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A hybrid Eulerian−Lagrangian model was developed to simulate gas−droplet−particle multiphase flow and the collision humidification between sorbe...
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Ind. Eng. Chem. Res. 2008, 47, 4861–4869

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SEPARATIONS Numerical Simulation of Multiphase Flow and Collision Humidification in the Multifluid Alkaline Spray Generator for a Novel Semidry Flue Gas Desulfurization System Yuegui Zhou,* Weicheng Cao, Lei Wang, and Mingchuan Zhang Institute of Thermal Energy Engineering, School of Mechanical Engineering, Shanghai Jiao Tong UniVersity, 800 Dong Chuan Road, Minhang, Shanghai, 200240, China

A hybrid Eulerian-Lagrangian model was developed to simulate gas-droplet-particle multiphase flow and the collision humidification between sorbent particles and spray droplets in the confined multifluid alkaline spray generator for a novel semidry flue gas desulfurization system. In this model, the motions of discrete phases were tracked simultaneously by using a stochastic trajectory approach, and a probability model of droplets catching particles was presented to judge whether sorbent particles were caught with direct simulation Monte Carlo method. Numerical humidification efficiency of sorbent particles is validated by the experimental one deduced from the measured desulfurization efficiency. And the effects of flue gas flow rate, spray droplet diameter, sorbent particle diameter, and particle injection location on the humidification efficiency were optimized. Numerical results show that the collision humidification efficiency of sorbent particles increases significantly at the axial distance of 1.67 times the generator diameter from the nozzle tip and reaches 78.5% without recirculation flow in the alkaline spray generator when the ratio of flue gas mass flow rate to spray water mass flow rate is 6.7. Moreover, there is an optimal droplet diameter ranging from 125 to 150 µm and an optimal particle injection location corresponding to the maximum humidification efficiency in this paper. 1. Introduction Compared with wet flue gas desulfurization (FGD), semidry FGD processes have been developed for medium and small boilers due to their advantages of a simple system, low cost, less space requirement, and no wastewater treatment. Typical semidry FGD processes include spray dryer absorption, limestone injection into the furnace and unreacted calcium (LIFAC), and duct sorbent injection.1,2 However, the spray dryer absorption process is restricted to be used widely in the old power plants for some reasons such as space limitations for relatively complicated equipment, needing a large spray dryer absorption tower, and heavy abrasion of atomizing nozzles due to spraying lime slurry. LIFAC and duct sorbent injection have the disadvantages of low desulfurization efficiency and sorbent utilization, mainly because the humidification efficiency of sorbent particles is only 25-30%, and most sorbent particles are not humidified by spray water droplets.3 In this situation, a novel compact semidry FGD process with a multifluid alkaline spray generator was proposed to improve the humidification efficiency of sorbent particles and the desulfurization efficiency.4 The purpose of using a multifluid alkaline spray generator is to separate sorbent particles from fly ash and to maintain higher concentrations of sorbent particles and water droplets in it. Thus, the humidification efficiency can be improved greatly, and then, the formed aqueous alkaline slurry is introduced into desulfurization duct to react with sulfur dioxide in flue gas. Experimental results showed that the collision humidification efficiency of sorbent particles was improved to nearly 75% and higher desulfurization efficiency was obtained.5 Recently, this novel FGD process has been successfully used for flue gas desulfurization system in a 75 t/h incinerator. * To whom correspondence should be addressed. Tel.: +86-2134206769. Fax: +86-21-34206115. E-mail: [email protected].

The most important step for this process is to improve the humidification efficiency of sorbent particles in the multifluid alkaline spray generator. Thus most sorbent particles are caught by spray water droplets to become aqueous lime slurry droplets, which react with sulfur dioxide from a slow gas–solid reaction to an instantaneous ionic reaction. Although the work on dust precipitation in spray scrubber has been conducted for a long time, there is little research on the particle-droplet collision and humidification in this kind of activation reactor. Ahlbeck6 established a one-dimensional humidification activation model in Coolside desulfurization process based on Calvert’s inertial impaction mechanism of the droplet-particle.7 On the other hand, in reference to Crawford’s droplet catching theory,8 Tang and Xu9 simulated the droplet-particle interaction in a 3D flow field with a nonslip model and predicted gas-droplet-solid multiphase flow and the collision between spray water droplets and solid particles. However, there was a large deviation between the experimental and predicted results because the interphase slip velocity was neglected in that model. The essential process of sorbent particles caught by spray droplets is the droplet-particle collision. The direct simulation technology of particle–particle collision has been developed rapidly in these years with the improvement of computer performance. A direct simulation Monte Carlo (DSMC) method was developed by Bird10,11 and was first used to simulate the rarefied gas flow. With the analogy on the motion of dispersed particles in gas–solid flow and the motion of molecules in dilute gas flow, the DSMC method has been used to simulate the particle–particle collision and droplet-droplet collision in multiphase flow12,13 and the particle–particle collision and cluster formation in a circulating fluidized bed.14–16 Recently, we have developed a new 3D computational fluid dynamics mathematical model to study gas-droplet-particle

