Computations of Fluid Dynamics of a 50 MWe Circulating Fluidized

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Ind. Eng. Chem. Res. 2010, 49, 5132–5140

Computations of Fluid Dynamics of a 50 MWe Circulating Fluidized Bed Combustor Liu Guodong,† Sun Dan,† Lu Huilin,*,† Jacques Bouillard,‡ Bai Yinghua,‡ and Wang Shuai‡ School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China, and INERIS, Parc Technologique ALATA, 60550 Verneuil en Halatte, France

Gas-particle two-phase turbulent flows are numerically studied in a 50 MWe circulating fluidized bed combustor. The dense flow of particles is modeled by the frictional stress models adopted from solid mechanics theory, and the dilute flow in the so-called rapid granular flow regime is modeled from the kinetic theory of granular flow. At low concentrations the viscosity due to the effect of the presence of particles is modeled by means of a semiempirical viscosity for fluidized catalytic cracking particles. The distribution of the velocity and concentration of particles in a circulating fluidized bed combustor is predicted. Simulations indicate that the dense regime with a high concentration of particles is in the bottom part and the dilute regime with a low concentration in the upper part of the furnace. The effect of secondary air on the flow behavior is analyzed, and the penetration length of the secondary air jet is computed in a 50 MWe circulating fluidized bed combustor. 1. Introduction Circulating fluidized bed (CFB) combustors use coal and other solid fuels such as biomass and agricultural and municipal waste as the primary source for power generation applications since they offer fuel flexibility, a broad turndown ratio, a relatively fast response to load changes, and lower SO2 and NOx emissions.1,2 A fundamental understanding of the flow behavior of the gas and particles is required for a better design of heat transferring surfaces in the CFB combustor. Due to complex gas-solid flow, chemical reactions, and heat transfer, modeling of CFB combustors is rather difficult.3,4 The fluid dynamics of this gas-solid two-phase flow is very complex and strongly dominated by particle to particle and gas to particle interactions, the geometrical arrangement of the parts, and the operation parameters. Computational fluid dynamics (CFD) is an emerging technique with great potential in providing detailed information on complex fluid dynamics. It is widely applied in industry to support engineering design for single-phase systems and has become a fundamental research component in multiphase systems, including fluidization. Mathematical modeling allows the testing of many variable combustion parameters in less time and at a lower cost. Therefore, mathematical modeling in the CFB combustion process is an attractive solution to enhance combustion performance and reduce pollutants. Investigations on CFB modeling have been carried out by many different researchers in the literature. A comprehensive review of studies concerning CFB combustion and their modeling was conducted.5 There must be a balance between the computational modeling and verification by experimental and operational results. In the Eulerian-Eulerian approach, the gas and particle phases are assumed to be continuous and fully interpenetrating in each control volume. Both phases are described in terms of separate conservation equations for mass and momentum. The interactions between the two phases are expressed as additional source terms added to the conservation equations. Currently, the twofluid model with the kinetic theory of granular flow is the most * To whom correspondence should be addressed. Tel.: +010 0451 86412258. Fax: +010 0451 86412202. E-mail: [email protected]. † Harbin Institute of Technology. ‡ Parc Technologique ALATA.

applicable approach to compute gas-solid flow in a CFB riser.6-10 This model is particularly appropriate when the particle loading is relatively high and can be applied with reasonable computing effort. The kinetic theory of granular flow is used to define the fluid properties of the solid phase through constitutive equations. A detailed discussion of granular flow model development was provided by Gidaspow.11 This is similar to the most widely used k-ε model for turbulence in singlephase flows. The energy associated with turbulence is used to calculate the turbulent diffusion of momentum. Therefore, this theory makes it possible to use a more fundamental approach to calculate the momentum transfer rates. Empiricism (use of a constant particle viscosity, or a pseudofluid) is avoided completely. Simulations using the models of kinetic theory of granular flow in the fluidized beds have been reported by many researchers.12-19 The main emphasis was on validating various models which were proposed for governing and closure equations and used for simulations of gas-solid fluidized beds.20-23 However, the formulation of some critical terms in CFD modeling of CFB combustors is still at a developing stage. The inclusion of chemistry and heat transfer modeling with fluidized bed two-phase flow in 3D CFD simulation will most likely require significant development before reliable results can be produced in the CFB combustors. Thus, it can be assumed that there is a need for comprehensive simplification modeling of fluidized bed combustors. The basic operating principle in a CFB combustor involves the suspension of solid particles by the fluidizing gas to facilitate better combustion and lower emissions through improved heat transfer and solids handling, so a better understanding of the dynamics of fluidized beds is a key issue in making improvements in efficiency, which can be achieved through numerical modeling. The main objective of the current work is to model the hydrodynamics of the gas and particles in a 50 MWe CFB combustor using a commercial CFD package (Fluent Inc.). The upgraded closure model for the solid phase, which includes a modified viscosity and pressure of particles, is used by means of the user-defined functions (UDFs) utility. Both the gas- and particle-phase velocity and particle concentration distributions in the CFB combustor are predicted. The effect of secondary air on the flow behavior is analyzed.

