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Numerical study on the spatial distribution of energy release during char combustion
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APPLIED ENERGY Applied Energy 85 (2008) 1060–1070 www.elsevier.com/locate/apenergy
Numerical study on the spatial distribution of energy release during char combustion Gu Ming-yan a,b,*, Zhang Ming-chuan a,*, Yu Juan a, Fan Wei-dong a, Tian Feng-guo a a
School of Mechanical Engineering, Shanghai Jiaotong University, 800 Dong Chuan Road, Shanghai 200240, China b School of Metallurgy and Resources, Anhui University of Technology, Maanshan Anhui 243002, China Received 23 September 2005; received in revised form 14 December 2007; accepted 19 December 2007
Abstract The energy distribution coefficient (Xc), the fraction of the total heat of reaction released at the char surface during combustion of char particles, was studied using the improved moving flame front (MFF) model. The energy distribution coefficient (Xc), considering homogeneous oxidation of CO in the boundary layer of the particle and reduction of CO2 at the surface, was derived explicitly. Under conditions in practical pulverized coal flames, the energy distribution coefficient (Xc) and the effective energy distribution coefficient (Xe), based on the heat-release calculated using the traditional single film model with CO as the only reaction product (SF-CO), were calculated and compared with the value commonly used in the SF-CO model. The results obtained show that the smaller the particle diameter, the greater the energy distribution coefficient. For the same particle diameter, the higher the particle temperature, the lower the energy distribution coefficient. Under the conditions of the calculation, the average value of the energy distribution coefficient Xc is approximately 0.7, and the average value of the effective SF-CO energy distribution coefficient is greater than 0.5, significantly larger than the value of 0.3 obtained by the traditional single film model. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Pulverized coal flame; Combustion of char particle; Energy distribution coefficient; Moving flame front (MFF) model; Single film (SF-CO) model
1. Introduction The combustion of char particles in an oxidizing environment is complicated by several heterogeneous and homogeneous reactions occurring simultaneously or in series. The continuous-film model of modern combustion theory and experiment have demonstrated that, the influences of the volumetric reaction of CO and the surface reduction of CO2 on the particle temperature and the overall combustion rate of char particle * Corresponding authors. Address: School of Mechanical Engineering, Shanghai Jiaotong University, 800 Dong Chuan Road, Shanghai 200240, China. Tel.: +86 21 3420 6768; fax: +86 21 3420 6115. E-mail addresses: [email protected] (M.-y. Gu), [email protected] (M.-c. Zhang).
0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2007.12.006
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
Nomenclature a As b cP d1 d2 dP D D0 f h H k Kd Ks L P q Q Qr Qc T t U V W Xc Xe
radius of particle (m) particle surface area (m2) radius of CO flame front (m) specific heat (J/(kg K)) internal diameter of primary air channel external diameter of primary air channel diameter of particle (m) inner diameter of burner inner diameter of combustion chamber scalar mixture fraction fluid enthalpy (J/kg) heat released of reaction (J/(kg K)) turbulent kinetic energy (m2/s2) bulk diffusion rate constant (kg/(m2 s Pa)) chemical kinetics rate constant (kg/(m2 s Pa)) length of combustion chamber partial pressure (Pa) burning rate of char (kg/(m2 s)) heat flux (J/m2 s) radiative heat flux (J/(m2 s)) convection heat flux (J/(m2 s)) temperature (K) time (s) axial velocity (m/s) radial velocity (m/s) angular velocity (m/s) energy distribution coefficient effective SF-CO energy distribution coefficient
Subscripts and superscripts g gas p particle s particle surface ox pure oxidation condition re pure reduction condition Char char CO carbon monoxide CO2 carbon dioxide O2 oxygen MFF improved moving flame front model SFS Traditional single film model ’ reaction 2C + O2 ? 2CO ” reaction C + CO2 ? 2CO ”’ reaction C + O2 ? CO2 Greek symbols C/ turbulent exchange coefficient e rate of eddy dissipation (m2/s3)
1061
1062
eP k q
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
particle absorptivity coefficient of thermal conductivity (W/(m K)) density (kg/m3)
are extremely complex. The primary product, CO, of the char surface oxidation reaction, can be burnt in the boundary layer of the particle, increasing the char particles’ surface temperature by several hundred Kelvin [1–3]. This phenomenon cannot be understood or predicted by the traditional single film with CO the only reaction product (SF-CO) model. However, because of the complexity of treating the highly nonlinear heat release and mass transfer coupling, the SF-CO model is still widely used in the numerical simulation of pulverized coal combustion [4–6]. In the SF-CO model, it is supposed that there is no further change in the primary combustion product, CO, in the boundary layer of the particle, thus the fraction of the total heat of char combustion released on or near the particle surface, termed in the present work the ‘‘energy distribution coefficient”, Xc, takes the value of 0.3, approximately [4,7]. In the past 20 years, much theoretical work on the combustion of char particles has been carried out. As a result, some explicit and semi-explicit expressions are available to calculate the combustion rate of a char particle [8–11], offering the possibility to easily analyze the influence of CO combustion in the boundary layer of the particle on the particle temperature and combustion rate. The present paper studies the energy distribution coefficient in combustion of char particles using the improved moving flame front (MFF) model. The improved MFF model takes into account the surface reactions of carbon with both oxygen and carbon dioxide, and the volumetric oxidation of carbon monoxide in the boundary layer of the particle, while it presents explicit algebraic expressions for the combustion rate and the particle temperature. The results of calculations using the improved MFF model are very close to the results obtained by solving the differential equations of the continuous-film model. However, the calculation time for the former is only a tiny fraction of that for the latter [3,10,11]. 2. Energy distribution coefficient In the calculation of pulverized coal combustion, the char particle temperature is calculated from the heat balance equation. Supposing that the temperature of a char particle is uniform, the energy equation for the particle is mP dðcP T s Þ ¼ Qc þ Qr þ Qb dt AS
