Energy Fuels 2010, 24, 6294–6300 Published on Web 11/30/2010
: DOI:10.1021/ef1013055
Numerical Simulation of the Effects of Block Height on the Gas-Solid Flow in a Fuel-Rich/Lean Burner by the Hard-Sphere Model Hao Zhou,* Guiyuan Mo, and Kefa Cen Zhejiang University, Institute for Thermal Power Engineering, State Key Laboratory of Clean Energy Utilization, Hangzhou, 310027, P. R. China Received September 25, 2010. Revised Manuscript Received November 4, 2010
The particle dispersion mechanisms in the gas-solid two-phase jet for a fuel-rich/lean burner have been numerically investigated by means of coupling the hard-sphere model with the computational fluid dynamics (CFD). In the computation of solid flow, the hard-sphere model was employed to deal with the particle-particle interactions. The numerical simulation was carried out based on the commercial software package Fluent. The influence of the collision block height on the particle distribution in the gas-solid fuel-rich/lean burner was investigated in this study. The particle-particle collision was simulated, and its effect on the fuel-rich/lean separating performance was evaluated. The results indicated that the particle-particle collision number and the concentration ratio increased with the collision block height increasing from 40 to 60 mm. A good fuel-rich/lean separating performance can be obtained with the collision block height of 60 mm. The particle dispersion between the fuel-rich side and the fuel-lean side became more uniform as a result of the particle-particle interactions. The corresponding experimental results were used to validate the numerical results with the hard-sphere model, and a better agreement between the simulation and experiments was achieved due to the particle-particle collisions.
1. Introduction Coal, as one of the most important fossil fuel, is widely used for power generation in the world. Most coal-fired power plants all over the world are now designed to meet the demand of high efficiencies and low pollutant emission. In recent years, to burn low volatile coal more efficiently and decrease the NOx emissions, a novel pulverized coal combustion technology called horizontal fuel-rich/lean burner has been employed in power station boilers in China.1,2 Various types of burner such as bend-type,3 louver-type,4 and collision-block-type2 have been adopted to separate the fuel/air mixture into a fuelrich stream and a fuel-lean stream. A collision-block-type fuel-rich/lean burner2 will be studied in this work, as shown in Figure 1. When a horizontal fuel-rich/lean burner is used in a tangentially fired boiler, a fuel-rich stream and a fuel-lean stream can be obtained by a fuel-rich/lean separator employed in the fuel conveying line. Because of the effect of the collision block, the coal particles are concentrated on the fuel-rich side over the central partition plate and a fuel-lean pulverized-coal flow will be formed on the other side of the partition plate. So there is a big difference
Figure 1. Sketch of the fuel-rich/lean burner.
in solid concentration between the fuel-rich stream and the fuel-lean stream. As reported by our previous study,5 the fuel concentration ratio between the fuel-rich side and the fuellean side can be regulated continuously by adjusting the height of the collision block. The fuel-rich stream faced the high-temperature flame when injected on the fuel-rich side. The lean fuel concentration on the fuel-lean side will result in oxidizing atmosphere near the water-cooled wall, and a high ash fusion temperature is achieved to prevent the furnace from slagging and fouling. As verified by field data,3,4 the nonstoichiometry combustion occurred and the NOx emissions can also be reduced under fuel-rich/lean combustion conditions. The designers of the fuel-rich/lean burner and the combusting system focus their attentions mainly on the particle dispersion characteristics and some detailed information on the complicated particle-particle interactions and particlefluid interactions. As one of the major criteria, the particle dispersion phenomenon between the fuel-rich and fuel-lean side is very important in evaluating the performance of the burner and the combusting system. Some studies on the testing and numerical simulating results have been reported
*To whom correspondence should be addressed. Telephone: þ86571-87952598. Fax: þ86-571-87951616. E-mail:
[email protected]. edu.cn. (1) Zhou, H.; Cen, K.; Fan, J. R. Experimental investigation on flow structures and mixing mechanisms of a gas-solid burner jet. Fuel 2005, 84, 1622–1634. (2) Zhou, H.; Cen, K.; Fan, J. R. Detached eddy simulation of particle dispersion in a gas-solid two-phase fuel rich/lean burner flow. Fuel 2005, 84, 723–731. (3) Wei, X.; Xu, T.; Hui, S. Burning low volatile fuel in tangentially fired furnaces with fuel rich/lean burners. Energy Convers. Manage. 2004, 45, 725–735. (4) Xu, M.; Sheng, C.; Yuan, J. Two-phase flow measurements and combustion tests of burner with continuously variable concentration of coal dust. Energy Fuels 2000, 14 (3), 533–538. r 2010 American Chemical Society
(5) Zhou, H.; Cen, K. F. Experimental measurements of a gas-solid jet downstream of a fuel-rich/lean burner with a collision-block-type concentrator. Powder Technol. 2006, 170, 94–107.