10.1021/ie901103t CCC: $40.75  2010 American Chemical Society Published on Web 11/03/2009

Ind. Eng. Chem. Res., Vol. 49, No. 11, 2010

2. Gas-Solids Flow Model Description In the CFB combustor, particles carried by gas are entrained out of the furnace chamber, shown in Figure 2. To maintain the bed solids, the entrained solids must be recirculated back to the bed. This is done in the return leg, which consists of a solids separator (normally a cyclone), a dipleg, and a loop seal connected to the furnace by a duct pipe. The particle seal is used to maintain the pressure balance that prevents gas and solids from entering the return device. The total air fed (to the combustor) is split into primary and secondary air flows. The primary combustion air is from the bed bottom through a distributor, and the secondary air flow is located above the feeding point of recirculating solids together with the additional sealing air, which would be considered as the secondary air. Therefore, the behavior of solid particles in a CFB combustor depends mostly on their size and density. The following assumptions are made for the modeling of a CFB combustor: (1) An isothermal process is assumed with the adiabatic flow of gas and particles. The chemical reactions and heat transfer are not considered in the simulations. Thus, the temperature of the gas and particle phases remains constant. In the CFB furnace, the gas temperature changes along the height due to combustion and heat transfer. The introduction of the complicated combustion makes the simulation of the CFB combustors difficult because a complex mechanism of heat transfer and chemical reactions needs to be modeled. The scaleup and optimal design of industrial CFB combustors cannot be carried out without considering the chemical reactions and heat transfer. Therefore, the models of combustion and heat transfer will be considered in the numerical simulations of the CFB combustor in the future. (2) The hydrodynamics in the furnace and return leg is considered, and the gas and particle flow in the superheater, economizer, and air heater is not considered in the present simulations. In a CFB combustor, solid particles are circulated around a loop into the bottom of the furnace. The solids exit the furnace top and are separated from the gas in a separator. Gas exits the top of the separator, while solids fall down into its standpipe to be recycled to the furnace by means of a nonmechanical valve. Therefore, investigation of fluid dynamic processes in the combustion chamber and in the return leg is required. (3) The bed material is a mixture with a mean diameter and density of particles. The mass of particles presented in the bed is constant. The particles are assumed to be inelastic, smooth, and monodispersed spheres. A key parameter for proper design and operation of a CFB combustor is the particle size distribution (PSD) of the bed inventory. It governs the solid circulation rate and heat transport from the combustion chamber into the heating surface. CFBs offer the possibility of removing the sulfur dioxide during combustion by adding limestone directly to the combustion chamber. The bed material consists of fresh fuel, limestone particles, and inert solids (ash) with different diameters and densities. If solids undergo size changes (growth or shrinkage), a wider size distribution of solids is created within the bed, which gives rise to a longer and irregular residence time of solids in the furnace. Therefore, to further develop a multifluid mathematical model, these effects in the simulations of a CFB combustor under various operating conditions should be considered. The model adopted is based on the fundamental concept of interpenetrating continua for gas-solid mixtures. According to this theory, different phases can emerge at the same time in the same computational volume. Such an idea is made possible by the introduction of a new dependent variable, εi, the concentration of each phase i. The fundamental equations of mass,

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momentum, and energy conservation are then solved for the gas and solid phases. Appropriate constitutive equations have to be specified to describe the physical rheological properties of each phase and to close the conservation equations. In this model, the solid viscosity and pressure are derived by considering the random fluctuation of the particle velocity and its variations due to particle-particle collisions and the actual flow field. Such random kinetic energy, or granular temperature, can be predicted by solving a fluctuating kinetic energy equation for particles, in addition to the mass and momentum equations. The solid viscosity and pressure can then be computed as a function of the granular temperature at any time and position. Adopting the second approximation distribution function allows us to apply the theory to both dense and dilute two-phase flows. A more complete discussion of the implemented kinetic theory model is given by Gidaspow.11 2.1. Continuity and Momentum Equation. The accumulation of mass in each phase is balanced by the convective mass flows (i ) gas, solids):11 ∂ (ε F ) + ∇ · (εiFivi) ) 0 ∂t i i