ð1Þ
where Qr is calculated from Qr ¼ rep ðT 4g T 4s Þ; Qc is calculated from Qc = (Tg Ts)km/a; Qb is the heat flux on the particle surface released by char combusting, presented in the form of a proportion of the heat release by complete combustion of char to CO2 [4,7]: Qb = Xc q H000 . When the traditional SF-CO model is used to calculate the char combustion rate, the primary combustion product is assumed to be CO and there is no further change in the primary combustion product in the boundary layer of the particle. Therefore, the heat flux at the particle surface released by char combustion is Qb = q H0 , and the corresponding energy distriQb qH 0 bution coefficient is X c ¼ qH 000 ¼ qH 000 0:3. On the other hand, if we assume that CO2 is immediately formed by burning CO at the particle surface, then, Xc = 1. In the numerical simulation of pulverized coal combustion, Xc is usually assumed to be an empirical value slightly larger than 0.3. But the value chosen has no strict theoretical foundation. In what follows, the energy distribution coefficient is deduced using the improved MFF model to calculate the char burning rate. Ignoring radiative heat exchange, the particle temperature in steady state is [3,11] a a a2 1 T s ¼ T g þ ðq0 H 0 q00 H 00 Þ 1 þ ðq0 þ q00 ÞH 000 ð2Þ b km b km km is the average coefficient of thermal conductivity of gas within the boundary layer. The radius of the CO flame front, b, is determined by [11]
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
b ¼ a
b q0 b q00 þ a ox q a re q
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ð3Þ
where P 2 þ 12 P g;CO b g;O2 ¼ a ox K d;O2 þ 1 1 P g;CO K d;O2 þ 1 2 P g;O K s;O K s;O 2
2
and
K d;CO2 P 2 1 þ Pg;CO K d;O2 b g;O2 ¼2 K d;CO2 a re 1þ
2
K s;CO2
Compared with the SF-CO model, in which there are no homogeneous reactions in the boundary layer of the particle, the relation between the equivalent heat flux Qb released by char combustion on the particle surface and the particle temperature is: a ð4Þ T s ¼ T g þ Qb km From Eqs. (2) and (4), Qb can be obtained as follows: a a Qb ¼ ðq0 þ q00 ÞH 000 þ ðq0 H 0 q00 H 00 Þ 1 b b
ð5Þ
q00 and q are given by [3,11] q a P g;CO2 þ K d;CO b 2 q ¼ 1 1 þ K d;CO 1 ab K s;CO2 h 2 i 1 1 P g;O2 þ q00 K s;O þ K d;O 1 ab 2 2 a q¼ 1 1 þ 1þb K s;O K d;O 00
2
ð6Þ
ð7Þ
2
q0 can be obtained by subtraction of Eqs. (6) and (7): q0 = q q00 . Qb can be calculated by substituting q0 , q00 , and b into Eq. (5). Therefore, the energy distribution coefficient, taking into consideration the oxidation of CO in the boundary layer of the particle and the surface reduction of CO2 is obtained as ðq0 þ q00 ÞH 000 ab þ ðq0 H 0 q00 H 00 Þ 1 ab ð8Þ XC ¼ qH 000 Substituting q = q0 + q00 into Eq. (8), we then find: a ðq0 H 0 q00 H 00 Þ 1 ab XC ¼ þ b qH 000
ð9Þ
In order to take into account CO combustion in the boundary layer of a particle and the surface reduction of CO2 on the basis of the traditional SF-CO model, this paper brings forward the concept of effective SF-CO energy distribution coefficient Xe: Xe ¼
QbMFF qSFS H 000
ð10Þ
where QbMFF is the equivalent heat released by char burning at the particle surface, calculated using the MFF model, and qSFS is the char burning rate calculated from the SF-CO model. This means that the coefficient Xe can be used directly in the traditional SF-CO model, taking into consideration CO oxidation in the boundary layer of the particle and the surface reduction of CO2, but with the computational program remaining unchanged. 3. Numerical calculation of the energy distribution coefficient For numerical simulation of pulverized coal combustion, we choose a specific pulverized coal burner as the subject for investigation, to study the energy distribution coefficient.
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3.1. Mathematical models The mathematical model is based on an Eulerian description of the continuous phase and a stochastic Lagrangian description for the coal particles. The gas-phase time-averaged continuity equation and conservation equations of momentum, turbulent kinetic energy (k), dissipation (e), enthalpy (h) and species (f) in cylindrical coordinates are [12] o o o o o/i o o/i o o/i ðqU /i Þ þ ðrqV /i Þ þ ðqW /i Þ ¼ CU rCU CU þ þ þ S U þ S UP ox ror roh ox ror roh ox or roh ð11Þ A standard k–e model is used for the modeling of turbulence. The computations are performed on a threedimensional non-uniform 55 45 11 grid. The continuity and momentum equations are solved using the SIMPLE algorithm [13]. Representative coal particle trajectories are calculated by solving the particle equation of motion for the three components [14]. The interaction of the conserved properties between the gasphase and coal particles is calculated using the Particle-Source-In-Cell technique [15]. The poly-disperse size distribution of coal is divided into discrete particle size groups, assuming a Rosin–Rammler distribution [16]. The radiant intensity is calculated by the discrete transfer method of Lockwood and Shah [17]. 3.2. Combustion chamber geometry and case description The data on the combustion chamber, coal properties and operating conditions are available in Refs. [6,18]. Fig. 1 is a schematic diagram of the pulverized coal combustion chamber. The test fuel is a high volatile bituminous coal. The coal properties, operating conditions and combustion parameters are given in Tables 1–4. 4. Results and discussions Figs. 2–4 are the results of calculations of the energy distribution coefficient for different particle diameters. Because the calculation of particle motion adopted a stochastic trajectory model, we randomly selected data for trajectories of particles having diameters of 10, 30, 50, 70, and 90 lm for statistical analysis. The data in the figures are for char burning following complete release of volatiles from the coal. Fig. 2 shows the ratio b/a, i.e. the ratio of the CO flame sheet radius in the boundary layer of a particle to the particle radius, for different particle diameters, and the corresponding values of the energy distribution d1
Primary air + Pulverized coal
D0
Secondary air
d2 L D
Fig. 1. Schematic of pulverized coal combustion chamber.
