Numerical simulation of flow behavior of liquid and particles in liquid–solid risers with multi scale interfacial drag method

Formation of particle clusters in liquid–solid circulating fluidized beds significantly affects macroscopic hydrodynamic behavior of the system. A multi scale interfacial drag coefficient (MSD) is proposed to determine effects of particle clusters on the mesoscale structure, by taking momentum and energy balance of dense phase, dilute phase and interphase into account. Based on the transportation and suspension energy-minimization method, the multi scale interfacial drag coefficient model used in this work is combined with the Euler–Euler two fluid model to simulate the heterogeneous behaviors of liquid–solid circulating fluidized bed. It was found that the reduction in drag coefficient is at least an important factor for the simulation of clusters formation, and the core-annulus flow is observed in the riser. The liquid–solid flow regime was significantly affected by the down-flow of particles in the form of clusters near the walls of the riser. The calculated concentration of particles inside the riser compared reasonably well with the available experimental data obtained by Razzak et al.     

Solid Flow Transition in Liquid and Three-Phase Fluidized Beds

Flow transition of solids in liquid and three phase fluidized beds of Newtonian and non-Newtonian fluids have been studied in a 15.2 cm-ID pyrex glass column. The relation between the fluid flow rate and the bed porosity in three phase fluidized beds have been determined in terms of effective volumetric flux of fluid phases from the modification of the Richardson and Zaki's equation. The modified particle Reynolds Number exhibited its maximum value with the variation of bed porosity in liquid and three phase fluidized beds. The drag coefficient changed its slope apparently at the bed porosity where the maximum value of the modified particle Reynolds number could be attained. At the flow transition condition, the continuity wave velocity, energy dissipation rate, and the continuity shock wave velocity found to have their maximum values. Also, the immersed heater-to-bed and wall-to-bed heat transfer coefficients, wall-to-bed mass transfer coefficient, liquid radial mixing coefficient and solid particle diffusivity in the literature data were found to have maximum values at the transition condition of liquid and three phase fluidized beds.     

Solid Flow Transition in Liquid and Three-Phase Fluidized Beds

ABSTRACT

Flow transition of solids in liquid and three phase fluidized beds of Newtonian and non-Newtonian fluids have been studied in a 15.2 cm-ID pyrex glass column. The relation between the fluid flow rate and the bed porosity in three phase fluidized beds have been determined in terms of effective volumetric flux of fluid phases from the modification of the Richardson and Zaki's equation. The modified particle Reynolds Number exhibited its maximum value with the variation of bed porosity in liquid and three phase fluidized beds. The drag coefficient changed its slope apparently at the bed porosity where the maximum value of the modified particle Reynolds number could be attained. At the flow transition condition, the continuity wave velocity, energy dissipation rate, and the continuity shock wave velocity found to have their maximum values. Also, the immersed heater-to-bed and wall-to-bed heat transfer coefficients, wall-to-bed mass transfer coefficient, liquid radial mixing coefficient and solid particle diffusivity in the literature data were found to have maximum values at the transition condition of liquid and three phase fluidized beds.     

Experimental and CFD-DEM numerical evaluation of flow and heat transfer characteristics in mixed pulsed fluidized beds

Pulsed fluidized beds can make gas-solid mix and contact more uniform, therefore obviously improving heat transfer efficiency. The mixed pulsed fluidized bed, whose total gas flow is composed of stable gas flow and pulsed gas flow, is proposed in this research. Firstly, the experimental device for drying particles in a mixed pulsed fluidized bed is established. Pressure signals with different frequencies and gas flow ratios are collected, and flow pattern diagrams are obtained through a high-speed camera. Secondly, the CFD-DEM parallel numerical simulation method is constructed to research the mixed pulsed fluidized bed performance. Particle mixing, motion and heat transfer characteristics under different pulse frequencies and flow ratios are studied. Results show that particles in the mixed pulsed fluidized bed exhibit regular periodic motion, thereby promoting the mixing effect of particles. Moreover the bubble nucleation point moves to the bottom of the bed with the increasing pulse frequency. When the total gas velocity is relatively low, particle mixing effect can be enhanced by increasing the proportion of pulsed gas. However, when the velocity is relatively high, particle mixing effect will be enhanced by decreasing the proportion.     