10.1021/ie071494c CCC: $40.75  2008 American Chemical Society Published on Web 06/18/2008

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multiphase flow and particle-droplet collision in the semidry FGD process. The probability submodel of droplets catching particles was established based on direct simulation Monte Carlo method to successfully simulate the humidification process of sorbent particles in the semidry FGD experimental setup.17 The objective of the present paper is to simulate and optimize gas-droplet-particle multiphase flow and particle-droplet collision humidification in the multifluid alkaline spray generator for a 75 t/h incinerator flue gas desulfurization system and to investigate the effects of flue gas flow rate, spray droplet diameter, sorbent particle diameter, and particle injection location on the collision humidification efficiency. 2. Mathematical Model Three-dimensional computational fluid dynamics mathematical model in the novel FGD process mainly includes a gas turbulent flow model, particle/droplet stochastic trajectory model, probability model of droplets catching particles, and droplet evaporation model. These submodels are described as follows. 2.1. Gas Turbulent Flow Model. The gas phase flow is described by elliptic, partial differential conservation equations for a Newtonian fluid in Cartesian coordinates. The gas phase conservation equations are time-averaged and solved by using a finite-difference formulation for the Navier–Stokes equations. The value of the eddy viscosity and subsequent closure of the equations can be achieved by using standard two-equation k-ε model. Each of these equations has the same general form and can be cast into the standard form as18 ∂ ∂φ ∂ (FV φ) ) (Γφ ) + Sφ + Spφ ∂xj j ∂xj ∂xj

(1)

where φ is the general dependent variable (mass, momentum, energy, species, etc.), Vj is the gas velocity, F is the fluid density, Γφ is the effective diffusivity, Sφ and Spφ represent the source terms of the gas phase and the interaction between the gas phase and the discrete phases, respectively. 2.2. Particle/Droplet Stochastic Trajectory Model. The Lagrangian approach is used to determine particle and droplet flow field by tracking the trajectories of particles and droplets throughout the computational domain. A particle or droplet moving in a gas flow field mainly experiences the forces on it because of gravity, gas-particle/droplet drag. Thus, the equation of the motion of a particle or droplet i (or the ith particle) is expressed as

|

f

mpi

|

dV pi 1 f f f f f f f ) CDπdpi2Fg V g + V ′g - V pi ( V g + V ′g - V pi) + mpi g dt 8 (2)

where mpi is the ith particle or droplet mass, dpi is the ith particle or droplet diameter, b V g is the gas time-averaged velocity, b Vg′ is the gas fluctuating velocity, and CD is the effective drag coefficient between gas phase and discrete phases expressed as

{

24 , Rep < 1 Rep CD ) 24 (1 + 0.15Re 0.687), 1 e Re < 1000 p p Rep g 1000 Re 0.44, p

Rep )

|

|

Fgdp V g - V p . µg f

The effective drag coefficient of droplets CD is adopted as19 CD ) 0.28 +

(

(3) Sti,j )

(4)

21 6 + Red √Red

(5)

