Kinetic Theory Of Granular Flow Research Articles

Numerical investigation of turbulent mass transfer processes in turbulent fluidized bed by computational mass transfer

Turbulent fluidized bed possesses a distinct advantage over bubbling fluidized bed in high solids contact efficiency and thus exerts great potential in applications to many industrial processes. Simulation for fluidization of fluid catalytic cracking (FCC) particles and the catalytic reaction of ozone decomposition in turbulent fluidized bed is conducted using the Eulerian–Eulerian approach, where the recently developed two-equation turbulent (TET) model is introduced to describe the turbulent mass diffusion. The energy minimization multi-scale (EMMS) drag model and the kinetic theory of granular flow (KTGF) are adopted to describe gas–particles interaction and particle–particle interaction respectively. The TET model features the rigorous closure for the turbulent mass transfer equations and thus enables more reliable simulation. With this model, distributions of ozone concentration and gas–particles two-phase velocity as well as volume fraction are obtained and compared against experimental data. The average absolute relative deviation for the simulated ozone concentration is 9.67% which confirms the validity of the proposed model. Moreover, it is found that the transition velocity from bubbling fluidization to turbulent fluidization for FCC particles is about 0.5 m·s–1 which is consistent with experimental observation.

Particle-resolved direct numerical simulation and bottom-up statistical analysis on solid-phase pressure in particle–fluid systems

Solid-phase stress is a major factor shaping the complex behaviors of particle–fluid systems. However, uncertainties and inconsistencies can be found among the various models proposed. This work pays attention to the effect of mesoscale structures, that is, the heterogeneity of particle distribution at a scale of statistical meaning but no significant flow field variation, on the solid-phase normal stress, or pressure. Using a bottom-up statistical method, the solid-phase pressure in liquid- and gas–solid flows is investigated by particle-resolved direct numerical simulation (PR-DNS). It is found that, in almost uniform liquid–solid flows, the solid-phase pressure is not well predicted by classical kinetic theory of granular flow (KTGF) due to the presence of interphase force, although KTGF applies much better to single-phase granular flows. In gas–solid flows, with increasing heterogeneity described by structural functions, the statistical solid-phase pressure becomes significantly larger than that in corresponding homogeneous flows. It reveals that mesoscale structures strongly affect solid-phase pressure, and suggests the deviation from classical KTGF in heterogeneous gas–solid flows can be attributed to both the interphase forces (mainly drag) and mesoscale structures. The coefficients in the solid-phase pressure models in KTFG are modified, fitting the statistical results of both homogeneous and heterogeneous particle–fluid flows.

Effective lateral dispersion of momentum, heat and mass in bubbling fluidized beds

The lateral dispersion of bed material in a bubbling fluidized bed is a key parameter in the prediction of the effective in-bed heat transfer and transport of heterogenous reactants, properties important for the successful design and scale-up of thermal and/or chemical processes. Computational fluid dynamics simulations offer means to investigate such beds in silico and derive effective parameters for reduced-order models. In this work, we use the Eulerian-Eulerian two-fluid model with the kinetic theory of granular flow to perform numerical simulations of solids mixing and heat transfer in bubbling fluidized beds. We extract the lateral solids dispersion coefficient using four different methods: by fitting the transient response of the bed to (1) an ideal heat or (2) mass transfer problem, (3) by extracting the time-averaged heat transfer behavior and (4) through a momentum transfer approach in an analogy with single-phase turbulence. The method (2) fitting against a mass transfer problem is found to produce robust results at a reasonable computational cost when assessed against experiments. Furthermore, the gas inlet boundary condition is shown to have a significant effect on the prediction, indicating a need to account for nozzle characteristics when simulating industrial cases.

