Scale and structure dependent drag in gas–solid flows

Drag plays a crucial role in hydrodynamic modeling and simulations of gas–solid flows, which is significantly affected by particle Reynolds number, solid volume fraction, heterogeneity, granular temperature, particle-fluid density ratio, and so on. To clarify and quantify the multiscale effects of these factors, large-scale particle-resolved direct numerical simulations of gas–solid flows with up to 115,200 freely moving particles are conducted. Both domain-averaged kinetic properties and local averaged dimensionless drag are sampled and analyzed. It is revealed that the complex scale-dependence of drag is attributed to the multiscale effects of heterogeneous structures and particle fluctuating velocity. The granular temperature and the scalar variance of solid volume fraction are also found to be scale-dependent. On account of these, a new drag correlation as the function of Froude number is proposed with consideration of scale-dependence.     

Experimental investigation and CFD simulation of liquid–solid–solid dispersion in a stirred reactor

For understanding the monosodium aluminate hydrate crystallization from the supersaturated aluminate solution containing red mud as the leaching liquor of bauxite, the liquid–solid–solid dispersion of a simulant system, i.e. glycerite, red mud and sand, in a stirred reactor has been experimentally investigated as well as simulated using computational fluid dynamics model (CFD) for the first time. The computational model is based on the Eulerian multi-fluid model along with RNG k–ε turbulence model, where Syamlal–obrien-symmetric drag force model (Syamlal, 1987) of the inter-phase momentum transfer between two dispersed solid phases is taken into account. A good agreement is obtained between the experimental data of solid distributions and the simulation results in the flow fields of liquid–solid–solid as well as liquid–solid systems. The solid suspension qualities of both liquid–solid and liquid–solid–solid systems in the stirred reactors with and without draft tube were also studied in detail based on mixing time, the standard deviation of solid concentration proposed by Bohnet and Niesmak (1980), the flow pattern and power number. The influence of the interaction between two dispersed solid phases on the suspension of red mud is found significantly greater than that of sand. The holdup of sand below the impeller is considerably larger than that above the impeller and the red mud dispersion approaches homogeneous in the reactor. The mixing time of liquid–solid–solid suspension is longer than that of liquid–solid suspension under the same conditions, and the mixing times of both systems in the stirred reactor with draft tube are longer than that in the reactor without draft tube. Furthermore, the distributions of sand and red mud in the reactor with draft tube were found less homogeneous than those without draft tube in most cases.     

An assessment of the ability of computational fluid dynamic models to predict reactive gas–solid flows in a fluidized bed

Fine grid, two dimensional simulations of reactive gas–solid flows occurring in a fluidized bed reactor were carried out using the Eulerian multi-fluid kinetic theory of granular flow (KTGF) approach in the commercial flow solver, ANSYS FLUENT 12.1. The fuel reactor of a pilot scale Chemical Looping Combustion rig, operated in the bubbling fluidization regime at the Vienna University of Technology, was simulated. Grid dependence studies were carried out as well as sensitivity studies to the fuel inlet condition and the inclusion of gas phase turbulence. Simulations could not accurately reproduce the experimental trend for the case when highly reactive nickel oxide was used as the oxygen carrier material, but in general satisfactory quantitative agreement was observed. The failure to correctly capture the experimental trend was primarily attributed to the fine length-scales at the feed gas inlets not being adequately resolved even at the finest grid investigated. The trend quickly worsened when coarser grids were used, indicating that the generality of the model is lost when grid dependence effects are present. A number of possible dimensional effects were also discussed. Subsequently, the model was used to successfully capture another experimental trend obtained with a much less reactive ilmenite oxygen carrier material. The model captured this trend correctly because the reaction was now limited by the reaction rate and not by species transfer to the large scale gas-emulsion interfaces. Results were therefore not as sensitive to the correct hydrodynamic modelling of the interface, especially near the gas inlets, and the model retained its generality over a wide range of operating conditions.     

Discrete particle simulation of solids motion in a gas–solid fluidized bed

The solids motion in a gas–solid fluidized bed was investigated via discrete particle simulation. The motion of individual particles in a uniform particle system and a binary particle system was monitored by the solution of the Newton's second law of motion. The force acting on each particle consists of the contact force between particles and the force exerted by the surrounding fluid. The contact force is modeled by using the analogy of spring, dash-pot and friction slider. The flow field of gas was predicted by the Navier–Stokes equation. The solids distribution is non-uniform in the bed, which is very diluted near the center but high near the wall. It was also found that there is a single solids circulation cell in the fluidized bed with ascending at the center and descending near the wall. This finding agrees with the experimental results obtained by Moslemian. The effects of the operating conditions, such as superficial gas velocity, particle size, and column size on the solids movement, were investigated. In the fluidized bed containing uniform particles better solids mixing was found in the larger bed containing smaller size particles and operated at higher superficial gas velocity. In the system containing binary particles, it was shown that under suitable conditions the particles in a fluidized bed could be made mixable or non-mixable depending on the ratios of particle sizes and densities. Better mixing of binary particles was found in the system containing particles with less different densities and closer sizes. These results were found to follow the mixing and segregation criteria obtained experimentally by Tanaka et al.     