6294
pubs.acs.org/EF
Energy Fuels 2010, 24, 6294–6300
: DOI:10.1021/ef1013055
Zhou et al. 4-7
12-21
about the concentrator separating characteristics. In our previous work, the vortex shedding process and its effect on the fuel-rich/lean separating performance was numerically investigated by the detached eddy simulation (DES) approach.2 In some numerical simulations on the gas-solid two-phase flow, the assumptions of dilute flow had been made and the particle-particle collisions were ignored.2,8,9 However, as reported by Tanaka and Tsuji,10 the particle-particle collisions may play an important role in the dilute two-phase flow. In their study of simulating the gas-solid two-phase flow in a vertical pipe, a hard-sphere model was used to deal with the particle-particle collisions. They found that the particle-particle collisions have a large effect on the diffusion of particles even in dilute conditions in which the particle volume fraction is 0 (10-4). The mass ratio of the fuel/air mixture in the pneumatic pipe is normally about 0.3-0.6 kg (coal)/kg (air), corresponding to the typical volume fraction ratios (solid to air) between 0.044 and 0.026%, then the conventional pulverized coal conveying flow can be considered as a dilute two-phase flow.11 However, in the regions upstream of the collision-block and adjacent to the partition plate, local concentrating occurs. The volume fraction ratios (solid to air) in those zones exceed the corresponding value in dilute two-phase conveying. In recent years, the gas-solid two-phase flow has been studied by means of numerical simulations. Some significant advances have been reported in investigating the behavior of
The gas-solid particulate flow during the past decades. Euler-Euler two-phase model12-15 and the Euler-Lagrange model10,16-21 are the two kinds of calculation models mainly used for the gas-solid flow. The hard-sphere model is based on the Euler-Lagrange model, and it takes the particle-particle collisions and particle-wall collisions into account.10 The objective of this work is to investigate the effect of the collision block height on the fuel-rich/lean separating performance and the influence of particle-particle interactions on the particle distribution by coupling the hard-sphere model with the computational fluid dynamics (CFD) using a 16-core computer. The particle motion was calculated by combining the Lagrange model and the hard-sphere approach. The gas motion was modeled by the RNG κ-ε two equation turbulent model. In the study of turbulent flows and the investigation of gas-solid interactions and mixing, the Reynolds Average Navier-Stokes (RANS) was widespreadly employed.7,22,23 The numerical results were validated by the gas-solid experiments. 2. Numerical Methods A hard-sphere approach10,24 and a soft-sphere approach16 are two kinds of the particle-particle collision models. The hardsphere approach was developed by Hoomans et al. to simulate the discrete particles in a two-dimensional gas-solid bed.25 The hard sphere approach is especially suitable for simulation of rigid granular particles in a relatively dilute flow.25,26 The soft-sphere model was developed by Tsuji et al. in the application of a 2-D fluidized bed simulation.16 Some mechanical models such as spring dashpot and slider have been made for the soft-sphere model.24 It has been widely used in numerical studies of granular particles, which are subjected to intensive mutual collisions in the contact-dominated dense particulate flow. In this study, the hard-sphere model reported by Tanaka and Tsuji10 was employed to deal with the particle-particle and particle-wall collisions. This model is based on