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Axisymmetric diffusers find wide applications in various industrial processes, including combustion systems, pneumatic conveying, and fluidized bed reactors. Understanding and accurately modeling the behavior of two-phase flows in these devices are critical for optimizing their performance and efficiency. Various aspects of the two-phase gas-solid flow, including particle-particle and particle-wall interactions, interphase momentum transfer, and phase segregation, are investigated. Our currently developed technique, which uses a cut-cell technique, is an established new method to handle the inclined wall of an axisymmetric diffuser. The near-wall cells are treated as five faces for the new grid; one is the inclined wall. This helps treat the boundary condition at the wall in an accurate physical way. The code FORTRAN, developed in-house, was used to solve the axisymmetric diffuser using a cut-cell technique. The results of this study will provide valuable insights into the behavior of gas-solid two-phase flows in axisymmetric diffuser. A parametric study of the impact of particles diameters (100 , 200 , and 300 μ m ), the solid volume loading ratios (0.005 , 0.008 , 0.01) , and cant angle (4.5 ∘ , 7 ∘ , 9.5 ∘) effect of axisymmetric diffuser on the local skin friction, pressure, velocity, turbulent kinetic energy, and separation zone. [ABSTRACT FROM AUTHOR]

Abstract Axisymmetric diffusers find wide applications in various industrial processes, including combustion systems, pneumatic conveying, and fluidized bed reactors. Understanding and accurately modeling the behavior of two-phase flows in these devices are critical for optimizing their performance and efficiency. Various aspects of the two-phase gas-solid flow, including particle-particle and particle-wall interactions, interphase momentum transfer, and phase segregation, are investigated. Our currently developed technique, which uses a cut-cell technique, is an established new method to handle the inclined wall of an axisymmetric diffuser. The near-wall cells are treated as five faces for the new grid; one is the inclined wall. This helps treat the boundary condition at the wall in an accurate physical way. The code FORTRAN, developed in-house, was used to solve the axisymmetric diffuser using a cut-cell technique. The results of this study will provide valuable insights into the behavior of gas-solid two-phase flows in axisymmetric diffuser. A parametric study of the impact of particles diameters ( 100 , 200 , and 300 μ m $100,\ 200,\ \text{and} \ 300\mu m$ ), the solid volume loading ratios ( 0.005 , 0.008 , 0.01 ) $(0.005,\ 0.008,\ 0.01)$ , and cant angle ( 4.5 ∘ , 7 ∘ , 9.5 ∘ ) $(4.5^{\circ},\ 7^{\circ},\ 9.5^{\circ}) $ effect of axisymmetric diffuser on the local skin friction, pressure, velocity, turbulent kinetic energy, and separation zone.

This study aims to provide insights into the intricate interactions between gas and liquid phases within flow components, which are pivotal in various industrial sectors such as nuclear reactors, oil and gas pipelines, and thermal management systems. Employing the Eulerian–Eulerian approach, our computational model incorporates interphase relations, including drag and non-drag forces, to analyze phase distribution and velocities within a complex U-bend system. Comprising two horizontal-to-vertical bends and one vertical 180-degree elbow, the U-bend system's behavior concerning bend geometry and airflow rates is scrutinized, highlighting their significant impact on multiphase flow dynamics. The study not only presents a detailed exposition of the numerical modeling techniques tailored for this complex geometry but also discusses the results obtained. Detailed analyses of local void fraction and phase velocities for each phase are provided. Furthermore, experimental validation enhances the reliability of our computational findings, with close agreement observed between computational and experimental results. Overall, the study underscores the efficacy of the Eulerian approach with interphase relations in capturing the complex behavior of the multiphase flow in U-bend systems, offering valuable insights for hydraulic system design and optimization in industrial applications. [ABSTRACT FROM AUTHOR]

The hydrodynamic behaviour of air-glass beads bubbling fluidized bed reactor containing spherical glass beads is numerically studied, using OpenFoam v7 CFD software. Both Gidaspow and Syamlal-O'Brien drag models are used to calculate momentum exchange coefficients. Simulation predictions of pressure loss, bed expansion rate, and air volume fraction parameters were compared and validated using data, existing in the literature obtained experimentally and performed by other numerical softwares. Pressure loss and rate of bed expansion were calculated with relative root mean square error (RMSE) equal to 0.65 and 0.095 respectively; Syamlal-O'Brien model is considered more accurate than Gidaspow model. Hence, numerical model reliability developed on OpenFoam was also proved. The hydrodynamic aspect study of the fluidized bed reactor was then performed, to analyse the impact of inlet air velocity (U) on particles motion. It was revealed that with U increment, air and glass beads axial velocities increase in the reactor centre and decrease in the sidewalls. Thus, a greater particle bed expansion is induced and the solid particles accumulated highly on the reactor sidewalls. In general, with the increase of U, the solid volume fraction decreases from 0.63 to 0.58 observed at 0.065 m/s and 0.51 m/s, respectively.

This study aims to provide insights into the intricate interactions between gas and liquid phases within flow components, which are pivotal in various industrial sectors such as nuclear reactors, oil and gas pipelines, and thermal management systems. Employing the Eulerian–Eulerian approach, our computational model incorporates interphase relations, including drag and non-drag forces, to analyze phase distribution and velocities within a complex U-bend system. Comprising two horizontal-to-vertical bends and one vertical 180-degree elbow, the U-bend system’s behavior concerning bend geometry and airflow rates is scrutinized, highlighting their significant impact on multiphase flow dynamics. The study not only presents a detailed exposition of the numerical modeling techniques tailored for this complex geometry but also discusses the results obtained. Detailed analyses of local void fraction and phase velocities for each phase are provided. Furthermore, experimental validation enhances the reliability of our computational findings, with close agreement observed between computational and experimental results. Overall, the study underscores the efficacy of the Eulerian approach with interphase relations in capturing the complex behavior of the multiphase flow in U-bend systems, offering valuable insights for hydraulic system design and optimization in industrial applications.