Heat transfer efficiency in gas–solid fluidized beds with flat and corrugated walls

Abstract Gas–solid fluidized bed reactors exhibit improved heat and mass transfer performance as compared to packed beds. Corrugated walls installed in narrow gas–solid bubbling fluidized bed (CWBFB) enclosures have been observed to decrease minimum bubbling velocity, reduce bubble size, improve gas distribution, provide stable operation, and minimize particle carryover or loss. Thorough analyses of the wall-to-bed heat transfer coefficient in flat- (FWBFB) and corrugated- (CWBFB) wall bubbling fluidized beds have been performed for a variety of operating conditions and geometric parameters. Fast-response self-adhesive heat flux probes and thermocouples were used to simultaneously measure the wall-to-bed heat flux, surface and bed temperatures, and were used to determine the heat transfer coefficient (HTC) at various axial and lateral locations. For a given set of parameters, a significant increase in HTC was observed at lower gas flow rates in CWBFB as compared to FWBFB. It was shown that CWBFB inventory required lower U mb (gas flow rate) as compared to FWBFB. Full 3-D transient Euler–Euler CFD simulations using the kinetic theory of granular flow were also performed, which confirmed the experimental results.

An inertial number regulated constitutive model for the gas-fluidization of binary mixtures across dilute and dense regimes

In this study, a constitutive model that is applicable to both dilute and dense regimes for simulating gas-particle flows with polydisperse particles is proposed. In dilute regime, solid stress is closed by kinetic theory of granular flow (KTGF). In dense regime, solid stress is closed by the η(Is) rheology. The transition from dilute to dense regimes is realized smoothly by the dynamic blending function χmix, which is a function of the inertial number of mixture Imix. The dynamic blending function χmix is also used to link the solid–solid drag force at different regimes. This new model was validated with the experimental data of polydisperse bubbling fluidized bed of Girimonte et al. (2018). When compared with the conventional baseline model, this new model improves the transition from dilute to dense regimes and the predictions in both density and size segregations.

A Comparative Study of Different CFD Codes for Fluidized Beds

Fluidized beds are pivotal in the process industry and chemical engineering, with Computational Fluid Dynamics (CFD) playing a crucial role in their design and optimization. Challenges in CFD modeling stem from the scarcity or inconsistency of experimental data for validation, along with the uncertainties introduced by numerous parameters and assumptions across different CFD codes. This study navigates these complexities by comparing simulation results from the open-source MFIX and OpenFOAM, and the commercial ANSYS FLUENT, against experimental data. Utilizing a Eulerian–Eulerian framework and the kinetic theory of granular flow (KTGF), the investigation focuses on solid-phase properties through the classical drag laws of Gidaspow and Syamlal–O’Brien across varied parameters. Findings indicate that ANSYS Fluent, MFiX, and OpenFOAM can achieve reasonable agreement with experimental benchmarks, each showcasing distinct strengths and weaknesses. The study also emphasizes that both the Syamlal–O’Brien and Gidaspow drag models exhibit reasonable agreement with experimental benchmarks across the examined CFD codes, suggesting a moderated sensitivity to the choice of drag model. Moreover, analyses were also carried out for 2D and 3D simulations, revealing that the dimensional approach impacts the predictive accuracy to a certain extent, with both models adapting well to the complexities of each simulation environment. The study highlights the significant influence of restitution coefficients on bed expansion due to their effect on particle–particle collisions, with a value of 0.9 deemed optimal for balancing simulation accuracy and computational efficiency. Conversely, the specularity coefficient, impacting particle–wall interactions, exhibits a more subtle effect on bed dynamics. This finding emphasizes the critical role of carefully choosing these coefficients to effectively simulate the nuanced behaviors of fluidized beds.

Numerical study of dense powder flow in a rotating drum: Comparison of CFD to experimental measurements

Designing chemical reactor equipment requires a thorough understanding of powder flow. Solid rheology modelling offers various models for this purpose. A comparative study of two different CFD models, the Kinetic Theory of Granular Flow (KTGF) and the dense granular flow (μI law), is proposed. Both models were confronted with experimental results obtained on a rotating drum for different rotation speeds and powder flowabilities. Image processing was used to compare the experimental gas/solid interfaces with those obtained from CFD. The KTGF model did not represent the powder rheology at low rotation speeds, regardless of the powder, whereas it was closer to experiments at higher speeds. The dense granular flow model was more appropriate for this system as it described the powder shape inside a rotating drum relatively well for each experiment. The latter model is recommended for modelling dense granular flows, while the KTGF is better suited to gas-solid flows.