the following assumptions: (1) the particle-particle collisions are considered to be instantaneous inelastic ones; (2) the particles are rigid spheres and any persistent particle deformation during a collision is neglected; (3) the particle-particle collisions between a pair of particles may occur at any point of time, while the multiple collision process at a point of time is not considered. Newton’s second law was used to calculate the motion of each individual particle without collision. During its movement, the particle may interact with the surrounding fluid. In this study, the drag force and gravity force were considered, while other forces such as the Saffman lift force and the Basset force were neglected. The drag force can be expressed as FD = 0.5FgApCD|uf - vp|(uf vp), AP = 0.25πdp2 is the particle cross-sectional area, and CD = (24/Re)fD is the drag coefficient. Then the nondimensional translational equation of motion of a particle is given by
(6) Fan, J. R.; Xia, Z. H.; Zhang, X. Y.; Cen, K. F. Numerical investigation on two-phase flow in rich/lean pulverized coal nozzles. Fuel 2000, 79, 1853–60. (7) Li, Z. Q.; Sun, R.; Wan, Z. X.; Sun, S. Z.; Wu, S. H.; Chen, L. Z. Gas-particle flow and combustion in the near-burner zone of the swirling stabilized pulverized coal burner. Combust. Sci. Technol. 2003, 175, 1979–2014. (8) Wicker, R. B.; Eaton, J. K. Structure of a swirling recirculating coaxial free jet and its effect on particle motion. Int. J. Multiphase Flows 2001, 27, 949–970. (9) Luo, K.; Klein, M.; Fan, J. R.; Cen, K. F. Effects on particle dispersion by turbulent transition in a jet. Phys. Lett. A 2006, 357, 345– 350. (10) Tanaka, T.; Tsuji, Y. Numerical simulation of gas-solid twophase flow in a vertical pipe: on the effect of inter-particle collision. ASME/FED Gas-Solid Flows 1991, 121, 123–128. (11) Zhou, H.; Cen, K. F. Experimental Investigations on Performance of Collision-Block-Type Fuel-Rich/Lean Burner: Influence of Solid Concentration. Energy Fuels 2007, 21, 718–727. (12) Deen, N. G.; Solberg, T.; Hjertager, B. H. Large eddy simulation of the Gas-Liquid flow in a square cross-sectioned bubble column. Chem. Eng. Sci. 2001, 56, 6341–6349. (13) Ortiz-Arroyo, A.; Larachi, F. Lagrange-Euler-Euler CFD approach for modeling deep-bed filtration in trickle flow reactors. Sep. Purif. Technol. 2005, 41, 155–172. (14) Sanyal, J.; Vahsquez, S.; Roy, S.; Dudukovic, M. P. Numerical simulation of gas-liquid dynamics in cylindrical bubble column reactors. Chem. Eng. Sci. 1999, 54, 5071–5083. (15) Moreau, M.; Simonin, O.; Bedat, B. Development of GasParticle Euler-Euler LES Approach: A Priori Analysis of Particle SubGrid Models in Homogeneous Isotropic Turbulence. Flow Turbulence Combust. 2010, 84, 295–324. (16) Tsuji, Y.; Kawaguchi, T.; Tanaka, T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technol. 1993, 77, 79–87. (17) Zhou, H.; Flamant, G.; Gauthier, D. DEM-LES of coal combustion in a bubbling fluidized bed Part 1: gas-solid turbulent flow structure. Chem. Eng. Sci. 2004, 59, 4193–4213. (18) Tsuji, T.; Yabumoto, K.; Tanaka, T. Spontaneous structures in three-dimensional bubbling gas-fluidized bed by parallel DEM-CFD coupling simulation. Powder Technol. 2008, 184, 132–140. (19) Cundall, P. D.; Strack, O. D. L. A discrete numerical model for granular assemblies. Geotechnique 1979, 29, 47–65. (20) Tsuji, Y.; Tanaka, T.; Yonemura, S. Cluster patterns in circulating fluidized beds predicted by numerical simulation (discrete particle model versus two-fluid model). Powder Technol. 1998, 95, 254–264. (21) Chu, K. W.; Yu, A. B. Numerical simulation of complex particle-fluid flows. Powder Technol. 2008, 179, 104–114.