(1)

where ε is the concentration of each phase, v is the velocity vector, and F is the density. Mass exchanges between the phases due to coal combustion are not considered. The momentum balance for the gas phase is given by the Navier-Stokes equation, modified to include an interphase momentum transfer term:11 ∂ (ε F v ) + ∇ · (εgFgvgvg) ) -εg∇p + εg∇ · τg + εgFgg ∂t g g g β(vg - vs)(2) where g is the acceleration due to gravity, p the thermodynamic pressure, β the interface momentum transfer coefficient, and τg the viscous stress tensor. The stress tensor of the gas phase can be represented as

{

}

1 τg ) µg [∇vs + (∇vs)T] - (∇ · vs)I 3

(3)

The solids phase momentum balance is given by11 ∂ (ε F v ) + ∇ · (εsFsvsvs) ) -εs∇p - εs∇ps + εs∇ · τs + ∂t s s s εsFsg + β(vg - vs)(4) The solids stress tensor can be expressed in terms of the bulk solid viscosity, ξs, and shear solids viscosity, µs, as

{

}

1 τs ) ξs∇ · vs + µs [∇vs + (∇vs)T] - (∇ · vs)I 3

(5)

2.2. Kinetic Theory of Granular Flow. There are two kinds of possible mechanisms inducing the fluctuations of particle velocity: interparticle collisions and particle interactions with turbulent fluctuations in the gas phase. Interparticle collisions play a crucial role in sufficiently dense suspensions. Equivalent to the thermodynamic temperature for gas, the granular temperature can be introduced as a measure of the energy of the fluctuating velocity of particles. The granular temperature, Θ, is defined as Θ ) 〈c′2〉/3, where c is the particle fluctuating velocity. The equation of conservation of the solid fluctuating energy can be found:11

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3 ∂ (ε F Θ) + ∇ · (εsFsΘ)vs ) (-∇psI + τs):∇vs + 2 ∂t s s ∇ · (ks∇Θ) - γs + φs + Dgs(6)

[

]

where ks is the thermal conductivity coefficient of the solid phase, γs the dissipation of fluctuating energy, φs the exchange of fluctuating energy between the phases, and I the unit tensor. The last two terms in eq 6 represent the interaction between gas turbulence and particle fluctuation. The dissipation fluctuating energy is11 γs ) 3(1 - e2)εs2Fsg0θ

( 4 d

)

θ - ∇ · vs π

(7)

The term Dgs is the rate of energy dissipation per unit volume resulting from the transfer of gas-phase fluctuations to the particle-phase fluctuations. In this study the value of Dgs is predicted using Koch’s expression24 as follows: dFs

Dgs )

( ) 18µg

2 4√πΘ d Fs

2

|vg - vs | 2

(8) τs )

The exchange of fluctuating energy between the gas and particles is9 φs ) -3βΘ

(9)

It accounts for loss of granular energy due to friction with the gas. 2.3. Stress Models of the Gas and Particle Phases. To fully describe the stress in each phase, as required for a two-fluid model, expressions for the gas and particle viscosities are needed. For the gas phase, the effective viscosity is determined: µg )

{

µg,l + µg,t Reg g 2300 Reg > 2300 µs,l

(10)

where Reg ) DFgvg/µg, D being the equivalent diameter. µg,l and µg,t are the laminar viscosity and the turbulent viscosity of the gas phase, respectively. The turbulent viscosity is determined from a k-ε turbulent model and expressed by µg,t ) CµFgk2/ε, where the equations of the turbulent kinetic energy, k, and turbulent kinetic energy dissipation rate, ε, are expressed by

(

of friction among particles in enduring contact. At high particle concentrations, individual particles interact with multiple neighbors through sustained contact. Under such conditions, the normal reaction forces and the associated tangential frictional forces of sliding contacts are the major contributions to the particle stresses. At low particle concentrations, however, the stresses are induced mainly by particle-particle collisions. The behavior of rapidly flowing granular materials, the particle-particle interactions of which are largely dominated by binary collisions, is described by the kinetic theory of granular flow.9 The same theory cannot be applied for slowly moving assemblies of granular materials, longer lasting contacts among particles of which transmit forces over relatively longrange stress chains.28,29 Savage26 and Srivastava and Sundaresan28 presented a frictional-kinetic closure for the particle-phase stress. This model assumes that the frictional and kinetic stresses are additive. Following Savage,26 the stress tensor of particles, τs, is simply the sum of the kinetic stress tensor τk and the frictional stress tensor τf. Each contribution evaluates as follows:

)

µt ∂ (ε F k) + ∇ · (εgFgvgk) ) ∇ · εg ∇k + εgGk - εgFgε ∂t g g σk (11)

( )

µt ∂ ε (ε F ε) + ∇ · (εgFgvgε) ) ∇ · ∇ε + εg [C1Gk ∂t g g σε k C2Fgε](12) Gk ) µt(∇vg + (∇vg)T):∇vg

{

τs,k + τs,f εs > εs,min τs,k εs e εs,min

(14)

where εs,min is the solid concentration at the transition point when frictional stresses become important. Kinetic-frictional theories based on this simple additive treatment have been used to examine a wide variety of flows such as flow down inclined chutes and vertical channels30,31 and flows in the bubbling fluidized bed32,33 and in the spouted beds.34,35 However, the discontinuity occurs at εs ) εs,min. From eq 14, the step transitioning not only causes numerical instabilities leading to slow convergence, but also is found to generate spurious solutions in numerical simulations. To address these problems, an approximate transitioning function is constructed to provide a smooth transition between the two regimes in the particle concentration space. To be more rigorous, this function should be dependent on the local concentration and shear rate. However, the results to date have been very promising for the case where the function is dependent only on the solid concentrations. The stitching function is used, and the stress tensor of the solids is expressed by τs ) (1 - φ1(εs))τs,k + φ1(εs)(τs,k + τs,f) φ1(εs) )

(15)

arctan[25(εs - εs,min)(εs,max - εs,min)-2] + 0.5 π (16)

The solids stress tensor incorporates the solid pressure and viscosity arising from particle momentum exchange due to translation, collision, and friction. Thus, the pressure and viscosity of particles are given as

(13)

ps ) (1 - φ1(εs))ps,k + φ1(εs)(ps,k + ps,f)

(17)

The empirical constants, C1, C2, Cµ, σk, and σε are 1.44, 1.92, 0.09, 1.0, and 1.3, respectively. In the CFB combustor, the concentration of particles varies from very dilute in the furnace chamber to packing in the cyclone and pipe leg. Depending on the way that momentum and energy are transferred in the solid phase, a gas-solid flow can be classified into three regimes:25-27 the macroviscous regime, where the disturbance flow field of one particle affects the motion of the surrounding particles, the grain-inertia regime, or a rapidly shearing regime which is dominated by direct collisions among particles, and in which the kinetic and collisional effects will be considered, and a plastic or slowly shearing regime, in which stresses arise because

µs ) (1 - φ1(εs))µs,k + φ1(εs)(µs,k + µs,f)

(18)

where ps,k and ps,f are the kinetic part and the frictional part of the solid pressure ps, respectively: ps,k ) εsFsΘ[1 + 2g0εs(1 + e)] ps,f ) F

(εs - εs,min)n (εs,max - εs)p

(19) (20)

The values of the empirical parameters of εs,min, F, n, and p are taken to be 0.5, 0.05, 2.0, and 5.0 for glass beads,25 respectively.


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The frictional viscosity is related to ps,f in an expression proposed by Schaeffer.29 The kinetic part µs,k and the frictional part µs,f are 4 µs,k ) εs2Fsdg0(1 + e) 5

Θπ +

10Fsd√πΘ 2 4 1 + g0εs(1 + e) (21) 96(1 + e)εsg0 5

[

µs,f )

]

ps,f sin(ψ)

(22)

2√I2D

where the value of ψ is taken to be 28.5° for glass beads.36 The bulk viscosity of the particles is as follows: 4 ξs ) εs2Fsdg0(1 + e) 3

Θ π

(23)

The theory of granular flow cannot be accurate in dilute suspensions.36 A dilute dispersed phase should obey the kinetic regime, where momentum and kinetic energy transport terms are dominated by the turbulent motion. On the other hand, collisions may have a rather weak influence on the transport properties, by modifying the particle effective mean-free path. This remains an issue in gas-solid flow models, as existing models perform unsatisfactorily. At a low concentration of particles, the particle presence effect will be considered. The particle presence effect gives rise to a stress only in the particulate phase. For simplification, the contribution of the particle present effect to the solid pressure is neglected. A viscosity µs,d effect arises from particles moving along the center line between the particles. The viscosity of the particles, µs, is simply evaluated as follows: µs )