Table 1 Dimension of combustion chamber [6,18] D0 (m)
L (m)
d1 (m)
d2 (m)
D (m)
0.6
3.0
0.022
0.035
0.056
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Table 2 Characteristics of coal [6,18] Proximate analysis (wt%, as received) Volatile Fixed carbon Moisture Ash
35.8 53.7 6.3 4.2
Ultimate analysis (wt%, as received) Carbon Hydrogen Sulphur Oxygen (by diff.) Nitrogen Particle average size (lm) Gross calorific value (MJ/kg)
72.6 5.05 1.55 15.31 1.29 45 29.29
Table 3 Coal combustion parameters [6,18] Coal devolatization parameters a1 (s1) a2 (s1) k1 (kJ/kmol) k2 (kJ/kmol)
3.7 105 1.5 1013 7.4 104 2.5 105
Carbon reaction (2C + O2 ? 2CO) A (kg/(m2 s Pa)) k (kJ/kmol)
0.86 1.495 105
Carbon reaction (C + CO2 ? 2CO) A (kg/(m2 s Pa)) k (kJ/kmol)
4.3 2.7 105
Table 4 Operating conditions [6,18] Coal feed rate (kg/h) Primary air flow rate (kg/h) Secondary air flow rate (kg/h) Primary air swirl number Secondary air swirl number Primary air temperature (°C) Secondary air temperature (°C)
14.0 31.3 120.0 0 1.03 80 300
coefficient Xc. From Fig. 2, it can be observed that, depending upon the particle diameter, when the particle temperature is below a certain value, CO burns on the particle surface, that is b/a = 1, and the corresponding value of the energy distribution coefficient is Xc = 1.0. This is because when the particle temperature is below this critical temperature the diffusion rate coefficient is larger than the chemical kinetic rate coefficient, and the primary product, CO, is directly oxidized to CO2 at the particle surface. The smaller the particle diameter, the larger the diffusion rate coefficient, and the wider the temperature range in which b/a = 1. From the comparison of energy distribution coefficients for the particle diameters dP = 10 lm and dP = 50 lm, it can be observed that, for dP = 10 lm, when the particle temperature is 2000 K, the CO flame front may still be located on the particle surface; whereas, for dP = 50 lm, the CO flame front separates from the surface when the particle temperature is about 1700 K, and the energy distribution coefficient decreases with increasing b/a.
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M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070 2.0 1.0 1.8 b/a
0.8
b/a xc
1.4
0.7
d p =10 μ m
1.2
xc
0.9
1.6
0.6
1.0
0.5
1000
1500 2000 2500 Particle temperature [K]
2.0 1.0 0.9
1.6
0.8
1.4
b/a xc
0.7
1.2
d p =30 μ m
0.6
1.0
xc
b/a
1.8
0.5 1200
1500 1800 2100 2400 Particle temperature [K]
2.0 1.0 0.9
1.6 b/a xc d p =50 μ m
1.4 1.2 1.0
0.8 xc
b/a
1.8
0.7 0.6 0.5
1400 1600 1800 2000 2200 2400 Particle temperature [K] 2.0 1.0 1.8
0.9
1.4 1.2
b/a xc d p =70 μ m
1.0 1400
0.8 xc
b/a
1.6
0.7 0.6 0.5
1600 1800 2000 2200 Particle tem perature [K]
2.0 1.0 1.6 1.4 1.2 1.0
0.9 b/a xc d p =90 μ m
0.8
xc
b/a
1.8
0.7 0.6 0.5
1400 1600 1800 2000 2200 Particle temperature [K]
Fig. 2. CO flame front radius and energy distribution coefficient.
Fig. 3 shows the range and probability of occurrence of the values for the energy distribution coefficient. From this figure, it is seen that, with increasing particle diameter, the probability of the energy distribution coefficient being 1.0 decreases from 90% when dP = 10 lm to about 4% when dP = 90 lm. The fraction of
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
d p = 10 μm
0.8 Probability
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0.6 0.4 0.2 0.0 0.5
0.6
0.7
0.8
0.9
1.0
Xc
0.25 d p = 30 μm
Probability
0.20 0.15 0.10 0.05 0.00 0.5
0.6
0.7
0.8
0.9
1.0
Xc
0.20 d p = 50 μm
Probability
0.16 0.12 0.08 0.04 0.00 0.5
0.6
0.7
0.8
0.9
1.0
Xc
0.20 d p = 70 μm
Probability
0.16 0.12 0.08 0.04 0.00 0.5
0.6
0.7
0.8
0.9
1.0
Xc
0.10 d p =90 μm
Probability
0.08 0.06 0.04 0.02 0.00 0.5
0.6
0.7
0.8
0.9
1.0
Xc
Fig. 3. Distributions of the energy distribution coefficient.
the total burning time during which combustion of CO occurs at the particle surface decreases markedly with increasing particle size.
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M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070 1.0
Xc , X e
0.9 0.8 0.7 0.6 0.5
Xc Xe d p = 10 μm
1200
1600 2000 2400 Particle temperature [K]
2800
1.0
Xc , Xe
0.9 0.8 0.7 0.6 0.5
Xc Xe d p = 30 μm
0.4 1200
1600 2000 2400 Particle temperature [K]
2800
1.0
X c , Xe
0.9 0.8 0.7 0.6 0.5 0.4
Xc Xe d p = 50 μm
1200
1600 2000 2400 Particle temperature [K]
1.0
Xc Xe
0.9 Xc , Xe
2800
0.8 0.7 0.6 0.5 0.4
d p = 70 μm 1200
1600 2000 2400 Particle temperature [K]
2800
1.0 Xc Xe
Xc , Xe
0.9 0.8 0.7 0.6 0.5
d p = 90 μm
0.4 1200
1600 2000 2400 Particle temperature [K]
2800
Fig. 4. Energy distribution coefficient and effective SF-CO energy distribution coefficient.
From the distributions of the energy distribution coefficient shown in Fig. 3, the typical values of Xc are X C ¼ 0:55 0:8; b > a ð12Þ X C ¼ 1:0; b ¼ a
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
Average Xc , Xe
1.0
1069
Xc Xe
0.8 0.6 0.4 0.2
X c (SF-CO)
0.0 0
20 40 60 80 Particle diameter [μm]
100
Fig. 5. Average energy distribution coefficient (1200–2400 K).