Some accuracy related aspects in two-fluid hydrodynamic sub-grid modeling of gas–solid riser flows

Sub-grid closures for filtered two-fluid models (fTFM) useful in large scale simulations of riser flows can be derived from highly resolved simulations (HRS) with microscopic two-fluid modeling (mTFM). Accurate sub-grid closures require accurate mTFM formulations as well as accurate correlation of relevant filtered parameters to suitable independent variables. This article deals with both of those issues. The accuracy of mTFM is touched by assessing the impact of gas sub-grid turbulence over HRS filtered predictions. A gas turbulence alike effect is artificially inserted by means of a stochastic forcing procedure implemented in the physical space over the momentum conservation equation of the gas phase. The correlation issue is touched by introducing a three-filtered variable correlation analysis (three-marker analysis) performed under a variety of different macro-scale conditions typical or risers. While the more elaborated correlation procedure clearly improved accuracy, accounting for gas sub-grid turbulence had no significant impact over predictions.     

Effect of anisotropic microstructures on fluid–particle drag in low-Reynolds-number monodisperse gas–solid suspensions

Local structural anisotropy prevails in gas–solid suspensions. It causes strong fluctuations in the drag on individual particles. In this work, the anisotropy of microstructures is quantified by a second-order structure tensor, which is determined with a directionally dependent mean free path length. Direct numerical simulations of low-Reynolds-number flows past anisotropic and isotropic BCC, FCC, and random arrays of monodisperse spheres in sufficiently large domains are performed. The results show that, at the same solid volume fraction, the differences between the mean drag in principal directions of anisotropic arrays and that in isotropic arrays correlate well with functions of eigenvalues of the structure tensor for the anisotropic arrays. Anisotropic drag models for different arrays are proposed. Assessment of the model for random arrays shows that it well captures fluctuations in the mean drag at microscales of several sphere diameters, where the traditional model fails to give satisfactory predictions.     

Minimum superficial fluid velocity in a gas–solid swirled fluidized bed

A swirl flow is achieved in a bed of solids by passing air through multiple fluid inlets, which are tangentially located at the base of a flat-based circular column. The minimum superficial velocities needed to achieve swirling of the bed are measured experimentally under varied conditions. An empirical correlation for the minimum swirl velocity has been proposed. The results indicate that a stable swirling regime operation of the bed is possible. There exists an upper limit of static bed depth beyond which stable swirling of entire bed is not possible. The minimum swirl velocities are found to be 1.2–1.3 times the minimum fluidization velocities predicted for conventional fluidized beds.     

Coupled CFD–DEM of particle-laden flows in a turning flow with a moving wall

The nature of the particle–solid interactions and particle–fluid interactions in rectangular duct bend geometry with/without a moving wall is studied, taking into account particle collision, colloidal, and hydrodynamic forces, and four way coupling between the fluid flow and particles. The focus is on systems where particles and fluid phase have similar length scales, fluid Reynolds number (Re_f) ∼ 1, and particle's Stokes number (St) ∼ 1. Particles move toward the walls of the channel near the bend, and have long residence times in these regions. Buoyancy force has negligible effect on particle motion, where adhesion and drag forces lead to particle motion and agglomeration patterns. The effect of a free surface on agglomeration sites in the turning flow is elucidated.     

Experimental and simulation study of nylon 6 solid–liquid extraction process

The solid–liquid extraction process of nylon 6 to eliminate small molecules, i.e., caprolactam(CL), cyclic dimers(CD) and cyclic trimers(CT), is investigated in detail by both batch extraction experiments and numerical simulations. In the batch extraction experiments, due to the small molecules attaching to the polymeric surface, the basic physical mechanism shifts from surface diffusion to internal diffusion as the extraction proceeded. The experimental data are well reproduced by a diffusion model consisting of two distinct steps, characterized as surface diffusion and internal diffusion. Furthermore, based on the established mass transfer mechanism and diffusion model of the two distinct steps, the equilibrium constants and internal diffusion coefficients of CL, CD and CT are acquired. An industrial countercurrent extraction tower is further simulated. It is found that the extraction efficiency of CL can be significantly improved by increasing the temperature at the bottom portion of the tower. The elimination of CD, which can be greatly promoted by a high-concentration CL-water solution, is controlled by mass transfer resistance, whereas the removal of CL is mainly affected by the equilibrium.     