Computational investigation of transportation and thermal characteristics in a bi-modal slurry flow through a horizontally placed pipe bend

In this study, we develop a three-dimensional computational model to explore the transportation and thermal characteristics of a bi-modal slurry flowing through a horizontally placed 90° pipe bend. The slurry comprises silica sand (SS) and fly ash (FA) granular, with varying combinations (65:35, 75:25, 85:15, 95:05, and 100:0). The computational investigation has been carried out for different carrier fluid's characteristics, including Prandtl number, and flow velocity (5 m/s), for efflux concentrations of Cw = 40–60% for each mixture. Validated with experimental data, the computational approach employs a two-phase Eulerian-Eulerian RNG k-ε turbulence model and the kinetic theory of granular flow. Results reveal that the 65:35 combination exhibits minimal pressure drop, and the 100:0 combination shows maximum heat transfer characteristics, particularly with low-viscosity fluid (Pr = 2.88) and high particle efflux concentration (Cw = 60%). The study also examines bend loss coefficients (Kt), concentration distribution, convective heat transfer coefficient (h), and Nusselt number (Nu) across different Prandtl fluids and efflux concentrations.

Study on the anisotropic flow characteristics of wet particles in liquid-solid fluidized beds

In liquid-solid fluidized beds, the presence of a liquid film around the surface of particles influences their collision behavior, leading in turn to the restitution coefficient no longer a constant. The present study introduces a dynamic restitution coefficient for wet particles to describe its dynamic variation during the process of particles colliding. The liquid-solid two-phase flow is simulated with Eulerian-Eulerian two-fluid method incorporating the anisotropic kinetic theory of granular flow based on second-order moment (SOM) model, in view of the anisotropy of particle fluctuations. This study aims to probe into the influence of liquid film and anisotropy of particle fluctuation on the particle-particle interactions and collision mechanisms. The predicted particle velocity and solid volume fraction are verified by the Limtrakul's et al. experiments. The simulated results show that the particle velocity fluctuations exhibit significant anisotropy, and the SOM model is superior to the KTGF model in capturing inhomogeneity and anisotropy of the flow field. The existence of a liquid film enhances energy dissipation during particle collisions and diminishes the anisotropy of particle velocity fluctuations. Also, the enhancement of particle density leads to a thicker liquid film and higher restitution coefficient, while the second-order moments are weakened and the anisotropy is remarkable. Furthermore, the effect of liquid viscosity on the liquid film thickness and restitution coefficient is more significant, where the particle fluctuations are reduced and the anisotropy is intensified by enhancing the liquid viscosity. In brief, both the liquid film and the anisotropy have impact on liquid-solid two-phase flow, by comparison, the effect of anisotropy is greater than liquid film.

Multi-phase modelling of loose, unsaturated soil’s continuous motion using a three-phase Eulerian approach

This paper develops a numerical model for loose, unsaturated soil to represent its mixing and motion using Computational Fluid Dynamics. It was found that existing models are not suitable for loose, unsaturated soil. The Herschel–Bulkley model is more appropriate for sludge and mud-like materials, and the Kinetic Theory of Granular Flow is inapt because it lacks yield stress. To mitigate these shortcomings, a novel three-phase Eulerian model is proposed, which combines these two models with an air phase. Each phase includes a physical characteristic of loose, unsaturated soil: the Herschel–Bulkley phase includes yield stress, a solid phase includes granular behaviour, and the air fraction adds porosity. To identify the model’s parameters, density is measured, and a slump test is performed. The radial run-out of the slump test is used to determine the required yield stress in the model. Test simulations showed clear improvements over the existing models by combining yield stress and granular, lumpy behaviour successfully. Application of the new model to a 3D screw conveyor simulation showcases its ability to simulate continuous soil motion phenomena, such as avalanching caused by a recirculatory flow, soil spilling over the flight and soil flowing back to the previous pitch.

