Kinetic Theory Of Granular Flow Research Articles

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.

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.

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.

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.

Investigation on multiphase flow of multi-size cuttings particles and non-Newtonian drilling fluids in oil and gas horizontal well drilling using kinetic theory of granular flow

Effective cuttings transport has long been a challenge in oil and gas horizontal drilling, and inadequate wellbore cleaning can result in severe drilling accidents including stuck pipe. The transportation of multi-size cuttings by non-Newtonian drilling fluids in the horizontal wellbore with a rotating drill pipe was systematically investigated using the kinetic theory of granular flow. Collisions between particles and their two-way coupling with drilling fluid turbulence were modeled. Flow regime of multi-size cuttings has been predicted, and effects of particle size composition characteristics were studied. The spatial inhomogeneity of the non-Newtonian fluid viscosity and the sedimentation of particles result in a complex stratified flow regime for multi-size cuttings transport. Cuttings concentration and drilling fluid axial velocity distributions both show swaying phenomena with drill pipe rotation. Moreover, the secondary flow regions appear with negative tangential velocities. The cuttings transport ratio (CTR = 0.846) is the best in the case of cuttings with different particle sizes injected in a uniform concentration. While in the case where the concentration of injected multi-size cuttings is negatively correlated with particle size, the cuttings velocity fluctuations caused by collisions and frictions are the most severe, and the borehole cleaning is the worst (CTR = 0.803).

Hydrodynamic characteristics of central pulse gas-liquid-solid circulating fluidized bed: Effect of gas and solid parameters

As an important multiphase reactor, gas-liquid-solid circulating fluidized bed is widely used in petroleum, chemistry, metallurgy, pharmacy and environment fields. In this work, a gas-liquid-solid circulating fluidized bed with central pulsating liquid flow was proposed and investigated to further improve the reaction rate of the reactor. The Eulerian-Eulerian- Eulerian method coupled with kinetic theory of granular flow is used to simulate the flow characteristics in the fluidized bed riser. At the same time, experiments under some operating conditions are carried out to verify the simulation results. The result shows that the relative motion of solids and liquid phase in the novel reactor is significantly increased compared with the conventional circulating fluidized bed. The continuous variation of the central pulse flow improved the pressure gradient fluctuation and mass transfer intensity. The radial/axial liquid-solid relative velocity regression formulas were obtained based on the numerical calculation results.

A solid-liquid mixing reactor based on swirling flow technology

Solid-liquid mixing is often applied in the chemical industry to keep solids in suspension for, amongst others, crystallization, adsorption, heterogeneous catalysis, etc. The most widely used technology to obtain a good degree of mixing is the mechanically stirred tank reactor. However, this technology is limited to small reactor volumes in case of high pressure/temperature processes due to sealing issues. An alternative for solid-liquid mixing is the application of swirling flow. This work studies the mixing capacities of a specially designed reactor geometry, the Swirling Flow Reactor (SFR). Computational Fluid Dynamics (CFD) is used to simulate the flow field and particle distribution in the SFR, where the RNG k−ϵ model and the Eulerian-Eulerian (E-E) multi-phase approach with a Kinetic Theory of Granular Flow (KTGF) model are applied for their proven effectiveness in the study of dense solid-liquid mixing problems. The effectiveness of mixing in the SFR is assessed by the axial particle distribution and homogeneity H. The mechanism of particle recirculation in the SFR is also identified, in which a Coanda jet flow (CoJF) formed by a specially designed inlet nozzle plays an important role in washing the reactor bottom surface. Additionally, Spectral Proper Orthogonal Decomposition (SPOD) is used to identify and reconstruct the coherent structures in the swirling flow. The results indicate that precessing coherent flow structures are present, which include the dominant double layer double helical vortex core and its second order harmonic, the double layer quadruple helical vortex core.

