Energy Minimization Multiscale Drag Model Research Articles

A Simplified Bubble Size Relation Compatible with the Energy Minimization Multiscale Drag Model for Studying Hydrodynamics in a 2D Gas–Solid Tapered Fluidized Bed

Gas–solid fluidized bed reactors are extensively utilized in direct reduced iron production. In practice, these reactors will have a wide particle size distribution, which is better handled by tapered fluidized beds due to their vertical velocity gradient. Herein, a simplified bubble size relation is proposed to remove implicit interdependency between the bubble size and its drag coefficient in the bubble‐based energy minimization multiscale (EMMS) heterogeneous drag model. Further, the proposed drag model is coupled with the two‐fluid kinetic theory of granular flow model to investigate hydrodynamics. The heterogeneous flow structure predicted by the model is similar to experiments. Further, the bulk parameters such as bed expansion ratio and bubble fraction obtained from the simulations using a simplified EMMS drag model are compared and are found to be in good agreement with the experimental findings, with mean relative deviations of 3.95% and 14.64%, respectively. The time‐averaged bubble fraction and bed expansion ratio are found to increase with air velocity and decrease with taper angle, whereas a reverse trend is observed for the mean particulate fluidized area fraction. Based on the current study, the taper angle between 5° and 10° is found to be most suitable.

Multiscale CFD Simulation of Multiphase Erosion Process in a Connecting Pipe of Industrial Polycrystalline Silicon Unit

Severe erosion phenomena often occur in industrial polycrystalline silicon units, leading to hydrogen leakage accidents and affecting long-term operation. It is favorable to use a computational fluid dynamics (CFD) simulation with the dense discrete phase model (DDPM) and the sub-grid energy-minimization multi-scale (EMMS) drag model to improve the prediction accuracy of complex multiphase erosion phenomena in a connecting pipe of an industrial polycrystalline silicon unit. Furthermore, the effect of droplet the specularity coefficient on boundary conditions is thoroughly considered. The predicted erosion behaviors are consistent with industrial data. The effects of operations parameters were discussed with three-dimensional CFD simulation, including droplet size and hydrogen volume fraction on erosion behaviors. The results indicated that the non-uniform multiphase erosion flow behavior near the wall can be simulated accurately with the EMMS drag model in a coarse mesh. A suitable droplet specularity coefficient such as 0.5 can also improve the accuracy of erosion position. Small liquid droplets, such as those of 30 μm size, will follow the gas phase better and have a lower erosion rate. The inertia effect of large droplets, such as those of 150 μm size, plays a dominant role, resulting in obvious erosion on the elbow walls. The erosion range and thinning rate enlarge with the increase in hydrogen volume fraction. A few silicon solid particles, such as 0.01% volume fraction, change local flow behaviors and probably cause the variation of local erosion positions. The process of erosion deformation first circumferentially extended and then accelerated at the local center position deeper.

Effect of the Scale-Up Process on the Reactor Performance within the Riser: Simulation Using Ozone Decomposition

Ozone decomposition in the riser is simulated with computational fluid dynamics in order to explore the scale-up effect on the chemical reaction performance. Glicksman’s full and simplified scaling rules are used to build two 1:3 scaled-up risers. The variation of cluster features during the scale-up process is approached with the energy minimization multiscale drag model. The comparison of axial and radial ozone concentrations between three cases indicates that the scale-up process exhibits less uniformity in the radial ozone distribution. The variation of cluster effect during the scale-up process has an evident effect on the gas–solid contact efficiency. The overall gas–solid contact efficiency is improved during the scale-up process with full set scaling rules.