Calibrating the frictional-pressure model from two-fluid simulation of fluidised beds in the defluidisation regime

The two-fluid simulation of a fluidised bed of non-adhesive particles, in which particles are represented as a continuous medium, requires a model for the pressure associated with particle contacts. While closures may be derived in the framework of the kinetic theory of granular flow for short-duration contacts, the frictional pressure associated with enduring particle contacts is generally modelled with an empirical closure involving several free parameters. This article proposes to use the experimental transition between the fluidised-bed and fixed-bed regimes in the determination of these parameters. The prediction of the minimum fluidisation velocity is shown to be governed by the frictional parameters, with either a discrete-element method or a two-fluid model. The shape of the particles, proxied by a sphericity coefficient, also influences the minimum fluidisation velocity. Such dependences of the model prediction can be used to select relevant frictional parameters, by comparison with experimental data or CFD-DEM simulation results.

Cohesive particle–fluid systems: An overview of their CFD simulation

AbstractSolid particles may experience different kinds of cohesive forces, which cause them to form agglomerates and affect their flow in multiphase systems. When such systems are simulated through computational fluid dynamics (CFD) programs, appropriate modelling tools must be included to reproduce this feature. In this review, these strategies are addressed for various systems and scales. After an introduction of the different forces (van der Waals, electrostatic, liquid bridge forces, etc.), the modelling approaches are categorized under three methodologies. For diluted slurries of very fine particles, many researchers succeeded with pseudo‐single phase approaches, employing a model for the non‐Newtonian rheology. This was especially popular for sludges in anaerobic digestions or certain types of soils. In other cases, continuum‐based approaches seem to be more adequate, including cohesiveness in the kinetic theory of granular flows or the restitution coefficient. Geldart‐A particles experiencing van der Waals forces are the primary focus of such studies. Finally, when each particle is modelled as a discrete element, the cohesive force can be directly specified; this is especially widespread for the wet fluidization case. For each of these approaches, a general overview of the main strategies, achievements, and limits is provided.

Influence of Frictional Stress Models on Simulation Results of High-Pressure Dense-Phase Pneumatic Conveying in Horizontal Pipe

Based on the two-fluid model, a three-zone drag model was developed, and the kinetic theory of granular flows and the Schneiderbauer solids wall boundary model were modified to establish a new three-dimensional (3D) unsteady mathematical model for high-pressure dense-phase pneumatic conveying in horizontal pipe. With this mathematical model, the influence of the three frictional stress models, namely Dartevelle frictional stress model, Srivastava and Sundaresan frictional stress model, and the modified Berzi frictional stress model, on the simulation result was explored. The simulation results showed that the three frictional stress models accurately predicted the pressure drop and its variations with supplementary gas in the horizontal pipe, with relative errors ranging from −4.91% to +7.60%. Moreover, the predicted solids volume fraction distribution in the cross-section of the horizontal pipe using these frictional stress models exhibited good agreement with the electrical capacitance tomography (ECT) images. Notably, the influence of the three frictional stress models on the simulation results was predominantly observed in the transition region and deposited region. In the deposited region, stronger frictional stress resulting in lower solids volume fraction and a higher pressure drop in the horizontal pipe were observed. Among the three frictional stress models, the simulation results with the modified Berzi frictional stress model aligned better with the experimental data. Therefore, the modified Berzi frictional stress model is deemed more suitable for simulating high-pressure dense-phase pneumatic conveying in horizontal pipe.