2.3. Probability Model of Droplets Catching Particles. 2.3.1. Model Assumption. (1) Droplets and particles are considered as spherical shape. The breakup and agglomeration between droplets and the collision between particles are neglected. (2) Particles are distributed homogeneously in cells at any time, and a droplet catches all the particles in its effective sweeping volume. (3) The droplets of the same trajectory have the same effective sweeping volume, inertial catching efficiency, and momentum change. 2.3.2. Inertial Catching Efficiency of a Droplet. The catching mechanisms include inertial impaction, interception, and Brownian diffusion when the particles flow around a droplet. Inertial impaction is the most important catching mechanism in the FGD process because the diameters of most sorbent particles are more than 1 µm, so only inertial impaction is taken into account in this model. The inertial catching efficiency of a droplet is defined as the ratio of the number of particles striking the droplet to the number that would strike it if the streamlines were not diverted by the droplet. Shi et al.20 show that the experimental inertial catching efficiency is lower than the theoretical one, and a correction factor k (k ) 0.80) is used to amend the droplet inertial catching efficiency. Equations 6 and 7 express the modified inertial catching efficiency of the jth class droplet catching the ith class particle. Only when Stokes number is more than the critical value Stcr can the particles be caught by a droplet through inertial collision. The value of critical Stokes number Stcr is 0.10 for spherical droplets.21 φi,j ) k

where Rep is the particle Reynolds number, expressed as f

Figure 1. Sketch of a droplet catching particles.

Sti,j Sti,j + 0.7

|

) |

2

FPdi2 Vj - Vi . 9µgDj f

f

(6)

(7)

2.3.3. Single Droplet Catching Probability. As shown in Figure 1, eq 8 shows the sweeping volume of a droplet to particles during each time step ∆t at the time n∆t, where n is the number of equivalent time steps. The effective sweeping

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volume of a droplet should be amended by eq 6 because of the diverted streamlines by the droplet.

|

|

Vn,j,i ) π ⁄ 4 × (Dj + di)2 f V i × ∆t Vj - f

(8)

According to the previous assumption, the single droplet catching probability per unit volume and per time step pn,j,i can be determined as the ratio of the effective sweeping volume of the droplet to the cell volume, expressed by eq 9

|

|

π f f φj,i (Dj + di)2 V j - V i ∆t 4 pn,j,i ) Vcell

(9)

In the model, a droplet trajectory represents Nj real droplets, which have the same effective sweeping volume and catching probability. So, the single trajectory catching probability per unit volume and per time step Xn,j,i is shown in eq 10 Xn,j,i ) 1.0 - (1.0 - pn,i,j)Nj

(10)

2.3.4. Probability of Droplets Catching Particles. When a sorbent particle passes through a cell, the probability to be caught in the cell during the course of ∆t is defined as the probability of droplets catching particles ηn,i. At the time n∆t, the probability of droplets catching particles in each cell is calculated by eq 11 when all the droplet trajectories are calculated during the course of ∆t. M

ηn,i ) 1.0 -

∏ (1 - X

k

n,j,i

)

(11)

k)1

where M is the total droplet trajectories that pass through the same cell during the course of ∆t at the time n∆t. 2.4. Droplet Evaporation Model. Because of very low solubility of calcium hydroxide and semihydrated calcium sulfite in water, the drying of slurry droplets is similar to that of water droplets. So the drying behavior of aqueous suspension droplets can be described as that of water droplets.22 Generally, the temperature and concentration profile along the droplet surface is assumed spherically symmetric and convection effects are taken into account by correlation laws. The transfer process is considered as quasisteady, and the pressure profile around the droplet and the thermophysical properties in the surrounding fluid are considered uniform. The “law of 1/3” is usually recommended for the calculation of reference temperature and vapor mass fraction, which gives Tf ) Ts + 1/3(Tg - Ts).23 The thermal equilibrium is assumed on the phase boundary of the droplet surface. Thus, the convective heat and mass transfer rates for a single spherical droplet are formulated by eqs 12 and 13. ˙ d ) πDdλg(Tf)(Tg - Ts)Nu0 Q m ˙ ) πDd

ln(1 + BT) BT

λg(Tf) Nu0 ln(1 + BM) Cp,g

(12)

(13)

where λg(Tf) is the thermal conductivity of the gas mixture in the film. Nu0 is calculated from the Ranz-Marshall correlation Nu0 ) 2.0 + 0.6Prd1/3Red1/2

(14)

The values BT and BM are Spalding heat and mass transfer numbers, respectively, expressed in eqs 15 and 16. BT )

Cp,g(Tg - Ts) Lat + Cp,l(Ts - Td)

(15)

BM )