The hydrodynamic behaviour of air-glass beads bubbling fluidized bed reactor containing spherical glass beads is numerically studied, using OpenFoam v7 CFD software. Both Gidaspow and Syamlal-O'Brien drag models are used to calculate momentum exchange coefficients. Simulation predictions of pressure loss, bed expansion rate, and air volume fraction parameters were compared and validated using data, existing in the literature obtained experimentally and performed by other numerical softwares. Pressure loss and rate of bed expansion were calculated with relative root mean square error (RMSE) equal to 0.65 and 0.095 respectively; Syamlal-O'Brien model is considered more accurate than Gidaspow model. Hence, numerical model reliability developed on OpenFoam was also proved. The hydrodynamic aspect study of the fluidized bed reactor was then performed, to analyse the impact of inlet air velocity (U) on particles motion. It was revealed that with U increment, air and glass beads axial velocities increase in the reactor centre and decrease in the sidewalls. Thus, a greater particle bed expansion is induced and the solid particles accumulated highly on the reactor sidewalls. In general, with the increase of U, the solid volume fraction decreases from 0.63 to 0.58 observed at 0.065 m/s and 0.51 m/s, respectively. [ABSTRACT FROM AUTHOR]

The present study investigates the hydrodynamics and mass transfer of the liquid–gas ejector using three-dimensional (air–water) and two-dimensional (CO2/air-MEA (Monoethanolamine) solution) computational fluid dynamics (CFD) modeling. For 3D simulation, validation of the CFD results of this ejector with experimental data (error less than 5%) showed high simulation accuracy. The effects of motive liquid flow rate and outlet pressure parameters on the air entrainment rate and air hold-up are also investigated. It was found that by increasing the outlet pressure by about 70% (from 3587 to 6127 Pag), the rate of gas entrainment and gas hold up decreased by about 37% and 20%, respectively. On the contrary, these parameters showed increasing behavior of about 74% and 15%, respectively, when the mass flow rate of liquid increased by about 21%. In addition, three-dimensional phenomena such as mixing shock and the location of its occurrence are examined, which is the reason for recirculation and vortex in the ejector. Next, by simulating a two-dimensional simulation and changing the inlet fluids to CO2/air-methanol amine, the ejector was designed to simultaneously increase the gas pressure and absorb carbon dioxide. A user-defined function code was used to express the mass transfer from the gas to the liquid phase. The results, in this case, showed that with increasing the outlet pressure of the ejector (from 0 to 2000 Pag), and enhancing the concentration of MEA solution (from 10% to 30%), the CO2 removal boosted from 83% to 95%. A similar behavior was shown when the L/G ratio increased from 3.5 to 5.5. This study serves as a showcase on how to do an exact design and analysis for liquid–gas ejectors in flare gas recovery systems. [ABSTRACT FROM AUTHOR]

A mathematical modeling approach was used to test different design modifications in a flash smelting settler to reduce the copper losses in slag, which is economically disadvantageous for copper processing using the pyrometallurgical route. The main purpose of this study was to find ways to reduce copper losses in slag by improving the settling and coalescence of copper matte droplets, in particular, the smallest droplet sizes of ≤100 µm. These improvements inside the flash smelting (FS) settler were targeted through different settler design modifications. Three different design schemes were tested using the commercial computational fluid dynamics (CFD) software, Ansys Fluent. These settler design modification schemes included the impact of various baffle types, positioning, the height inside the settler, and settler bottom inclinations. Simulations were carried out with and without coalescence and the results were compared with normal settler design. The results revealed that the settling phenomenon and coalescence efficiency were improved significantly with these design modifications. It was concluded that a single baffle design was optimal for reducing copper losses and increasing coalescence efficiency instead of using multiple baffle arrangements. The top-mounted baffle outperformed the bottom-mounted baffle and inclined settler design. [ABSTRACT FROM AUTHOR]

Gas-particle flows in circulating fluidized beds (CFB) with wide particle size distributions were simulated using the Eulerian-Eulerian approach to analyze the effects of the particle phase division and the applicability of the particle-particle drag model. The results indicate that the simulation is not accurate by just using a single average particle diameter when the particle size distribution includes a critical particle diameter. A binary particle phase division criterion was then developed to establish two particle phases representing two types of particles with different flow patterns. Coupling the Eulerian-Eulerian approach with the new criterion enabled accurate predictions of the pressures, particle volume fractions, and particle mass circulation rates that were in agreement with experimental data. The influences of different particle-particle drag models were also investigated to show that the simulation using the Syamlal model was not accurate due to the overestimated particle-particle drag, while the results without particle-particle drag and with the Manger model were similar and much more accurate. Moreover, the flow mechanism for the non-uniformity of particle circulation rates in the parallel circulating loops of the CFB boiler was revealed. This study improves the Eulerian-Eulerian simulations of fluidization with wide particle size distributions and further deepens the understanding of flow characteristics in CFB. [ABSTRACT FROM AUTHOR]

A numerical scheme for the effects of vibration on nanofluid pool boiling heat transfer was developed. For this purpose, a horizontal flat vibrating heated surface was considered. To model this phase-change phenomenon, the Eulerian-Eulerian approach was employed accompanied by the Rensselaer Polytechnic Institute (RPI) model to estimate the boiling heat flux on a solid surface, based on transient simulation. The k-ε turbulence model was used for simulating the Reynolds stresses appearing in the averaged Navier Stokes equation. The effects of the amplitude and frequency of vibration, nanofluid concentration along with magnitude of the heat flux on pool boiling heat transfer characteristics including heat transfer coefficient (HTC), vapor volume fraction and nanofluid velocity were studied. New analytical correlations for analyzing the heat transfer coefficient and nanofluid velocity based on the wall superheat temperature, amplitude and frequency of vibration were also developed. Results showed that applying mechanical vibration increased the boiling curve slope and the heat transfer coefficient. As a consequence, an increase of up to 30.11% and 17.5% in the heat transfer rate was achieved at lower heat fluxes for higher amplitude and frequency of oscillations, respectively. [ABSTRACT FROM AUTHOR]

Wall-to-bed (or wall-to-fluid) heat transfer issues in trickle bed reactors (TBR) has an important impact on operation and efficiency in this category of reactors. In this study, the hydrodynamic and thermal behavior of trickle bed reactors was simulated by means of computational fluid dynamics (CFD) technique. The multiphase behavior of trickle bed reactor was studied by the implementation of the Eulerian-Eulerian multiphase approach. Also, bed porosity effect was modeled by porosity function method. In order to study the effect of operating parameters on wall-to-bed heat transfer, the influence of catalyst particle diameter and catalytic bed porosity was investigated on wall-to-bed Nu number. The results showed that the enhancement of catalytic bed porosity from 0.36 to 0.5 decreases the Nu number about 15% due to a reduction of liquid velocity adjacent to the reactor wall. Also, the increase of particle diameter from 4 to 6 millimeter decreases wall-to-bed Nu number about 15% owing to a reduction in liquid phase volume fraction.