Validation of an anisotropic model of turbulent flows containing dispersed solid particles applied to gas–solid jets

A mathematical model of turbulent flows containing dispersed solid particles is described together with its application to gas–solid jets. Flow fields are predicted by solution of the density-weighted transport equations expressing conservation of mass and momentum, with closure achieved through the k–? turbulence model and a second-moment closure. The particle phase is calculated using a Lagrangian particle tracking technique which involves solving the particle momentum equation in a form that accounts for the spatial, temporal and directional correlations of the Reynolds stresses experienced by a particle. The two phases are coupled via modification of the fluid-phase momentum equations. Predictions of the complete model are validated against available experimental data on a number of single-phase and two-phase, gas–solid jet flows with various particle loadings, and both mono- and poly-dispersed particle size distributions. Overall, predictions of the models compare favourably with the data examined, with results obtained from the anisotropic second-moment turbulence closure being superior to eddy viscosity-based predictions.     

CFD simulation of impeller shape effect on quality of mixing in two-phase gas–liquid agitated vessel

Mixing efficiency in two-phase gas–liquid agitated vessel is one of the important challenges in the industrial processes. Computational fluid dynamics technique (CFD) was used to investigate the effect of four different pitched blade impellers, including 15°, 30°, 45° and 60°, on the mixing quality of gas–liquid agitated vessel. The multiphase flow behavior was modeled by Eulerian–Eulerian multiphase approach, and RNG k − ε was used to model the turbulence. The CFD results showed that a strong global vortex plays the main role on the mixing quality of the gas phase in the vessel. Based on the standard deviation criterion, it was observed that the axial distribution of the gas phase in the 30° impeller is about 55% better than the others. In addition, the results showed that the 30° impeller has a uniform radial distribution over the other impellers and the maximum gas phase holdup in the vessel. Investigation of the power consumption of the impellers showed that the 30° impeller has the highest power consumption among the other pitched blade impellers. Also, examine the effect of same power condition for pitched blade impellers showed that the 30° impeller has the best mixing quality in this condition.     

Numerical simulation of micro-mixing in gas–liquid and solid–liquid stirred tanks with the coupled CFD-E-model

The coupled CFD-E-model for multiphase micro-mixing was developed, and used to predict the micro-mixing effects on the parallel competing chemical reactions in semi-batch gas–liquid and solid–liquid stirred tanks. Based on the multiphase macro-flow field, the key parameters of the micro-mixing E-model were obtained with solving the Reynolds-averaged transport equations of mixture fraction and its variance at low computational costs. Compared with experimental data, the multiphase numerical method shows the satisfactory predicting ability. For the gas–liquid system, the segregated reaction zone is mainly near the feed point, and shrinks to the exit of feed-pipe when the feed position is closer to the impeller. Besides, surface feed requires more time to completely exhaust the added H⁺ solution than that of impeller region feed at the same operating condition. For the solid–liquid system, when the solid suspension cloud is formed at high solid holdups, the flow velocity in the clear liquid layer above the cloud is notably reduced and the reactions proceed slowly in this almost stagnant zone. Therefore, the segregation index in this case is larger than that in the dilute solid–liquid system.     

On the effects of the flow macro-scale over sub-grid modelling in dense gas–solid fluidized flows

Multiscale modelling of gas–particle fluidized flows is frequently approached by means of sub-grid modelling, which provides constitutive closures for filtered formulations applied to large scale simulations. A widely practiced procedure for the derivation of sub-grid models consists of filtering over predictions from highly resolved simulations under two-fluid modelling. The present work is intended as a contribution in this field by providing new supporting evidence for the enhancement of sub-grid closure models. Most of the efforts in the area have been directed to providing sub-grid models dependent on meso-scale filtered effects alone, and under low gas Reynolds number suspension conditions. In this work, macro-scale conditions are added to the analysis thereby accounting for flow topology, particularly for dense gas–solid fluidized flows. Two macro-scale variables are considered in the simulations, namely the domain average solid volume fraction and the domain average gas Reynolds number. So, in addition to the usual meso-scale filtered markers, relevant filtered parameters are also related to those macro-scale conditions. The filtered parameters of interest here are the effective interphase drag coefficient and filtered and residual stresses in both of the phases. Various domain average solid volume fractions and domain average gas Reynolds numbers were enforced, thereby providing for a variety of macro-scale dense conditions. It was found that both these macro-scale parameters considerably affect the meso-scale and the resulting filtered parameters of dense gas–solid flows, even though this occurs in a milder way when compared to results for dilute flow conditions available in the literature.     