A frictional–collisional model for bedload transport based on kinetic theory of granular flows: discrete and continuum approaches

In this work, the modelling of collisional bedload transport is investigated with a focus on the continuum modelling of the granular flow. For this purpose, a frictional–collisional approach, combining a Coulomb model with the kinetic theory of granular flows, is developed. The methodology is based on a comparison with coupled fluid–discrete simulations that the classical kinetic theory model fails to reproduce. This inaccuracy may be explained by the assumptions of negligible interparticle friction and the absence of a saltation model in the continuum approach. In order to provide guidelines for the modelling, the fluctuating energy balance is computed in the discrete simulations and systematically compared with the kinetic theory laws. Interparticle friction is shown to affect the radial distribution function and to increase the energy dissipation, in agreement with previous observations. In addition, a saltation regime is identified, leading to departure from the viscosity and pseudo-thermal diffusivity laws of the kinetic theory in the dilute regime. Based on these observations, modifications to account for interparticle friction are included in the two-fluid model, and the kinetic theory is coupled with a saltation model. The results show that for inelastic frictional particles, interparticle friction controls energy dissipation, and the macroscopic behaviour of the granular flow does not depend on the microscopic particle properties. The proposed model reproduces the$\mu (I)$rheology in the dense regime of the granular flow. Finally, the model is evaluated with experiments, showing significant improvements concerning the granular flow modelling.

Numerical investigation of bed-to-tube heat transfer in a shallow fluidized bed containing mixed-size particles

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.

Estimation of energy consumption and transportation characteristics for slurry flow through a horizontal straight pipe using computational fluid dynamics

The energy expense of slurry transportation through the pipeline plays a vital role in the economics of various modern industries, such as mining, crude oil, petroleum, and mineral processing. Therefore, it is essential to develop a suitable condition by which we can efficiently transport slurry without affecting the environment and capital costs. To solve these problems, a steady state three-dimensional multiphase Eulerian RNG k–ε turbulence model based on the kinetic theory of granular flow is developed to investigate transportation parameters like pressure distribution, concentration distribution, head loss, settling velocity, and specific energy consumption. Four different particles named bottom ash, glass beads, iron ore, and silica sand with five different sizes, 125, 200, 275, 350, and 440 μm are transported through 3.8 m long straight pipe having 54 mm pipe diameter. The trends of various transportation properties with varying flow velocity (Vm = 1–5 m/s) and efflux concentration (Cw = 40%–60%) are presented. The numerically obtained results for different slurries and water are in good agreement with the past experimental data available in the literature. The computational finding shows that the transportation of bottom ash requires minimum energy, whereas silica sand needs the maximum. In addition, the degree of deviation into transportation properties increases with the particle size, efflux concentration, and flow velocity.

Numerical study of ice slurry flow and heat transfer in successive U-bends as part of tubular heat exchangers

Using ice slurry can assist the energy saving in cooling systems. Ice slurries are used as secondary refrigerant in large cooling systems. They are mixtures of tiny ice particles in water and an antifreezing agent. The cooling can be stored in ice particles during off-peak conditions and released during peak condition. The stored cooling in ice slurry must be delivered to the desired system through a heat exchanger. Successive U-bend pipes commonly exist in tubular heat exchangers. However, this configuration has not been investigated yet for ice slurries. The present study aims to investigate the heat transfer of these mixtures in successive in-plane U-bends as part of heat exchangers. Mass transfer between ice slurry and fluid is the main important part of this problem which is considered in the present study. For the simulation of ice slurry, the Eulerian two-fluid numerical method is used along with the consideration of mass transfer between two phases and the kinetic theory of granular flow for ice particles viscosity. Nusselt number and pressure drops are mainly studied for different geometric configurations. The length between two bends are changed from 50 to 400 mm and the radius of curvatures of the bends are changed from 50 to 100 mm. The results of the study indicated that the average Nusselt number increases with the radius of curvature and distance between two U-bend pipes. Two successive U-bends neutralize each other's centrifigual effects, then ice particles have chances to rearrange and reduce the wall temperature in each bend. This effect is more prominent in higher distances between two bends and higher radii of curvature. At low radius of curvatures, the variation of distance between two bends has stronger effect on heat transfer of the system; in such a way that by doubling the distance between two bends, the Nusselt number increases 4.1% and 1.5% respectively for radius of curvatures 50 mm and 100 mm. Also it was shown that by increasing the radius of curvature and distance between two U-bend pipes the skin friction coefficient increases. It can be seen that by increasing the ratio of the distance between two bends to the radius, the performance evaluation criterion (PEC) increases.