The hydrodynamics of circulating fluidized beds (CFBs) is a complex phenomenon that can drastically vary depending on operational setup and geometrical configuration. A research of the literature shows that studies for the prediction of key variables in CFB systems operating at high temperature still need to be implemented aiming at applications in energy conversion, such as combustion, gasification, or fast pyrolysis of solid fuels. In this work the computational fluid dynamics (CFD) technique was used for modeling and simulation of the hydrodynamics of a preheating gassolid flow in a cylindrical bed section. For the CFD simulations, the twofluid approach was used to represent the gassolid flow with the kepsilon turbulence model being applied for the gas phase and the kinetic theory of granular flow (KTGF) for the properties of the dispersed phase. The information obtained from a semiempirical model was used to implement the initial condition of the simulation. The CFD results were in accordance with experimental data obtained from a benchscale CFB system and from predictions of the semiempirical model. The initial condition applied in this work was shown to be a viable alternative to a more common constant solid mass flux boundary condition.
Circulating fluidized bed reactors are systems in which gassolid heterogeneous reactions take place in a fast fluidization regime. One of the most successful applications of this technology is the combustion of lowgrade fuels, such as biomass, waste, and coal with high ash content. Fluidized beds provide high specific transfer rates, high solids throughput, and thermal uniformity within the reactor [
The total particulate material circulating in the system, the solids inventory, is an important parameter for an efficient design of CFB for combustion applications. Together with the gas superficial velocity it drives the bed particles along the loop. The pressure drop and the particle residence time are strongly related to the solid distribution in the fast bed zone (riser). Moreover, the solid distribution also affects the mass and heat transfer rates. For combustion and gasification purposes, quartz sand is commonly used as inert material due to its relatively low cost and excellent performance at high temperatures. In such systems, the amount of solid inert material can reach up to 97% of the total mass in the solids inventory [
Several studies have been carried out to describe the hydrodynamic behavior of the gassolid flow in CFB systems, based on empirical and theoretical analysis at high or environmental temperatures [
In a different approach to the mathematical model of CFBs, the literature has shown the successful application of the CFD technique for the simulation of many gassolidfluidized bed applications. Great attention has been given to the hydrodynamics in the riser component of the CFB unit. Some works have studied the behavior of FCC catalyst [
The EulerianEulerian approach is commonly applied to describe a gassolid system. Also known as the twofluid model, it treats the gas as well as the particulate phases as fluids, which introduces some variables that are difficult to determine for the solid phase. Thus, the kinetic theory of granular flow has been widely applied [
Cases where the available experimental data provide only the total solids inventory of the CFB loop are inappropriate for the simulation of individual components, such as risers. For the determination of initial and boundary conditions, many authors [
A schematic view of the benchscale CFB unit installed at University of Campinas is provided in Figure
Experimental assembly setup, adapted from Behainne [
Preheated air is supplied to the riser by a screw compressor, while the solids are fed in by a screw feeder located at the bottom of the solids hopper. Solids that are fluidized in the riser and dragged by the gas phase are collected by a tangential cyclone, which is responsible for releasing the solids into the standpipe. The Lvalve controls the solid reinjection into the riser, creating a circulating system. Fine particles escaping the unit are collected by a bag filter located before the stack. Temperature measurement points are placed along the riser. Table
Geometrical and physical properties of the system.
Riser internal diameter, 
0.102 m 
Standpipe/Lvalve diameter, 
0.063 m 
Riser height, 
4.0 m 
Particle density, 
2,700 kg/m^{3} 
Particle Sauter mean diameter, 
353 
Particle specific heat, 
830 J/kg K 
Minimum fluidization velocity^{1}, 
0.06 m/s 
Particle transport velocity^{2}, 
5.78 m/s 
Particle Geldart group  B 
^{
1}Wen and Yu [
Yang [
A set of several experimental tests were conducted on this unit, as reported by Hory et al. [
Operational conditions of the CFB unit.
Pressure, 
Atmospheric 
Temperature, 
673 K 
Fluidization velocity in riser, 
6 m/s 
Total solids inventory, 
6.5 kg 
Aeration mass rate at Lvalve, 
2 kg/h 
Two approaches were employed in the numerical investigation of the CFB unit, each with a specific aim. Initially a semiempirical model was assembled to determine key operational variables of a CFB system. This model was based on mathematical correlations obtained from the literature. The results produced by the semiempirical model were applied to determine boundary and initial conditions of the second approach, a CFD study of the hydrodynamics of the gassolid flow in the unit’s riser section. Both model strategies are presented in more detail as follows.
The practical hydrodynamic model presented by Basu [
Semiempirical CFB mathematical model.
Riser  
Height (  