Numerical simulation on adsorption of CO2 using K2CO3 particles in the bubbling fluidized bed

AbstractWith the increase of greenhouse gas emissions, global warming has become an urgent problem, and the use of solid adsorbents to capture CO2 gas in flue gas has attracted more and more attention. In this study, the process of CO2 capture by K2CO3 particles in the bubbling fluidized bed (BFB) is numerically simulated with Eulerian–Eulerian(E–E) two fluid model incorporating with the kinetic theory of granular flows (KTGF). The results are verified through a detailed comparison with experimental data from Ayobi et al. Furthermore, Regarding the fundamental factors influencing CO2 adsorption rate is revealed, diminishing the inlet gas superficial velocity and augmenting the particle size of the solid adsorbent both contribute to improve adsorption performance. Specifically, the adsorption rate increases from 76.7% to 81.7% at the gas superficial velocity reducing from 1.10 to 0.71 m/s, while the adsorption rate from 77.6% to 79.7% with the particle size ranging from 400 to 600 μm. Additionally, the study delves into an exploration of fluid dynamic characteristics pertaining to gas particles within the bubbling fluidized bed while systematically considering varied inlet gas superficial velocities and particle sizes.

Effects of tube configurations on the heat transfer and hydrodynamic behavior in a gas-solid fluidized bed

The study of surface-to-bed heat transfer and flow characteristics in a gas-solid fluidized bed with different immersed tube configurations were investigated using the Eulerian-Eulerian method coupled with the kinetic theory of granular flow (KTGF) computationally. Compared with cases of in-line configurations, the staggered configurations increased the heat transfer coefficients (HTC) of the center-immersed heating tube. Moreover, it was found that with an increase in the rows and columns of the configurations, the HTCs increased and decreased respectively. The surface-to-bed heat transfer process was investigated combined with the particle renewal mechanism, and it was demonstrated that the HTCs were significantly affected by the surrounding packet fraction distribution and the packet residence time on the immersed heating surface. The results could be quantitatively employed to aid the heating tube configuration in designing the external heat exchanger (EHE) of a circulating fluidized bed (CFB) boiler for the treatment of municipal solid waste (MSW).

Simple generalization of kinetic theory for granular flows of nonspherical, oriented particles

Simple generalization of kinetic theory for granular flows of nonspherical, oriented particles

Influence of distributor plate design on mixing characteristics of rice husk biomass in a bubbling fluidized bed gasifier: An experimental and CFD study

This study investigates the mixing characteristics of rice husk biomass in a bubbling fluidized bed gasifier (BFBG) using different distributor plates: perforated, 45° slotted, and hybrid plates. The study explores the fluidization characteristics of a biomass/sand mixture using three distributor plates, observing the maximum difference in initial minimum fluidization velocity (Umf,i) and final minimum fluidization velocity (Umf,f) for perforated plate, indicating axial mixing and segregation, while the 45° slotted plate represents uniform bed expansion and fluidization, and the hybrid plate exhibits an intermediate behavior. Axial and lateral biomass distribution is also studied, and it is found that with the 45° slotted plate the highest axial distribution of rice husk is observed at the lower portion due to lateral and swirling flow whereas perforated plate causes the highest deviation at the lower portion but approaches ideal mixing at the mid and upper sections due to axial dominant flow. The hybrid plate exhibits a blend of axial and lateral flows, resulting in intermediate axial distribution at lower and upper section of gasifier. Radially, the perforated plate has the highest concentration of biomass at maximum height whereas the 45° slotted plate has concentration near the walls, and the hybrid plate has optimal mixing throughout. The hybrid plate also achieves the highest mixing index at all air velocities. Overall, the study provides insights into biomass mixing in BFBGs and highlights the superior performance of the hybrid distributor plate.The CFD study also carried out to complement the experimental results in terms of pressure drop and mixing behavior by employing different distributor plats. Multiphase two fluid model (TFM) with kinetic theory of granular flow has been employed for CFD simulations with the engagement of k-epsilon turbulence model. The simulation results are in good agreement with experimental results in terms of bed pressure drop quantitatively and mixing characteristics of rice husk biomass qualitatively.