A unified EMMS-based constitutive law for heterogeneous gas-solid flow in CFB risers

Energy minimization multi-scale (EMMS) drag model has been demonstrated to be very successful in quantifying the effect of mesoscale structure on the effective interphase drag force of heterogeneous gas-solid flow in circulating fluidized bed (CFB) risers, however, a corresponding model for the effective particle phase stress is not yet available. To this end, an EMMS drag model was extended to predict the granular temperature of particles inside the dilute phase and the dense phase as well as the granular temperature of clusters. A model for the effective particle phase stress was then developed based on the concept of multiscale analysis in EMMS model. It was shown that the experimentally measured granular temperature, granular pressure and granular viscosity as a function of mean solid concentration can be predicted reasonably well. The agreement demonstrates its effectiveness in the quantification of the effect of mesoscale structure on the particle phase stress, thus establishing a unified EMMS-based model for the constitutive law of heterogeneous gas-solid flow in CFB risers.

Hydrodynamics in commercial-scale internally circulating fluidized beds with different central downcomer outlets

Standpipes, or downcomers, are commonly used in fluidized beds to transport particles. The outlet structure of the downcomer greatly affects the performance of flow from it and even overall reactor performance. In this study, the hydrodynamics in commercial-scale internally circulating fluidized beds (ICFBs) with central downcomers having different outlet structures was investigated using computational fluid dynamics simulations with an energy minimization multi-scale drag model. The predicted results closely agreed with experimental data. Results showed that in an ICFB with a downcomer outlet directly open to the bed (model A), nearly 12.7% to 5.4% of the gas in the draft tube bypasses into the downcomer. In the ICFB models B and C with a conic baffle below the downcomer, the gas bypass is significantly weakened or even eliminated when the diameter of the conic baffle is 1.1 times that of the downcomer (model C). In addition, the solids circulation mass flux in ICFBs increased by about 62.5%, from 126.8kg/(m2s) in model A to 206kg/(m2s) in model C.

A computational particle fluid-dynamics simulation of hydrodynamics in a three-dimensional full-loop circulating fluidized bed: Effects of particle-size distribution

A computational particle fluid-dynamics model coupled with an energy-minimization multi-scale (EMMS) drag model was applied to investigate the influence of particle-size distribution on the hydrodynamics of a three-dimensional full-loop circulating fluidized bed. Different particle systems, including one monodisperse and two polydisperse cases, were investigated. The numerical model was validated by comparing its results with the experimental axial voidage distribution and solid mass flux. The EMMS drag model had a high accuracy in the computational particle fluid-dynamics simulation of the three-dimensional full-loop circulating fluidized bed. The total number of parcels in the system (Np) influenced the axial voidage distribution in the riser, especially at the lower part of the riser. Additional numerical simulation results showed that axial segregation by size was predicted in the two polydisperse cases and the segregation size increased with an increase in the number of size classes. The axial voidage distribution at the lower portion of the riser was significantly influenced by particle-size distribution. However, radial segregation could only be correctly predicted in the upper region of the riser in the polydisperse case of three solid species.

A comprehensive CFD combustion model for supercritical CFB boilers

A combustion model of a large-scale supercritical circulating fluidized bed (CFB) boiler was developed for comprehensive computational-fluid-dynamics analysis. The model incorporates gas–solid hydrodynamics, coal combustion, heat transfer on heat exchange surfaces in the furnace, and heat transfer between furnace and working medium in the heat transfer tubes. In simulating the dense and dilute phases in the furnace, the gas–solid hydrodynamics is based on the Euler–Euler model and energy-minimization multiscale drag model. Coal combustion entails evaporation, devolatilization, char combustion, gas homogeneous reaction, and pollutant emission. The coefficient of heat transfer between gas–solid and the waterwall is estimated using the cluster renewal model, and for radiation, the discrete ordinate model is used. Moreover, thermohydraulic processes in the membrane wall are also included in the heat transfer process. The model was successfully applied in simulations of a 350-MW supercritical CFB boiler. Detailed distributions of solids concentration, oxygen, heat flux, and working medium temperature in the boiler furnace are presented.

