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Numerical Simulation and Optimization of NO Emissions in a Precalciner Lai Huang,† Jidong Lu,*,† Zhijuan Hu,‡ and Shijie Wang† State Key Laboratory of Coal Combustion, Huazhong UniVersity of Science and Technology, Hubei, Wuhan 430074, People’s Republic of China, and Tianjin Cement Industrial Design and Research Institute, Tianjin 300400, People’s Republic of China ReceiVed September 3, 2005. ReVised Manuscript ReceiVed October 29, 2005
For cement plants, great attention is being given to the emission of the pollutant gases, especially NO. Because of the increasingly stringent emission constraints at cement plants, it is becoming more important to predict emissions accurately and then decrease the release quantity. The precalciner is an important apparatus in the cement production process, in that it can reduce not only the heat loading of the rotary kiln but also the NO emission, because of its relative low operating temperature. In this paper, the NO release was simulated based on the full-scale modeling for the precalciner and the model results were compared with measurements to validate the simulation models. The optimum cases of air staging and fuel staging were analyzed by executing a simulation technique on the restructuring precalciner with no effect on the operation process, and the conclusion is that the fuel staging case is the optimum method economically.
1. Introduction Cement production involves the thermal conversion of a raw material consisting of ∼75%-80% CaCO3 to clinker. Raw material is produced by finely grinding and homogenizing the raw materials. It is subsequently preheated by heat exchange with the hot process gases, then calcined, converted to clinker, cooled by heat exchange with coal combustion air, and finally ground with gypsum to form cement. The pyroprocessing operations typically occur in a kiln system, which comprises a preheater, a precalciner, a rotary kiln, and a clinker cooler. The function of the preheater is preheating the raw materials, and then the preheated raw materials enter into the precalciner to decompose previously, the partially decomposed raw materials flow with the flue into the rotary kiln and decompose further. The precalciner systems are being increasingly used in the cement industry for intermediate feed conditioning, prior to the conventional rotary cement kiln. Advantages include the ability to use a wide range of fuel types and quality, and to increase significantly the production capacity of kilns, thereby helping to reduce the mechanical problems associated with increasing kiln size. The calcination of CaCO3 is strongly endothermic and the most energy demanding reaction. The fuels most commonly used for cement production are pulverized coal or petcoke. Large fuel consumption results in cement production having a significant emission potential for combustion-generated pollutants, of which NOx is a major concern. NOx is primarily formed at two positions in kiln systems for cement clinker production: in the rotary kiln and precalciner (Figure 1). In the rotary kiln, NOx is formed both from atmospheric N2 and from fuel-bound nitrogen, whereas, in the precalciner, only NOx can be formed from fuel-bound nitrogen, because of the low operating tem* Author to whom correspondence should be addressed. Tel.: 86-2787548586. Fax: 86-27-87545526. E-mail:
[email protected]. † Huazhong University of Science and Technology. ‡ Tianjin Cement Industrial Design and Research Institute.
peratures. Because of the high clinkering temperature, it is difficult to reduce NOx formation significantly in the rotary kiln. Therefore, primary measures for reducing NOx formation have mainly been focused on optimizing precalciner design, with respect to controlling NOx emission. Focus has particularly been on in-line precalciner-type kiln systems, where the flue gas from the rotary kiln is passed through the precalciner. This is because this type of kiln system allows NOx from the rotary kiln to react with the fuel fired in the precalciner and thereby be partially reduced to N2.11 The air-staging and fuel-staging techniques have been used in boiler for reducing NOx emission maturely,2-7 and these techniques can be drawn to reduce NOx emission for the precalciner. The influences on NOx emission in the precalciner are sophisticated with fuel type (bovey coal, bituminous coal, or anthracite coal), combustion type (oxidized or deoxidized atmosphere), burn condition (premix or diffuse combustion), and raw material decomposition (raw material types). Therefore, (1) Jensen, L. S. NOx from cement production-reduction by primary measures, Ph.D. Thesis, Technical University of Denmark, Lyngby, Denmark, 1990. (2) Hill, S. C.; Smoot, L. D.; Smith, P. J. Prediction of Nitrogen Oxide Formation in Turbulent Coal Flames. In The 20th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1984; pp 13911400. (3) Fiveland, W. A.; Wessel, R. A.; Eskinazi, D. Pollutant Model for Predicting Formation and Reduction of Nitric Oxides in Three-Dimensional, Pulverized-Fuel-Fired Furnaces. Presented at The 24th National Heat Transfer Conference, Pittsburgh, PA, 1987. (4) Wennerberg, D. Prediction of Pulverized Coal and Peat Flames. Combust. Sci. Technol. 1991, 58, 25-41. (5) Truelove, J. S.; Holcmbe, D. Measurement and Modeling of Coal Flame Stability in a Pilot Scale Combustor. In The 23th Symposium (International) on Combustion; The Combustion Institute, Pittsburgh, PA, 1990; pp 963-971. (6) Abbas, T.; Costa, M.; Costen, P.; Lockwood, F. C. Nitrous Oxide Emission From an Industry Type Pulverized Coal Burner. Combust. Flame 1991, 87, 104-108. (7) Epple B.; Schnell, U. Modeling and Simulation of Coal Combustion Processes in Utility Bolier Furnaces. Presented at the ICHMT 2nd International Forum on Expert Systems and Computer Simulation in Energy Engineering, Erlangen, Germany, March 17-20, 1992, Paper No. 12L.
