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     

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     

Characteristic time scales for predicting the scalar flux at a free surface in turbulent open‐channel flows

The purpose of this study is to predict the turbulent scalar flux at a free surface subject to a fully developed turbulent flow based on a hydrodynamic analysis of turbulence in the region close to the free surface. The effect of the Reynolds number on turbulent scalar transfer mechanisms is extensively examined. A direct numerical simulation technique is applied to achieve the purpose. The surface‐renewal approximation is used to correlate the free‐surface hydrodynamics and scalar transport at the free surface. Two types of characteristic time scales have been examined for predicting turbulent scalar flux. One is the time scale derived from the characteristic length and velocity scale at the free surface. The other is the reciprocal of the root‐mean‐square surface divergence. The results of this study show that scalar transport at the free surface can be predicted successfully using these time scales based on the concept of the surface‐renewal approximation. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Effect of liquid volume in the gas‐separator on the hydrodynamics of airlift reactors

Gas hold‐up and liquid circulation velocity measurements were made using a 167 dm³ external loop airlift reactor. The gas‐separator was of the open channel configuration. The reactor height was 2.5 m with riser and downcomer diameters of 0.19 m and 0.14 m respectively. The systems investigated were Newtonian air–water and air–glycerol with the superficial air velocity varying between 0.02 and 0.12 m s⁻¹. The ratio of the liquid volume in the gas‐separator to the liquid volume in the reactor (volume‐ratio) was varied from 0.0% to 37%, to find its minimum critical value for optimum operation of the airlift reactor. For the air–water system, discernible effects of the volume‐ratio on riser and, downcomer gas hold‐ups and liquid circulation velocity were observed at volume ratios ≤7%. Beyond this value, the volume‐ratio had no effect. For a viscous and foaming air–glycerol system the critical volume‐ratio was increased to 19%. New and simple correlations for predicting gas hold‐up in the riser, gas hold‐up in the downcomer, and liquid circulation velocity were developed with reasonable accuracy. © 1999 Society of Chemical Industry     

Quantifying the uncertainty introduced by discretization and time‐averaging in two‐fluid model predictions

The two‐fluid model (TFM) has become a tool for the design and troubleshooting of industrial fluidized bed reactors. To use TFM for scale up with confidence, the uncertainty in its predictions must be quantified. Here, we study two sources of uncertainty: discretization and time‐averaging. First, we show that successive grid refinement may not yield grid‐independent transient quantities, including cross‐section–averaged quantities. Successive grid refinement would yield grid‐independent time‐averaged quantities on sufficiently fine grids. Then a Richardson extrapolation can be used to estimate the discretization error, and the grid convergence index gives an estimate of the uncertainty. Richardson extrapolation may not work for industrial‐scale simulations that use coarse grids. We present an alternative method for coarse grids and assess its ability to estimate the discretization error. Second, we assess two methods (autocorrelation and binning) and find that the autocorrelation method is more reliable for estimating the uncertainty introduced by time‐averaging TFM data. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5343–5360, 2017     

Hydrodynamics of upflow anaerobic sludge blanket reactors

The hydrodynamic characteristics of upflow anaerobic sludge blanket (UASB) reactors were investigated in this study. A UASB reactor was visualized as being set‐up of a number of continuously stirred tank reactors (CSTRs) in series. An increasing‐sized CSTRs (ISC) model was developed to describe the hydrodynamics of such a bioreactor. The gradually increasing tank size in the ISC model implies that the dispersion coefficient decreased along the axial of the UASB reactor and that its hydrodynamic behavior was basically dispersion‐controlled. Experimental results from both laboratory‐scale H₂‐producing and full‐scale CH₄‐producing UASB reactors were used to validate this model. Simulation results demonstrate that the ISC model was better than the other models in describing the hydrodynamics of the UASB reactors. Moreover, a three‐dimensional computational fluid dynamics (CFD) simulation was performed with an Eulerian‐Eulerian three‐phase‐fluid approach to visualize the phase holdup and to explore the flow patterns in UASB reactors. The results from the CFD simulation were comparable with those of the ISC model predictions in terms of the flow patterns and dead zone fractions. The simulation results about the flow field further confirm the discontinuity in the mixing behaviors throughout a UASB reactor. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

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.     

Three‐dimensional CFD‐PBM coupled model of the temperature fields in fluidized‐bed polymerization reactors

A three‐dimensional (3‐D) computational fluid dynamics model, coupled with population balance (CFD‐PBM), was developed to describe the gas–solid two‐phase flow in fluidized‐bed polymerization reactors. The model considered the Eulerian–Eulerian two‐fluid model, the kinetic theory of granular flow, the population balance, and heat exchange equations. First, the model was validated by comparing simulation results with the classical calculated data. The entire temperature fields in the reactor were also obtained numerically. Furthermore, two case studies, involving constant solid particle size and constant polymerization heat or evolving particle‐size distribution, polymerization kinetics, and polymerization heat, were designed to identify the model. The results showed that the calculated results in the second case were in good agreement with the reality. Finally, the model of the second case was used to investigate the influences of operational conditions on the temperature field. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

Direct numerical simulation of the turbulent flow in a baffled tank driven by a Rushton turbine

We present a direct numerical simulation (DNS) of the turbulent flow in a baffled tank driven by by a Rushton turbine. The DNS is compared to a Large Eddy Simulation (LES), a Reynolds Averaged Navier‐Stokes (RANS) simulation, Laser Doppler Velocimetry data, and Particle Image Velocimetry data from the literature. By Reynolds averaging the DNS‐data, we validate the turbulent viscosity hypothesis by demonstrating strong alignment between the Reynolds stress and the mean strain rate. Although the turbulent viscosity ν_T in the DNS is larger than in the RANS simulation, the turbulent viscosity parameter C_μ = ν_T?/k², is an order of magnitude smaller than the standard 0.09 value of the k‐? model. By filtering the DNS‐data, we show that the Smagorinsky constant C_S is uniformly distributed over the tank with C_S ≈ 0.1. Consequently, the dynamic Smagorisnky model does not improve the accuracy of the LES. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

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     

LES–Lagrangian‐particles‐simulation of turbulent reactive flows at high Sc number using approximate deconvolution model

Large eddy simulation (LES) with the approximate deconvolution model is combined with Lagrangian particles simulation (LPS) for simulating turbulent reactive flows at high Schmidt numbers Sc. The LES is used to simulate velocity and nonreactive scalar while reactive scalars are simulated by the LPS using the mixing volume model for molecular diffusion. The LES–LPS is applied to turbulent scalar mixing layers with a second‐order isothermal irreversible reaction at Sc = 600. The mixing volume model is implemented with the IEM, Curl's, and modified Curl's mixing schemes. The mixing volume model provides a correct decay rate of nonreactive scalar variance at high Sc independently of the number of particles. The statistics in the LES–LPS with the IEM or modified Curl's mixing scheme agree well with the experiments for both moderately‐fast and rapid reactions. However, the LPS with the Curl's mixing scheme overpredicts the effects of the rapid reaction. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2912–2922, 2016     

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     

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     

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