- Email: [email protected]
Simulation of ash deposit in a pulverized coal-fired boiler
Fuel 80 (2001) 645±654
www.elsevier.com/locate/fuel
Simulation of ash deposit in a pulverized coal-®red boiler J.R. Fan*, X.D. Zha, P. Sun, K.F. Cen Department of Energy Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China Received 6 May 2000; accepted 23 August 2000
Abstract A model has been developed to simulate deposit growth under slagging conditions. The model was coupled with a comprehensive combustion code to predict the ¯ow ®eld, the temperature ®eld and the deposit growth behavior. The predictions indicate that the numerical model can be used to optimize the design and operation of pulverized coal-®red boilers. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Pulverized coal-®red; Slagging; Flow ®eld; Temperature ®eld; Deposit growth
1. Introduction
2. Mathematical models
The accumulation of furnace deposits is one of the many dif®culties faced by utility operators all over the world. Slagging not only reduces the thermal ef®ciency of a furnace, but also affects its integrity due to corrosion, erosion or impact on the bottom tubes. Slagging when severe can lead to substantial ®nancial losses to an operator. Although soot blowing and wall blowing are routinely used to manage deposition, unexpected or uncontrolled deposition can still occur at locations inaccessible to the cleaning devices, or at locations where the bonding strength between the wall and the deposit is too strong for cleaning equipment to be effective. Deposition problems are frequenting associated with a change in fuel characteristics and/or boiler operating conditions. Predictive indices and deposition models help designers and operators to diagnose and correct operational problems due to the deposition. These models also provide insight into the deposition behavior of a particular coal or coals. In recent years, considerable advances have been made in developing models to predict ash deposition behavior. Improved methods have been developed which utilize a more accurate description of the coal, as well as a mathematical description of the ¯y ash transport and sticking in order to approximate the deposition rate [1]. This paper describes our efforts to simulate the ash deposition behavior in a pulverized coal-®red boiler.
2.1. The ¯ow ®eld and heat transfer models In this work, a Lagrangian/Eulerian approach has been employed for gas±solid two-phase ¯ow simulation. The gas phase is described by Navier±Stokes equations, coupled with appropriate equations for density and viscosity. For closure of the turbulence equations, we use both a k± 1 model and a RNG k± 1 model, then make a comparison between them. The general Eulerian equation for the gas phase takes the form div rvf 2 div G grad f S f
where Sf is the source terms of the gas phase, G f the effective viscosity that is summarized in Table 1 for the different variable f . Where f represents the variables u, v, w, k and 1 , (coordinate velocities, turbulent ¯uctuation energy and turbulent energy dissipation) [2±4] A modi®ed SIMPLER method [5] has been employed to determine velocities and pressures using a non-staggered grid system in Cartesian coordinates as demonstrated in the following part. The heat transfer equation is ruc p TDyDz 1 rvcp TDxDz 1 rwcp TDxDy lx TDyDz 1 ly TDyDz 1 lz TDyDz 1 Qradiation 2 4K1 sT 4 DV 1 Qreaction DV
* Corresponding author. Tel.: 186-571-795-1764; fax: 186-571-7991863. E-mail address: [email protected] (J.R. Fan).
1
2
Where, r is the density, l the conducting coef®cient, s the Stenfan±Boltsman constant, T the temperature, cp the speci®c heat, u, v, and w the velocity, Qradiation is the radiation
0016-2361/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0016-236 1(00)00134-4
646
J.R. Fan et al. / Fuel 80 (2001) 645±654
Nomenclature Coal-particle area Ap Drag coef®cient CD Cg Gas molar concentration Speci®c heat Cp Cm,C1,C2 Empirically determined constants Binary diffusivity Dw Particle diameter dp E Activation energy g Gravitational vector h Enthalpy K Reaction-rate coef®cient Mass-transfer coef®cient Kc k Mean turbulent kinetic energy M Molecular weight Particle mass mp Nu Nusselt number Particle number density np p Sticking probability Q Particle-to-gas heat-transfer rate R Gas constant r Particle reaction rate The volatile production rate rv Gas source term for variable f Sf t Time T Temperature u Velocity along x-direction v Velocity along y-direction v Velocity vector w Velocity along z-direction X Mole fraction x,y,z Cartesian coordinate Y Pyrolysis coef®cient Greek letters f Deposit porosity F General variables 1 Emissivity, or dissipation rate of turbulence m Viscosity r Density s k, s 1 Turbulent Prandtl and Schmidt numbers Subscripts c Convection, or coal daf Daf coal eff Effective g Gas h Char l Char oxidation reaction m Mean p Particle r Radiation v Volatiles w Moisture
energy transfer, which is modeled by using Monte Carlo method [6], Qreaction is the heat energy released during coal combustion, which is modeled as a source term after completing particle tracing. 2.2. Combustion models The equation of motion for a particle is m p dvp =dt mp g 1