Numerical Simulation of Fluidization Behavior and Chemical Performance for Hydrochlorination of Silicon Tetrachloride in a Fluidized Bed Reactor

Exploring the fluidization behaviors and chemical performance in silicon tetrachloride (SiCl4) hydrochlorination processes within a fluidized bed reactor (FBR) poses significant challenges. In this study, we developed an Eulerian-granular model (EGM) by integrating the Eulerian–Eulerian two-fluid model with the kinetic theory of granular flow (KTGF). The effect of fluidization velocities on the flow regime, heat transfer, and chemical reaction performance were investigated. The applicability of the simulation method and the validity of the model were confirmed through comprehensive comparisons, including the simulated values of the maximum bed expansion height (Hmax) with theoretical values derived from empirical formulas and the simulated gas temperature profile with Hsu’s experimental data. The results indicate that the present EGM can be feasible to describe the variation of the flow regime within the FBR. An increase in bed voidage over time, coinciding with transitions in the flow regime, can be observed. Particularly noteworthy was the attainment of a more uniform distribution of SiCl4 under the bubbling fluidization state. Furthermore, the FBR possess high heat transfer characteristics, and the reaction gas can reach the set temperature of the bed after entering a small distance (about 10 mm). The presence of circulating bubbles within the FBR enhances the mixing uniformity of the SiCl4 reaction gas and silicon particles, particularly in the central and upper regions of the bed under the bubbling fluidization state. As a result, the predicted highest concentration of SiHCl3 was 13.08% and the conversion rate of SiCl4 was 28.97% under the bubbling fluidization state. Our results can provide a theoretical basis for further understanding of the hydrochlorination process of SiCl4 within the FBR.

Validation of an improved two-fluid model with particle rotation for gas-solid fluidized bed

Gas-solid fluidized beds are widely applied in chemical and process engineering. It is of significance to establish a reasonable and effective mathematical model to explore the hydrodynamics of gas-particle system for industrial applications. As a less computationally demanding alternative to the discrete descriptions, two-fluid model considering kinetic theory of granular flow is often adopted to describe the fluidized behaviors of particles, but it cannot characterize the rotation of particles and its influence on the fluidized behaviors. In this study, to address the rotation effect of the fluidized particles, a two-fluid model combining the classical fluid and micropolar fluid is established, namely CMTFM. In the CMTFM, classical fluid is used to describe the motion of gas phase, while micropolar fluid is adopted to describe the motion of particle phase, and the rotation of particles and its influence on the hydrodynamics of the gas-particle system are characterized by the degree of freedom of microrotation and the improved drag force based on micropolar viscosities. In the calculation of the gas-solid bubbling fluidized bed, we investigated the influence of the microstructure parameters, particle-particle collision restitution coefficient and inlet velocity, and the results are compared to those from TFM model and experiments. Through the analysis, it manifests that pressure drop and expansion height of the fluidized bed under the consideration of the microrotation effect are closer to the experiments, which demonstrates the feasibility and advantage of the classical-micropolar two-fluid model.

Numerical investigation of the effect of the location of an immersed tube in a fluidized bed on heat transfer of surface-to-bed

The study of heat transfer characteristics within an external heat exchanger (EHE) in circulating fluidized bed (CFB) boilers for the treatment of municipal solid waste (MSW) is of great significance for improving energy utilization. An Eulerian-Eulerian approach coupled with the kinetic theory of granular flow (KTGF) was used in this work and the effect of the immersed tube location on hydrodynamics and heat transfer characteristics in a gas-solid fluidized bed was investigated. The model accuracy was validated by the reference result. It was shown that the tube location has a significant effect on heat transfer of surface-to-bed, with increasing height of the tube from 0.2 m to 0.5 m, the average heat transfer coefficient (HTC) of the immersed surface decreased from 302 to 274 W/(m2K). Meanwhile, the specific process of particle renewal on the tube surface and the impact of the particle renewal mechanism on heat transfer were investigated.