10.1021/ef0502857 CCC: $33.50 © 2006 American Chemical Society Published on Web 11/25/2005
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Figure 1. Schematic plan of the production position of NO.
then absorb heat from the surrounding gas and decompose. The temperature in the DD-PRC is approximately in the range of 11101400 K. The processes of coal combustion and raw material calcination occur simultaneously, and the all inlet materials exit from the outlet located in the upper body of the DD-PRC.
3. Mathematical Models 3.1. Fluid Phase. The fluid phase turbulence is modeled using a renormalization group (RNG) k- model.8 The motion of the gas phase is described by the elliptic partial differential conservation equations for a Newtonian fluid in a threedimensional cylindrical coordinate system. The general form of the differential equations for the gas phase is given by the following equation:
div(FνΦ) - div(ΓΦ grad Φ) ) SΦ + SP,Φ
Figure 2. Abridged general view of the 2500 t/d dual combustion and denitrator process precalciner (DD-PRC): (A) front view and (B) top view.
the aim of the paper is to simulate the full-scale operating dual combustion and denitrator process precalciner (DD-PRC) and compare the model results with measurements results to validate the mathematical model, and then optimize the operation at the air staging or fuel staging condition to reduce the NOx emission. 2. Structure and Process Description Figure 2 illustrates a schematic view of DD-PRC. The exhaust gas from the end of rotary kiln is fed into the DD-PRC from the bottom inlet, the tertiary air and the raw material enter into the chamber through inlet pipes, and the coal and the secondary air flow into the DD-PRC from two pipes at certain angles. The temperature of exhaust gas is ∼1400 K, and the tertiary air temperature is ∼1100 K. The coal particles are heated to ignition temperature, and they release a great amount of heat to raise the temperature of the surrounding gas and the raw material particles,
(1)
Here, SΦ is the source term of the gas phase, SP,Φ the source term from the interaction with the particle phase, and ΓΦ the effective viscosity. The detail forms for different variables Φ are summarized in Table 1. In Table 1, p represents fluid pressure, the parameters u, V, and w represent the three velocity components, k represents the turbulent kinetic energy, and represents the turbulent dissipation rate. The Reynolds stress terms in the conservation equations are approximated using the Boussinesq eddy viscosity model. 3.2. Particle Phase. The motion of the particle phase is treated by solving the Lagrangian equations for the trajectory of a statistically significant sample of individual particles; the sample represents several of the real particles with the same properties. The motion of the particle is determined by varying the velocity components derived from a stochastic model developed by Fan et al.8 The particle trajectories are tracked throughout the computational domain, and the interaction between the particles and the gas is incorporated by the proper cross source terms in the balance equations of mass, momentum, and energy. The coal particles are assumed to be composed of volatile matter, char, ash, and moisture; their evolution is (8) Fan, J. R.; Zhang, X. Y.; Chen, L. H.; Cen, K. F. New Stochastic Particle Dispersion Modeling of a Turbulent Particle-laden Round Jet. Chem. Eng. J. 1997, 66, 207-215.