The present study investigates the hydrodynamics and mass transfer of the liquid–gas ejector using three-dimensional (air–water) and two-dimensional (CO2/air-MEA (Monoethanolamine) solution) computational fluid dynamics (CFD) modeling. For 3D simulation, validation of the CFD results of this ejector with experimental data (error less than 5%) showed high simulation accuracy. The effects of motive liquid flow rate and outlet pressure parameters on the air entrainment rate and air hold-up are also investigated. It was found that by increasing the outlet pressure by about 70% (from 3587 to 6127 Pag), the rate of gas entrainment and gas hold up decreased by about 37% and 20%, respectively. On the contrary, these parameters showed increasing behavior of about 74% and 15%, respectively, when the mass flow rate of liquid increased by about 21%. In addition, three-dimensional phenomena such as mixing shock and the location of its occurrence are examined, which is the reason for recirculation and vortex in the ejector. Next, by simulating a two-dimensional simulation and changing the inlet fluids to CO2/air-methanol amine, the ejector was designed to simultaneously increase the gas pressure and absorb carbon dioxide. A user-defined function code was used to express the mass transfer from the gas to the liquid phase. The results, in this case, showed that with increasing the outlet pressure of the ejector (from 0 to 2000 Pag), and enhancing the concentration of MEA solution (from 10% to 30%), the CO2 removal boosted from 83% to 95%. A similar behavior was shown when the L/G ratio increased from 3.5 to 5.5. This study serves as a showcase on how to do an exact design and analysis for liquid–gas ejectors in flare gas recovery systems.

This work is devoted to a numerical study of inflow swirl on the flow field in a spouted bed. The Eulerian-Eulerian multiphase model was used to simulate the hydrodynamics of a gas-solid flow in a 2D axisymmetric spouted bed under an unsteady laminar regime. The results of the simulations are validated with the experimental data obtained by He et al. (Can. J. Chem. Eng. Vol. 72, pp. 229–234 and pp. 561–568, 1994). The comparison of the results shows that the numerically obtained profiles of the time-averaged axial solid velocity agree well with the experimentally measured values. The results of the simulations revealed that the slightly increase in the swirling ratio of the inlet flow leads to an enhanced spouting process, while a strong swirling ratio has an adverse effect on the mixing between gas and solid particles. Thus, the use of the inflow swirl enables control of dynamics of spouted beds. Unlabelled Image • Numerical study of inflow swirl on the flow field in a spouted bed. • Slightly increase in the swirling ratio of the inlet flow leads to an enhanced spouting process. • Strong swirling ratio has an adverse effect on the mixing between gas and solid particles. [ABSTRACT FROM AUTHOR]

The present work deals with the investigation of the gas-solid flow in a horizontal pipe using the Eulerian-Eulerian modeling approach for a particle size range of 2 μ m ≤ d p ≤ 20 μ m at solid volume fractions of 0.001 and 0.10 which is missing in the existing literature. An extensive study has been performed to investigate the effect of the particle-wall collision and particle-particle collision, solid volume fraction, particle size and inlet slip ratio on two-phase pressure drop and Nusselt number. The effect of the collisions is found to be prominent only at higher solid volume fraction (10%). Under the particle size considered in the present study, interestingly, the pressure drop shows completely opposite trend under two different solid volume fraction situations which has not been reported in earlier studies due to the consideration of relatively large-sized particles. On the other hand, the Nusselt number gets reduced with an increase in the particle size. The effect of the inter-particle collision is found to affect the pressure drop significantly under the current operating conditions. Both the pressure drop and Nusselt number increases with an increase in the solid volume fraction. Similarly, an increase in the inlet slip ratio increases the Nusselt number, whereas it reduces the pressure drop. [ABSTRACT FROM AUTHOR]

Accurate prediction of SO2 absorption efficiency under different physical and chemical parameters is of significant importance for desulfurization of the flue gas. In order to understand the mechanism of SO2 absorption inside a bubble-dispersion tower, a three-dimensional twin Eulerian model together with two-film theory was applied to simulate the flue gas desulfurization processes in a bubble-dispersion tower. After comparing the predicted desulfurization efficiencies by using calculated gas holdup with the experimental parameters, the deviation of simulated model with the measured ones was small. Moreover, it was observed that the larger the fractional hole area, the better desulfurization performance. The bubble tower showed fine adaptability when the superficial gas velocity varies from 0.3 to 0.7 m/s. Also, there was a positive correlation between the SO2 removal ability and the hydrogen ion concentration. Considering the crystallization of calcium sulfite, the PH of slurry tank inside bubble tower is recommended to be set between 5.5 and 6, and the initial CaCO3 mass fraction is suggested to be set around 10–15% under prediction conditions. Moreover, the SO2 absorption capability could be increased by lifting the initial liquid height, while the SO2 removal efficiency would level off when tube insertion depth/column diameter H/D was over 0.128, so the H/D is suggested to be set from 0.08 to 0.128 to achieve high SO2 absorption and avoid soil erosion. It was observed that the smaller the size of bubbles generated in the slurry, the higher SO2 absorption efficiency could be. [ABSTRACT FROM AUTHOR]

In this work, a full-loop 3D computational fluid dynamics (CFD) numerical simulation of the chemical looping gasification (CLG) process of lignite in a circulating fluidized bed (CFB) was performed using a two-fluid Eulerian-Eulerian model. The results showed that the CFD simulation effectively captured the axial and radial velocities of the particles. More radial flow occurred in the bottom part of the riser and inside the cyclone. The exothermic reaction became dominant within 7s, while the heat-absorbing reaction became dominant between 7 and 15s. The aggregation regions of syngas moved up with that of the high-temperature zone, and CO was the main contributor to the syngas. The particle size in the range of 175–225 μm was inversely proportional to the size of the average heat transfer coefficient (HTC) in the riser. Extremely small particle size saturated the bed, suppressing the HTC. The peak of the HTC was 387.7 W/(m2·K), which occurred in the upper-middle region of the riser and reached. The maximum HTC average value was 180.6 W/(m2·K). Finally, experimental data were used to verify the reliability of the model. [Display omitted] • Simulation of a CLG fuel reactor in a circulating fluidized bed. • Contribute to understanding the rapid fluidization behavior of particles in CFB. • The spatial-temporal distribution of components in riser was investigated. • The spatial-temporal distribution of temperature in riser was investigated. • A study of the heat transfer properties of lignite for the CLG process in a CFB. [ABSTRACT FROM AUTHOR]