YFs - YFg 1 - YFs

(16)

where YF is the water vapor mass fraction; Lat is the latent heat of vaporization at the temperature Ts; subscripts g, s, and d refer to the conditions at external gas flow, the droplet surface, and the initial droplet, respectively; Cp,g is the average gas specific heat in the film; and Cp,l is the liquid specific heat. According to the classical vaporization theory, the heat transfer number BT is taken to be equal to BM. 2.5. Numerical Method and Physical Problem Description. 2.5.1. Numerical Method. The gas phase and discrete phase equations are solved in Cartesian coordinates. Gas turbulent flow model is standard k-ε model. Pressure-velocity coupling is realized by SIMPLEC algorithm. The discrete phases begin to be calculated after the gas equations are convergent, and the source terms of the discrete phases to the gas phase are also calculated. The interphase coupling is realized by using PSIC (particle source in cell) algorithm. The simulation process of droplets catching particles is described as follows. (1) At the time (n + 1)∆t, all the droplets trajectories are computed during the time step ∆t. Therefore, the probability of droplets catching particles ηn+1,i can be counted in each cell. The evaporation of droplets is calculated at the end of time step ∆t. Droplets tracking will be ended when the droplets flow out of the computational domain. (2) Subsequently, all the particles trajectories are computed at the time (n + 1)∆t. When the particle trajectory is calculated during the time step ∆t, a random number R is taken from a random number generator and compared with the probability of droplets catching particles ηn+1,i. If R is less than or equal to ηn+1,i, the particle is caught by droplets in the cell, and the calculation of particle trajectories is ended. The particles tracking will also be ended when the particles flow out of the computational domain. 2.5.2. Physical Problem Description. The FGD process with a multifluid alkaline spray generator was used for flue gas desulfurization system of a 75 t/h incinerator, shown in Figure 2a. A small amount of hot flue gas entrained sorbent particles into the multifluid alkaline spray generator, and sorbent particles are collided and humidified to form lime slurry droplets by spray water droplets at higher particle and droplet concentrations. Then, the formed alkaline spray droplets were induced into the existing or retrofitted flue gas duct to react with SO2 in flue gas and the slurry droplet evaporation for 2–4 s residence time. The reaction product is controlled to be dry before the particulate collection system. It is important to improve the collision humidification efficiency between sorbent particles and spray water droplets and to make most sorbent particles humidified. The multifluid alkaline spray generator was a vertical cylinder with an internal diameter of 0.9 m and a height of 2.5 m, shown in Figure 2b. The entrance cross section was divided into an internal annulus with a diameter of less than 0.48 m, and an external annulus from 0.48 to 0.90 m. A Y-jet twin-fluid nozzle was located at the center of the generator to spray water to fine droplets with a distance of 0.20 m from the nozzle tip. The total flue gas flow rate in the alkaline spray generator was 2.06 m3/s (STP) and the flue gas temperature was 473 K. The flue gas flow rate in the internal annulus was 0.57 m3/s, which entrained sorbent particles into the generator at base condition. The spray water mass flow rate was 0.28 kg/s with mean droplet diameter of 100 µm, and the initial velocity of spray jet was 50 m/s with spray cone angle of 20°. The sorbent particles were evenly injected from the internal annulus with the mass flow rate of 0.069 kg/s and mean particle diameter of 75 µm. The wall of the cylindrical generator was approximately

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Figure 2. Sketch of the novel FGD process with a multifluid alkaline spray generator: (a) schematic of FGD process; (b) schematic of alkaline spray generator.

Figure 3. Phase velocity fields at base condition: (a) gas phase velocity; (b) spray droplet velocity; (c) sorbent particle velocity.

treated as stepwise grids and the grid nodes is 28 × 52 × 28 in the computational domain. 3. Results and Discussion 3.1. Gas-Droplet-Particle Multiphase Flow Characteristic and Particle Collision Humidification Efficiency. Figure 3 shows the flow velocity fields of the gas phase, spray droplets, and sorbent particles in the confined alkaline spray generator, respectively. It can be seen that the flue gas flow in the generator is induced and accelerated by high speed spray jet, which causes higher gas velocity in the central area of spray jet and lower gas velocity at the surrounding region of it. And, the gas velocity becomes more and more uniform with the increasing axial distance. The spray jet first expands with the axial distance and then contracts inside with the interaction of the surrounding flue gas flow, and the spray jet diameter is 0.56 m at the outlet of

Figure 4. Axial gas velocity profiles at different cross sections.