Fig. 4 shows the comparison between the dependence on particle size and temperature of the energy distribution coefficient Xc and the effective SF-CO energy distribution coefficient Xe. From Fig. 4 it can be observed that the patterns of variation of the effective SF-CO energy distribution coefficient Xe and the energy distribution coefficient Xc with particle temperature are similar. Different trends occur for small particles and under low particle temperature (<1600–1800 K) conditions, where the energy distribution coefficient is equal to 1.0 and the effective SF-CO energy distribution coefficient of most particles is less than 1.0 and decreasing with increasing particle temperature. By comparing Xe and Xc it can be observed that, at a given particle temperature, almost all the Xe are less than Xc by 0.2–0.3 on average, except under the condition that CO burns at the particle surface. This is because, within the particle temperature range investigated (1200– 2400 K), the influence of surface reduction of CO2 is comparatively small, and taking into account the oxidation of CO in the boundary layer of the particle increases the resistance to oxygen diffusion to the char surface (see Eq. (7)). Thus, the burning rate of a char particle calculated using the MFF model will be smaller than the combustion rate calculated using the SF-CO model, namely, qMFF < qSFS. Therefore, from Eq. (10), we see that Xe < Xc. Fig. 5 shows the average values of the energy distribution coefficient and the effective SF-CO energy distribution coefficient for different particle diameters over the range of particle temperatures investigated. From Fig. 5, we can see that the energy distribution coefficients is typically near 0.7, except for the case of particles having diameters of 10 lm when the energy distribution coefficient is close to 1.0. Compared with the energy distribution coefficient used by SF-CO model (Xc = 0.3), the effective SF-CO energy distribution coefficient Xe for the particle of 10 lm has a difference of about 0.6, and the difference for the particle of 30 lm is about 0.3. The average effective SF-CO energy distribution coefficient for other particle diameters is about 0.5, which is higher than the value normally used (Xc = 0.3) by about 0.2. This indicates that, by taking into account the homogeneous oxidation of CO in the boundary layer of a char particle, the fraction of the heat of combustion gained by the particle is found to increase with decreasing particle size. 5. Conclusions A method with which to determine the energy distribution coefficient for the char combustion process was developed using the improved moving flame front (MFF) model. Values of the energy distribution coefficient during the char combustion process were obtained for different particle sizes. A comparison of energy distribution coefficients from the MFF model and from the traditional Single Film with CO the only reaction product (SF-CO) model was presented using the effective SF-CO energy distribution coefficient. (1) The energy distribution coefficient considering the oxidation of CO in the boundary layer of a particle is larger than the energy distribution coefficient obtained when neglecting the oxidation of CO in the boundary layer of the particle. For the fuel characteristic parameters adopted for the calculations presented in this article, the average energy distribution coefficient is more than twice the energy distribution coefficient obtained using the SF-CO model (>0.6 versus 0.3).
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(2) The effective SF-CO energy distribution coefficient follows the same trend of variation with particle size as the energy distribution coefficient, but the effective SF-CO energy distribution coefficient is smaller. The average effective SF-CO energy distribution coefficient is approximately 0.5 or greater, which is 0.2 higher than the value of 0.3 used in the traditional SF-CO model. (3) The energy distribution coefficient is related to the fuel characteristic parameters and particle diameter. The smaller the particle diameter, the higher the energy distribution coefficient. The temperature range over which the energy distribution coefficient is equal to 1.0 (all of the heat of char combustion released at, or near, the char surface) is wider for smaller char particles than for larger ones.
Acknowledgements The authors of this paper gratefully acknowledge financial supports from the Chinese National Natural Science Fund, Grant No. 50476018, and The Special Fund for Key Fundamental Research of China, Grant No. 2004CB217703 and No. 2006CB200303, and the great help from Prof. P.M. Walsh in the University of Alabama at Birmingham, USA, in preparing the manuscript. References [1] Makino A, Law CK. Quasi-steady and transient combustion of a carbon particle: theory and experimental comparisons. In: 21st Symposium (international) on combustion. Pittsburg: The Combustion Institute; 1986. p. 183–91. [2] Lee JC, Yetter RA, Dryer FL. Transient numerical modeling of carbon particle ignition and oxidation. Combust Flame 1995;101:387–98. [3] Yu J. Study and modeling on the interaction of volatile flame, CO flame and char particle combustion. PhD dissertation. Shanghai JiaoTong University, 2003. [4] Kurose R, Makino H, Suzuki A. Numerical analysis of pulverized coal combustion characteristics using advanced low-NOx burner. Fuel 2004;83:693–703. [5] Xu M, Azrvedo JLT, Carvalho MG. Modelling of the combustion process and NOx emission in a utility boiler. Fuel 2000;79:1611–9. [6] Lockwood FC, Mahmud T, Yehia MA. Simulation of pulverized coal test furnace performance. Fuel 1998;77:1329–37. [7] Sun XX. Combustion experimental technology and method of pulverized coal utility boiler. Beijing: Electric Power Press; 2002 [in Chinese]. [8] Libby PA, Blake TR. Theoretical study of burning carbon particle. Combust Flame 1979;36:139–69. [9] Fu WB. The macro-general rules of coal combustion theories. Beijing: Tsinghua University Press; 2003 [in Chinese]. [10] Zhang MC, Yu J, Xu XC. A new flame sheet model to reflect the influence of the oxidation of CO on the combustion of a carbon particle. Combust Flame 2005;143:150–8. [11] Zhang MC, Yu J. An improved moving flame front model for combustion of a carbon particle with finite-rate heterogeneous oxidation and reduction. In: Proceedings of 6th Asia-Pacific conference on combustion, Nagoya, Japan, 20–23 May 2007, p. 158–61. [12] Han CY, Xu MH, Zhou HC, Qiu JR. Pulverized coal combustion. Beijing: Science Press; 2001 [in Chinese]. [13] Patankar SV. Numerical heat transfer and fluid flow. New York: Hemisphere Publishing Corporation; 1980. [14] Zhou LX. Theory and numerical modeling of turbulent gas-particle flows and combustion. Beijing, New York, Florida: Science Press, CRC Press; 1993. [15] Crowe CT, Sharma NP, Stock DE. The particle-source-in cell model for gas-dropper flows. Trans ASME J Fluids Eng 1977;99:325–32. [16] Field MA, Gill DW, Morgan BB, Hawksley PGW. The combustion of pulverized coal. Leatherhead, Surrey: BCURA; 1967. [17] Lockwood FC, Shan NG. A new radiation method for incorporation in general combustion prediction procedures. In: Eighteenth symposium (international) on combustion. Pittsburg: The Combustion Institute; 1981. p. 1405–14. [18] Godoy S, Hirji KA, Lockwood FC. Combustion measurements in a pulverized coal-fired furnace. Combust Sci Tech 1988;59:165–82.