{

µs,k εs > εs,dil µs,d εs e εs,dil

(24)

where εs,dil is the solid concentration at the transition point when the kinetic effect becomes important. For the phasic viscosity, the following expression is used: µs,d ) εsµs,0

(25)

The coefficient of the phasic viscosity is similar to those suggested by Ishii and Mishima,37 and is consistent with Einstein’s equation for the effective viscosity of dilute suspensions. At low concentrations and a high gas velocity, solids can be transported in a dilute flowing suspension. Matsen38 stated that, for a very dilute system at εs,dil g 0.9997, the effective drag was that of an isolated particle.39 Here, we set εs,dil ) 0.9997 as the first approximation. Miller and Gidaspow determined the solid viscosity from a mixture momentum balance, neglecting transient effects and assuming that the gas and solid velocity gradients were of the same order.40 They found that the solid viscosity could be approximated by the solid concentration multiplied by a constant µs ) 5εs (P). More recent particle viscosity data of FCC particles obtained by using the particle image velocity technique showed that a better correlation for viscosity, partially based on the kinetic theory of granular flow, was expressed by41 εsµs,d ) 0.165εs1/3[1 - (εs/εs,max)1/3]-1

Figure 1. Distribution of viscosity as a function of the concentration of particles.

(26)

Figure 1 shows the distribution of viscosity as a function of the concentration of particles. When the particle concentration is

Figure 2. Schematic of the circulating fluidized bed combustor.

less than εs,dil, the viscosity of the particles is increased. The calculated viscosity decreases, and then increases with an increase of the particle concentration without a jump at εs ) εs,min. Note that in this work the model is applied in combination with the kinetic stress and the frictional stress. The assumption captures both the shear flow regime where the kinetic and collisional contributions dominate and the quasi-static flow regime where friction dominates. Only when the solid concentration is extremely dilute (εs,dil g 0.9997) is the gas-solid flow treated as a uniformly dispersed particulate flow.42 The solid viscosity is a data point input into the model. The correlation for particulate viscosity given by eq 26 is a semiempirical equation based on kinetic theory. The viscosity increases to the 1/3 power due to isentropic compression.11 The radial distribution function is based on Bagnold’s equation. To address the step transitioning (discontinuity) problem, the hyperbolic tangent blending function is used in the numerical simulations of the bubbling fluidized bed43 and spouted bed.44 The transitioning function provides a smooth transition between the two granular regimes in the particle concentration space. 2.4. Interphase Momentum Exchange. To couple the momentum transfer between the gas and particle phases, a model for the drag force is required. Gidaspow11 proposed a drag law that was a combination of the Ergun45 and the Wen and Yu46 experimental correlations. This drag law has been widely used in the literature. For solid concentrations greater than 0.2, the Ergun correlation is used, whereas for values less than or equal to 0.2, the Wen and Yu expression is employed. This transition proposed by Gidaspow11 makes the drag law discontinuous in solid concentration though it is continuous in Reynolds number. Physically, the drag force is a continuous function of both the solid concentration and Reynolds number, and therefore, the continuous forms of the drag law may be needed to correctly

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Table 1. Parameters and Dimensions of the Furnace of the Model Used parameter

unit

value

parameter

unit

value

height of the furnace width of the furnace depth of the furnace outer diameter of the cyclone vortex finder diameter of the cyclone superficial velocity particle-particle coefficient of restitution wall-particle coefficient of restitution

m m m m m m/s -

31.46 4.77 8.61 4.0 2.0 5.0 0.95 0.95

diameter of the particles density of particles operating temperature gas density kinetic viscosity of the gas specularity coefficient maximum solid volume fraction static height of the particles

mm kg/m3 °C kg/m3 m2/s m

0.5 2200 850 0.315 136 × 10-6 0.5 0.63 3.0, 5.0

simulate gas-solid fluidized beds. To avoid discontinuity of the two correlations, the switch function is introduced to give a smooth transition from one regime to the other: β ) φgs150