the generator. When sorbent particles issues from the internal annulus of the entrance cross-section, most of them are entrained into the spray jet core region and humidified by spray water droplets to form aqueous slurry droplets. Figure 4 traces the axial evolution of the radial profiles of flue gas velocity. The gas velocity is higher in the center of the generator and lower toward the wall. Far from the inlet, it approaches the velocity profile in a fully developed pipe flow. Since there is no negative velocity at each cross-section, it can be concluded that no recirculating zone appears in the generator at base condition because of enough high surrounding flue gas flow rate for the entrainment of spray jet. Figure 5 shows the dimensionless velocity profile in the spray jet region plotted against the normalized radial coordinate. Here, the gas velocity is normalized with respect to the peak centerline velocity and the radial coordinate with respect to the distance from the centerline where the gas velocity is half of the peak centerline gas velocity. The result shows that the dimensionless gas

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Figure 5. Dimensionless gas velocity profiles across the jet.

Figure 8. Gas temperature contour.

Figure 6. Droplet axial velocity distribution at different axial distances.

Figure 9. Particle number density distribution.

Figure 7. Particles axial velocity distribution at different axial distances.

velocity profile in the spray region is self-similarity, which is the same as single-phase jet. It agrees with the calculated results of evaporating spray jets in concurrent gas–solid pipe flows.24 Figures 6 and 7 show the radial profile of the axial velocity of spray droplets and sorbent particles at different axial distances, respectively. The axial velocity distribution of droplets and particles is axisymmetric in the radial direction and the maximal magnitude is located at the centerline of the cylindrical generator. The axial velocity of droplets first decays sharply because of the entrainment of spray jet and then becomes

relatively uniform at the outlet of the cylindrical generator. The axial velocity of sorbent particles increases significantly at the initial axial distance due to the induction and acceleration of the spray jet and, then, gradually decays and becomes uniform at the outlet. Comparing Figures 6 and 7, it is found that the slip velocity between droplets and particles is large at the axial distance of 1.67 times the generator diameter from the nozzle tip which contributes to improve the collision frequency between spray droplets and sorbent particles. Figure 8 shows the gas temperature distribution in the alkaline spray generator. The gas temperature at the spray jet core region is relatively low due to the evaporation of the spray jet. However, the gas temperature surrounding the spray jet is high, which can accelerate the evaporation of droplets near the wall and prevent the droplets from the possible deposition on the wall. Figure 9 shows the number density distribution of sorbent particles in the alkaline spray generator. The number density of sorbent particles is high adjacent to the nozzle inlet when they are injected from the internal annulus of the entrance cross section. Then it decreases gradually with the increasing axial distance because a great number

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Figure 10. Cumulative particle humidification efficiency with the height of the generator.

of sorbent particles are entrained into the spray jet core region and caught by spray droplets to form the aqueous slurry droplets. And, only a few sorbent particles turbulently disperse outside in the region surrounding the spray jet. Figure 10 indicates the variation of cumulative catching efficiency of sorbent particles with the increasing height of the alkaline spray generator. It can be seen that the collision humidification efficiency between sorbent particles and spray droplets first increases significantly with the increasing height and reaches 90% of the total efficiency at the axial distance of 1.67 times the generator diameter from the nozzle tip. Then, it increases slowly with further increasing height. It can be concluded that sorbent particles are caught and humidified by spray droplets mainly at the axial distance of 1.67 times the generator diameter because of large slip velocity between spray droplets and sorbent particles with comparison of the axial velocity distributions in Figures 6 and 7. The results show that the numerical collision humidification efficiency of sorbent particles is 67.4% by using a multifluid alkaline spray generator. The experimental humidification efficiency of sorbent particles ranged from 66.7% to 75.0%, which was deduced from the measured SO2 removal efficiency by comparison with removal efficiency of spray dryer absorption at the same conditions in our previous experiments.5 Therefore, the numerical humidification efficiency of sorbent particles agrees well with the experimental one, which validates the probability model of droplets catching particles. 3.2. Effect of Main Parameters on Humidification Efficiency in the Multifluid Alkaline Spray Generator. 3.2.1. Effect of the Flue Gas Flow Rates. The flue gas flow rate in the multifluid alkaline spray generator significantly affects the performance of flue gas desulfurization system. The recirculation flow in the confined generator and the deposition of droplets on the wall will happen if the surrounding flue gas flow rate is too low to afford the entrainment of high speed spray jet. On the other hand, high flue gas flow rate in the generator will significantly decrease the concentrations of particles and droplets and lower the collision humidification efficiency and desulfurization efficiency. Therefore, it is necessary to investigate the effect of flue gas flow rate on gas-droplet-solid multiphase flow and the collision humidification efficiency in the multifluid alkaline spray generator. Figure 11 shows the gas velocity fields in the generator at different flue gas flow rates respectively. There is no recirculation flow in the alkaline spray generator when the flue gas flow rate decreases from 2.06 to 1.44 m3/s because the flue gas flow