1 rC v 2 vp uvg 2 vp uAp 1 Freaction 2 D g 3
where Freaction vp 2dmp =dt is the force exerted on the coal-particle due to sudden momentum change when devolatilization occurs, the direction of the reaction force is modeled stochastically, compared to drag force this force is smaller in quantity but important for particle trajectory. When the particle has advanced in the furnace, reaction processes like vaporization, devolatilization and char combustion should be taken into consideration. Diffusion-limited vaporization of moisture from the coalparticle is described by rw Mw Num Cg Dwm Ap Xwp 2 Xwg =dp 1 2 Xwp rp =rw
4
Use the equations 0
dV=dt Vdaf 2 VK exp E=RT 0
Vdaf QVdaf
5 6
to describe the formation of volatile matter from coal dust. Char is produced in competition with volatile production as expressed by rhm rv 1 2 Ym =Ym
7
Char assumes to be oxidized heterogeneously by a gaseous oxidizer that diffuses to the particle, is absorbed, reacts with carbon, and is then described as CO. The char-oxidizing rate is rhl
Ap np 2 Mhp mg f1 Kcp1 Kp1 j p Cog Cg Mg Ap np Cg j p Kp1 1 Kcp1 1 rp
8
The total reaction rate for the coal-particle is rp rv 1 rhl 1 rw
9
The carbon reaction rate is rh rhm 2 rhl
10
The mass change of a particle follows: dmp =dt mw 1 mv 1 mh
11
Where mw, mv and mh are the rate of mass change when the coal-particle is evaporated, devolatilized and char-oxidized respectively. The conservation of particle energy is mp dhp =dt Qc 1 Qr 1 Qw 1 Qv 1 Qh
12
J.R. Fan et al. / Fuel 80 (2001) 645±654
647
Table 1 Eulerian conservation equations and identi®cation of terms in Eq. (1) Conservative equation
f
G
Sf
Mass (continuity) x-Direction momentum
1 u
0 meff
0
y-Direction momentum
v
m eff
2
z-Direction momentum
w
m eff
2
2p 2 2u 2 2v 2 2w 1 1 1 m eff meff meff 2x 2x 2x 2y 2x 2z 2x
2p 2 2u 1 meff 1 2y 2x 2y 2p 2 2u 1 2 meff 1 2z 2x 2z
2 2v meff 1 2y 2y 2 2v meff 1 2y 2z
2 2w meff 2z 2y 2 2w meff 2z 2z
Turbulent kinetic energy k meff =s k Gk 2 r1 Dissipation rate of 1 meff =s 1 1=k C1 Gk 2 C2 1 turbulent kinetic energy ( " # ) 2u 2 2v 2 2w 2 2u 2v 2 2v 2w 2 2w 2u 2 1 Gk meff 2 1 1 1 ; meff mt 1 m; 1 1 1 1 2x 2y 2z 2y 2x 2z 2y 2x 2z
mt Cm rk2 =1; Cm 0:09; C1 1:44; C2 1:92; s k 1:0; s 1 1:3
molten coal-particles entrained by gas collides on the wall and wall-cooling surfaces. Then they are cooled and frozen to slag. The slags mainly appear on the radiant heating surfaces. In order to predict the deposition mechanism with mathematical models, the following issues must be addressed: (1) ash formation, (2) ¯uid dynamics and particle transport, (3) particle impaction and sticking, (4) deposit growth as a function of location in the combustion chamber, (5) deposit properties and strength development, (6) heat transfer through the deposit, (7) the effect of deposition on operating conditions (e.g. temperatures and heat ¯uxes) in the combustor, and (8) deposit structure and its effect on ¯ow patterns in the combustion facility [8,9].
where Qc, Qr, Qw, Qv and Qh are referring to heat related to gas-particle convection, radiation and heat release during evaporation, devolatilization and char-oxidation along the trajectory of the particle. The EBU-Arrhenius model models gas phase turbulent combustion process Wfu min Wfu;A ; Wfu;T Wfu;A ArYfu YO2 exp 2E=RT Wfu;T
13
1 r min Yfu ; YO2 CE R
Equations with the form of dx=dt f x; t are integrated using a ®ve-stage Runge±Kutta method as described in Refs. [2,7].
2.3.1. Particle impaction rates Although a limited number of particle trajectories were adequate for the combustion simulations, more information was required to approximate impaction rates at the wall.
2.3. Slagging models In the coal combustion process, the molten or fractional Table 2 Coal properties Proximate analysis (%)
Ultimate analysis (%)
MS
Ash
VM
FC
C
H
O
N
S
6.00
21.82
16.72
55.46
64.89
2.83
2.4
0.98
1.08
Heating value (MJ/kg) 28.27
Table 3 The percentages of various size classes of pulverized coal Particle diameter (mm) Percentage (%) Particle diameter (mm) Percentage (%)
5 20.22 160 1.42
20 28.04 180 0.94
40 17.95 200 0.62
60 11.61 220 0.41
80 7.58 240 0.27
100 4.96 260 0.18
120 3.27 280 0.12
140 2.16 300 0.25
648
J.R. Fan et al. / Fuel 80 (2001) 645±654
Fig. 2. The predicted pro®le of temperature ®eld: (a) vertical central cross section; and (b) secondary burner plane (height 15.722 m). Fig. 1. The predicted pro®le of ¯ow ®eld.
Consequently, a stochastic separated ¯ow (SSF) model [10] was added as a postprocessor to calculate particle impaction rates. In this model, the in¯uence of turbulent velocity ¯uctuations in the gas phase on the particle trajectories is accounted for through random particle-eddy interactions.
Velocity ¯uctuations are assumed to be isotropic and are obtained by sampling a Gaussian PDF with a standard deviation of 2k=30:5 : The particle motion within an eddy is modeled deterministically by solving the instantaneous particle momentum equation. Velocity ¯uctuations are assumed to remain constant during a particle-eddy interaction [11,12].