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Table 1. Eulerian Conservation Equations and Identification of Terms in Eq 1a Φ 1
S ) SΦ + SP,Φ
ΓΦ 0
SP,m
∂u ∂V ∂w ∂ ∂p 1 ∂ 1 ∂ - + µ + rµ + µ + SP,u ∂x ∂x eff ∂x r ∂r eff ∂x r ∂θ eff ∂x
(
u
µeff
V
µeff
w
µeff
k
µeff/σk
µeff/σ
( )
)
(
(
)
)
[
(
)
]
(
)
2µeff 1 ∂w V r∂(w/r) ∂u ∂V ∂ ∂p 1 ∂ 1 ∂ Fw2 + + + + SP,V µeff + rµeff + µeff ∂r ∂x ∂r r ∂r ∂r r ∂θ ∂r r r ∂θ r r µ ∂(w/r) FVw 1 ∂w 2V eff ∂V 1 ∂p 1 ∂ 1 ∂ ∂u 1 ∂V w ∂ µ + r + + + SP,w µ + rµ + + r r ∂r r ∂θ r r ∂θ ∂x eff r ∂θ r ∂r eff r ∂θ r r ∂θ eff r ∂θ µeff ∂u 2 ∂V 2 ∂w V 2 ∂u ∂V 2 ∂w 1 ∂V ∂w w 2 ∂u 2 FGk - F + SP,k, Gk ) 2 + + + + + + + + + F ∂x ∂r r∂θ r ∂r ∂x ∂x r∂θ r ∂θ ∂r r 2 η[1 - (η/η0)]b GkCRNG - C2F + SP, CRNG ) C1 k k 1 + β η3 -
(
)
)] [ ( { [( ) ( ) (
[ (
)] (
) )] ( ) ( ) (
)}
0
a The following variables and constants are used throughout this table: µ 2 eff ) µt + µ, µt ) CµFk /, Cµ ) 0.085, C1 ) 1.42, C2 ) 1.68, β0 ) 0.015, η0 ) 4.38, σk ) σ ) 0.7179. b In this equation, η ) Sk/ and S ) (FGk/µt)1/2.
described in sequence by drying, devolatilization, and char combustion, the particle diameters are treated as constant, and the density changes with time. The coal-devolatilization is modeled by a two-step mechanism and the product gas resulting from the coal-devolatilization participates in the gaseous reaction. The residual char particles are considered to be spherical, and they burn under the control of a combination of external oxygen transfer and internal kinetic rates. A shrink-core model for raw material calcination is used:
1 - (1 - γ)1/3 )
k0 E Pe - PCO2 exp t DP RT Pe
log Pe ) -
(
)
9300 + 6.86 T
(a) The release rate of fuel nitrogen is proportional to the volatile rate; (b) The content distributions of nitrogen in char and in volatile are uniform; (c) Volatile nitrogen is instantaneously released by means of HCN; (d) The transform rate of nitrogen char to NO is proportional to the char combustion rate; and (e) Thermal-NO and prompt-NO can be ignored. The reaction mechanism is characterized through
(2) (3)
Here, γ is the decomposition ratio (γ ) M′raw_material/ Mraw_material, where M′raw_material is the mass of decomposed raw material and Mraw_material is the original mass of raw material (0 e γ e 1)), k0 is the decomposition rate constant, and the variables E, R, T, and DP represent, respectively, the activation energy, the molar gas constant, the temperature of raw material particle, and the diameter of raw material particle; Pe represents the equilibrium CO2 pressure for raw material calcinations,9 PCO2 is the partial pressure of CO2, and t is the time. It is specified that E ) 92 465 J/mol, and k0 ) 0.004428 m/s (for PCO2 e Pe) or k0 ) 0 m/s (for PCO2 > Pe). 3.3. Formation of NO. It is known that the NO formation mechanism is rather complex, part of which is still not yet clear. Although probability density function (PDF) models have been introduced to simulate the reaction mechanism numerically, it is difficult to apply this type of model to the coal combustion in multiphase reaction flows, because of the great computational demand. Considering the present state of engineering application and numerical computation, the mechanic model of De’Soete10 is adopted here to simulate the fuel-NO formation. This model has been used widely,3,11-13 and its characteristics are as follows: (9) Mu¨ller, A.; Stark, J. Contribution to the Kinetics of Calcium Carbonate Dissociation. ZKG Int. 1979, 32, 78-82. (10) De’Soete, G. G. Overall Reaction Rates of NO and N2 Formation From Fuel Nitrogen. In The 15th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1975; pp 1093-1102. (11) Hill, S. C.; Smoot, L. D.; Smith, P. J. Prediction of Nitrogen Oxide Formation in Turbulent Coal Flames. In The 20th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1984; pp 13911400.