rate is high enough to afford the entrainment of spray jet. However, a small recirculation zone in the generator appears when the flue gas flow rate decreases to 1.24 m3/s and expands with lower flue gas flow rate. The recirculation zone in the generator should be avoided because it would result in the backmixing and deposition of aqueous particles or droplets on the wall. Therefore, the flue gas flow rate in the generator should be controlled above 1.44 m3/s, i.e. the ratio of the flue gas mass flow rate to spray water mass flow rate is above 6.7. Figure 12 indicates the effect of flue gas flow rate on cumulative catching efficiency of sorbent particles. The cumulative catching efficiency of particles increases greatly when the flue gas flow rate decreases because the concentrations of sorbent particles and spray droplets and the slip velocity between droplets and particles obviously increase. Thus, the collision frequency between sorbent particles and spray droplets is improved, and most sorbent particles are humidified by spray water droplets. It is also found that the collision humidification efficiency of sorbent particles reaches 78.5% when the flue gas flow rate is 1.44 m3/s, which is significantly higher than that of 25% in duct sorbent injection.3 It shows that the collision humidification efficiency and desulfurization efficiency of the FGD process with the multifluid alkaline spray generator can improve dramatically. Compared with spray dryer FGD process, the novel compact FGD process discards the complicated lime slurring system and avoids the abrasion and blockage of atomizers by spraying water instead of lime slurry. 3.2.2. Effect of Droplet Diameters. Droplet velocity fields of different diameters are shown Figure 13. Droplets of different diameters with the same initial spray cone angle have different spatial distributions, and the spray jet diameter increases with the increasing of droplet diameter because large droplets can easily maintain their initial jet direction due to large particle inertia and relaxation time. It agrees with the experimental results of droplet spatial distribution.25 Figure 14 shows the effect of mean droplet diameters on particle humidification efficiency at the same spray water mass flow rate and sorbent particle diameters of 45 and 75 µm, respectively. It is found that the particle humidification efficiency gradually increases to the maximal magnitude and then decreases with the increasing of droplet diameter, and the particle humidification efficiency increases with the increasing of sorbent particle diameter. At the same spray water mass flow rate, the small droplet diameter enlarges the total droplet surface area and the volume of droplet sweeping particles, which improves the collision frequency between droplets and particles. On the other hand, the droplet velocity of small diameter can decay sharply due to small inertia, which decreases the slip velocity and the collision frequency between spray droplets and sorbent particles. Therefore, it is concluded that an optimal droplet diameter ranges from 125 to 150 µm corresponding to higher collision humidification efficiency in this paper. And, the numerical results show that the optimal droplet diameter ranges from 80 to 100 µm for the semi-industrial experimental setup of the same FGD process.17 Both results show that the optimal droplet diameter is relative to the structure size and spray water parameter of the multifluid alkaline spray generator, and the similarity ratio of the optimal droplet diameter in two scale-up generators is Cdp ) )

(

CFs1-nCl(2-n)⁄2Cµn CFP

0.9 ) [( 0.38

) 1.44

)

1⁄(1+n)

(2-0.625)⁄2 1⁄(1+0.625)

]

Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4867

Figure 11. Gas velocity fields at different gas flow rates: (a) 1.65; (b) 1.44; (c) 1.24; (d) 1.03 m3/s.

Figure 12. Cumulative particle humidification efficiency with the height at different gas flow rates.

Figure 14. Effect of droplet diameters on particle humidification efficiency.

Most sorbent particles are induced by spray jet to concentrate toward the jet core region and efficiently caught by spray droplets when injected from the internal annulus. Therefore, the particle number density decreases at the outlet of the alkaline spray generator. When injected from the whole entrance cross section, sorbent particles adjacent to the spray jet are caught by droplets, which reduces the particle number density, and less particles injected from the external annulus are caught by droplets, which results in high particle number density. However, only a small number of sorbent particles are entrained into the spray jet core and caught by droplets when injected from the external annulus, and there is high particle number density at the outlet of the generator.