J.R. Fan et al. / Fuel 80 (2001) 645±654
649
Ts the temperature of the deposit surface. Factors which are expected to in¯uedce sticking probability include particle viscosity, surface tension, velocity, and angle of impact, as well as the chemical and physical state of the surface upon which deposition is occurring. The sticking probability of a particle of composition i was therefore de®ned as m m . mref pi Tps ref m 15 pi Tps 1 m # mref where, we assume mref 1 £ 105 Pa´s: 2.3.3. Deposit properties In order to model deposit growth and heat transfer, it was necessary to describe the thermal and physical properties of the deposit. The properties include the deposit thickness, porosity, ¯uidity, thermal conductivity and so on. Among these properties, the porosity is the major factor which in¯uence the total properties of the deposit. The porosity of deposit can be described as: Vl f 1 2 1 2 f0 1 1 2 f0 16 Vs where f is the deposit porosity, f 0 the initial porosity of the deposit, Vl the volume of the liquid, and Vs the volume of the solid [9]. Note that, the deposit will be solid when the viscosity is bigger than critical viscosity mcr 105 Pa´s: And zero porosity is reached before the deposit is completely liquid. The thickness of deposit can be described as: li mi =rp 1 2 fi
17
where li is the thickness, mi the mass per area, r p the solid particle density, f i the deposit porosity, and i refers to the current time step. The thermal conductivity, which is also an important property of deposit, can be described as: k 1 2 Fks 1 Fkg Fig. 3. The particle trajectories of four different diameters.
2.3.2. Particle sticking A model was also needed to predict which of the impacting particles would stick based on particle temperature and composition. The capture ef®ciency hcap or fraction of the impacting particles, which adhere to the surface was approximated by the following expression: [13]
h
N X i1
18
where kg is the thermal conductivity of the gas phase, ks the thermal conductivity of the solid, F the fraction of the conductivity attributable to the gas. In these, 2n 1 12 19 F n 2 21 1 1 fn where n is an empirical parameter n 6:5; f the porosity of the deposit [14]. 2.4. Numerical approach
pi Tps 1 1 2 pi Tps ps Ts
14
where pi(Tps) is the sticking probability of particles of composition i, Tps the particle temperature on impaction, ps(Ts) the sticking probability of the deposit surface, and
Our model is used to predict the ¯ow ®eld, temperature ®led, particle transport and deposit behaviors in a 300 MW (electrical output) W-shaped pulverized coal-®red utility boiler. Our numerical results were obtained using 68 £ 86 £ 50 (29 2400) non-uniform grids. Grid-dependence tests
650
J.R. Fan et al. / Fuel 80 (2001) 645±654
Fig. 4. The total particles mass cohered to the furnace: (a) front wall; (b) right side wall; (c) back wall; (d) left side wall; (e) ash hopper; and (f) top wall.
were conducted. The calculation begins by solving the gas ¯ow-®eld equations assuming that the particles are absent. Using the ¯ow-®eld particles' trajectories, their temperatures and burnout histories are determined. The mass, momentum and energy source terms for each cell is calculated. The source terms are included in the gas-phase equations and the ¯ow ®eld is then recalculated. The process is repeated until further repetition fails to change the solution. Thus, the mutual interaction of the gas and particles is accounted for. A modi®ed SIMPLER method [5] has been employed to determine velocities and pressures of gas ¯ow ®eld using a non-staggered grid system in Cartesian coordinates. A ®ve-stage iteration method is used in integrating the conventional difference equations for the particle. For an initial-value problem of the ®rst-order
difference equation, dy=dx f x; y;
y x0 y0 ;
20
the numerical solution at the n 1 1 step is yn11 yn 1 Dtn 0:1185k1 1 0:5190k3 1 0:5061k4 2 0:1800k5 1 0:0364k6 ;
21
where Dtn is the time step and k1 2 k6 are the following derivatives: k1 f xn ; yn ; k2 f xn 1 Dtn =4; yn 1 Dtn k1 =4;
22
3Dtn 3Dtn k1 9Dtn k2 ; yn 1 1 ; k 3 f xn 1 8 32 32
23
J.R. Fan et al. / Fuel 80 (2001) 645±654
651
Fig. 4. (continued)
12Dtn 1932Dtn k1 ; yn 1 13 2197 ! 7200Dtn k2 7296Dtn k3 1 2 2197 2197
The adjustment to the time step Dtn is controlled by the error
k4 f xn 1
24
!1=4 ;
27
where 1 is an empirical constant and
k5 f xn 1 Dtn ; yn 1 439Dtn k1 =216 2 8Dtn k2 1 3680Dtn k3 =513 2 845Dtn k4 =4104
1Dt un 0:84 p n dn1
25
Dtn 8Dtn k1 3544Dtn k3 ; yn 2 1 2Dtn k2 2 2 27 2565 ! 1859Dtn k4 11Dtn k5 2 (26) 1 4104 40
p dn11
Dtn
k1 128k3 2197k4 k5 2k6 2 2 1 1 ; 360 4275 75240 50 55 28
k6 f xn 1
if un . 1; then the results satisfy the equation udn11 =Dtn u , 1;
29
652
J.R. Fan et al. / Fuel 80 (2001) 645±654
Fig. 4. (continued)
where the error in the n 1 1 step is dn11 yn11 2 yn11 :
30
Here, yn11 is the actual solution and yn11 the numerical solution. If udn11 u is the given value, the numerical solution yn11 is accepted. Otherwise, the time step Dtn is decreased and the calculations repeated. If un , 1; then the results do not satisfy Eq. (19). Using u nDtn to replace Dtn, the calculation is again repeated. Our ®ve-stage iteration method reduces the solution time
by a factor of four compared to the four-stage Runge±Kutta method, which is used in Ref. [15]. 3. Results and discussions The analysis of the coal used is presented in Table 2. A continuous distribution of coal-particle sizes was represented by using 16 different particle diameters. The mass fractions for various size classes are shown in Table 3.