The nitrogen in coal is released, along with the pulverized coal pyrolysis and the char combustion, and it then reacts with gas and generates inter-component HCN. Even though there are other NHj components produced, it is assumed that all the interproductions are HCN as in the mechanism model of De’Soete. The release rate Rcoal-HCN of nitrogen in coal is proportional to the mass weakening rate (Sp) during coal pyrolysis and char combustion (eq 5):
RcoalfHCN )
27 N SY 14 p coal
(5)
In the above model, the number 27 is the molecular weight of HCN, 14 is the molecular weight of nitrogen, and YNcoal is the mass fraction of nitrogen in coal. After its production, the HCN oxidizes and becomes NO, and the reaction rate is12
(
RHCNfNO ) 1011FYHCN(YO2)b exp -
)
33700 Tg
(6)
where YHCN and YO2 are the mass fractions of component HCN and O2, and the exponent coefficient b, as proposed by De’Soete,10 can be expressed as a linear function of oxygen concentration XO2: (12) Fiveland, W. A.; Wessel, R. A.; Eskinazi, D. Pollutant Model for Predicting Formation and Reduction of Nitric Oxides in Three-Dimensional, Pulverized-Fuel-Fired Furnaces. Presented at the 24th National Heat Transfer Conference, Pittsburgh, PA, 1987. (13) Coelho, L. R.; Azevedo, J. L. T.; Carvalho, M. G. Numerical Simulation and Comparison of NOx Emissions from a Low NOx Front Wall Fired Boiler for Different Operating Conditions. In Proceedings of the 3rd International Symposium on Coal Combustion (ISCC), Beijing, PRC, Sept. 18-21, 1995; pp 617-624.
NO Emission in Precalciner
{
(for ln(XO2) e -5.5)
b ) 1.0 b ) 0.2 - 0.8 ln(XO2) b ) 0.071(-ln(XO2) - 3.0) b ) 0.0
(for -5.5 < ln(XO2) e -4.5)
2.5
(for -4.5 < ln(XO2) e -3.0) (for -3.0 < ln(XO2))
Energy & Fuels, Vol. 20, No. 1, 2006 167
}
Table 2. Parameters of Inlets
(7)
(
)
30 000 Tg
(10)
3.4. Transportation Equations of HCN and NO. The concentration of NO can be obtained by solving the transportation equations and variances of component mass fraction of YHCN and YNO in a cylindrical coordinate system (see eq 11):
)
∂Yj ∂ ∂ ∂ ∂ Γ + (FwYj) + (rFVYj) + (FuYj) ) ∂x r ∂r r ∂θ ∂x Yj ∂x ∂Yj ∂ ∂ ΓYj ∂Yj ΓYjr + + SYj (j ) HCN, NO) (11) r ∂r ∂r r ∂θ r ∂θ
)
(
)
1109 1383 338 338 1043
amount (wt %) 1.24 30.45 48.04 20.27
Ultimate Analysis carbon hydrogen oxygen (by difference) nitrogen sulfur
62.14 3.238 10.698 1.22 1.194
specific energy (LHV)b of coal (MJ/kg)
25.33
b
Note: ad means “air-dry”. Lower heating value. Table 4. Components Analysis of Raw Material
RNO+CaO ) (39816 × 108)FgYNOYCOe(-8920/Tg)
(
21.94 15.34 2.1 2.32 44.69
Proximate Analysis
a
the reaction rate is
(
tertiary air exhaust gas coal secondary air raw material
moisture volatile matter fixed carbon ash
(8)
(9)
temp (K)
component
Because the deoxidation action of char on NO is very limited,3,11 it is neglected in this work. In the precalciner, the CaO forms from the decomposition of raw material, and it has a catalysis effect on the NO reduced to N2:14 CaO 1 NO + CO 98 CO2 + N2 2
mass flow (kg/s)
Table 3. Proximate and Ultimate Analysis of Coal(ad)a
Simultaneously, the generated NO is deoxidized to N2 by HCN, and the reaction rate is12
RNOfN2 ) (3 × 1012)FYHCNYNO exp -
constituent
Here, the reaction source items of YHCN and YNO are determined by the NO formation mechanism:3
SYHCN ) RcoalfHCN - RHCNfNO - RNOfN2
(12)
SYNO ) RHCNfNO - RNOfN2 - RNO+CaOfN2
(13)
The NO model is based on the solution of transport equations for two conserved scalars. The chemistry is modeled by the equilibrium model, which assumes that the chemistry is rapid enough for chemical equilibrium to exist at the molecular level. It computes species from conserved scalars using an algorithm based on the minimization of Gibbs free energy. The NO model can account for the interaction of turbulence and chemistry. In addition, a conservation equation for the two conserved scalars variance (Y′j2) is introduced as
( ) ()
∂Y′j2 ∂Y′j 2 ∂ ∂ (FuiY′j2) ) ΓYj + Cgµt - CdF Y′j2 ∂xi ∂xi ∂xi ∂xi k (for i ) x, r, θ; j ) HCN, NO) (14) The conserved scalar variance is used in the closure model describing turbulence chemistry interactions. (14) Tsujimura, M.; Furusawa, T.; Kunii, D. Catalytic reduction of nitric oxide by carbon monoxide over calcined limestone. J. Chem. Eng. Jpn. 1983, 16, 132-136.