Figure 13. Droplet velocity fields with different droplet diameters: (a) 50; (b) 100; (c) 200 µm.

3.2.3. Effect of Particle Injection Locations. Figure 15 shows the particle number density distribution in the central longitudinal section of the alkaline spray generator when sorbent particles are injected from three different locations.

The effect of sorbent particle injection locations on particle humidification efficiency is shown in Figure 16. The sorbent particle collision humidification efficiency is significantly higher when injected from the internal annulus than when injected from the whole cross section or the external annulus. It can be well explained by different particle number density distributions in Figure 15. Therefore, the particle injection location also affects significantly the collision humidification efficiency between sorbent particles and spray droplets, and

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Figure 15. Distribution of particle number density at different particle injected locations: (a) particles injected from inner annulus; (b) particles evenly injected from inlet cross-section; (c) particles injected from external annulus.

(3) Decreasing the flue gas flow rate in the multifluid alkaline spray generator can improve the collision humidification efficiency between sorbent particles and spray droplets but may result in the recirculation flow. The collision humidification efficiency can reach 78.5%, which is significantly higher than that of 25% in simple duct sorbent injection, and there is no recirculation zone in the generator when the ratio of the flue gas mass flow rate to spray water mass flow rate is above 6.7. (4) There is an optimal particle injection location for higher collision humidification efficiency when sorbent particles are injected from the internal annulus of the entrance cross section near the spray jet. Acknowledgment Figure 16. Effect of particle injected locations on particle humidification efficiency.

The authors are grateful for the support provided by the National Natural Science Foundation of the People’s Republic of China (50606023).

the optimal one is the internal annulus of the entrance cross section near the spray jet.

Nomenclature

4. Conclusion A 3D computational fluid dynamics mathematical model is developed to simulate gas-droplet-particle multiphase flow and the collision humidification between sorbent particles and spray droplets in the multifluid alkaline spray generator for a semidry flue gas desulfurization system, and the numerical collision humidification efficiency is validated by the experimental results. And, the effects of main structure and operation parameters including flue gas flow rate, spray droplet diameter, sorbent particle diameter, and particle injection location on the humidification efficiency are optimized. (1) The dimensionless gas velocity profile in the spray region is self-similarity, which is the same as single-phase jet. (2) The collision humidification efficiency between sorbent particles and spray droplets increases significantly with the height of the generator and reaches 90% of the total efficiency at the axial distance of 1.67 times the generator diameter from the nozzle tip. And, an optimal droplet diameter ranges from 125 to 150 µm corresponding to higher humidification efficiency at the given structure and operation parameters in this paper.

B ) mass and heat transfer number C ) similarity ratio CD ) drag coefficient Cp ) specific heat, J/(kg K) d ) particle diameter, m D ) droplet diameter or cylinder diameter, m g ) gravity acceleration, m/s2 Lat ) latent heat, J/kg k ) correction factor of inertial catching efficiency M ) total droplet trajectory number in a cell at time n∆t m ) mass, kg N ) particle number of a trajectory Nu ) Nusselt number Pr ) Prandtl number p ) droplet catching probability per unit volume per time step R ) random number Re ) Reynolds number St ) Stokes number T ) temperature, K X ) single trajectory catching probability per unit volume per time step

Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4869 x ) x coordinate Y ) mass fraction V ) effective sweeping volume of the droplet in a time step or cell volume, m3 V ) velocity, m/s Greek Letters Γ ) effective diffusivity, kg m-1 s-1 φ ) dependent variable η ) probability of droplets catching particles by droplets per unit volume per time step φ ) inertial catching efficiency of a droplet µ ) gas viscosity, kg/(m s) F ) density, kg/m3 ∆t ) time step, s Subscripts d ) droplet F ) mass fraction g ) gas phase i ) ith group particle, i ) 1–5 j ) coordinate, j ) 1–3 or jth group particle, j ) 1–5 n ) number at time n∆t, n ) 0, 1, 2. p ) particle or droplet s ) droplet surface

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ReceiVed for reView November 3, 2007 ReVised manuscript receiVed March 9, 2008 Accepted March 10, 2008 IE071494C