Abstract Experimental and numerical investigations of ignition in combustors with multiple burners have recently emerged and have provided new insights on the last phase of ignition in gas turbine-like annular geometries where the flame propagates from burner to burner. Previous comparisons between calculations and experiments of light-round in a laboratory scale annular combustion chamber have demonstrated the ability of large-eddy simulation to predict such processes for perfectly premixed conditions and, more recently, for n-heptane spray injection. The present analysis focuses on two additional operating points with liquid n-heptane sprays and the turbulent flame propagation in the two-phase mixture is examined through the behavior of its leading points. The validation of the light-round process is characterized in terms of ignition delays. The detailed analysis of the propagation through the definition of a leading point enables to highlight some key phenomena responsible for the flame behavior, such as the influence of the liquid droplet spray and its vaporization in the chamber. Calculations indicate that the volumetric expansion due to the chemical reaction at the flame induces a strong azimuthal flow in the fresh stream at a distance of several sectors ahead of the flame, which modifies conditions in this region. This creates heterogeneities in the gas composition and wakes on the downstream side of the swirling jets formed by the injectors, with notable effects on the motion of the leading point and on the absolute flame velocity. [ABSTRACT FROM AUTHOR]

The dynamics of dust lifting behind a passing shock wave has been extensively studied in recent years. Nevertheless, only a few studies have focused on the problem of dust lifting by a rarefaction wave. Therefore, the first objective of this research was to create a three-dimensional computational fluid dynamics (CFD) model of experiments and simulations shown in literature. For this, the Eulerian-Eulerian approach was selected as the modelling technique. The second part of the research was devoted to performing own experiments, as well as their numerical simulations. The process of dust lifting was recorded using a high-speed camera in two pressure chambers with different diameters using a solenoid valve to initiate depressurization. It turned out that the particle layer showed similarities to a fluidized particle bed when exposed to the rarefaction wave. After the rarefaction wave arrived at the particle bed, the bed expanded upwards with visible bubbles forming and expanding inside, eventually breaking through the top of the bed and spouting dust further up the chamber. A combination of smaller particle diameter, smaller pressure chamber diameter and higher initial pressure gave the highest amount of particle dispersion. [ABSTRACT FROM AUTHOR]

This paper deals with the injection of twin oblique nanofluid jets into a channel with water cross-flow. In this regard, the effects of different geometric and physical parameters including the velocity, distance, and angles of the jets as well as the nanoparticles volume fraction therein are studied. The Eulerian-Eulerian two-phase model is employed to analyze the present problem. By solving separate equation sets for water and the nanoparticles, this approach provides the possibility of behavior prediction for each of the phases inside the flow field, separately. The accuracy of the current simulations is confirmed by comparing the obtained results with available experimental data. The results show that replacement of a single jet with twin jets increases the heat exchange from the target surface and makes its distribution more uniform along the surface. In addition, it is found that rise in the velocity and distance of the jets leads to heat transfer improvement. However, the effect of the nanoparticles volume fraction in the injected nanofluid on the heat transfer rate of the target surface is strongly dependent to the nanoparticles penetration into the water cross-flow. Closer scrutiny of the results reveals that the injection angles of the twin jets play an important role in the nanoparticles penetration as well as their distribution pattern inside the flow field and thereby, by adjusting these angles, the heat exchange from the target surface can be improved. [ABSTRACT FROM AUTHOR]

• Bed-to-tube heat transfer in fluidized bed with mixed-size particles are simulated. • Average HTC increases nonlinearly with the proportion of small-size component. • Local HTC is improved by enlarging the size difference between components. • A modified heat transfer correlation for complex particle systems is proposed. Mixed-size particles with low processing cost have great potential to act as the absorbing media in the next-generation concentrated solar power plants. However, the research on the heat transfer from the particles to heated surfaces in gas–solid fluidized beds is limited. In this paper, the bed-to-tube heat transfer coefficient (HTC) in a shallow fluidized bed with immersed tubes is determined numerically. The Eulerian–Eulerian approach that incorporated the kinetic theory of granular flow has been implemented in a two-dimensional model. The distribution of the local HTC around the tube is investigated for various particle systems. The results show that the HTC reaches a maximum at the upper right (45°) and upper left (135°) of the tube, respectively, indicating a strong relation between the local HTC and solid volume fraction (SVF). The average HTC increases as the mean particle size gets smaller. For monosized particles, the HTC increases from 925 W/(m2·K) to 3033 W/(m2·K) as the particle size decreases from 300 to 100 µm. For binary particles, the growth in the HTC is nonlinear, with an increase in growth rate being observed as the small-size component becomes dominant. For mixed-size particles with the same mean size, a higher HTC can be achieved by enlarging the size difference between the components. A modified correlation for predicting the bed-to-tube HTC is established. Besides, the impacts of gas velocity and temperature, and heat radiation on the bed-to-tube HTC are discussed. It is found that an optimal gas velocity exists to maximize the average HTC and SVF simultaneously, while the gas temperature has a minor contribution. Due to the small heat transfer temperature difference, the effect of thermal radiation on the HTC can be neglected even though the bed temperature reaches 800 °C. [ABSTRACT FROM AUTHOR]

Airborne diseases, including COVID-19, are transmitted by respiratory droplets, which makes the study of the evolution of these droplets important to control the transmission. However, the evolution of the droplets is complex, being a multiphase, polydisperse, multicomponent system undergoing evaporation. To numerically investigate such multiphase flows, there are mainly two approaches. One is the Eulerian–Lagrangian (E–L) approach, which is widely used due to its ability to trace the dispersion and evaporation of individual droplets. However, this approach generally has high costs and difficulty in post-processing. The other one is the Eulerian–Eulerian (E–E) approach, which, though having lower costs, is less adopted because of its failure to treat the features of polydispersity and evaporation. In order to take advantage of the low-costs of E–E approach, the population balance equation (PBE) is combined with the E–E approach to trace the polydisperse evaporating droplets. Two PBE solving methods, sectional method (SM) and quadrature based moment method (QBMM), are used and compared. The codes are developed based on the OpenFOAM library and their abilities to predict size changes of evaporating droplets, evolution of expelled airflow front, and aerosols concentration are assessed by using the experimental and numerical results in literature. Good agreements with the reported results are found, indicating the reliability of the CFD-PBE approaches. The SM and QBMM are finally applied in the transport of cough droplets in a 3D chamber. The suspending trends of small droplets and the falling trends of the large droplets are obtained by both methods. The droplets are found to be able to travel a distance longer than 2 m, which is valuable for the guidelines of social distancing. Additionally, the advantages and disadvantages of SM and QBMM are discussed. • The E–E approach is coupled with the PBE to trace the respiratory droplets. • Sectional method and quadrature based moment method are used to solve the PBE. • The CFD-PBE approach is verified and validated with data in literature. • The approach is applied in the dispersion and evaporation of cough droplets. [ABSTRACT FROM AUTHOR]