Numerical investigation of binary particle mixing in gas-solid fluidized bed with a bubble-based drag EMMS model

Heterogeneous flow structure of bubbling deeply affects gas–solid momentum transfer in a binary gas–solid fluidized bed. This work presented a binary particle bubble-based Energy Minimum Multi-scale (EMMS) model, and an assumption that bubble-emulation drag force acting on solid 1 and solid 2 depending on each solid volume ratio in the emulation phase was applied to simplify the force balance of the binary particle-phase. The bubble-based EMMS drag was incorporated in the Eulerian multi-fluid model to predict the mixing behaviors of two binary particle systems. The simulation results agree well with the experimental observations in terms of binary solid mixing, bed expansion, and bubble diameter. Compared with the prediction results by the Gidaspow drag model, the jetsam solid fraction and bubble size predicted by the present drag model is in more agreement with the measured results, which indicate the EMMS drag model is an alternative choice for modeling binary gas–solid bubbling system.     

MODELING OF SOLID FLOWS IN A FLUIDIZED BED WITH SECONDARY TANGENTIAL AIR INJECTION IN THE FREEBOARD

Abstract

The Vortexing Fluidized-Bed Combustion (VFBC) technique was recently developed for small- and medium-scale coal-burning boiler applications. Experimental observations showed that the general solid flows in the freeboard of a vortexing fluidized bed consisted of three successive stages: (1) spirally ascending motion before colliding the freeboard wall, (2) bouncing on the wall, and (3) sliding on the wall and exiting the freeboard. This study attempts to model these three stages of solid flows. The dimensionless governing equations for particle motion in the swirling field were presented taking into account the interactions of particle inertia, centrifugal force, viscous fluid drag, and gravity. Numerical solutions of particle velocities and trajectories were pursued, and effects of particle momentum transfer number, Froude number, and particle-wall restitution coefficient were delineated. The experimental validation of solid flows in the swirling freeboard was furnished with an 18 cm ID laboratory fluidized bed.     

Dynamic forces on an immersed cylindrical tube and analysis of particle interaction in 2D-gas fluidized beds

The interactions of bubbles and particles with fixed cylindrical tubes in two-dimensional fluidized beds were investigated by experiments and by simulations, based on results for single bubbles impinging on a tube. The experimental results based on PIV analysis support our previous force origin model and indicate that the model is able to successfully model bubble behavior and particle motion around fixed objects. The simulation results give useful predictions, dynamic force induced on a tube consists of the force from pressure gradient, fluid viscous force and particle contact force. The predominant force component is from the pressure gradient. As bubbles directly interact with a tube, the particle contact force contribution briefly becomes predominant.Bubble behavior and particle motion are greatly affected by the state of the emulsion phase as the medium of the fluidized bed into which gas is injected. Hence the dynamic forces on immersed objects are directly affected by the state of the emulsion phase.     

Multi-fluid modelling of hydrodynamics in a dual circulating fluidized bed

In this work, a multi-fluid model based on the Eulerian-Eulerian framework is used to study the gas-solid hydrodynamics, such as solid distribution, particle motion and solid velocity, in a three-dimensional (3D) dual circulating fluidized bed (DCFB). The influence of four different drag force models, including two classic models, i.e. Gidaspow, EMMS drag model and two recent drag models, i.e. Rong and Tang drag model, on hydrodynamics in DCFB are assessed. Numerical results show that the characteristics of solid distribution and velocity in different sections are distinct. For qualitative analysis, all the drag models can predict a reasonable radial solid distribution and pressure distribution, but only the EMMS, Rong and Tang drag model can capture the phenomenon of dense solid concentration in the low part. For quantitative analysis, the solid circulating rate predicted by the EMMS drag model is the closest to the experimental value while the Gidaspow drag model shows the most significant deviation. The overall assessments confirm that the drag model selection has a significant influence on the simulations of gas-solid flow in DCFBs. This study sheds lights on the design and optimization of fluidized bed apparatuses.     