CPFD study of a full-loop three-dimensional pilot-scale circulating fluidized bed based on EMMS drag model

For the purpose of process optimization and scale-up, coupling energy-minimization multi-scale (EMMS) drag model with computational particle fluid dynamics (CPFD) is a good option for large scale three dimensional full-loop circulating fluidized bed (CFB) simulation. In this study, such integration is applied for a complex CFB with six cyclones, based on Barracuda platform, to investigate the gas-solids flow dynamic characteristics in scaled-up system, especially in the dense flow region, and to characterize different fluidization regimes. The simulation results are compared with those obtained from Wen-Yu model, in terms of axial pressure distribution, solid volume fraction, particle recirculation, etc., and are evaluated against available measurement data. The result demonstrates that EMMS drag model can predict the axial pressure distribution well, especially in the dense region, which gives an S-shape solid volume fraction in the axial direction and two-core-annulus structures (‘M’ shape) in the radial direction. Meanwhile, EMMS drag model provides smaller drag force between the gas phase and the solids that the particle recirculation fluxes inside and outside the riser is relatively smaller. With the increase of superficial gas velocity, three different fluidization regimes, including multiple bubble regime, exploding bubble regime and turbulent fluidization regime, are identified based on EMMS drag model. The results show that the dense region is clear at the multiple and exploding bubble regimes; while the particle volume fraction and mass flow rate in the riser top are larger than those in the middle at the turbulent fluidization regime, which gives a guidance that the riser height is limited that particles do not have enough space to distribute.

CFD simulation of gas-liquid-solid flow in slurry bubble columns with EMMS drag model

The drag models reflecting the complex phase interactions are of critical importance in the CFD simulation of gas-liquid or gas-liquid-solid flows. In this study, we demonstrate that the Dual-Bubble-Size (DBS) drag model based on the Energy-Minimization Multi-Scale (EMMS) concept, is capable of effectively predicting the distribution of gas holdup in slurry bubble columns. For solid-free or low solid loading systems, a thorough comparison of the DBS-Global and other drag models indicates that, without any fitting parameters, the DBS-Global drag model prediction on the radial distribution of gas holdup and solid hydrodynamics is in conformity with experiments over a wide range of superficial gas velocities. The three-fluid and two-fluid models are also compared in this work, indicating that the three-fluid model in combination with the DBS-Global drag model gives the best prediction. Previous experiments show that the effects of solid presence on hydrodynamics become pronounced at high solid loading conditions. The prediction of the original DBS-Global drag model deviates from the experiments at high solid loading conditions, and the solid effects need to be taken into account. This work then proposes a modified drag model for simulating three-phase systems at high solid concentration. The new model is capable of accurately predicting the local gas holdup for the systems of solid loading of 25% or 40%. Further fundamental study of the solid effect on the change of flow structure and dominant mechanisms in gas-liquid flow is required.

Numerical Study of the Scaling Rules for Riser with Consideration of Cluster Effect

The validation of scaling rules with the consideration of cluster effect is investigated by two-fluid models. Glicksman’s full and simplified scaling rules are used to build two 1:3 scaled-up risers. The cluster features within different particle classes or operation conditions are approached with the energy minimization multiscale drag model. The comparison of axial and radial solids concentration between three cases indicates that the simplified set scaled riser produces a poor fit throughout the length of the riser and that the full set scaled riser produces a good similarity only toward the top half of the riser. The analysis of cluster characteristics of three cases illustrates that the accurate repetition of the clusters is essential for the hydrodynamic similarity. The simplified set scaled riser presents lower cluster characteristic values along the riser, and the full set presents poor similarity of cluster characteristics in the riser’s bottom region.