The circulating fluidized bed, separated by horizontal baffles, was studied both experimentally and numerically by CFD methods. The pressure distribution in a large-scale cold-flow column with a diameter of 700 mm with a circulating fluidized bed of a microspheric catalyst was measured experimentally for the superficial velocity range from 0.05 to 1.0 m/s. The column was sectioned in height by four rows of horizontal baffles made of several angle bars. For this column design 3D CFD simulations were performed based on the Eulerian–Eulerian approach (two-fluid model) with standard closures and using a coarse computational grid. Comparison of the results of the experiment and transient simulations showed that simulation allows estimating the pressure distribution in a fluidized gas-solid apparatus with an error not exceeding 5%. This prediction accuracy can be sufficient for important practical applications, for example, for the calculation and design of the apparatus or the choice of the design of distributive baffles. The pressure distribution over the height of the column is largely determined by the distribution of the catalyst particles inside column. For example, the contribution of the particle weight to the static pressure is approximately 96% for the superficial velocity Wo ∼ 0.1 m/s. Therefore, this kind of simulation can provide useful information for the distribution of solid particles in a fluidized bed apparatus. This is important for a large number of users of commercial CFD packages, which are engaged in the design of devices that provide optimal hydrodynamic conditions. [ABSTRACT FROM AUTHOR]

The Eulerian-Eulerian approach is used to simulate the two phase flow of air and water in a dissolved air flotation (DAF) tank. Unsteady simulation is adopted to obtain the quasi-steady result. The two dimensional model cannot capture the three dimensional feature of flow pattern in the tank. The three dimensional model reproduces the stratification structure observed in the experiment and obtains the satisfactory volume fraction of air bubbles in the separation zone. To account for the turbulence effect, four two-equation turbulence models are evaluated. Although all turbulence models capture the stratification structure in the separation zone, the re-normalization group theory (RNG) k-e model obtains the best agreement with the experimental data. The effect of bubble diameter on the performance of DAF tank is simulated. Small air bubbles can form a big range of high volume fraction of air bubbles, which helps to remove the suspended matters. [ABSTRACT FROM AUTHOR]

A full-scale three-dimensional Eulerian-Eulerian numerical model was established considering absorbing reactions in which the two-film theory model was adopted to describe the absorption process of SO 2 and NO x . The established model was firstly verified by the industrial operation data of a 2 × 220 m 2 sintering flue gas desulfurization tower. Then, using the model, numerical simulations of simultaneous desulfurization and denitration process were carried out based on three different methods including spraying-inside tower oxidation absorption of the composited NaClO 2 /NaClO/Ca(OH) 2 slurry, oxidation absorption of the composited NaClO 2 /NaClO/Ca(OH) 2 slurry and bubble absorption of Ca(OH) 2 slurry. Numerical results revealed that the first method, spraying-inside tower oxidation absorption of the composited NaClO 2 /NaClO/Ca(OH) 2 slurry had the best performance on denitration without influencing on the desulfurization efficiency. The result was then further verified by an industrial scale test on a 2 × 220 m 2 sintering flue gas desulfurization tower. [ABSTRACT FROM AUTHOR]

• A data-driven modeling (DDM) framework is established for Eulerian-Eulerian approach. • The implementation of the DDM framework is verified for an artificial problem. • Bubble tracking data set is filtered in Frenet frame to obtain bubble drag coefficients. • The performance of the data-driven drag model is discussed using a pipe flow case study. Interfacial force closures in the two-fluid model play a critical role for the predictive capabilities of void fraction distribution. However, the practices of interfacial force modeling have long been challenged by the inherent physical complexity of the two-phase flows. The rapidly expanding computational capabilities in the recent years have made high-fidelity data from the interface-captured direct numerical simulation become more available, and hence potential for data-driven interfacial force modeling has prevailed. In this work, we established a data-driven modeling framework integrated to the HZDR multiphase Eulerian-Eulerian framework for computational fluid dynamics simulations. The data-driven framework is verified in a benchmark problem, where a feedforward neural network managed to capture the non-linear mapping between bubble Reynolds number and drag coefficient and reproduce the void distribution resulting from the baseline model in the test case. The second focus is on utilizing the bubble tracking data set to form a closure for the bubble drag in the turbulent bubbly flow, in which the drag coefficient is set to be correlated with the bubble Reynolds number and the Eötvös number. Pseudo-steady state filtering in the Frenet Frame was carried out to obtain the drag coefficient from the turbulent bubbly flow data. The performance of the data-driven drag model is also examined through a case study, where improvement of model's prediction near-wall is regarded necessary. Discussion and further plans of investigation are provided. [ABSTRACT FROM AUTHOR]