J.R. Fan et al. / Fuel 80 (2001) 645±654
653
Fig. 5. The cohesive mass of particles at the central line of front wall.
Fig. 1 shows the predicted results of ¯ow ®eld in the furnace. The pressure gradient obtained from thermal calculation is imposed in the SIMPLER method to couple to calculate the ¯ow ®eld near the platen. The ¯ow ®eld shown in Fig. 1(b) is taken from a cross-section of one of the secondary burners vertical height at 15.722 m. Fig. 2 shows the temperature ®eld of furnace. Fig. 2(a) is the temperature pro®les of vertical central cross section and Fig. 2(b) is the temperature pro®les of secondary burner plane at height 15.722 m. Fig. 3 shows the predicted tracks of four different particles of respective size of 20, 50, 80 and 110 mm in diameter. The residence time of 20 mm particle is 20 s whereas that of the 50 mm particle is 14 s. From the ®gure, it can be concluded that the smaller the particles, the better the distribution of the gas ¯ow. Fig. 4 shows the total particles mass cohered to the front wall, right sidewall, back wall, left side wall, dust hopper and top wall. It is a statistical conclusion and can give
instructive guide to investigate the ash deposit behaviors in the furnace. We can conclude that the particles mass cohered at the wall is different at different point. The deposits at those points which particles impact regularly grow rapidly. The growth rate of deposits is proportional to the impact probability. Fig. 5 shows the cohesive mass of particles at the central line of front wall along the furnace height. It can be seen from the ®gure that the mass cohered to wall at about 23 m height is biggest. And it is also bigger than other place at the height from 15 to 25 m height. It is because the burners are located at this region. The particles are comparatively denser than the other place. So the particle mass cohered to wall at near-burners region is bigger. The another region where the cohesive particle mass is also bigger is the outlet of furnace, which is about 40 m height. In this region, the denser particle density and higher particle and wall surface temperature lead to the rapid growth of deposit. Fig. 6 shows the calculated porosity of the deposit as a
Fig. 6. The calculated deposit porosity at the central line of front wall.
654
J.R. Fan et al. / Fuel 80 (2001) 645±654
Fig. 7. The calculated deposit depth at the central line of front wall.
function of furnace height along the central line of front wall. The porosity of deposit is relative to the thermal conductivity. And the porosity of deposit is also relative to the coal chemistry and wall conditions. Fig. 7 shows the calculated depth of the deposit as a function of furnace height along the central line of front wall. It can also be seen that the deposit depth is bigger at near-burners region. The reasons are that the probability of particle impacting to the wall in this region is bigger and the temperature of wall surface is higher than other places. The particles, which impact to the wall, are easier to be captured. Similar to the Fig. 5, another region of bigger deposit depth is the outlet of the furnace, which is about 40 m height along the furnace.
4. Conclusion A model has been developed to simulate deposit growth under slagging conditions. The model was coupled with a comprehensive combustion code to predict the ¯ow ®eld, the temperature ®eld and the deposit growth behavior in a pulverized coal-®red boiler. Some useful conclusion can be deduced to guide the investigation of deposit growth. The deposits grow rapidly at those places where the particles' impacting probability and the temperature of wall surface are high. The numerical simulation on ash deposit can give convenient and effective way to investigate the deposit behavior in the combustion reactor.
Acknowledgements This project is supported by the Special Funds for Major State Basic Research Project of People's Republic of China. References [1] Lee FCC, Riley GS, Lockwood FC. Applications of advanced technology to ash-related problems in boilers. New York: Plenum Press, 1996. [2] Fan JR, Liang XH, Xu QS, Zhang XY, Cen KF. Energy 1997;22:847. [3] Launder BE, Spalding DB. Mathematical models of turbulence. New York: Academic Press, 1972. [4] Spalding DB. 13th Symposium (International) on combustion. The Combustion Institute, Pittsburgh, PA, 1971. p. 49. [5] Rahman MM, Miettinen A, Siikonen T. Numerical heat transfer. Part B 1996;30:291. [6] Hammersley JM, Handscomb DC. Monte Carlo methods. New York: Wiley, 1964. [7] Smoot LD, Pratt DT. Pulverized-coal combustion and gasi®cation. New York: Plenum Press, 1979. [8] Wang H, Harb JH. Prog Energy Combust Sci 1997;23:267. [9] Richards GH, Slater PN, Harb JN. Energy & Fuels 1993;7:774. [10] Shuen JS, Solomon ASP, Qhang QF, Faeth GM. AIAA J 1985;23:396. [11] Wilemski G, Srinivasachar S, Saro®m AF. In: Benson SA, editor. Inorganic transformations and ash deposition during combustion. New York: Engineering Foundation Press, ASME, 1992 (p. 545). [12] Baxter LL, Hardesty DR. Coal combustion science, Quarterly Progress Report, Sandia Report 1991:SAND91±S8233. [13] Walsh PM, Sayre AN, Loehden DO, Monroe LS, Beer JM, Saro®m AF. Prog Energy Combust Sci 1990;16:327. [14] Sugarawa A, Yoshiwaza Y, Aust. J Phys 1961;14:469. [15] Hill SC, Smoot LD. Energy & Fuels 1993;7:874.