dvp fD ðuf - vp Þ þ g0 ¼ dt St
ð1Þ
(22) Bilrgen, H.; Levy, E. K. Mixing and dispersion of particle ropes in lean phase pneumatic conveying. Powder Technol. 2001, 119, 134–152. (23) Yilmaz, A.; Levy, E. K. Formation and dispersion of ropes in pneumatic conveying. Powder Technol. 2001, 114, 168–185. (24) Cundall, P. A.; Strack, O. D. L. Discrete numerical-model for granular assemblies. Geotechnique 1979, 29, 47–65. (25) Hoomans, B. P. B.; Kuipers, J. A. M.; Briels, W. J.; Van, W. P. M. Discrete particle simulation of bubble and slug formation in a twodimensional gas-fluidisedbed: a hard-sphere approach. Chem. Eng. Sci. 1996, 51, 99–118. (26) Yamamoto, Y.; Potthoff, M.; Tanaka, T.; Kajishima, T.; Tsuji, Y. Large-eddy simulation of turbulent gas-particle flow in a vertical channel: effect of considering inter-particle collisions. J. Fluid Mech. 2001, 442, 303–334.
6295
Energy Fuels 2010, 24, 6294–6300
: DOI:10.1021/ef1013055
Zhou et al.
where νp is the particle translational velocity and fD is the modified factor for the Stokes drag force. For Rep e 1000, fD = 1 þ 0.15Rep0.687; for Rep > 1000, fD = 0.0183Rep and Rep is the particle Reynolds number.27 g0 is the nondimensional gravity acceleration vector, and g0 = gLr/Ur2 (g is the gravity acceleration, Lr is the characteristic length scale, and Ur is the characteristic velocity scale). The particle Stokes number St is expressed as ð2Þ
Figure 2. Sketch of particle-particle collision between particle pi and particle pj.10.
where Fp is the particle density, dp is the particle diameter, and μ is the fluid dynamics viscosity. The rotational motion of a particle is induced only by the particle-particle collisions, particle-wall collisions, and friction, while the rotation caused by the fluid is not considered in this work. As a result, the rotational motion of a particle can be simulated as ω_ p ¼ T p =I p ð3Þ
for both particle-particle collisions and particle-wall collisions. The influence of the restitution coefficient on the particle-particle collisions was examined by Ouyang and Yu et al.28 γ is the coefficient of friction, and it is used only when the sliding motion between two colliding particles occurs. The collision detection is very important for the calculation of the hard-sphere model, because the particle-particle collisions between a pair of particles occurs only at any point of time. As shown in Figure 2, Δr(t) and Δr(t þ dt) are the distance between two colliding particles “i” and “j” at any initial time t and the terminal distance after a time step dt, respectively. The following equation for k must have real roots k1 and k2 when the particle-particle collision occurs during this time step. Also k1 and k2 should satisfy 0 e k1 < 1, k1 < k2. ð12Þ ΔrðtÞ þ kðΔrðt þ dtÞ - ΔrðtÞÞ ¼ ðdpi þ dpj Þ=2
St ¼ Fp Ur dp 2 =ð18μLr Þ
where ωp,Tp, and Ip are the particle rotational velocity, torque, and the moment of inertia, respectively. Tp can be defined as Tp ¼ r J=Δt
ð4Þ
where J is the collision impulsive force in a contact time Δt. The particle angular velocity was only used for the particle-particle collision calculation, but the Saffman lift force was not considered in this work. After the particle-particle collision occurs, the postcollision velocities of the two particles i and j can be calculated according to the governing equations for the collision processes: 0