• CCU for industrial processes is proposed by using CaL and Chemical Looping cycles. • Mass and energy balances of the chemical looping cycle are implemented in MATLAB. • NiFe 2 O 4 and Fe 2 O 3 are compared for the conversion of 1 t / h of CO 2. • CFD and a User Defined Function reproduce the reaction conditions in the oxidizer. The present work assesses the potential of reducing CO 2 emissions associated with steel production through the introduction of a decarbonization process downstream of a steel mill eventually producing an alternative fuel/syngas. The analysed system is composed of a calcium looping process for CO 2 separation followed by a chemical looping section for syngas production from CO 2 and H 2 O s. The main units in the chemical looping cycle are: the oxidizer, where a flux of CO 2 and H 2 O s reacts with an oxygen carrier to produce CO and H 2 ; the air reactor, where the oxidation of the oxygen carrier is completed by the interaction with air; the reducer, where the reduced oxygen carrier is regenerated to the initial state (Fe 2 O 3 or NiFe 2 O 4 in the present case) through an endothermic reaction occurring at high temperatures. A MATLAB model was created to determine the molar flow rate of the components flowing through the thermochemical cycle and the thermal power associated with each unit at the operating conditions. The analysis is carried out focusing on the treatment of 1 t / h of CO 2 , resulting in 7.1 t / h of NiFe 2 O 4 or 12.1 t / h of Fe 2 O 3. The syngas at the outlet from the oxidizer reactor is composed of equimolar H 2 and CO with a mass flow rate of 0.05 t / h and 0.64 t / h , respectively. A separate MATLAB model was developed to identify the experimental conditions necessary to reach fluidization of FeO particles in a lab-scale oxidizer reactor (u m f = 0.162 m / s). Companion CFD simulations were carried out to evaluate the hydrodynamics of the lab-scale oxidizer reactor and the associated reaction kinetics (Langmuir-Hishelwood) above minimum fluidization conditions with the aim of assessing the assumptions performed in the MATLAB in terms of conversion rates. For the imposed inlet velocity conditions of the gas mixture (2.6 times above the minimum fluidization velocity) large bubbles with low frequency are observed, while full consumption of the reactant gases is achieved during the first 15 s of simulation, due to the significant reaction rate (2.6 k m o l / s m 3). The results of the CFD simulation and the comparison with existing literature allow to validate the assumptions on the oxidizer conversion and the overall accuracy of the model. [ABSTRACT FROM AUTHOR]

A three-dimensional computational fluid dynamic (CFD) model has been developed for simulating full-loop solid circulation in a dual circulating fluidized bed (DCFB) chemical loop combustion (CLC) reactor model. The standard k-ε turbulence model and kinetic theory of granular theory based Eulerian multiphase model were used to describe the gas and solid motions, respectively. The simulations focused on the investigation of solid circulation in a CLC reactor model which consists of an air reactor (AR, height of 1.36 m, diameter of 0.05 m) and a fuel reactor (FR, height of 0.97 m, diameter of 0.054 m). Key gas–solid flow behaviors related to gas–solid circulation behaviors, e.g. the transient flow regime, solid velocity, solid distribution and circulation characteristics, were numerically investigated. It was found that a core–annulus flow structure appeared in FR. The influences of FR and LLS fluidization flow rate on global and internal circulation rate were studied separately. With FR fluidization flow rate increasing, the time-averaged axial solid volume fraction in the top region of FR first increased and then decreased. The influences of FR and LLS fluidization rate on circulation dynamic characteristics, including circulation fluctuation strength and circulation stability, were also numerically investigated in this work. [ABSTRACT FROM AUTHOR]

In the present study, laminar forced convection of copper-oxide nanofluid in a trapezoidal microchannel-heat-sink (MCHS) is studied using the Eulerian–Eulerian two-phase approach. The incompressible, three dimensional and steady state conservation equations are solved using finite volume method. The substrate material is assumed to be silicon, mean diameter of spherical nanoparticles are considered 100 nm and in the 1–4% volume concentration range. The effects of viscous dissipation, Brownian motion and geometry change on thermal performance of MCHS are evaluated. It is observed that the Brownian motion depends on three parameters, namely, nanofluid inlet temperature, nanoparticles diameter and volume fraction. Also, it is found that with the increase in aspect factor at constant Re, average Nusselt number and pressure drop reduce, while at a specified length of MCHS, average Nusselt number decreases. Finally, it is shown that considering the viscous dissipation, pressure drop varies very slowly, while with the increase in nanoparticles volume fraction and therefore increase in viscous dissipation, heat transfer reduces non-linearly. [ABSTRACT FROM AUTHOR]

A three-dimensional model is developed for computational fluid dynamics analysis of soot filtration processes in a wall flow–type particulate filter based on an Eulerian–Eulerian numerical approach. The primary objective of this study is to accurately capture the local values of filtration parameters, such as volume porosity, collection efficiency, and soot mass deposited, through isotropically discretized computational grids within the multi-layered porous wall regions. Most commercial computational fluid dynamics codes do not have the ability to generate structured mesh with ordered cell index or allow expressing mathematical recursive operation or handling time array through defined user field functions. For these reasons, it is difficult to utilize the code in situations where complex algorithms and mathematical treatments are required. Therefore, custom-build user subroutines, written with C++ programming language, are developed and integrated with the model to calculate localized soot mass distributions in each layer of porous wall. New recursive and computationally efficient algorithms are developed utilizing the functional attributes of the computational fluid dynamics code and coupled with the modified unit collector mechanism in order to obtain temporal and local filtration efficiency. Simulations enabled quantitative visualization of the detailed filtration processes along the filter wall and channel, including the time evolution of filtration parameters, which is difficult to detect experimentally. The model revealed correlations between wall flow pattern and rearrangement behaviors of filtration parameters and provided insights into the soot cake layer profiles with respect to both the length and the width of the channel. [ABSTRACT FROM PUBLISHER]

This paper presents a theoretical analysis of the effect produced by Venturi devices in gas wells. The first part of our methodology consists of performing steady-state simulations to fit experimental and theoretical pressure profiles. These simulations were carried out in Aspen Plus® to reproduce gas production in wells. The results in our case study have indicated that the flow pattern corresponds to a mist type. Then CFD simulations have been used to reproduce the gas–liquid flow through a Venturi device based on ANSYS CFX®. It has been observed that the Venturi increases the gas volume fraction and easy formation of smaller bubbles, which tend to flow in the center of the well. CFD simulations were carried out assuming an Eulerian–Eulerian approach for the bubbles dispersion through the Venturi device. The RNG k–ε model and the homogeneous MUSIG model are used to include the turbulence effect and to represent the bubbles population balance, respectively. Thus the numerical evidence indicates that Venturi-devices promote a flow pattern where the pressure drop decreases and hence it can increase the gas production in certain types of gas wells. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with spherical nanoparticles size effects on thermal performance and pressure drop of a nanofluid in a trapezoidal microchannel-heat-sink (MCHS). Eulerian–Eulerian two-phase numerical approach is utilized for forced convection laminar, incompressible and steady three dimensional flow of copper-oxide nanoparticles with water as base fluid at 100 to 200nm diameter and 1% to 4% volume concentration range. Continuity, momentum, energy and volume conservation equations are solved at whole of the computational domain via finite volume method. Obtained results signify that pressure drop increases 15% at Re =500 and 1% volume concentration while nanoparticles diameter increases from 100 to 200nm. By increasing volume concentration, nanoparticles size effect becomes more prominent and it is observed that increment rate of pressure drop is intensified for above 150nm particles diameter. Unlike the pressure drop, heat transfer decreases with an increase in nanoparticles diameter. Also, it is observed that with an increase in nanoparticles diameter, average Nusselt number of base fluid decreases more than that of the nanoparticles and this signifies that base fluid has more efficacy on thermal performance of copper-oxide nanofluid. [Copyright &y& Elsevier]