CFD simulation of solids residence time distribution in a CFB riser

Solids residence time distribution (RTD) in circulating fluidized bed risers is a critical parameter for evaluating reactor performances, however, it is still very difficult to be predicted via computational fluid dynamics (CFD) simulation due to the complexity of particle clustering phenomenon. This paper tries to establish an effective CFD model to reasonably predict solids RTD of gas–solids riser flows by means of properly addressing the paramount role of particle clusters in determining solids RTD. The gas–solids hydrodynamic characteristics were solved by Eulerian–Eulerian model, where an energy minimization multi-scale (EMMS) drag model was applied to modify the gas–solids drag force to account for the influence of particle clusters. The motion of tracer particles was calculated using species transport equation, where the diffusion coefficient of particles, a vital parameter indicating particle diffusion capacity, was investigated thoroughly. The established CFD model was validated against the available experimental data in the literature. It was shown that axial profiles of solids volume fraction and radial profiles of solids mass flux can be well predicted with EMMS drag model, but not with homogeneous drag model. The proper prediction of bed hydrodynamics is also very crucial to the success of solids RTD simulation. On the other hand, the effect of the diffusion coefficient of particles, the magnitude of which can span a range from 10−5m2/s to 10m2/s, is minor when compared with the convective transport mechanism, at least for the specific cases we studied. In addition, the importance of the sampling time resolution and tracer injection time for a RTD curve was addressed. The simulation results showed that a low time resolution often results in the loss of some micro-scale information, i.e. drastically smoothing the fluctuations of the RTD curve, and an inappropriate assessment of the tracer injection time can lead to a significant change of the RTD curve.

Coarse grid simulation of heterogeneous gas–solid flow in a CFB riser with EMMS drag model: Effect of inputting drag correlations

Two-fluid model combined with Energy-Minimization Multi-Scale (EMMS) drag model has been accepted as an effective method to simulate the hydrodynamics of heterogeneous gas–solid flow in circulating fluidized beds. In the EMMS drag model, a drag correlation obtained from homogeneous fluidization and/or packed bed, denoted as traditional drag correlation, is necessary to describe the homogeneous gas–solid interactions within three (dilute-phase, dense-phase and inter-phase) sub-systems. In this article we study the effects of different traditional drag correlations on the effective inter-phase drag force of clustered gas–solid flow within the framework of EMMS drag model, and their consequent effects on CFD results. It was shown that due to the proper consideration of meso-scale structural effect, CFD results using the EMMS drag model are in a reasonable agreement with experimental data (including radial and axial solid concentration profiles and root mean square of local solid concentration), and are slightly affected by different inputting traditional drag correlations. Present conclusion is quite different from the one obtained in previous studies, where coarse grid simulation with traditional drag correlation failed to predict the hydrodynamics of CFB risers and was sensitive to the traditional drag correlation used. Therefore, the EMMS drag model appears as an advantage over traditional drag correlations, since it is not only insensitive to the empirical input, but also gives much better agreement with experiments.

Coarse grid simulation of heterogeneous gas–solid flow in a CFB riser with polydisperse particles

Industrial fluidized beds usually show a wide particle size distribution which significantly affects the performance of gas–solid two-phase reactors. However, in traditional CFD models the particle size distribution is often represented by the Sauter mean diameter no matter whether the distribution is wide or narrow, which cannot reflect the effects of the particle size distribution on its operation. In this study, a simplified population balance model (PBM) is combined with two-fluid model (TFM) and the Energy Minimization Multi-Scale (EMMS) drag model for simulating heterogeneous gas–solid flow. The EMMS drag model is used to characterize the effects of meso-scale clustering structures on the inter-phase drag force. The current model is compared with the model with the assumption of single particle diameter, and is used to study the segregation and mixing characteristics in a riser. It was shown that (i) for the specific cases we studied, particle polydispersity has a negligible effect on the time-averaged axial solid concentration profiles but has a notable effect on the particle velocity distributions, (ii) the experimental hydrodynamics as well as segregation and mixing patterns in a riser with a continuous particle size distribution can be predicted reasonably well by present combined TFM–EMMS–PBM method.