APPLIED ENERGY Applied Energy 85 (2008) 1060–1070 www.elsevier.com/locate/apenergy
Numerical study on the spatial distribution of energy release during char combustion Gu Ming-yan a,b,*, Zhang Ming-chuan a,*, Yu Juan a, Fan Wei-dong a, Tian Feng-guo a a
School of Mechanical Engineering, Shanghai Jiaotong University, 800 Dong Chuan Road, Shanghai 200240, China b School of Metallurgy and Resources, Anhui University of Technology, Maanshan Anhui 243002, China Received 23 September 2005; received in revised form 14 December 2007; accepted 19 December 2007
Abstract The energy distribution coefficient (Xc), the fraction of the total heat of reaction released at the char surface during combustion of char particles, was studied using the improved moving flame front (MFF) model. The energy distribution coefficient (Xc), considering homogeneous oxidation of CO in the boundary layer of the particle and reduction of CO2 at the surface, was derived explicitly. Under conditions in practical pulverized coal flames, the energy distribution coefficient (Xc) and the effective energy distribution coefficient (Xe), based on the heat-release calculated using the traditional single film model with CO as the only reaction product (SF-CO), were calculated and compared with the value commonly used in the SF-CO model. The results obtained show that the smaller the particle diameter, the greater the energy distribution coefficient. For the same particle diameter, the higher the particle temperature, the lower the energy distribution coefficient. Under the conditions of the calculation, the average value of the energy distribution coefficient Xc is approximately 0.7, and the average value of the effective SF-CO energy distribution coefficient is greater than 0.5, significantly larger than the value of 0.3 obtained by the traditional single film model. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Pulverized coal flame; Combustion of char particle; Energy distribution coefficient; Moving flame front (MFF) model; Single film (SF-CO) model
1. Introduction The combustion of char particles in an oxidizing environment is complicated by several heterogeneous and homogeneous reactions occurring simultaneously or in series. The continuous-film model of modern combustion theory and experiment have demonstrated that, the influences of the volumetric reaction of CO and the surface reduction of CO2 on the particle temperature and the overall combustion rate of char particle * Corresponding authors. Address: School of Mechanical Engineering, Shanghai Jiaotong University, 800 Dong Chuan Road, Shanghai 200240, China. Tel.: +86 21 3420 6768; fax: +86 21 3420 6115. E-mail addresses: [email protected] (M.-y. Gu), [email protected] (M.-c. Zhang).
0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2007.12.006
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
Nomenclature a As b cP d1 d2 dP D D0 f h H k Kd Ks L P q Q Qr Qc T t U V W Xc Xe
radius of particle (m) particle surface area (m2) radius of CO flame front (m) specific heat (J/(kg K)) internal diameter of primary air channel external diameter of primary air channel diameter of particle (m) inner diameter of burner inner diameter of combustion chamber scalar mixture fraction fluid enthalpy (J/kg) heat released of reaction (J/(kg K)) turbulent kinetic energy (m2/s2) bulk diffusion rate constant (kg/(m2 s Pa)) chemical kinetics rate constant (kg/(m2 s Pa)) length of combustion chamber partial pressure (Pa) burning rate of char (kg/(m2 s)) heat flux (J/m2 s) radiative heat flux (J/(m2 s)) convection heat flux (J/(m2 s)) temperature (K) time (s) axial velocity (m/s) radial velocity (m/s) angular velocity (m/s) energy distribution coefficient effective SF-CO energy distribution coefficient
Subscripts and superscripts g gas p particle s particle surface ox pure oxidation condition re pure reduction condition Char char CO carbon monoxide CO2 carbon dioxide O2 oxygen MFF improved moving flame front model SFS Traditional single film model ’ reaction 2C + O2 ? 2CO ” reaction C + CO2 ? 2CO ”’ reaction C + O2 ? CO2 Greek symbols C/ turbulent exchange coefficient e rate of eddy dissipation (m2/s3)
1061
1062
eP k q
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
particle absorptivity coefficient of thermal conductivity (W/(m K)) density (kg/m3)
are extremely complex. The primary product, CO, of the char surface oxidation reaction, can be burnt in the boundary layer of the particle, increasing the char particles’ surface temperature by several hundred Kelvin [1–3]. This phenomenon cannot be understood or predicted by the traditional single film with CO the only reaction product (SF-CO) model. However, because of the complexity of treating the highly nonlinear heat release and mass transfer coupling, the SF-CO model is still widely used in the numerical simulation of pulverized coal combustion [4–6]. In the SF-CO model, it is supposed that there is no further change in the primary combustion product, CO, in the boundary layer of the particle, thus the fraction of the total heat of char combustion released on or near the particle surface, termed in the present work the ‘‘energy distribution coefficient”, Xc, takes the value of 0.3, approximately [4,7]. In the past 20 years, much theoretical work on the combustion of char particles has been carried out. As a result, some explicit and semi-explicit expressions are available to calculate the combustion rate of a char particle [8–11], offering the possibility to easily analyze the influence of CO combustion in the boundary layer of the particle on the particle temperature and combustion rate. The present paper studies the energy distribution coefficient in combustion of char particles using the improved moving flame front (MFF) model. The improved MFF model takes into account the surface reactions of carbon with both oxygen and carbon dioxide, and the volumetric oxidation of carbon monoxide in the boundary layer of the particle, while it presents explicit algebraic expressions for the combustion rate and the particle temperature. The results of calculations using the improved MFF model are very close to the results obtained by solving the differential equations of the continuous-film model. However, the calculation time for the former is only a tiny fraction of that for the latter [3,10,11]. 2. Energy distribution coefficient In the calculation of pulverized coal combustion, the char particle temperature is calculated from the heat balance equation. Supposing that the temperature of a char particle is uniform, the energy equation for the particle is mP dðcP T s Þ ¼ Qc þ Qr þ Qb dt AS