Decay constant, Kunii and Levenspiel [  


Choking voidage, Yang [  


Solids circulation flux, Yang [  


Terminal velocity of particles, Basu [  


where 











Superficial gas velocity, Perales et al. [  


Axial voidage fraction, Davidson [  


Internal solids reflux, Davidson [  


Solids inventory, Behainne and Martins [  




Pressure drop, Behainne and Martins [  


 
Cyclone  
Swift geometrical configuration, Basu [  




Pressure drop, Muschelknautz and Greif [  


Wall friction coefficient, Basu [  


Tangential gas velocity, Muschelknautz and Greif [  


Gas exit tube radius, Muschelknautz and Greif [  


Parameters of cyclone design, Muschelknautz and Greif [ 





Velocity at exit  


 
Standpipe/solids recycle valve  
Height above the aeration point, Knowlton [  


Pressure drop in the vertical leg of the Lvalve, Knowlton [  


Pressure drop in the Lvalve, Geldart and Jones [  


Pressure drop in the riser above the solids return level,  
Behainne and Martins [  


Aeration mass flow rate, Geldart and Jones [  


Solids inventory, Behainne and Martins [  

The total solids inventory is calculated as the sum of individual values for the riser and the standpipe/Lvalve, since the particles of the CFB system are mainly concentrated in those components.
For a better understanding of the behavior of the gassolid flow in the riser, a CFD study was carried out. CFD can produce detailed information on multiphase flows, which is not always readily obtained on experimental units. The gassolid flow information produced can also be used to aid in the improvement of the system design.
The governing equations for the momentum, turbulence, and energy transport were used to describe the phenomena involved in the multiphase flow inside the riser. The gassolid system was represented by the EulerianEulerian approach, which considers each phase as a fluid. For describing the turbulence in the gas phase, the realizable kepsilon model was applied and the solid phase was modeled by the KTGF, following the general approach adopted by many authors for multiphase flow in risers. The main equations in the model are presented in Table
Hydrodynamic and thermal models for the twofluid gassolid flow approach.
Continuity  


Gasphase momentum  




Gasphase stress tensor  


Solidphase momentum  


Solidphase stress tensor  


Solidphase pressure, Ogawa et al. [ 



Particleparticle restitution coefficient, Jiradilok et al. [ 



Radial distribution function, Ogawa et al. [ 



Solidphase bulk viscosity, Lun et al. [ 



Solidphase shear viscosity, Gidaspow [ 





Gassolid drag, Gidaspow [ 









Energy balance  


Heat exchange, Ranz and Marshall [ 




The solid stress tensor was described through the KTGF, which accounts for the solid viscosity and pressure terms. The granular temperature was related to the kinetic turbulent energy of the particle and the transport equation derived from it in the kinetic theory is simplified to an algebraic formulation. As for the thermal balance in the riser, a transport equation was solved for each phase. The pressure work, kinetic energy, and viscous heating were neglected as the flow occurs at low Mach numbers [
Only the riser was considered for the CFD simulation, since this is the section of interest in most of industrial applications and where experimental data was collected for validation. This simplification also avoids extracomputational efforts for simulating the very dense regions in the Lvalve, through which the solids return to the riser. A hexahedral mesh containing approximately 400 thousand control volumes was created for the riser. A set of finer and coarser mesh was also created, whereas the refinement of the one selected was sufficient for producing grid independent results for the nonisothermal multiphase flow. The mean equivalent cell length to particle diameter for the selected grid was around 37. Details of the geometry and numerical grid are shown in Figure
Details of (a) the generated geometry, (b) numerical mesh of the top section, and (c) numerical mesh of the bottom section of the riser for the CFD simulation.
Atmospheric air represented the continuum phase and quartz sand the dispersed phase. The boundary conditions are described in Table
Boundary conditions for the CFD riser simulation.
Gas phase  Solid phase  

Main inlet  Mass flow rate:  
 