ð5Þ
vj ¼ vj - J=mp, j
0
ð6Þ
ωi ¼ ωi þ rp, i =I p, i n J
0
ð7Þ
0
ð8Þ
vi ¼ vi þ J=mp, i
ωj ¼ ωj þ rp, j =Ip, j n J
where |Δr(t) þ k(Δr(t þ dt) - Δr(t))| is the relative distance between the two particles at the point of time when collision occurs, and dp is the diameter of the particle. When a particle interacts with the wall, the interaction between the particle and wall can be treated as one specific case of the regular particle-particle collisions and the mass of wall is infinite, then Me will equal mp in the particle-wall collisions. The governing equations of the gas phase are the mass conservation equation and the momentum conservation equation, defined as follows
where νi and νj are velocities of the colliding particles denoted as particle “i” and “j”, while ωi and ωj are corresponding angular velocities of them. The 0 denotes the postcollision variables. mp is the particle mass, rp the radius of particle, and Ip the moment of inertia. J is the impulsive force experienced by particle “i”, and it can be obtained from the following equation: J ¼ jn n þ jt t
ð9Þ
jn ¼ - ð1 þ eÞMe vr 3 n
ð10Þ
) 2 jt ¼ min - Me t 3 ðvr þ ri ωi n þ rj ωj nÞ, γjn 7
DF þ r 3 ðFuÞ ¼ 0 Dt
ð13Þ
DðFuÞ þ r 3 ðFuuÞ ¼ - rp þ r 3 ðτÞ þ Fg Dt
ð14Þ
where F is the gas density, u is the gas velocity, t is the time, p is the pressure, and τ is the fluid viscous stress tensor. The gas motion was modeled by the RNG κ - ε two equations turbulent model in this work. In the present study, the numerical work was carried out by means of coupling the hard-sphere model and the computational fluid dynamics with Fluent as a platform. The hard-sphere model code was incorporated into the commercial CFD software packages Fluent through its user-defined functions (UDF). Chu and Yu developed a three-dimensional CCDM model based on Fluent to simulate the gas-solid flow in pneumatic conveying bends.29
(
ð11Þ
In the above equations, jn and jt are the normal and the tangential components of the impulse J, respectively; νr is the relative velocity between the particles i and j defined as νr = νi - νj; Me is the efficient mass defined as Me = mp,i mp,j/(mp,i þ mp,j); n is the normal unit vector pointing from the center of particle “i” to the center of particle “j”, while t is the unit vector in the tangential direction at the contact point perpendicular to n; and e is the coefficient of restitution determined by the particle material. In this work, the properties of the wall were considered to be the same as those of the particle. So a restitution coefficient was used
3. Computational Conditions The experimental study of the gas-solid jet downstream of a fuel-rich/lean burner was described in our previous paper.5 The full industrial-scale fuel-rich/lean burner studied in the experiments was designed for a 300 MWe capacity utility boiler. It consisted of a collision-block-type concentrator and a coal nozzle. Because of the geometrical restrictions of the test
(27) Clift, R.; Grace, J. R.; Weber, M. E. Bubbles, Drops, and Particles; Academic Press: New York, 1978. (28) Ouyang, J.; Yu, A. B.; Pan, R. H. Simulation of Gas-Solid Flow in Vertical Pipe by Hard-Sphere Model. Part. Sci. Technol. 2005, 23, 47– 61.
(29) Chu, K. W.; Yu, A. B. Numerical Simulation of the Gas-Solid Flow in Three-Dimensional Pneumatic Conveying Bends. Ind. Eng. Chem. Res. 2008, 47, 7058–7071.