ð1Þ
where Qr is calculated from Qr ¼ rep ðT 4g T 4s Þ; Qc is calculated from Qc = (Tg Ts)km/a; Qb is the heat flux on the particle surface released by char combusting, presented in the form of a proportion of the heat release by complete combustion of char to CO2 [4,7]: Qb = Xc q H000 . When the traditional SF-CO model is used to calculate the char combustion rate, the primary combustion product is assumed to be CO and there is no further change in the primary combustion product in the boundary layer of the particle. Therefore, the heat flux at the particle surface released by char combustion is Qb = q H0 , and the corresponding energy distriQb qH 0 bution coefficient is X c ¼ qH 000 ¼ qH 000 0:3. On the other hand, if we assume that CO2 is immediately formed by burning CO at the particle surface, then, Xc = 1. In the numerical simulation of pulverized coal combustion, Xc is usually assumed to be an empirical value slightly larger than 0.3. But the value chosen has no strict theoretical foundation. In what follows, the energy distribution coefficient is deduced using the improved MFF model to calculate the char burning rate. Ignoring radiative heat exchange, the particle temperature in steady state is [3,11] a a a2 1 T s ¼ T g þ ðq0 H 0 q00 H 00 Þ 1 þ ðq0 þ q00 ÞH 000 ð2Þ b km b km km is the average coefficient of thermal conductivity of gas within the boundary layer. The radius of the CO flame front, b, is determined by [11]
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
b ¼ a
b q0 b q00 þ a ox q a re q
1063
ð3Þ
where P 2 þ 12 P g;CO b g;O2 ¼ a ox K d;O2 þ 1 1 P g;CO K d;O2 þ 1 2 P g;O K s;O K s;O 2
2
and
K d;CO2 P 2 1 þ Pg;CO K d;O2 b g;O2 ¼2 K d;CO2 a re 1þ
2
K s;CO2
Compared with the SF-CO model, in which there are no homogeneous reactions in the boundary layer of the particle, the relation between the equivalent heat flux Qb released by char combustion on the particle surface and the particle temperature is: a ð4Þ T s ¼ T g þ Qb km From Eqs. (2) and (4), Qb can be obtained as follows: a a Qb ¼ ðq0 þ q00 ÞH 000 þ ðq0 H 0 q00 H 00 Þ 1 b b
ð5Þ
q00 and q are given by [3,11] q a P g;CO2 þ K d;CO b 2 q ¼ 1 1 þ K d;CO 1 ab K s;CO2 h 2 i 1 1 P g;O2 þ q00 K s;O þ K d;O 1 ab 2 2 a q¼ 1 1 þ 1þb K s;O K d;O 00
2
ð6Þ
ð7Þ
2
q0 can be obtained by subtraction of Eqs. (6) and (7): q0 = q q00 . Qb can be calculated by substituting q0 , q00 , and b into Eq. (5). Therefore, the energy distribution coefficient, taking into consideration the oxidation of CO in the boundary layer of the particle and the surface reduction of CO2 is obtained as ðq0 þ q00 ÞH 000 ab þ ðq0 H 0 q00 H 00 Þ 1 ab ð8Þ XC ¼ qH 000 Substituting q = q0 + q00 into Eq. (8), we then find: a ðq0 H 0 q00 H 00 Þ 1 ab XC ¼ þ b qH 000
ð9Þ
In order to take into account CO combustion in the boundary layer of a particle and the surface reduction of CO2 on the basis of the traditional SF-CO model, this paper brings forward the concept of effective SF-CO energy distribution coefficient Xe: Xe ¼
QbMFF qSFS H 000
ð10Þ
where QbMFF is the equivalent heat released by char burning at the particle surface, calculated using the MFF model, and qSFS is the char burning rate calculated from the SF-CO model. This means that the coefficient Xe can be used directly in the traditional SF-CO model, taking into consideration CO oxidation in the boundary layer of the particle and the surface reduction of CO2, but with the computational program remaining unchanged. 3. Numerical calculation of the energy distribution coefficient For numerical simulation of pulverized coal combustion, we choose a specific pulverized coal burner as the subject for investigation, to study the energy distribution coefficient.
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3.1. Mathematical models The mathematical model is based on an Eulerian description of the continuous phase and a stochastic Lagrangian description for the coal particles. The gas-phase time-averaged continuity equation and conservation equations of momentum, turbulent kinetic energy (k), dissipation (e), enthalpy (h) and species (f) in cylindrical coordinates are [12] o o o o o/i o o/i o o/i ðqU /i Þ þ ðrqV /i Þ þ ðqW /i Þ ¼ CU rCU CU þ þ þ S U þ S UP ox ror roh ox ror roh ox or roh ð11Þ A standard k–e model is used for the modeling of turbulence. The computations are performed on a threedimensional non-uniform 55 45 11 grid. The continuity and momentum equations are solved using the SIMPLE algorithm [13]. Representative coal particle trajectories are calculated by solving the particle equation of motion for the three components [14]. The interaction of the conserved properties between the gasphase and coal particles is calculated using the Particle-Source-In-Cell technique [15]. The poly-disperse size distribution of coal is divided into discrete particle size groups, assuming a Rosin–Rammler distribution [16]. The radiant intensity is calculated by the discrete transfer method of Lockwood and Shah [17]. 3.2. Combustion chamber geometry and case description The data on the combustion chamber, coal properties and operating conditions are available in Refs. [6,18]. Fig. 1 is a schematic diagram of the pulverized coal combustion chamber. The test fuel is a high volatile bituminous coal. The coal properties, operating conditions and combustion parameters are given in Tables 1–4. 4. Results and discussions Figs. 2–4 are the results of calculations of the energy distribution coefficient for different particle diameters. Because the calculation of particle motion adopted a stochastic trajectory model, we randomly selected data for trajectories of particles having diameters of 10, 30, 50, 70, and 90 lm for statistical analysis. The data in the figures are for char burning following complete release of volatiles from the coal. Fig. 2 shows the ratio b/a, i.e. the ratio of the CO flame sheet radius in the boundary layer of a particle to the particle radius, for different particle diameters, and the corresponding values of the energy distribution d1
Primary air + Pulverized coal
D0
Secondary air
d2 L D
Fig. 1. Schematic of pulverized coal combustion chamber.