Abstract: In dilute two-phase flows, the accurate prediction of the temperature of the dispersed phase can be of paramount importance. Indeed, processes such as evaporation or chemical reactions are strongly non-linear functions of heat transfer between the carrier and dispersed phases. This study is devoted to the validation of an Eulerian description of the dispersed phase – the Mesoscopic Eulerian Formalism (MEF) – in the case of non-isothermal flows. Direct Numerical Simulations using the MEF are compared to a reference Lagrangian simulation for a two-dimensional non-isothermal turbulent jet laden with solid particles. The objectives of this paper are (1) to study the influence of the thermal inertia of particles on their temperature distribution and (2) conduct an a posteriori validation of the MEF, which was recently extended to non-isothermal flows. The focus is on the influence of additional terms in the MEF governing equations, namely heat fluxes arising from the Random Uncorrelated Motion (RUM). Results show that mean and rms of particle temperature are strongly dependent of the thermal Stokes number. The mean temperature is satisfactorily predicted by the MEF, comparing to the Lagrangian reference. Under the conditions of the present study, the RUM heat fluxes have a marginal influence on the mean particle temperature. However, a significant impact was observed on the magnitude of particle temperature fluctuations. Neglecting the RUM heat fluxes leads to erroneous results while the Lagrangian statistics are recovered when it is accounted for in the regimes of low to moderate thermal Stokes number. [Copyright &y& Elsevier]

Abstract: Turbulent polydispersed multiphase flows are encountered in many engineering and environmental applications and particularly in combustion applications, spray polydispersity is the norm rather than the exception. In this review we summarize the current state of Eulerian transport models for turbulent polydispersed particulate flows without size class discretization. The stochastic nature of both carrier and dispersed phase justifies a stochastic approach to describe the behavior of such systems. In this regard Brownian motion of a single microscopic particle is discussed to intuitively introduce the subject and point out the need for a stochastic representation of the phenomena based on stochastic differential equations (SDEs). Understanding the stochastic tools and mathematical framework based on Langevin equation is compulsory for the rest of this review but here we restrict our coverage to definitions and general remarks and give references for further readings. A stochastic foundation based on Langevin equation is defined for fluid and particle and derivation of the transport equation up to third order statistics without binning the particle diameter is discussed based on corresponding Fokker–Planck equation. Terms that appear in the process of contracting a probability density function (PDF) causing closure problems are identified. The Maximum entropy method is discussed as a tool for closure of particle acceleration terms in Eulerian transport equations followed by current closure issues such as realizability and generality. [Copyright &y& Elsevier]

The Eulerian-Eulerian approach is used to simulate flow in a dense granular bed subjected to a slight, vertical, sinusoidal vibration. The bottom of the bed was subjected to a vertical vibration, ASin(ωvt)J0(kmx), where J represents the profile of the bottom wall and is the first kind of Bessel function. The governing equations of the gas phase and particle phase are described and the results of the model with different vibration frequencies and amplitudes are presented. Bubble formation and upward and downward heaping were observed at different amplitudes and frequencies. The results of the model confirm that there is a change from upward to downward heaps according to the strength of the vibration. In addition, the location of the bubble and the shape of the heaping at the interface of the bed depend on the strength of the vibration and the profile of the bottom of the container. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents the results of numerical simulations of the fluid flow in milli torus reactor operated as airlift without agitation. CFD simulations were performed in 3D using FLUENT 6.2.16 numerical software. Unstructured mesh for prediction of gas hold up inside the milli torus reactor was investigated. An Eulerian–Eulerian multi-fluid approach was applied with a k − ɛ turbulence model. The inter-phase drag forces were used. For simplification of the solution, the bubbles inside the reactor were assumed to have the same size. The computed gas hold up was compared with the experimental data, a good agreement was obtained for unstructured meshing. For such mesh, simulations were validated with experimental residence time distribution (RTD) determination. [Copyright &y& Elsevier]

Abstract: This study characterizes the hydrodynamics of an industrial scale lift engager which circulates the catalyst between the reactor and regenerator sections of a continuous catalytic reformer in an oil refinery. The flow of Geldart D particles in this unit was simulated using a granular Eulerian model. Before studying the influence of the operating parameters, the effect of several model parameters such as the drag and the frictional pressure models on the predictions was carried out. Whilst all of the drag models investigated in this study (Gidaspow and Syamlal–O’Brien models) gave qualitatively similar results, the choice of the frictional pressure model affected the simulation results in a rather astounding manner. The KTGF based frictional pressure model gave inconsistent results as both catalyst velocity and its volume fraction increased along the lift line. However, the Johnson and Jackson model overcame this drawback. Interestingly, both KTGF based and Johnson and Jackson models gave similar results for the flow inside a simple riser. Therefore, it can be concluded that for complex flow domains having both dilute and dense phase flows, the most widely used KTGF model may not be appropriate and Johnson and Jackson model should be used instead. After optimizing the selection of model parameters, simulations were conducted to study the effect of the lift gas velocity. It was observed that a lower lift gas velocity leads to large-scale fluctuations in the outlet mass flow rate. The simulation results were also compared with the previously reported studies on the riser flow with a reasonable qualitative agreement. [Copyright &y& Elsevier]