εs2µg 2 2

εg d

Fgεs |v - vs | + εgd g 3CdεgεsFg |vg - vs | -2.65 εg (27) (1 - φgs) 4d

+ 1.75

with φgs ) Cd )

arctan[150 × 1.75(0.2 - εs)] + 0.5 π 24 (1 + 0.15(Re)0.687) Re Cd ) 0.44

Re < 1000

Re g 1000

(28a) (28b) (28c)

where Re is the Reynolds number, Re ) dFg|vg - vs|/µg. Leboreiro et al.47 employed a linear interpolation in the simulations of bubbling fluidized beds. Physically, the drag force is a continuous function of both the solid concentration and Reynolds number, and therefore, the continuous forms of the drag law may be needed to simulate flow of particles in the CFB combustors. Note that the correlations by Ergun45 and Wen and Yu46 were originally developed on the basis of experiments with homogeneous systems. However, the distribution in circulating fluidized bed combustors is heterogeneous. The drag monotonously increases with an increase of the solids concentration, which is in contrast to the experimentally observed reduction of the drag due to the formation of clusters. Therefore, the effect of the cluster structure on the drag force should be taken into account in the calculation of the momentum exchange. 2.5. Boundary Conditions. The flow behavior of the gas and particle phases is simulated in a commercial CFB combustor of a CFB boiler generating 220 t/h of steam. Figure 2 shows a

Figure 3. Effect of the mesh density on the averaged porosity along the height.

schematic of the boiler system.48,49 The combustor is 8.61 m × 4.77 m in cross-section and 31.46 m high (the height is defined in this study as the distance above the distributor). It is equipped with two hot cyclones and two loop seals. The crosssection of the furnace area increases gradually from 2.5 m2 at the distributor to 41.07 m2 in the furnace with the diverging section ending 3.23 m above the distributor. Table 1 summarizes the parameters used in the simulations. Two gas exits leading to hot cyclones (barrel diameter, 4.0 m; barrel length, 3.3 m; length of the cone section, 5.8 m; dipleg diameter, 0.35 m) are located symmetrically at the rear wall at the top of the combustor. Two recycle inlets for return of particles collected in cyclones penetrate the rear wall in the lower part of the combustor. Coal is fed there together with recycled solids. At the inlet, the velocities of the primary air and particles are specified. The concentration of particles is zero. The inlet mass flux of gas is specified at the loop seal. The periodic boundary condition for the solid phase is used. The inlet solid mass flux at the loop seal equals that at the exit of the cyclone. The gas pressure is not specified at the inlet because of the incompressible-gas-phase assumption (relatively low pressure drop system). At the outlet, the pressure is specified (atmospheric). Initially, the velocities of both the gas and particles are set at zero. The static height of the bed materials and the mass of particles in the return leg remain constant. At the wall, the gas tangential and normal velocities are set at zero (no slip condition). The normal velocity of the particles is also set at zero. The following boundary equations apply for the tangential velocity and granular temperature of particles at the wall:50

Θw ) -

6µsεs,max

∂vs,w πFsεsg0√3Θ ∂n

(29)

√3πFsεsvsg0Θ3/2 ksθ ∂θw + ew ∂n 6εs,maxew

(30)

vt,w ) -

where ew is the restitution coefficient at the wall. 2.6. Simulation Code and Computation Procedures. The set of governing equations presented in section 2.1, section 2.2, section 2.3, and section 2.4 is solved by a CFD code (Fluent 6.2). The stress model and the drag force coefficient model are incorporated by means of the UDFs utility. The typical values of the relaxation factors are 0.2-0.4. A time step of 0.0001 s with 50 iterations per time step is chosen. This iteration is adequate to achieve convergence for the majority of time steps. First-order discretization schemes for the convection terms are used. The relative error between two successive iterations is specified by using a convergence criterion of 10-5 for each scaled residual component. The governing equations are solved by a finite volume technique. The phase-coupled SIMPLE algorithm is applied for the pressure-velocity coupling, which is based on total volume continuity, and the effects of the


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Figure 4. Instantaneous concentration of particles in a CFB combustor.

Figure 5. Instantaneous concentration at three different positions.

interfacial coupling terms are fully incorporated into the pressure correction equation. Grids are created in a CAD program called GAMBIT and exported into Fluent. To validate the numerical results, the grid dependence is first examined to minimize the numerical uncertainty. A mesh refinement study is used to examine the effects of the mesh density on the solution with a coarse mesh (325 575 unstructured elements), medium mesh (582 236 unstructured elements), and fine mesh (884 138 unstructured elements). For comparison, the variations of the averaged porosity along the height of the riser for the three meshing schemes are shown in Figure 3. The plotted values are obtained by spatially averaging the porosities over the crosssection and over time. The analysis of the axial porosity shows that the change in the results between the medium and fine grids is much lower compared to that between the coarse and medium grids. The absolute variation in the averaged porosity between the medium and fine grids has a value of 0.4%. Therefore, the simulation runs have been done with the medium grid to ensure high computational accuracy within the constraints of the available computational resources. The time-averaged distributions of flow variables are computed by covering a period of 80 s corresponding to 6-7 weeks of computational time on a PC (80 GB hard disk, 512 MB of RAM, and 2.4 GHz CPU). The time-averaged results are obtained by averaging results from 40.0 to 80.0 s. 3. Simulations and Discussions Figure 4 shows the instantaneous concentration of particles in the CFB combustor. Simulations show that the bed begins to expand once gas is introduced. Some particles hit the top wall and fall down. Some particles close to the cyclone are dragged by the gas into the cyclone. At the initial stage, the flow of particles into the cyclone is high, leading to particle accumulation at the apex of the cyclone. Some particles may exit the system from the vortex

