenon in an industrial classifying hydrocyclone of body diameter 355 mm is studied by a computational fluid dynamics model. In the model, the turbulent flow of gas and liquid is modeled using the Reynolds Stress Model, and the interface between the liquid and air core is modeled using the volume of fluid multiphase model. The outcomes are then applied in the simulation of particle flow described by the stochastic Lagrangian model. The results are analyzed in terms of velocity and force field in the cyclone. It is shown that the pressure gradient force plays an important role in particle separation, and it balances the centrifugal force on particles in the radial direction in hydrocyclones. As particle size decreases, the effect of drag force whose direction varies increases sharply. As a result, particles have an apparent fluctuating velocity. Some particles pass the locus of zero vertical velocity (LZVV) and join the upward flow and have a certain moving orbit. The moving orbit of particles in the upward flow becomes wider as their size decreases. When the size is below a critical value, the moving orbit is even beyond the LZVV. Some fine particles would recircuit between the downward and upward flows, resulting in a relatively high separation efficiency and the “fish‐hook” effect. Numerical experiments were also extended to study the effects of cyclone size and liquid viscosity. The results suggest that the mechanisms identified are valid, although they are quantitatively different. © 2009 American Institute of Chemical Engineers AIChE J, 2010