www.elsevier.com/locate/fuel
Simulation of ash deposit in a pulverized coal-®red boiler J.R. Fan*, X.D. Zha, P. Sun, K.F. Cen Department of Energy Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China Received 6 May 2000; accepted 23 August 2000
Abstract A model has been developed to simulate deposit growth under slagging conditions. The model was coupled with a comprehensive combustion code to predict the ¯ow ®eld, the temperature ®eld and the deposit growth behavior. The predictions indicate that the numerical model can be used to optimize the design and operation of pulverized coal-®red boilers. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Pulverized coal-®red; Slagging; Flow ®eld; Temperature ®eld; Deposit growth
1. Introduction
2. Mathematical models
The accumulation of furnace deposits is one of the many dif®culties faced by utility operators all over the world. Slagging not only reduces the thermal ef®ciency of a furnace, but also affects its integrity due to corrosion, erosion or impact on the bottom tubes. Slagging when severe can lead to substantial ®nancial losses to an operator. Although soot blowing and wall blowing are routinely used to manage deposition, unexpected or uncontrolled deposition can still occur at locations inaccessible to the cleaning devices, or at locations where the bonding strength between the wall and the deposit is too strong for cleaning equipment to be effective. Deposition problems are frequenting associated with a change in fuel characteristics and/or boiler operating conditions. Predictive indices and deposition models help designers and operators to diagnose and correct operational problems due to the deposition. These models also provide insight into the deposition behavior of a particular coal or coals. In recent years, considerable advances have been made in developing models to predict ash deposition behavior. Improved methods have been developed which utilize a more accurate description of the coal, as well as a mathematical description of the ¯y ash transport and sticking in order to approximate the deposition rate [1]. This paper describes our efforts to simulate the ash deposition behavior in a pulverized coal-®red boiler.
2.1. The ¯ow ®eld and heat transfer models In this work, a Lagrangian/Eulerian approach has been employed for gas±solid two-phase ¯ow simulation. The gas phase is described by Navier±Stokes equations, coupled with appropriate equations for density and viscosity. For closure of the turbulence equations, we use both a k± 1 model and a RNG k± 1 model, then make a comparison between them. The general Eulerian equation for the gas phase takes the form div rvf 2 div G grad f S f
where Sf is the source terms of the gas phase, G f the effective viscosity that is summarized in Table 1 for the different variable f . Where f represents the variables u, v, w, k and 1 , (coordinate velocities, turbulent ¯uctuation energy and turbulent energy dissipation) [2±4] A modi®ed SIMPLER method [5] has been employed to determine velocities and pressures using a non-staggered grid system in Cartesian coordinates as demonstrated in the following part. The heat transfer equation is ruc p TDyDz 1 rvcp TDxDz 1 rwcp TDxDy lx TDyDz 1 ly TDyDz 1 lz TDyDz 1 Qradiation 2 4K1 sT 4 DV 1 Qreaction DV
* Corresponding author. Tel.: 186-571-795-1764; fax: 186-571-7991863. E-mail address: [email protected] (J.R. Fan).
1
2
Where, r is the density, l the conducting coef®cient, s the Stenfan±Boltsman constant, T the temperature, cp the speci®c heat, u, v, and w the velocity, Qradiation is the radiation
0016-2361/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0016-236 1(00)00134-4
646
J.R. Fan et al. / Fuel 80 (2001) 645±654
Nomenclature Coal-particle area Ap Drag coef®cient CD Cg Gas molar concentration Speci®c heat Cp Cm,C1,C2 Empirically determined constants Binary diffusivity Dw Particle diameter dp E Activation energy g Gravitational vector h Enthalpy K Reaction-rate coef®cient Mass-transfer coef®cient Kc k Mean turbulent kinetic energy M Molecular weight Particle mass mp Nu Nusselt number Particle number density np p Sticking probability Q Particle-to-gas heat-transfer rate R Gas constant r Particle reaction rate The volatile production rate rv Gas source term for variable f Sf t Time T Temperature u Velocity along x-direction v Velocity along y-direction v Velocity vector w Velocity along z-direction X Mole fraction x,y,z Cartesian coordinate Y Pyrolysis coef®cient Greek letters f Deposit porosity F General variables 1 Emissivity, or dissipation rate of turbulence m Viscosity r Density s k, s 1 Turbulent Prandtl and Schmidt numbers Subscripts c Convection, or coal daf Daf coal eff Effective g Gas h Char l Char oxidation reaction m Mean p Particle r Radiation v Volatiles w Moisture
energy transfer, which is modeled by using Monte Carlo method [6], Qreaction is the heat energy released during coal combustion, which is modeled as a source term after completing particle tracing. 2.2. Combustion models The equation of motion for a particle is m p dvp =dt mp g 1