finder due to strong particle-particle interaction. At the same time, an equal mass flux of particles will be added into the furnace from the loop seal to keep a constant inventory. Finally, macroscopically steady state flow is established, where the input and output rates of particles are equal. From Figure 4 it can be seen that there are many more particles near the wall than in the center, especially near the wall close to the cyclone side Figure 5 shows the instantaneous concentration of particles at three different positions. From a given initial condition, particles go through the furnace and finally reach the so-called statistical steady state regime. For practical purposes, this regime is reached when all the flow parameters start to oscillate around well-defined means. The averaged values are obtained by spatially averaging over time from 40.0 to 80.0 s. Figure 6 shows the distribution of averaged velocities of the gas phase and particles at three different heights. The velocities of the gas phase and particles are higher in the center regime than near the walls. The velocity of the particles is negative at the west wall and the east wall, which means the particles flow down close to the walls. At the front wall, the velocity of the particles is negative, which means the particles flow down. However, it is positive at the rear wall, which indicates the particles flow up. The particles in the separator and dipleg return to the furnace from a loop seal by secondary air. Thus, particles near the west wall flow up with secondary air. Therefore, the secondary air influences the motion of the particles in the furnace. Figure 7 shows the distributions of the particle concentration at three different heights. The concentration of particles is low in the center and high near the walls. The recirculating solids from the loop seal return to the furnace at the rear wall. This causes the particle concentration to be high at the rear wall and low at the front wall. An unsymmetrical distribution of the concentration of particles is found. From the west wall, the concentration of particles decreases, reaches the minimum in the center, and then increases at the east wall. From Figure 6, the low gas velocity causes particles to accumulate near the wall and generates a large resistance force to fluid flow. Consequently, gas tends to flow through the center, and more particles accumulate near the wall. The structure of the core with a low concentration and the annulus with a high concentration is formed in the furnace, which causes solid backmixing. This flow structure in the furnace is characterized by the phenomena that the particle concentration is higher near the wall than that in the center, particles always move upward in the center zone but can be either upward or downward near the wall, and the gas velocity is higher near the center and lower near the wall. This indicates that the arrangement of solid circulation ports is indeed important for the hydrodynamics of the gas and particles in the furnace.

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Figure 6. Profile of the velocities of the gas and particles at three heights.

Figure 7. Distributions of the concentrations of particles at three heights.

Figure 8. Profile of the porosity along the height at two inventories of particles.

Figure 8 shows the cross-sectional particle concentration distribution along the height. An S-shaped profile in the axial solids distribution exists. The solid concentration varies significantly, being usually high in the bottom and low in the top of the CFB combustor. The predicted pressure distribution along the height in the CFB combustor is shown in Figure 9. Most of the pressure drops take place over the first meters of the furnace (i.e., bottom bed). The pressure drop gradient is much lower in the upper part than in the lower part of the furnace. In a CFB combustor, the secondary air injection is mainly employed to control the nitrogen oxide formation, enhance mixing, and stimulate solid flow. The total combustion air is split into primary and secondary streams, where the secondary air is injected into the furnace at a certain height above the distributor. Understanding the hydrodynamics of the gas and solids movement resulting from the introduction of secondary air can have consider-

Figure 9. Profile of the gas pressure along the height at two inventories of particles.

able significance in improving the design. The typical local gas jet observed in the simulation is presented in Figure 10. The air jet ejects into the furnace at an incline angle. The secondary air jet will be turned on upward due to the interaction of the gas and solids. The local circulation of gas with particles is formed. Thus, the mixing of particles is improved. Due to the transfer of momentum, the jet cross-section increases with a decrease of the gas velocity along the jet to maintain the constant gas flow rate inside the jet, and the penetration length is varied. There are different definitions of jet penetration length used in the literature. The maximum penetration length of the secondary air jet is considered to be the distance from the orifice to the end of the curvature. Figure 11 shows the penetration length as a function of the secondary air velocity. The penetration length increases with an increase of the secondary air velocity. The numerical results are in agreement with data calculated by empirical correlations.51