Effect of flow pulsation on fluidization degree of gas-solid fluidized beds by using coupled CFD-DEM

In this paper, the effect of inlet flow type on fluidization of a gas-solid fluidized bed was studied by using numerical simulations. Gas-solid fluidized beds are widely used in processes such as heating, cooling, drying, granulation, mixing, segregating and coating. To simulate the gas-particle flows, the unresolved surface CFD‐DEM was used considering Eulerian–Lagrangian approach. The fluid phase was modeled by computational fluid dynamics (CFD) while the solid phase was solved by discrete element method (DEM), and the coupling between gas and solid phases was considered to be four-way. The uniform and pulsed flows were injected through three nozzles located at the bottom of a rectangular bed. Three types of pulsed flow were considered: sinusoidal, rectangular and relocating. The fluidized bed behavior was discussed in terms of minimum fluidization velocity (MFV), pressure drop, bubble formation, bed expansion, particles velocity and, gas-solid interaction and particle contact forces. The results of different simulations indicated that the minimum fluidization velocity of the beds fluidized by pulsed flows was decreased by up to 33%. The influence of the pulsation amplitude on the minimum fluidization velocity was more significant than that of the pulsation frequency. The bed expansion and particles average velocity were increased by the pulsed flows, while the pressure drop and interaction force were decreased. As the pulsation frequency increased, the pressure drop and gas-solid interaction force increased, although size of the bubbles and bed expansion decreased. It was also observed that in large vibration frequencies, the bubbles became more regular. In the sinusoidal flow, the velocity and contact force between the particles were initially increased by frequency and in larger frequencies they were decreased.     

MODELING OF SOLID FLOWS IN A FLUIDIZED BED WITH SECONDARY TANGENTIAL AIR INJECTION IN THE FREEBOARD

The Vortexing Fluidized-Bed Combustion (VFBC) technique was recently developed for small- and medium-scale coal-burning boiler applications. Experimental observations showed that the general solid flows in the freeboard of a vortexing fluidized bed consisted of three successive stages: (1) spirally ascending motion before colliding the freeboard wall, (2) bouncing on the wall, and (3) sliding on the wall and exiting the freeboard. This study attempts to model these three stages of solid flows. The dimensionless governing equations for particle motion in the swirling field were presented taking into account the interactions of particle inertia, centrifugal force, viscous fluid drag, and gravity. Numerical solutions of particle velocities and trajectories were pursued, and effects of particle momentum transfer number, Froude number, and particle-wall restitution coefficient were delineated. The experimental validation of solid flows in the swirling freeboard was furnished with an 18 cm ID laboratory fluidized bed.     

CFD-DEM simulations of a fluidized bed with droplet injection: Effects on flow patterns and particle behavior

As one of the most preferred technologies, fluidized beds with droplet injection have been widely applied in a variety of industries attribute to the advantages of excellent mixing effect as well as consecutive interphase contact. However, pronounced slugging and gas channeling may occur with the existence of droplets, where a large proportion of bed solids would be lumped together. This study focused on the hydrodynamics and cohesive-like characteristics of solid particles in a pseudo-2D droplet gas-solid fluidized bed via two-way coupled CFD-DEM numerical simulations with the consideration of droplets coating process and liquid bridge force. Results revealed that the existence of droplets would lead to poor fluidization characteristics. It could be summarized that the increase of surface tension would lead to inadequate mixing. At the same time, larger value of liquid viscosity would cause a slower particle motion, while cases that exhibited vigorous fluidization corresponded to smaller values of viscosity. The influences cast by different contact angles were also studied and results showed that choosing an appropriate contact angle is of paramount importance to the optimization of the fluidization quality. It was also found that the more droplets injected, the worse the mixing behavior, while changing the number of droplets injected had no significant effect on the flow pattern and particle motion.     

Numerical simulation of hydrodynamic characteristics in a gas–solid fluidized bed

The fluidization of quartz particles as bed materials in the fluidized bed has significant influences on the combustion and gasification of refused derived fuels. Three-dimensional (3-D) simulations and analyses are performed for Geldart B particles using the computational fluid dynamics (CFD) method based on the kinetic theory of granular flows (KTGF) to investigate the hydrodynamic behavior. The drag models of Syamlal–O’Brien, Gidaspow, and Wen and Yu are selected to analyze the applicability of the kinetic model. The pressure drop, velocity distribution and solid volume fraction are studied numerically when the gas inlet velocity is changed. The results show that the increase of superficial gas velocity would lead to heterogeneous expansion of solid volume fraction and velocity distributions in both the dense phase zone and free board with a similar distribution pattern. The near wall particles form a dense phase structure with the solid volume fraction being greater than 0.3.     