Table 1 Dimension of combustion chamber [6,18] D0 (m)
L (m)
d1 (m)
d2 (m)
D (m)
0.6
3.0
0.022
0.035
0.056
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Table 2 Characteristics of coal [6,18] Proximate analysis (wt%, as received) Volatile Fixed carbon Moisture Ash
35.8 53.7 6.3 4.2
Ultimate analysis (wt%, as received) Carbon Hydrogen Sulphur Oxygen (by diff.) Nitrogen Particle average size (lm) Gross calorific value (MJ/kg)
72.6 5.05 1.55 15.31 1.29 45 29.29
Table 3 Coal combustion parameters [6,18] Coal devolatization parameters a1 (s1) a2 (s1) k1 (kJ/kmol) k2 (kJ/kmol)
3.7 105 1.5 1013 7.4 104 2.5 105
Carbon reaction (2C + O2 ? 2CO) A (kg/(m2 s Pa)) k (kJ/kmol)
0.86 1.495 105
Carbon reaction (C + CO2 ? 2CO) A (kg/(m2 s Pa)) k (kJ/kmol)
4.3 2.7 105
Table 4 Operating conditions [6,18] Coal feed rate (kg/h) Primary air flow rate (kg/h) Secondary air flow rate (kg/h) Primary air swirl number Secondary air swirl number Primary air temperature (°C) Secondary air temperature (°C)
14.0 31.3 120.0 0 1.03 80 300
coefficient Xc. From Fig. 2, it can be observed that, depending upon the particle diameter, when the particle temperature is below a certain value, CO burns on the particle surface, that is b/a = 1, and the corresponding value of the energy distribution coefficient is Xc = 1.0. This is because when the particle temperature is below this critical temperature the diffusion rate coefficient is larger than the chemical kinetic rate coefficient, and the primary product, CO, is directly oxidized to CO2 at the particle surface. The smaller the particle diameter, the larger the diffusion rate coefficient, and the wider the temperature range in which b/a = 1. From the comparison of energy distribution coefficients for the particle diameters dP = 10 lm and dP = 50 lm, it can be observed that, for dP = 10 lm, when the particle temperature is 2000 K, the CO flame front may still be located on the particle surface; whereas, for dP = 50 lm, the CO flame front separates from the surface when the particle temperature is about 1700 K, and the energy distribution coefficient decreases with increasing b/a.
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0.8
b/a xc
1.4
0.7
d p =10 μ m
1.2
xc
0.9
1.6
0.6
1.0
0.5
1000
1500 2000 2500 Particle temperature [K]
2.0 1.0 0.9
1.6
0.8
1.4
b/a xc
0.7
1.2
d p =30 μ m
0.6
1.0
xc
b/a
1.8
0.5 1200
1500 1800 2100 2400 Particle temperature [K]
2.0 1.0 0.9
1.6 b/a xc d p =50 μ m
1.4 1.2 1.0
0.8 xc
b/a
1.8
0.7 0.6 0.5
1400 1600 1800 2000 2200 2400 Particle temperature [K] 2.0 1.0 1.8
0.9
1.4 1.2
b/a xc d p =70 μ m
1.0 1400
0.8 xc
b/a
1.6
0.7 0.6 0.5
1600 1800 2000 2200 Particle tem perature [K]
2.0 1.0 1.6 1.4 1.2 1.0
0.9 b/a xc d p =90 μ m
0.8
xc
b/a
1.8
0.7 0.6 0.5
1400 1600 1800 2000 2200 Particle temperature [K]
Fig. 2. CO flame front radius and energy distribution coefficient.
Fig. 3 shows the range and probability of occurrence of the values for the energy distribution coefficient. From this figure, it is seen that, with increasing particle diameter, the probability of the energy distribution coefficient being 1.0 decreases from 90% when dP = 10 lm to about 4% when dP = 90 lm. The fraction of
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
d p = 10 μm
0.8 Probability
1067
0.6 0.4 0.2 0.0 0.5
0.6
0.7
0.8
0.9
1.0
Xc
0.25 d p = 30 μm
Probability
0.20 0.15 0.10 0.05 0.00 0.5
0.6
0.7
0.8
0.9
1.0
Xc
0.20 d p = 50 μm
Probability
0.16 0.12 0.08 0.04 0.00 0.5
0.6
0.7
0.8
0.9
1.0
Xc
0.20 d p = 70 μm
Probability
0.16 0.12 0.08 0.04 0.00 0.5
0.6
0.7
0.8
0.9
1.0
Xc
0.10 d p =90 μm
Probability
0.08 0.06 0.04 0.02 0.00 0.5
0.6
0.7
0.8
0.9
1.0
Xc
Fig. 3. Distributions of the energy distribution coefficient.
the total burning time during which combustion of CO occurs at the particle surface decreases markedly with increasing particle size.
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Xc , X e
0.9 0.8 0.7 0.6 0.5
Xc Xe d p = 10 μm
1200
1600 2000 2400 Particle temperature [K]
2800
1.0
Xc , Xe
0.9 0.8 0.7 0.6 0.5
Xc Xe d p = 30 μm
0.4 1200
1600 2000 2400 Particle temperature [K]
2800
1.0
X c , Xe
0.9 0.8 0.7 0.6 0.5 0.4
Xc Xe d p = 50 μm
1200
1600 2000 2400 Particle temperature [K]
1.0
Xc Xe
0.9 Xc , Xe
2800
0.8 0.7 0.6 0.5 0.4
d p = 70 μm 1200
1600 2000 2400 Particle temperature [K]
2800
1.0 Xc Xe
Xc , Xe
0.9 0.8 0.7 0.6 0.5
d p = 90 μm
0.4 1200
1600 2000 2400 Particle temperature [K]
2800
Fig. 4. Energy distribution coefficient and effective SF-CO energy distribution coefficient.
From the distributions of the energy distribution coefficient shown in Fig. 3, the typical values of Xc are X C ¼ 0:55 0:8; b > a ð12Þ X C ¼ 1:0; b ¼ a
M.-y. Gu et al. / Applied Energy 85 (2008) 1060–1070
Average Xc , Xe
1.0
1069
Xc Xe
0.8 0.6 0.4 0.2
X c (SF-CO)
0.0 0
20 40 60 80 Particle diameter [μm]
100
Fig. 5. Average energy distribution coefficient (1200–2400 K).