1 rC v 2 vp uvg 2 vp uAp 1 Freaction 2 D g 3
where Freaction vp 2dmp =dt is the force exerted on the coal-particle due to sudden momentum change when devolatilization occurs, the direction of the reaction force is modeled stochastically, compared to drag force this force is smaller in quantity but important for particle trajectory. When the particle has advanced in the furnace, reaction processes like vaporization, devolatilization and char combustion should be taken into consideration. Diffusion-limited vaporization of moisture from the coalparticle is described by rw Mw Num Cg Dwm Ap Xwp 2 Xwg =dp 1 2 Xwp rp =rw
4
Use the equations 0
dV=dt Vdaf 2 VK exp E=RT 0
Vdaf QVdaf
5 6
to describe the formation of volatile matter from coal dust. Char is produced in competition with volatile production as expressed by rhm rv 1 2 Ym =Ym
7
Char assumes to be oxidized heterogeneously by a gaseous oxidizer that diffuses to the particle, is absorbed, reacts with carbon, and is then described as CO. The char-oxidizing rate is rhl
Ap np 2 Mhp mg f1 Kcp1 Kp1 j p Cog Cg Mg Ap np Cg j p Kp1 1 Kcp1 1 rp
8
The total reaction rate for the coal-particle is rp rv 1 rhl 1 rw
9
The carbon reaction rate is rh rhm 2 rhl
10
The mass change of a particle follows: dmp =dt mw 1 mv 1 mh
11
Where mw, mv and mh are the rate of mass change when the coal-particle is evaporated, devolatilized and char-oxidized respectively. The conservation of particle energy is mp dhp =dt Qc 1 Qr 1 Qw 1 Qv 1 Qh
12
J.R. Fan et al. / Fuel 80 (2001) 645±654
647
Table 1 Eulerian conservation equations and identi®cation of terms in Eq. (1) Conservative equation
f
G
Sf
Mass (continuity) x-Direction momentum
1 u
0 meff
0
y-Direction momentum
v
m eff
2
z-Direction momentum
w
m eff
2
2p 2 2u 2 2v 2 2w 1 1 1 m eff meff meff 2x 2x 2x 2y 2x 2z 2x
2p 2 2u 1 meff 1 2y 2x 2y 2p 2 2u 1 2 meff 1 2z 2x 2z
2 2v meff 1 2y 2y 2 2v meff 1 2y 2z
2 2w meff 2z 2y 2 2w meff 2z 2z
Turbulent kinetic energy k meff =s k Gk 2 r1 Dissipation rate of 1 meff =s 1 1=k C1 Gk 2 C2 1 turbulent kinetic energy ( " # ) 2u 2 2v 2 2w 2 2u 2v 2 2v 2w 2 2w 2u 2 1 Gk meff 2 1 1 1 ; meff mt 1 m; 1 1 1 1 2x 2y 2z 2y 2x 2z 2y 2x 2z
mt Cm rk2 =1; Cm 0:09; C1 1:44; C2 1:92; s k 1:0; s 1 1:3
molten coal-particles entrained by gas collides on the wall and wall-cooling surfaces. Then they are cooled and frozen to slag. The slags mainly appear on the radiant heating surfaces. In order to predict the deposition mechanism with mathematical models, the following issues must be addressed: (1) ash formation, (2) ¯uid dynamics and particle transport, (3) particle impaction and sticking, (4) deposit growth as a function of location in the combustion chamber, (5) deposit properties and strength development, (6) heat transfer through the deposit, (7) the effect of deposition on operating conditions (e.g. temperatures and heat ¯uxes) in the combustor, and (8) deposit structure and its effect on ¯ow patterns in the combustion facility [8,9].
where Qc, Qr, Qw, Qv and Qh are referring to heat related to gas-particle convection, radiation and heat release during evaporation, devolatilization and char-oxidation along the trajectory of the particle. The EBU-Arrhenius model models gas phase turbulent combustion process Wfu min Wfu;A ; Wfu;T Wfu;A ArYfu YO2 exp 2E=RT Wfu;T
13
1 r min Yfu ; YO2 CE R
Equations with the form of dx=dt f x; t are integrated using a ®ve-stage Runge±Kutta method as described in Refs. [2,7].
2.3.1. Particle impaction rates Although a limited number of particle trajectories were adequate for the combustion simulations, more information was required to approximate impaction rates at the wall.
2.3. Slagging models In the coal combustion process, the molten or fractional Table 2 Coal properties Proximate analysis (%)
Ultimate analysis (%)
MS
Ash
VM
FC
C
H
O
N
S
6.00
21.82
16.72
55.46
64.89
2.83
2.4
0.98
1.08
Heating value (MJ/kg) 28.27
Table 3 The percentages of various size classes of pulverized coal Particle diameter (mm) Percentage (%) Particle diameter (mm) Percentage (%)
5 20.22 160 1.42
20 28.04 180 0.94
40 17.95 200 0.62
60 11.61 220 0.41
80 7.58 240 0.27
100 4.96 260 0.18
120 3.27 280 0.12
140 2.16 300 0.25
648
J.R. Fan et al. / Fuel 80 (2001) 645±654
Fig. 2. The predicted pro®le of temperature ®eld: (a) vertical central cross section; and (b) secondary burner plane (height 15.722 m). Fig. 1. The predicted pro®le of ¯ow ®eld.
Consequently, a stochastic separated ¯ow (SSF) model [10] was added as a postprocessor to calculate particle impaction rates. In this model, the in¯uence of turbulent velocity ¯uctuations in the gas phase on the particle trajectories is accounted for through random particle-eddy interactions.
Velocity ¯uctuations are assumed to be isotropic and are obtained by sampling a Gaussian PDF with a standard deviation of 2k=30:5 : The particle motion within an eddy is modeled deterministically by solving the instantaneous particle momentum equation. Velocity ¯uctuations are assumed to remain constant during a particle-eddy interaction [11,12].