6296
Energy Fuels 2010, 24, 6294–6300
: DOI:10.1021/ef1013055
Zhou et al.
Table 1. Physical and Numerical Parameters properties
value
inlet area (mm mm) air temperature (°C) inlet velocity (m/s) Reynolds number fluid CFD cell type damping coefficient restitution coefficient nondimensional time step
160 120 20 14 1.74 105 air hexahedral 0.3 0.9 0.001
Figure 3. Schematics of computational grids (3D view).
Table 2. Numerical Simulation Cases collision relative particle mean particle solid block height collision diameter density concentratin case (mm) block height ( μm) (kg/m3) (kg/kg) 1 2 3
40 50 60
0.25 0.3125 0.375
14.3 14.3 14.3
2700 2700 2700
0.31 0.31 0.31
rig, the burner must be scaled so that it can be installed in the test facility. A scale ratio of 1/2.708 was employed to make a model burner with a nozzle width of 160 mm and a height of 120 mm. A 3 mm-thick partition plate was located at the center of the nozzle to separate the fuel/air mixture into a fuelrich stream and a fuel-lean stream. As illustrated in Figure 1, the simulated burner had the same size as the one in our previous experiments. The inlet sectional area of the burner is 160 120 mm2. The velocity-inlet boundary condition was used for the gas inlet, and the inlet velocity was set to be 14 m/s (ux = 0, uy = 0, uz = 14), with the flow Reynolds number of 1.74 105. The gas outlet boundary condition was set to be outflow. The parameters of the present numerical simulations are shown in Table 1. The effects of the collision block height on the concentrating performance and on the mixing characteristics of the fuelrich/lean jet were investigated. The fuel-rich/lean ratio was adjusted by changing the height of the collision block, and three cases were studied, as listed in Table 2. In this particle dispersion simulation, all coal particles are assumed to be rigid spheres. The coal particles with RosinRammler size distribution (the mean diameter 14.3 μm) and a particle density of 2700 kg/m3 were used as the material conveyed. The solids concentration in the primary air was kept as 0.31 kg/kg in all cases. The schematics of the computational grids for a 3D gassolid two-phase flow in the fuel-rich/lean burner are shown in Figure 3. Hexahedral CFD cells were employed in the computational area. There were altogether about 1.6 million meshes and the side length of the hexahedral mesh was about 2 mm. The minimum mesh volume was 5.49 10-9 m3, and the maximum mesh volume was 9.2 10-9 m3. No noticeable change in the simulation results can be obtained with finer meshes in the trial grid test. The particle tracking was carried out after the air flow entered the quasi-steady state; in other words, at this time the air flow turbulent quantities vary with time but keeping a certain average values. Also this time was considered to be the nondimensional time t = 0. For each case, 396 particles were injected into the air flow field at the nozzle with even distribution every five time steps and their initial velocities were equal to the local gas-phase velocity. When gas-solid flow became quasi-steady, the total number of particles tracked were about 4.4 105, 4.2 105, and 3.9 105 for cases of h = 40, h = 50, and h = 60 mm, respectively.
Figure 4. Gas velocity magnitude in the midplane of the burner.
4. Results and Discussion Figure 4 shows the gas velocity magnitude for three cases at the nondimensional time t = 15.8. At the top zone of the collision block, the gas velocity became greater. With the increase in the collision block height, the area of peak velocity increased. Downstream of the collision block, there was a region with low velocity. As reported in our previous work on the detached eddy simulation of the fuel-rich/lean burner,2 the large scale vortex structures were found downstream of the collision block. Figure 5 presents plots of the gas velocity profiles in a vertical middle line at the exit of the burner. There was a velocity difference between the fuel-rich and fuel-lean streams, and the differences increased with the height of the collision block. A deviation of ∼7 m/s in the gas velocity was achieved with 6297
Energy Fuels 2010, 24, 6294–6300
: DOI:10.1021/ef1013055
Zhou et al.