Temperature: 900 K  
 
Secondary inlet  Mass flow rate:  Mass flow rate: 

recirculation function;  
Temperature: 624 K  Temperature: 624 K  
 
Outlet  Pressure: 0 Pa  Pressure: 0 Pa 
 
Walls  No slip  Free slip 
Heat flux: −175 W/m^{2}  Heat flux: −175 W/m^{2} 
In order to reproduce the behavior of the gassolid flow in a vertical riser, transient simulations were considered. The numerical formulation followed the finite volume method by means of the commercial software Ansys Fluent 12.0. For the interpolation of the discretized partial differential equations, the firstorder upwind scheme was used. The convergence criterion was established as 10^{−3} in absolute values. Reduced underrelaxation factors were chosen to improve the stability of the solution. The time step of 10^{−5} s was initially adopted and gradually increased to a maximum value of 10^{−4} s.
As the main purpose of the semiempirical model was to ease the preliminary system setup for the CFB unit, a validation was carried out comparing its results to those obtained from the experimental data shown in Table
Input data used in the semiempirical model based on Hory et al. [
Internal diameter of the riser column, 
0.102 m 
Height of the secondary air injection, 
0.9 m 
Solids reflux ratio, 
0.066 
Operation temperature, 
673 K 
Operation pressure, 
101.3 kPa 
Voidage fraction bottom region of the riser, 
0.9 
Solid sphericity, 
0.75 
^{
1}Values supported by Basu [
The results obtained from the semiempirical model for each section of the CFB unit are presented in Table
Results obtained from the semiempirical model.
Riser  Particle terminal velocity corrected by sphericity, 
3.04 m/s 
Superficial gas velocity, 
5.54 m/s  
Solids circulation flux in the riser, 
20.93 kg/m^{2}·s  
Choking voidage, 
0.9969  
Voidage fraction at the riser exit, 
0.9962  
Riser height, 
4.00 m  
Riser heighttointernal diameter ratio, 
39.2  
Solids inventory in the total riser height, 
3.52 kg  
Pressure drop in the total riser height, 
4,268 Pa  
Solids return level above the riser base  0.45 m  
Pressure drop in the riser measured above the solids return level, 
3,077 Pa  
 
Cyclone  Volumetric gas flow entering the cyclone, 
0.045 m/s 
Solidtogas mass ratio at the cyclone entrance, 
3.8  
Gas velocity at the inlet section of the cyclone, 
14.83 m/s  
Cyclone dimensions [m]: 
—  
Gas velocity at the cyclone exit, 
10.90 m/s  
Pressure drop in the cyclone, 
271 Pa  
 
Standpipe and Lvalve  Internal diameter of the standpipe and the Lvalve, 
0.063 m 
Circulating solids flux in the standpipe and the Lvalve, 
55.2 kg/m^{2}·s  
Solids velocity in the moving bed, 
0.04 m/s  
Horizontal section of the Lvalve, 
0.36 m  
Aeration level above of the horizontal section center line, 
0.13 m  
Aeration mass flow rate in the Lvalve, 
1.97 kg/h  
Height of the solids above the aeration point, 
0.50 m  
Height of the standpipe, 
2.71 m  
Pressure drop in the Lvalve, 
3,917 Pa  
Pressure drop in the standpipe, 
7,265 Pa  
 