J.R. Fan et al. / Fuel 80 (2001) 645±654
649
Ts the temperature of the deposit surface. Factors which are expected to in¯uedce sticking probability include particle viscosity, surface tension, velocity, and angle of impact, as well as the chemical and physical state of the surface upon which deposition is occurring. The sticking probability of a particle of composition i was therefore de®ned as m m . mref pi Tps ref m 15 pi Tps 1 m # mref where, we assume mref 1 £ 105 Pa´s: 2.3.3. Deposit properties In order to model deposit growth and heat transfer, it was necessary to describe the thermal and physical properties of the deposit. The properties include the deposit thickness, porosity, ¯uidity, thermal conductivity and so on. Among these properties, the porosity is the major factor which in¯uence the total properties of the deposit. The porosity of deposit can be described as: Vl f 1 2 1 2 f0 1 1 2 f0 16 Vs where f is the deposit porosity, f 0 the initial porosity of the deposit, Vl the volume of the liquid, and Vs the volume of the solid [9]. Note that, the deposit will be solid when the viscosity is bigger than critical viscosity mcr 105 Pa´s: And zero porosity is reached before the deposit is completely liquid. The thickness of deposit can be described as: li mi =rp 1 2 fi
17
where li is the thickness, mi the mass per area, r p the solid particle density, f i the deposit porosity, and i refers to the current time step. The thermal conductivity, which is also an important property of deposit, can be described as: k 1 2 Fks 1 Fkg Fig. 3. The particle trajectories of four different diameters.
2.3.2. Particle sticking A model was also needed to predict which of the impacting particles would stick based on particle temperature and composition. The capture ef®ciency hcap or fraction of the impacting particles, which adhere to the surface was approximated by the following expression: [13]
h
N X i1
18
where kg is the thermal conductivity of the gas phase, ks the thermal conductivity of the solid, F the fraction of the conductivity attributable to the gas. In these, 2n 1 12 19 F n 2 21 1 1 fn where n is an empirical parameter n 6:5; f the porosity of the deposit [14]. 2.4. Numerical approach
pi Tps 1 1 2 pi Tps ps Ts
14
where pi(Tps) is the sticking probability of particles of composition i, Tps the particle temperature on impaction, ps(Ts) the sticking probability of the deposit surface, and
Our model is used to predict the ¯ow ®eld, temperature ®led, particle transport and deposit behaviors in a 300 MW (electrical output) W-shaped pulverized coal-®red utility boiler. Our numerical results were obtained using 68 £ 86 £ 50 (29 2400) non-uniform grids. Grid-dependence tests
650
J.R. Fan et al. / Fuel 80 (2001) 645±654
Fig. 4. The total particles mass cohered to the furnace: (a) front wall; (b) right side wall; (c) back wall; (d) left side wall; (e) ash hopper; and (f) top wall.
were conducted. The calculation begins by solving the gas ¯ow-®eld equations assuming that the particles are absent. Using the ¯ow-®eld particles' trajectories, their temperatures and burnout histories are determined. The mass, momentum and energy source terms for each cell is calculated. The source terms are included in the gas-phase equations and the ¯ow ®eld is then recalculated. The process is repeated until further repetition fails to change the solution. Thus, the mutual interaction of the gas and particles is accounted for. A modi®ed SIMPLER method [5] has been employed to determine velocities and pressures of gas ¯ow ®eld using a non-staggered grid system in Cartesian coordinates. A ®ve-stage iteration method is used in integrating the conventional difference equations for the particle. For an initial-value problem of the ®rst-order
difference equation, dy=dx f x; y;
y x0 y0 ;
20
the numerical solution at the n 1 1 step is yn11 yn 1 Dtn 0:1185k1 1 0:5190k3 1 0:5061k4 2 0:1800k5 1 0:0364k6 ;
21
where Dtn is the time step and k1 2 k6 are the following derivatives: k1 f xn ; yn ; k2 f xn 1 Dtn =4; yn 1 Dtn k1 =4;
22
3Dtn 3Dtn k1 9Dtn k2 ; yn 1 1 ; k 3 f xn 1 8 32 32
23
J.R. Fan et al. / Fuel 80 (2001) 645±654
651
Fig. 4. (continued)
12Dtn 1932Dtn k1 ; yn 1 13 2197 ! 7200Dtn k2 7296Dtn k3 1 2 2197 2197
The adjustment to the time step Dtn is controlled by the error
k4 f xn 1
24
!1=4 ;
27
where 1 is an empirical constant and
k5 f xn 1 Dtn ; yn 1 439Dtn k1 =216 2 8Dtn k2 1 3680Dtn k3 =513 2 845Dtn k4 =4104
1Dt un 0:84 p n dn1
25
Dtn 8Dtn k1 3544Dtn k3 ; yn 2 1 2Dtn k2 2 2 27 2565 ! 1859Dtn k4 11Dtn k5 2 (26) 1 4104 40
p dn11
Dtn
k1 128k3 2197k4 k5 2k6 2 2 1 1 ; 360 4275 75240 50 55 28
k6 f xn 1
if un . 1; then the results satisfy the equation udn11 =Dtn u , 1;
29
652
J.R. Fan et al. / Fuel 80 (2001) 645±654
Fig. 4. (continued)
where the error in the n 1 1 step is dn11 yn11 2 yn11 :
30
Here, yn11 is the actual solution and yn11 the numerical solution. If udn11 u is the given value, the numerical solution yn11 is accepted. Otherwise, the time step Dtn is decreased and the calculations repeated. If un , 1; then the results do not satisfy Eq. (19). Using u nDtn to replace Dtn, the calculation is again repeated. Our ®ve-stage iteration method reduces the solution time
by a factor of four compared to the four-stage Runge±Kutta method, which is used in Ref. [15]. 3. Results and discussions The analysis of the coal used is presented in Table 2. A continuous distribution of coal-particle sizes was represented by using 16 different particle diameters. The mass fractions for various size classes are shown in Table 3.