Figure 5. Gas velocity profiles in vertical middle line at the exit of the burner.
Figure 7. Particle spatial distribution in the midplane of the burner.
became more obvious and the particle-particle interactions may happen more frequently in these zones. Figure 7 presents the particle spatial distribution considering the particle-particle collisions for three cases at t = 15.8. When the collision block height was 40 mm (case 1), the fuel-rich/lean separator cannot separate the air-coal flow efficiently. The fuel-rich/lean mean concentration ratio was 1.16. As illustrated in Figure 7a, the particle concentration in the fuel-rich side was almost equal to that in the fuel-lean side. Figure 7b shows the spatial distribution of the particles in case 2. The fuel-rich/lean mean concentration ratio was 1.42, and a better separating performance can be achieved than in case 1. Figure 7c presents the spatial distribution of the particles with the collision block height of 60 mm. It can be seen that the particle concentration in the fuel-rich side was much larger than that in the fuel-lean side. The fuel-rich/ lean mean concentration ratio was 1.97 in case 3. The fuel-rich/ lean separator had the good ability to separate the coal-air flow into a fuel-rich stream and a fuel-lean stream. The particle characteristics in the burner were in accordance with the results provided by Zhou et al.2 and Fan et al.6 The time history of the particle-particle collision frequencies was obtained to quantitatively investigate the particleparticle collisions and the effect on the particle distribution, as shown in Figure 8. The particle-particle collision frequency indicated the number of particle-particle collisions that happened in one nondimensional time step. As reported by Wang, the accumulation effect and the turbulent transport effect were the influence factors on the particle-particle collisions.30 In this work, the collision frequency of the
Figure 6. Particle concentration profiles in the midplane of the burner.
h = 60 mm (case 3). A larger velocity difference between the fuel-rich and fuel-lean streams was favorable for flame stability. Figure 6 shows the particle concentration profiles in the midplane of the burner. In the regions upstream of the collision-block and adjacent to the partition plate, the solid concentration was higher than that in other places. With the increase of the collision block height, local concentrating
(30) Wang, L. P.; Wexler, A. S.; Zhou, Y. Statistical mechanical description and modeling of turbulent collision of inertial particles. J. Fluid Mech. 2000, 415, 117–153.
6298
Energy Fuels 2010, 24, 6294–6300
: DOI:10.1021/ef1013055
Zhou et al.
Figure 10. Time history of the global dispersion function distribution.
Figure 8. Time history of the particle-particle collision frequency.
Figure 11. Influence of collision block height on the fuel-rich/lean mean concentration ratio.
Figure 9. The average particle-particle collision number.