Fig. 4 shows the comparison between the dependence on particle size and temperature of the energy distribution coefficient Xc and the effective SF-CO energy distribution coefficient Xe. From Fig. 4 it can be observed that the patterns of variation of the effective SF-CO energy distribution coefficient Xe and the energy distribution coefficient Xc with particle temperature are similar. Different trends occur for small particles and under low particle temperature (<1600–1800 K) conditions, where the energy distribution coefficient is equal to 1.0 and the effective SF-CO energy distribution coefficient of most particles is less than 1.0 and decreasing with increasing particle temperature. By comparing Xe and Xc it can be observed that, at a given particle temperature, almost all the Xe are less than Xc by 0.2–0.3 on average, except under the condition that CO burns at the particle surface. This is because, within the particle temperature range investigated (1200– 2400 K), the influence of surface reduction of CO2 is comparatively small, and taking into account the oxidation of CO in the boundary layer of the particle increases the resistance to oxygen diffusion to the char surface (see Eq. (7)). Thus, the burning rate of a char particle calculated using the MFF model will be smaller than the combustion rate calculated using the SF-CO model, namely, qMFF < qSFS. Therefore, from Eq. (10), we see that Xe < Xc. Fig. 5 shows the average values of the energy distribution coefficient and the effective SF-CO energy distribution coefficient for different particle diameters over the range of particle temperatures investigated. From Fig. 5, we can see that the energy distribution coefficients is typically near 0.7, except for the case of particles having diameters of 10 lm when the energy distribution coefficient is close to 1.0. Compared with the energy distribution coefficient used by SF-CO model (Xc = 0.3), the effective SF-CO energy distribution coefficient Xe for the particle of 10 lm has a difference of about 0.6, and the difference for the particle of 30 lm is about 0.3. The average effective SF-CO energy distribution coefficient for other particle diameters is about 0.5, which is higher than the value normally used (Xc = 0.3) by about 0.2. This indicates that, by taking into account the homogeneous oxidation of CO in the boundary layer of a char particle, the fraction of the heat of combustion gained by the particle is found to increase with decreasing particle size. 5. Conclusions A method with which to determine the energy distribution coefficient for the char combustion process was developed using the improved moving flame front (MFF) model. Values of the energy distribution coefficient during the char combustion process were obtained for different particle sizes. A comparison of energy distribution coefficients from the MFF model and from the traditional Single Film with CO the only reaction product (SF-CO) model was presented using the effective SF-CO energy distribution coefficient. (1) The energy distribution coefficient considering the oxidation of CO in the boundary layer of a particle is larger than the energy distribution coefficient obtained when neglecting the oxidation of CO in the boundary layer of the particle. For the fuel characteristic parameters adopted for the calculations presented in this article, the average energy distribution coefficient is more than twice the energy distribution coefficient obtained using the SF-CO model (>0.6 versus 0.3).
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(2) The effective SF-CO energy distribution coefficient follows the same trend of variation with particle size as the energy distribution coefficient, but the effective SF-CO energy distribution coefficient is smaller. The average effective SF-CO energy distribution coefficient is approximately 0.5 or greater, which is 0.2 higher than the value of 0.3 used in the traditional SF-CO model. (3) The energy distribution coefficient is related to the fuel characteristic parameters and particle diameter. The smaller the particle diameter, the higher the energy distribution coefficient. The temperature range over which the energy distribution coefficient is equal to 1.0 (all of the heat of char combustion released at, or near, the char surface) is wider for smaller char particles than for larger ones.
Acknowledgements The authors of this paper gratefully acknowledge financial supports from the Chinese National Natural Science Fund, Grant No. 50476018, and The Special Fund for Key Fundamental Research of China, Grant No. 2004CB217703 and No. 2006CB200303, and the great help from Prof. P.M. Walsh in the University of Alabama at Birmingham, USA, in preparing the manuscript. References [1] Makino A, Law CK. Quasi-steady and transient combustion of a carbon particle: theory and experimental comparisons. In: 21st Symposium (international) on combustion. Pittsburg: The Combustion Institute; 1986. p. 183–91. [2] Lee JC, Yetter RA, Dryer FL. Transient numerical modeling of carbon particle ignition and oxidation. Combust Flame 1995;101:387–98. [3] Yu J. Study and modeling on the interaction of volatile flame, CO flame and char particle combustion. PhD dissertation. Shanghai JiaoTong University, 2003. [4] Kurose R, Makino H, Suzuki A. Numerical analysis of pulverized coal combustion characteristics using advanced low-NOx burner. Fuel 2004;83:693–703. [5] Xu M, Azrvedo JLT, Carvalho MG. Modelling of the combustion process and NOx emission in a utility boiler. Fuel 2000;79:1611–9. [6] Lockwood FC, Mahmud T, Yehia MA. Simulation of pulverized coal test furnace performance. Fuel 1998;77:1329–37. [7] Sun XX. Combustion experimental technology and method of pulverized coal utility boiler. Beijing: Electric Power Press; 2002 [in Chinese]. [8] Libby PA, Blake TR. Theoretical study of burning carbon particle. Combust Flame 1979;36:139–69. [9] Fu WB. The macro-general rules of coal combustion theories. Beijing: Tsinghua University Press; 2003 [in Chinese]. [10] Zhang MC, Yu J, Xu XC. A new flame sheet model to reflect the influence of the oxidation of CO on the combustion of a carbon particle. Combust Flame 2005;143:150–8. [11] Zhang MC, Yu J. An improved moving flame front model for combustion of a carbon particle with finite-rate heterogeneous oxidation and reduction. In: Proceedings of 6th Asia-Pacific conference on combustion, Nagoya, Japan, 20–23 May 2007, p. 158–61. [12] Han CY, Xu MH, Zhou HC, Qiu JR. Pulverized coal combustion. Beijing: Science Press; 2001 [in Chinese]. [13] Patankar SV. Numerical heat transfer and fluid flow. New York: Hemisphere Publishing Corporation; 1980. [14] Zhou LX. Theory and numerical modeling of turbulent gas-particle flows and combustion. Beijing, New York, Florida: Science Press, CRC Press; 1993. [15] Crowe CT, Sharma NP, Stock DE. The particle-source-in cell model for gas-dropper flows. Trans ASME J Fluids Eng 1977;99:325–32. [16] Field MA, Gill DW, Morgan BB, Hawksley PGW. The combustion of pulverized coal. Leatherhead, Surrey: BCURA; 1967. [17] Lockwood FC, Shan NG. A new radiation method for incorporation in general combustion prediction procedures. In: Eighteenth symposium (international) on combustion. Pittsburg: The Combustion Institute; 1981. p. 1405–14. [18] Godoy S, Hirji KA, Lockwood FC. Combustion measurements in a pulverized coal-fired furnace. Combust Sci Tech 1988;59:165–82.