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Note that the present model is restricted in many aspects. It is necessary to add heat transfer and combustion submodels. The latter includes the drying, devolatilization, and primary fragmentation of fresh fuel particles and combustion of char and volatiles. For further model development, the size distribution of particles needs to be considered by means of the population balance of particles with the consideration of fragmentation and attrition. We also recognize that the model is required to be validated by comparing its predictions to experiments in circulating fluidized bed combustors, which will be of interest for further investigation. Acknowledgment

Figure 10. Instantaneous gas flow at the local secondary air ports.

This work was supported by the Natural Science Foundation of China through Grant No. 50776023 and the National Key Project of Scientific and Technical Supporting Programs funded by the Ministry of Science and Technology of China (Grant No. 2006BAA03B01-07). Nomenclature

Figure 11. Distribution of the penetration length of the secondary air jet.

The lower secondary air jet is close to the distributor. Thus, the penetration length of the upper secondary air jet is larger than that of the lower secondary air jet due to the interaction of inlet primary air. In the simulations, it is observed that the jet can reach the opposite wall at high jet velocity. This may cause the undesired erosion of the wall in real applications. Results indicate that the maximum penetration length is in the range of 0.5-1.3 m at a secondary air velocity of 50-90 m/s. Simulations indicate that the secondary air jet affects the flow of the gas phase and particles in the dense regime, and further study is required at different velocities of primary air and secondary air jet. 4. Conclusions The flow behavior of the gas and particles is simulated by taking the stress models of macroscopic fluid dynamics into account in the CFB combustor. Special emphasis has been made on different flow patterns in the CFB combustor, which are more limited in the literature. For gas stresses, the different viscosities used depend on the local Reynolds number. For the solid phase, the frictional stress models of the dense flow are based on the solid mechanics theory, the dilute flow is modeled from the kinetic theory of granular flow, and at low concentrations the viscosity, due to the effect of the presence of particles, is modeled by means of a semiempirical particle viscosity. Simulations show the distribution of the velocity, concentration, and gas pressure in the furnace. In this paper we show that it is possible to integrate the modified stress models for the entire CFB combustor.

C ) constant, dimensionless Cd ) drag coefficient, dimensionless d ) particle diameter, m D ) depth of the bed, m Dgs ) rate of energy dissipation, kg m-1 s-3 e ) restitution coefficient, dimensionless F ) constant, dimensionless g ) acceleration due to gravity, m s-2 g0 ) radial distribution function, dimensionless Gs ) circulation mass flux, kg s-1 H ) height, m I ) unit tensor I2D ) second invariant of the deviator of the strain rate tensor for the solid phase, s-2 k ) turbulent kinetic energy, m2 s-2 ks ) granular conductivity, kg m-1 s-1 p ) fluid pressure, Pa ps ) solid pressure, Pa Re ) Reynolds number, dimensionless t ) time, s ug ) superficial gas velocity, m s-1 v ) velocity component, m s-1 W ) width of the furnace, m x, y, z ) coordinates, m Greek Letters τ ) stress tensor, Pa τf ) frictional stress, Pa τk ) kinetic stress, Pa Θ ) granular temperature, m2 s-2 ξs ) bulk viscosity, kg m-1 s-1 µg ) gas viscosity, kg m-1 s-1 µs ) shear viscosity of particles, kg m-1 s-1 φ1 ) stitching function φs ) exchange of fluctuating energy, kg m-1 s-3 F ) density, kg m-3 ε ) turbulent kinetic energy dissipation rate, m2 s-3 εg ) porosity, dimensionless εs ) concentration of particles, dimensionless εs,dil ) solids concentration at the transition point, dimensionless εs,max ) maximum solids concentration, dimensionless γs ) energy dissipation rate, kg m-1 s-3 β ) drag coefficient, kg m-3 s-1

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φgs ) stitching function σ ) constant, dimensionless Subscripts f ) frictional part g ) gas phase l ) laminar flow k ) kinetic part s ) solid phase t ) turbulent flow w ) wall

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ReceiVed for reView July 8, 2009 ReVised manuscript receiVed October 2, 2009 Accepted October 21, 2009 IE901103T

Computations of Fluid Dynamics of a 50 MWe Circulating Fluidized

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