particles in three cases was studied. The particle-particle collision frequency varied with the development of the gassolid flow. However, when the gas-solid two-phase flow became the quasi-steady state, the particle-particle collision frequency would stay at a certain level. It was clear that the particle-particle collision number increased with the increasing of the collision block height. Figure 9 shows the average particle-particle collision number in a nondimensional time step after the gas-solid two-phase flow became the quasi-steady state. The particle-particle collision frequencies were about 147.98, 155.85, and 166.81 in cases 1, 2, and 3, respectively. With the collision block height increasing, the particles had more opportunities to collide with each other, and the particle-particle collision frequency became greater. The particle-particle interactions occurred more frequently with the collision block height increasing from 40 to 60 mm. To evaluate the influence of the particle-particle collision on the dispersion characteristics of particles, the global dispersion function DX(t) was obtained, and it can be defined as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Nt uX DX ðtÞ ¼ t ðXi ðtÞ - Xm ðtÞÞ2 =Nt ð15Þ
values of DX(t) in case 1 were smaller than those in cases 2 and 3. The DX(t) increased with the increasing of the collision block height. Transverse distribution became more obvious when the collision block height increased. There was a difference between DX(t) values considering the particle-particle collisions and those without the particle-particle collisions. The values of the global dispersion functions with the particleparticle collisions were smaller than those without the particleparticle collisions. This demonstrated that the spanwise dispersion of the particles decreased due to the effect of the particle-particle collisions. To analyze the particle dispersion pattern with various collision block height and the effect of particle-particle collisions, the fuel-rich/lean mean concentration ratio at the exit of the burner was obtained. Figure 11 presents the influence of the collision block height on the fuel-rich/lean mean concentration ratio at the exit of the burner. The particles distributed almost equally in the fuel-rich side and fuel-lean side when the collision block height was 40 mm. It can be seen that the fuel-rich/lean mean concentration ratio was about 1.16, which was nearly equal to the experimental results. The concentration ratio increased to 1.43 and 1.97 with h = 50 mm and h = 60 mm, respectively. The particles distributed mainly in the fuel-rich side of the gas-solid jet. A good fuel-rich/lean separating performance can be obtained with the collision block height of 60 mm. The concentration ratio between the fuel-rich side and the fuel-lean side became larger with the increasing of the collision block height. Figure 11 shows that the values of the concentration ratio with the particle-particle collisions are smaller than those
i¼1
where Nt is the total number of particles at simulation time t, Xi(t) and Xm(t) is the transverse displacement of particle i and the mean transverse displacement of the different particles at simulation time t, respectively. Figure 10 shows the time history of the global dispersion function distribution in three cases. It can be seen that the 6299
Energy Fuels 2010, 24, 6294–6300
: DOI:10.1021/ef1013055
Zhou et al.
without the particle-particle collisions. The particle dispersion between the fuel-rich side and the fuel-lean side became more uniform as a result of the particle-particle interactions. The numerical results with the hard-sphere model are validated by the gas-solid experiments.5 Figure 11 presents the fuel-rich/lean mean concentration ratio at the exit of the burner for experimental results. A better agreement with the experiment was achieved in the fuel-rich/lean mean concentration ratio due to the particle-particle collisions. When studies are carried out on the gas-solid two phase flow in the burner, pneumatic pipe, and other engineering devices with a high mass ratio of the fuel/air mixture, the particle-particle collisions may play a very important part in the numerical simulations.
this study. The particle-particle interactions were simulated and their effect on the fuel-rich/lean separating performance was evaluated. With the collision block height increasing from 40 to 60 mm, the particles have more opportunities to collide with each other and the particle-particle collision numbers increase. The fuel-rich/lean mean concentration ratio between the fuelrich side and the fuel-lean side became greater with the increasing of the collision block height. A good fuel-rich/lean separating performance can be obtained with the collision block height of 60 mm. Studies show that the particle dispersion between the fuel-rich side and the fuel-lean side become more uniform as a result of the particle-particle interactions. The numerical simulation results were validated by the corresponding experiments, and a better agreement between the simulation and experiments was achieved due to the particle-particle collisions.
5. Conclusions The particle dispersion mechanisms of the gas-solid twophase flow in a fuel-rich/lean burner were numerically investigated by coupling the hard-sphere model and CFD. The hard-sphere model was employed for the solid flow to deal with the particle-particle and particle-wall interactions, and the computational fluid dynamic for the gas flow was carried out through the commercial software package Fluent. The influence of the collision block height on the particle distribution in the gas-solid fuel-rich/lean burner was investigated; three cases with various collision block height were studied in
Acknowledgment. This work was supported by National Basic Research Program of China (Grant 2009CB219802), Program for New Century Excellent Talents in University (Grant NCET07-0761), a Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant 200747), Zhejiang Provincial Natural Science Foundation of China (Grant R107532), and Zhejiang University K.P.Chao’s High Technology Development Foundation (Grant 2008RC001), the Fundamental Research Funds for the Central Universities.
6300