Study of hydrodynamic characteristics of particles in liquid–solid fluidized bed with modified drag model based on EMMS

Flow behavior of solid phases is simulated by means of Eulerian–Eulerian in a liquid–solid fluidized bed with modified drag model based on energy-minimization multi-scale (EMMS) method. The modified EMMS drag coefficient is characterized by the treatment of the particle-rich dense phase and the liquid-rich dilute phase as the two interpenetrating continua. It was shown that the modified EMMS drag coefficient can predict reasonably the solid concentration profiles in a liquid–solid fluidized bed. The distributions of solid velocity, granular temperature and granular pressure are predicted. The phenomenon of back-mixing near the wall is found in the liquid–solids fluidized beds.     

Numerical investigation of hydrodynamics in liquid-solid circulating fluidized beds under different operating conditions

A computational fluid dynamics (CFD) model was employed to investigate the hydrodynamics of the liquid–solid circulating fluidized bed (LSCFB). The numerical simulations of the flow in the LSCFB under different operating conditions, including different superficial liquid velocities, superficial solid velocities, particle densities and shapes, are carried out using the CFD model developed in the previous work. The numerical predictions show correct trends and good agreements with the experimental data. It is demonstrated that the radial non-uniformity and axial uniformity exist in the flow structures under different operating conditions. By increasing the superficial solid velocity, the average solids holdup and radial non-uniformity increase, while the opposite trends are observed by increasing the superficial liquid velocity. Besides, the solids holdup decreases with the decrease in the particle density. It is also observed that all the flow distributions in the radial and axial directions in LSCFBs are more uniform than those in GSCFBs.     

Evaluation of direct quadrature method of moment for the internally circulating fluidized bed simulation with ultrafine particles

In the framework of the Euler-Euler gas–solid two-fluid model, the particle population balance equation is solved by the direct quadrature method of moment. The dynamic process of ultrafine particle movement and aggregation in an internally circulating fluidized bed is simulated. The distribution of the concentration and velocity of the agglomerates in the flow process is given, and the changes of the moments in the bed are shown. The effects of different breakage coefficients and inlet gas rates on the concentration distribution of agglomerates are compared. The results show that the particle size decreases with the increase of breakage coefficient, and the time required to reach steady fluidization state increases; the higher the inlet velocity, the better the effect of circulating particles in the bed. When there is a certain gas velocity difference between the two sides, the effect of circulating particles in the bed is better.     

Hydrodynamic studies on fluidization of Red mud: CFD simulation

Hydrodynamic studies are carried out for the fluidization process using fine i.e. Geldart-A particles. Effects of superficial velocity on bed pressure drop and bed expansion is studied in the present work. Commercial CFD software package, Fluent 13.0 is used for simulations. Red mud obtained as waste material from Aluminum industry having average particle size of 77 microns is used as the bed material. Eulerian–Eulerian model coupled with kinetic theory of granular flow is used for simulating unsteady gas–solid fluidization process. Momentum exchange coefficients are calculated using the Gidaspow drag functions. Standard k–ε model has been used to describe the turbulent pattern. Bed pressure drop and bed expansion studies are simulated by CFD which are explained with the help of contour and vector plots. CFD simulation results are compared with the experimental findings. The comparison shows that CFD modeling is capable of predicting the hydrodynamic behaviors of gas–solid fluidized bed for fine particles with reasonable accuracy.     