J.R. Fan et al. / Fuel 80 (2001) 645±654
653
Fig. 5. The cohesive mass of particles at the central line of front wall.
Fig. 1 shows the predicted results of ¯ow ®eld in the furnace. The pressure gradient obtained from thermal calculation is imposed in the SIMPLER method to couple to calculate the ¯ow ®eld near the platen. The ¯ow ®eld shown in Fig. 1(b) is taken from a cross-section of one of the secondary burners vertical height at 15.722 m. Fig. 2 shows the temperature ®eld of furnace. Fig. 2(a) is the temperature pro®les of vertical central cross section and Fig. 2(b) is the temperature pro®les of secondary burner plane at height 15.722 m. Fig. 3 shows the predicted tracks of four different particles of respective size of 20, 50, 80 and 110 mm in diameter. The residence time of 20 mm particle is 20 s whereas that of the 50 mm particle is 14 s. From the ®gure, it can be concluded that the smaller the particles, the better the distribution of the gas ¯ow. Fig. 4 shows the total particles mass cohered to the front wall, right sidewall, back wall, left side wall, dust hopper and top wall. It is a statistical conclusion and can give
instructive guide to investigate the ash deposit behaviors in the furnace. We can conclude that the particles mass cohered at the wall is different at different point. The deposits at those points which particles impact regularly grow rapidly. The growth rate of deposits is proportional to the impact probability. Fig. 5 shows the cohesive mass of particles at the central line of front wall along the furnace height. It can be seen from the ®gure that the mass cohered to wall at about 23 m height is biggest. And it is also bigger than other place at the height from 15 to 25 m height. It is because the burners are located at this region. The particles are comparatively denser than the other place. So the particle mass cohered to wall at near-burners region is bigger. The another region where the cohesive particle mass is also bigger is the outlet of furnace, which is about 40 m height. In this region, the denser particle density and higher particle and wall surface temperature lead to the rapid growth of deposit. Fig. 6 shows the calculated porosity of the deposit as a
Fig. 6. The calculated deposit porosity at the central line of front wall.
654
J.R. Fan et al. / Fuel 80 (2001) 645±654
Fig. 7. The calculated deposit depth at the central line of front wall.
function of furnace height along the central line of front wall. The porosity of deposit is relative to the thermal conductivity. And the porosity of deposit is also relative to the coal chemistry and wall conditions. Fig. 7 shows the calculated depth of the deposit as a function of furnace height along the central line of front wall. It can also be seen that the deposit depth is bigger at near-burners region. The reasons are that the probability of particle impacting to the wall in this region is bigger and the temperature of wall surface is higher than other places. The particles, which impact to the wall, are easier to be captured. Similar to the Fig. 5, another region of bigger deposit depth is the outlet of the furnace, which is about 40 m height along the furnace.
4. Conclusion A model has been developed to simulate deposit growth under slagging conditions. The model was coupled with a comprehensive combustion code to predict the ¯ow ®eld, the temperature ®eld and the deposit growth behavior in a pulverized coal-®red boiler. Some useful conclusion can be deduced to guide the investigation of deposit growth. The deposits grow rapidly at those places where the particles' impacting probability and the temperature of wall surface are high. The numerical simulation on ash deposit can give convenient and effective way to investigate the deposit behavior in the combustion reactor.
Acknowledgements This project is supported by the Special Funds for Major State Basic Research Project of People's Republic of China. References [1] Lee FCC, Riley GS, Lockwood FC. Applications of advanced technology to ash-related problems in boilers. New York: Plenum Press, 1996. [2] Fan JR, Liang XH, Xu QS, Zhang XY, Cen KF. Energy 1997;22:847. [3] Launder BE, Spalding DB. Mathematical models of turbulence. New York: Academic Press, 1972. [4] Spalding DB. 13th Symposium (International) on combustion. The Combustion Institute, Pittsburgh, PA, 1971. p. 49. [5] Rahman MM, Miettinen A, Siikonen T. Numerical heat transfer. Part B 1996;30:291. [6] Hammersley JM, Handscomb DC. Monte Carlo methods. New York: Wiley, 1964. [7] Smoot LD, Pratt DT. Pulverized-coal combustion and gasi®cation. New York: Plenum Press, 1979. [8] Wang H, Harb JH. Prog Energy Combust Sci 1997;23:267. [9] Richards GH, Slater PN, Harb JN. Energy & Fuels 1993;7:774. [10] Shuen JS, Solomon ASP, Qhang QF, Faeth GM. AIAA J 1985;23:396. [11] Wilemski G, Srinivasachar S, Saro®m AF. In: Benson SA, editor. Inorganic transformations and ash deposition during combustion. New York: Engineering Foundation Press, ASME, 1992 (p. 545). [12] Baxter LL, Hardesty DR. Coal combustion science, Quarterly Progress Report, Sandia Report 1991:SAND91±S8233. [13] Walsh PM, Sayre AN, Loehden DO, Monroe LS, Beer JM, Saro®m AF. Prog Energy Combust Sci 1990;16:327. [14] Sugarawa A, Yoshiwaza Y, Aust. J Phys 1961;14:469. [15] Hill SC, Smoot LD. Energy & Fuels 1993;7:874.