• Air injection shifts oil droplets to the central region and enhances the separation efficiency. • The migration velocity of oil droplets toward the center is increased using air injection. • The length of the reverse flow region is increased by the air injection. • Air injection with the small diameter of air bubbles enhances the separation efficiency. The need to have an efficient oil-water separator leads to improve and optimize the hydrocyclones. One way to improve the efficiency of a deoiling hydrocyclone is using air injection. In the present study, the effects of air injection on the three-phase flow field, oil droplet distribution, separation efficiency, and the working principles of deoiling hydrocyclones are investigated using the Eulerian-Eulerian multi-fluid model. The numerical results of two and three-phase flow are in good agreement against the experimental data. The oil core which is formed at the center of the deoiling hydrocyclones disappeared due to the air injection. The injected air creates an air-core inside the deoiling hydrocyclone and flows out through the overflow. The results show that the air injection increases the migration velocity of oil droplets and the length of the reverse flow region, leading to the enhancement of the separation efficiency. The air injection also increases the turbulence level and consequently increases the breakup rate of the oil droplets inside the deoiling hydrocyclone with air injection. Therefore, the air-liquid ratio and the injected bubble diameter should be regulated to increase the efficiency of the air-injected deoiling hydrocyclone. The results of different air injection diameters show that the small injection diameter is preferable due to the more penetration inside the deoiling hydrocyclone and increase the reverse flow region. The simulation results show that the air injection with bubble diameter of 42 μm increases the hydrocyclone efficiency up to 95.6%. [ABSTRACT FROM AUTHOR]

[Display omitted] • An Eulerian-Eulerian approach was used to predict the efficiency curve of cyclones. • The particle polydispersity was considered by the local mean diameter. • The local mean diameter was calculated by solving a population balance equation. • The polydisperse global efficiency was closer to experimental than the monodisperse. • The efficiency curve was in agreement with experimental data from the literature. Predicting the efficiency curve plays a decisive role in cyclone separator design, and a way to do this is through numerical simulations. However, the use of an Eulerian–Lagrangian approach requires high computational cost. Thus, this study proposes an Eulerian-Eulerian approach in which the characteristic diameter is calculated using a population balance equation. Monodisperse and polydisperse simulations with two to eight quadrature points were carried out for the cyclone presented by Huang et al. (2018), and the results were compared with their experimental data. The worst polydisperse simulation shows a global efficiency error of 3.4 % , while the monodisperse error was 27.3 %. The efficiency curve error was less than 3 % for simulations with more than seven quadrature points. The use of the four-way and two-way coupling models resulted in an efficiency curve error of 2.1 % and 4.4 % , respectively. The efficiency curve errors lower than 3 % for the different cases show the feasibility of the proposed model. [ABSTRACT FROM AUTHOR]

Abstract: The bed flow regimes and the hydrodynamics in a 2D countercurrent staged fluidised bed were simulated using Computation Fluid Dynamics (CFD). Based on the two-fluid theory, an Eulerian–Eulerian approach coupled with kinetic theory of granular flow (KTGF) for the solid phase was applied. The predictions were compared with the experimental results of Kuo and Cheng (2006). The calculated and experimental results both showed a non-growth flow regime, a dilute flow regime, an oscillating flow regime, a bubbling flow regime and a flooding flow regime on the perforated plate at different operating conditions. The values of the predicted pressure drop across the bed at steady state for the dilute flowing regime and the bubbling flowing regime agreed quantitatively well with the previous experimental results, although the time to reach the steady state was different. The calculated flow regime map as functions of the gas velocities and solids feeding rates agreed qualitatively with the experiments. [Copyright &y& Elsevier]

Abstract: Simultaneous solution algorithms for Eulerian–Eulerian gas–solid flow models are presented and their stability analyzed. The integration algorithms are based on dual-time stepping with fourth-order Runge–Kutta in pseudo-time. The domain is solved point or plane wise. The discretization of the inviscid terms is based on a low-Mach limit of the multi-phase preconditioned advection upstream splitting method (MP-AUSMP). The numerical stability of the simultaneous solution algorithms is analyzed in 2D with the Fourier method. Stability results are compared with the convergence behaviour of 3D riser simulations. The impact of the grid aspect ratio, preconditioning, artificial dissipation, and the treatment of the source terms is investigated. A particular advantage of the simultaneous solution algorithms is that they allow a fully implicit treatment of the source terms which are of crucial importance for the Eulerian–Eulerian gas–solid flow models and their solution. The numerical stability of the optimal simultaneous solution algorithm is analyzed for different solids volume fractions and gas–solid slip velocities. Furthermore, the effect of the grid resolution on the convergence behaviour and the simulation results is investigated. Finally, simulations of the bottom zone of a pilot-scale riser with a side solids inlet are experimentally validated. [Copyright &y& Elsevier]

This paper studies the Eulerian–Lagrangian and Eulerian–Eulerian approaches for the simulation of interaction between free surface flow and particles. The dynamics of the fluid as well as the transport of the particles in the Eulerian description is solved using the lattice Boltzmann method. To minimize artificial diffusion in particle transport the lattice Boltzmann method with direction-dependent stabilization is proposed. The interaction between the fluid and particles is ensured using the particulate immersed boundary method, where the two-ways coupling algorithm is considered. The developed Eulerian–Lagrangian and Eulerian–Eulerian schemes are compared with each other and validated against results from literature. Both schemes are applied to free surfaces flow problems with complex geometries similar to real gravity casting problems with fillers. [ABSTRACT FROM AUTHOR]

• A 3D CFD model is used for biomass combustion in a bubbling fluidized bed furnace. • Several sub-models of solid hydrodynamics and combustion process are incorporated. • Solid hydrodynamics is investigated by using inert particles. • Combustion behaviour of two different biomass fuels are studied. • Predicted results are compared with experimental analysis. Biomass combustion in a bubbling fluidized bed has become a competitive technology due to its unique advantages of fuel flexibility and less pollutant emission. Numerical modelling of bubbling fluidized bed is a complex issue and recent models can't describe the fuel movement and conversion due to the complicated combustion phenomena. In this work, a simplified comprehensive three dimensional numerical model is used to study different biomass combustion process in a bubbling fluidized bed combustor including all necessary steps to define solid movement and conversion using CFD software AVL Fire. The hydrodynamic behaviour and combustion of the solid fuel is observed under different working conditions. Two different biomass fuels, wood pellet and olive stone are used to study the combustion phenomena. Solid conversion process is modelled comprehensively including evaporation, devolatilization, homogeneous and heterogeneous char reactions with a detailed heat transfer process. Eulerian-Eulerian approach is used to represent the transport of mass exchange, momentum and energy for solid and gas phases through different user defined subroutines. Various scalers are used to optimize the solid volume fraction, bed temperature distribution, solid velocity, heat transfer coefficients, gas species concentration and reaction rates for the solid phase as well as for the gas phase. Numerical results are compared with the existing results available in the literature and found reasonable agreement. High combustion rate is observed due to vigorous agitation of the solid bed. Two solid high temperature regions are located along the height of the combustor and they exist separately at the inlet and dilute zone. [ABSTRACT FROM AUTHOR]