Total solids inventory in the CFB system  8.20 kg 
Comparison of the semiempirical model results for (a) superficial gas velocity (
In Figure
According to these results, the amount of solids in the riser corresponds to approximately 43% of the total solids inventory. This information produced by the semiempirical model was used for setting the initial condition for the CFD simulation of the riser. Thus an initial packed bed was set at the base of the riser corresponding to the stipulated solid mass.
The simulation was carried out for 10 s, during which time a quasisteady state was achieved. At the initial seconds of simulation, the inert bed was observed to begin a rapid fluidization, reaching the riser’s exit and starting to return to the riser. Nevertheless, only after 5 seconds of simulation, transient statistics averages were collected for the main variables in order to analyze the riser characteristics.
The multiphase flow in fluidized beds (risers) is known for its chaotic behavior, as can be observed by the solid phase mass flux leaving the riser (Figure
CFD simulation results of solid phase mass flux leaving the riser: (a) time history fluctuations and (b) power spectral density.
The oscillatory characteristic of the mass flux at the exit can be explained by the continuous disappearance and formation of clusters along the riser, which determines the solid radial distribution and the vertical displacement of particles into the column, also to be observed in Figure
In Figure
Pressure drop in the riser as given by the semiempirical model and the CFD simulations.
Timeaveraged CFD axial profiles for (a) pressure at the center line and (b) solid phase volume fraction calculated as an area average at several cross section planes along the height of the riser.
Instantaneous solidphase volume fraction at 8, 9, and 10 seconds and the mean time average on an axial plane of the riser.
The CFD simulation indicates that the voidage fraction is not strongly segregated into a bottom dense region and an upper dilute one, but these regions are still clearly identified. Higher solid volume fraction zones were observed to occur close to the recirculation inlet height and at the Tshaped exit. This differs from the semiempirical model assumption of a much denser region at the bottom, a mean volume fraction of 0.1 against 0.04 from the simulation, thus explaining the lower pressure at the base of the riser.
Although the CFD model showed only a small difference between a denser region at the bottom and a more dilute above, the coreannulus behavior of the gassolid flow found in the fast fluidization regime was verified. This configuration is commonly found in fast fluidization gassolid flow in risers [
Karri and Knowlton [
CFD simulation solid phase mean radial profiles of (a) volume fraction; (b) axial velocity component at 1.5 m, 2.5 m, and 3.5 m.
Furthermore, the thermal behavior of the gassolid flow along the riser was analyzed. Figure
Timeaveraged gas phase temperature profile at the axial central position in the riser compared with the experimental data.
As described previously, fluidizing gas heated in a GLP burner is introduced by the main inlet flow. The system loses thermal energy through the walls and by heating the solids returning to the system through the Lvalve. To account for the heat loss, the heat flux at the wall was estimated considering only the external natural convection for a vertical cylinder with a constant mean external wall temperature of 338 K and an atmospheric temperature of 303 K. The total amount of heat lost to the environment under this condition was around 175 W/m^{2}, which was set as the thermal boundary condition at the walls. This approximation was considered more realistic than an adiabatic wall. From the base of the riser to the lateral inlet, a temperature reduction was observed due to the return of the recirculated particles and the injection of auxiliary gas. In that region, the simulated results showed some deviation from the experimental measurement. However, the difference was lower than 22 K for the second and third points. Above that region, where the flow is more developed, a better agreement was found.
A practical semiempirical model based on hydrodynamic correlations from experimental data was proposed for determination of the main characteristics of a benchscale CFB unit. This model predicts the solids inventory in components of the system, thereby providing important information for more detailed simulations through a CFD approach. The semiempirical model was validated with experimental information obtained from a benchscale CFB unit operating under precombustion conditions. Deviation for key operational parameters, such as superficial gas velocity, solids inventory, and aeration mass flow rate in the recirculating valve were below 30%.
CFD simulations of the riser of the CFB unit were also carried out. In these simulations the realizable kepsilon model described the turbulence of the continuous phase and the KTGF was applied to the description of the dispersed phase flow in the twofluid model of the riser section of the CFB. The hydrodynamics verified the coreannulus model, which is also confirmed by most of the studies found in literature on fast fluidization beds. The solid circulation rate showed good agreement with the semiempirical model predictions. The simulated thermal profile in the riser showed small underpredicted values with respect to the experimental data, not larger then 3%.
The study also showed the viability of applying the semiempirical correlations to determine the solids inventory as an initial condition to a CFD simulation. By this approach less computational time is required to attain the pseudosteady state than it would be to initialize the same simulation with an empty riser and constant
Decay constant
Area,
Archimedes number
Solidtogas mass ratio at the entrance of the cyclone
Drag coefficient
Diameter, m
Friction coefficient
Gravity, m/
Radial distribution
Circulation mass flux, kg/
Height of the secondary air injection, m
Total height of the riser, m
Inventory, kg
Thermal conductivity, W/m.K
Model factor
Length, m
Mass rate, kg/h
Nusselt number
Pressure, Pa
Internal recirculation rate
Reynolds number
Time, s
Temperature, K
Velocity, m/s
Velocity, m/s
Volume,
Model parameter
Model parameter
Interphase momentum exchange coefficient, kg/
Volume fraction
Sphericity
Solid bulk viscosity, P·s
Shear viscosity, Pa·s
Granular temperature,
Density, kg/
Shear stress, Pa
Velocity, m/s
Stress tensor, Pa
Solid stress tensor, Pa.
Cyclone
Choking
Entry
Falling
Gas phase
Phase index
Lvalve
Minimum fluidization
Nonspherical
Outlet
Riser
Solid phase
Standpipe
Solids return level
Terminal
Transport
Wall.
This work was supported by the national agency CNPq.