A fundamental CFD study of the gas–solid flow field in fluidized bed polymerization reactors

A Eulerian–Eulerian model incorporating the kinetic theory of granular flow was applied to describe the gas–solid two-phase flow in fluidized bed polymerization reactors. The model parameters were examined, and the model was validated by comparing the simulation result with the classical calculated data. The effects of distributor shape, solid particle size, operational gas velocity and feed manner on the flow behavior in the reactor were also investigated numerically. The results show that with the increase of solid particle diameter, the bubble numbers decrease and the bubble size increases, resulting in a smaller bed expansion ratio. Bed expansion ratio increases with increasing the gas inlet velocity. Moreover, the final fluidized qualities are almost the same for the plane distributor case and the triangle distributor case. There exists a tempestuous wiggle from side to side in the bed at the continuous feed manner, which could not be obtained at a batch feed manner.     

Coarse grid simulation of bed expansion characteristics of industrial-scale gas–solid bubbling fluidized beds

Two-fluid modeling of the hydrodynamics of industrial-scale gas-fluidized beds proves a long-standing challenge for both engineers and scientists. In this study, we suggest a simple method to modify currently available drag correlations to allow for the effect of unresolved sub-grid scale structures, by assuming that the particles inside each computational cell are presented in the form of a two-phase structure. This method would thus make it possible to simulate the hydrodynamics of industrial-scale bubbling fluidized beds of Geldart B and D particles with a coarse computational mesh. It is shown that with the proposed modification of the drag force correlation, the experimentally measured bed expansion characteristics of industrial-scale bubbling fluidized beds can be reasonably predicted at acceptable computational cost. Also the simulation result for the macroscopic solid circulation pattern is in qualitative agreement with the experimental data.     

Numerical simulation of local and global mixing/segregation characteristics in a gas–solid fluidized bed

Researches on solids mixing and segregation are of great significance for the operation and design of fluidized bed reactors. In this paper, the local and global mixing and segregation characteristics of binary mixtures were investigated in a gas–solid fluidized bed by computational fluid dynamics-discrete element method (CFD-DEM) coupled approach. A methodology based on solids mixing entropy was developed to quantitatively calculate the mixing degree and time of the bed. The mixing curves of global mixing entropy were acquired, and the distribution maps of local mixing entropy and mixing time were also obtained. By comparing different operating conditions, the effects of superficial gas velocity, particle density ratio and size ratio on mixing/segregation behavior were discussed. Results showed that for the partial mixing state, the fluidized bed can be divided into three parts along the bed height: complete segregation area, transition area and stable mixing area. These areas showed different mixing/segregation processes. Increasing gas velocity promoted the local and global mixing of binary mixtures. The increase in particle density ratio and size ratio enlarged the complete segregation area, reduced the mixing degree and increased the mixing time in the stable mixing area.     

Reduction of nitrogen oxides from simulated exhaust gas by using plasma–catalytic process

Removal of nitrogen oxides (NO_x) using a nonthermal plasma reactor (dielectric-packed bed reactor) combined with monolith V₂O₅/TiO₂ catalyst was investigated. The effect of initial NO_x concentration, feed gas flow rate (space velocity), humidity, and reaction temperature on the removal of NO_x was examined. The plasma reactor used can be energized by either ac or pulse voltage. An attempt was made to utilize the electrical ignition system of an internal combustion engine as a high-voltage pulse generator for the plasma reactor. When the plasma reactor was energized by the electrical ignition system, NO was readily oxidized to NO₂. Performance was as good as with ac energization. Increasing the fraction of NO₂ in NO_x, which is the main role of the plasma reactor, largely enhanced the NO_x removal efficiency. In the plasma–catalytic reactor, the increases in initial NO_x concentration, space velocity (feed gas flow rate) and humidity lowered the NO_x removal efficiency. However, the reaction temperature in the range up to 473 K did not significantly affect the NO_x removal efficiency in the presence of plasma discharge.     

Numerical simulations and validation of gas–solid flows in a fluidized-bed roaster based on the CFD-DPM model

In view of the complex gas–solid flow characteristics in a fluidized-bed roaster, the discrete phase model (DPM) provided by ANSYS software was used to numerically analyze the model using a coupled algorithm. The asymmetric flow phenomenon in the transition section at the top of the furnace was found to be unfavourable to the gas–solid flow, and an inverted U-shaped furnace structure was proposed to optimize the transition section at the top of the furnace. A large cold experimental setup was built to verify the model. The results showed that the air velocity is mainly in the axial upward direction; under the action of the gas, the solid particles and the air velocity are basically in the same direction. The main furnace and subfurnace connection section changes the movement of the gas–solid mixture, and its unreasonable structure leads to the asymmetric flow phenomenon of the gas–solid fluid at the top of the furnace. Compared with the previous furnace structure, the uniformity of gas–solid flow in the optimized ‘inverted U-shaped’ structure has been significantly improved. The cold experimental results are in good agreement with the numerical simulation results, which verifies the accuracy of the proposed model.