CPFD simulation of circulating fluidized bed risers

This study investigated the applicability of computational particle fluid dynamics (CPFD) numerical schemes for simulating flows in circulating fluidized bed (CFB) risers. Gas–solid flows were simulated in CFB risers containing Geldart A particles with both low and high solid fluxes as well as in a CFB riser containing Geldart B particles for three flow conditions using CPFD. The results are compared to experimental data and previous two-fluid model (TFM) simulations. The time-averaged axial and radial distributions of the solid concentration show that the bottom-dense, upper-dilute and core-annulus heterogeneous structures were successfully captured by the CPFD calculations, but only qualitatively. The results differ from experimental data for Geldart A particles and high solid fluxes, although they were more accurate than two-fluid simulations with conventional drag models. Two-fluid modeling with the EMMS (energy minimization multi-scale) drag model gave more accurate results than the CPFD simulations. The results indicate that the drag force in the CPFD scheme is still overestimated, although the cumulative method used to compute drag force is more accurate than the proportional method in the two-fluid model. An EMMS drag model which takes into account the intrinsic heterogeneity in the CFB risers is needed for the CPFD scheme. The effect of the realistic particle size distribution was seen in the by CPFD results. CFB risers with Geldart A and B particles are calculated using CPFD scheme. The results are more accurate than two-fluid model simulations with the same drag model. A drag model accounting for heterogeneities in CFB risers is needed for CPFD simulation to agree well with experimental data. The effect of particle size distribution is detected by CPFD simulation. ► CFB risers with Geldart A and B particles are calculated using CPFD scheme. ► The capability of CPFD for calculating flows in CFB risers is promising. ► Comparing to TFM, the CPFD scheme is indicated to be more advanced. ► A drag model accounting for heterogeneities in CFB risers is needed for CPFD. ► The effect of particle size distribution is detected by CPFD calculation.

MP-PIC simulation of CFB riser with EMMS-based drag model

MP-PIC (multi-phase particle in cell) method combined with the EMMS (energy minimization multi-scale) drag force model was implemented with the open source program MFIX to simulate the gas–solid flows in CFB (circulating fluidized bed) risers. Calculated solid flux by the EMMS drag agrees well with the experimental value; while the traditional homogeneous drag over-predicts this value. EMMS drag force model can also predict the macro- and meso-scale structures. Quantitative comparison of the results by the EMMS drag force model and the experimental measurements show high accuracy of the model. The effects of the number of particles per parcel and wall conditions on the simulation results have also been investigated in the paper. This work proved that MP-PIC combined with the EMMS drag model can successfully simulate the fluidized flows in CFB risers and it serves as a candidate to realize real-time simulation of industrial processes in the future.

The simulation and experimental validation on gas-solid two phase flow in the riser of a dense fluidized bed

Gas-solid flow in dense CFB (circulating fluidized bed)) riser under the operating condition, superficial gas 15.5 m/s and solid flux 140 kg/m2s using Geldart B particles (sand) was investigated by experiments and CFD (computational fluid dynamics) simulation. The overall and local flow characteristics are determined using the axial pressure profiles and solid concentration profiles. The cold experimental results indicate that the axial solid concentration distribution contains a dilute region towards the up-middle zone and a dense region near the bottom and the top exit zones. The typical core-annulus structure and the back-mixing phenomenon near the wall of the riser can be observed. In addition, owing to the key role of the drag force of gas-solid phase, a revised drag force coefficient, based on the EMMS (energy-minimization multi-scale) model which can depict the heterogeneous character of gas-solid two phase flow, was proposed and coupled into the CFD control equations. In order to find an appropriate drag force model for the simulation of dense CFB riser, not only the revised drag force model but some other kinds of drag force model were used in the CFD. The flow structure, solid concentration, clusters phenomenon, fluctuation of two phases and axial pressure drop were analyzed. By comparing the experiment with the simulation, the results predicted by the EMMS drag model showed a better agreement with the experimental axial average pressure drop and apparent solid volume fraction, which proves that the revised drag force based on the EMMS model is an appropriate model for the dense CFB simulation.