Experimental study on the fluidization discharging characteristics of Geldart-C kaolin powders in a blow tank with pulsed gas

Kaolin powders have been suggested to be able to adsorb heavy metal vapor from coal-fired flue gas. However, due to the influence of inter particle forces, such as liquid bridge force, it is difficult to realize stable pneumatic conveying. In the present work, the fluidization characteristics of kaolin powders were investigated. A series of unstable flow phenomena such as agglomeration, channeling, and slugging occurred during the fluidization process. Also, the fluidization discharging characteristics of kaolin powder in an optimized blow tank were experimentally studied. The results indicated that the introduction of pulsed gas can effectively destroy agglomeration and thus improving the stability of discharging. Visual experiments in pseudo-2D fluidized bed were also confirmed the destructive effect of pulsed gas on agglomeration. With an increase in either fluidization gas velocity U_f or pulsed gas velocity v_pulsed, the mass flow rate of kaolin powder G first increased and then decreased. Finally, drying experiments demonstrated that there is free water on the surfaces of the kaolin powders. The analysis of forces indicated that the liquid bridge force F_lb between particles is much larger than the particle gravity F_g. The liquid bridge force might be one of key reasons for kaolin powder agglomerating.     

Study on hydrodynamic characteristics of the liquid-solid circulating fluidized bed with a central pulsating nozzle by numerical approach

Pulsating fluidization is gaining increasing attention due to its superiority in efficiency improvement. A novel type of liquid–solid circulating fluidized bed with a central pulsating nozzle was proposed to improve the reaction efficiency in this work. Based on Eulerian-Eulerian two-fluid model and the kinetic theory of granular flow, the hydrodynamic characteristics in the riser was investigated by three-dimensional numerical simulation. The effects of pulsating liquid flow and particle properties on the distributions of solids holdup, the radial velocity of the particles, the slip velocity and the radial mixing degree were studied. The simulation results showed that with the addition of the central pulsating liquid flow, the particles displayed apparent radial motion, and the interphase mixing degree as well as the interphase mass transfer efficiency were enhanced. Based on the numerical results, the regression formulas of the axial and radial slip velocities were obtained respectively.     

A modified drag model for power-law fluid-particle flow used in computational fluid dynamics simulation

A modified drag model for the power-law fluid-particle flow considering effects of rheological properties was proposed. At high particle concentrations (ε_s ≥ 0.2), based on the Ergun equation, the cross-sectional shape and the tortuosity of the pore channel are considered, and the apparent flow behavior index and consistency coefficient of the power-law fluid at the surface of the particles are corrected. At low particle concentrations (ε_s < 0.2), based on the Wen-Yu drag model, the modified Reynolds number for power-law fluid and the relational expression between drag coefficient for single particle and Reynolds number that considers the effect of the flow behavior index are adopted. Numerical simulations for the power-law fluid-particle flow in the fluidized bed were carried out using the non-Newtonian drag model. The effects of rheological parameters on the drag coefficient were analyzed. The comparisons of simulation and experiment show that the modified drag model predicts reasonable void fraction under different rheological parameters, particle diameters, and liquid velocities in both low particle concentrations and high particle concentrations. The increase in flow behavior index and consistency coefficient increases the drag coefficient between the two phases and decreases the average particle concentration within the bed.     

A study of gas and solid mixing behaviors in a three partitioned fluidized bed

A previously unknown partitioned fluidized bed gasifier (PtFBG) has been developed for improving coal gasification performance. The basic concept of the PtFBG is a fluidized bed divided into two parts, a gasifier and a combustor, by a partitioned wall. Char is burnt in the combustor and the generated heat is supplied to the gasifier along with the bed materials. During that time, highly concentrated CO₂ is inevitably generated in the combustor. Therefore, vigorous solid mixing is an essential precondition as well as minimizing horizontal gas mixing. In this study, gas and solid mixing behaviors were verified in a cold model three partitioned fluidized bed (3-PtFB). Glass beads with an average diameter of 150 μm and a particle density of 2500 kg/m³ were used as bed materials. For the gas mixing experiments, CO₂ and N₂ were introduced into the beds through each distributor. Then, outlet gas flow rates and concentrations were measured by gas flow meters and an IR gas analyzer respectively. The calculated gas exchange ratios ranged from 3% to 10% with varying gas flow rates. For the solid mixing experiments, 1000 μm polypropylene particles with a density of 883 kg/m³ were continuously fed into the reactor. Then, the polypropylene particles were distributed to the entire beds evenly. Solid mixing behaviors were very analogous to liquid mixing behaviors in a continuous stirred tank reactor (CSTR).