component
amount (wt %)
loss on ignition, LOI SiO2 Al2O3 + TiOS2 Fe2O3 CaO MgO K2O Na2O SO3 Cl
36.02 13.12 3.03 1.84 42.78 2.13 0.63 0.07 0.17 0.003
Table 5. Components of Exhaust Gas component
value
CO2 O2 CO N2 NO
15% 0% 0.9096% 84.09% 750 mg/Nm3
The calculation of NO formation during pulverized coal combustion in the DD-PRC follows from the post-processor method,8 which assumes that the consumed oxygen, generated heat, and gas-phase parameters have no effects on the main combustion and decomposition reactions. Thus, it is easy to incorporate the method to the computation of gas and solid twophase flow, heat transfer, pulverized coal combustion, and carbonate decomposition in the DD-PRC. 4. Models: Validation and Discussions The numerical simulation with the models mentioned previously is executed on the in-line 2500 t/d DD-PRC, and the source of the CFD code is developed in Fortran 90. The operating parameters are listed in Table 2. The proximate and ultimate analyses of the coal and the compositional analysis of the raw materials are presented in Tables 3 and 4, respectively. Table 5 lists the component volume fractions of the exhaust gas from the rotary kiln. Figures 3 and 4 present the contours of the temperature and concentration of oxygen, NO, and CO. Figures 3A and 4A show the variation of temperature along the height of the DD-PRC. The highest temperature region occurs at the areas of the exhaust gas inlet and coal and
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Figure 3. Contours of temperature, O2, NO, and CO at the section of tertiary air inlet: (A) temperature, T (K); (B) O2 content (%); (C) NO concentration (mg/Nm3); and (D) CO content (ppm).
Figure 4. Contours of temperature, O2, NO, and CO at the section of the outlet: (A) temperature (K), (B) O2 content (%), (C) NO concentration (mg/Nm3), and (D) CO content (ppm).
secondary air inlets, and then the temperature decreases, because of the strongly endothermic reaction of the raw materials.
Figures 3B and 4B present the oxygen contours at the sections of tertiary air inlet and outlet accordingly. The oxygen concen-
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Energy & Fuels, Vol. 20, No. 1, 2006 169
Figure 5. NO concentration versus the number of measurements. Table 6. Comparisons between Simulation and Measurements prediction temperature of outlet burnout ratio of coal decomposition of raw material average concentration of NO at outlet
1170 K 92.2% 89.17% 832 mg/Nm3
measurement (average) error 1176 K 94.3% 91.26% 776 mg/Nm3
0.51% 2.22% 2.29% 7.22%
tration increases from the exhaust gas inlet to the area of coal and secondary air inlets, and then decreases from the area of coal and secondary air inlets to the outlet area because of the consumption of coal combustion and the release of the CO2 generated by coal combustion and raw material decomposition reactions. Figures 3C and 4C are the NO concentration contours. The concentration of NO coming from the rotary kiln is ∼750 mg/ Nm3, and the NO concentration then decreases at the region of coal inlets, because of the reducibility of CO, which is generated plentifully (see Figures 3D and 4D), and the CaO from the raw material decomposition acts as the catalyst (see eq 9). The NO concentration increases from the region of coal inlets to the area of the outlet, because the fuel NO is produced from the coal combustion. The temperature of the DD-PRC is 90%, the decomposition ratios of raw material increase, and the NO concentrations are lower than the original condition, when both air staging and fuel staging are taken into consideration. The burnout ratio of case 1 is the highest in the three optimum cases, because the coal quantity is smaller than the original
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Figure 7. Comparison of different cases: (A) temperature (K), (B) burnout ratio (%), (C) decomposition ratio (%), and (D) NO concentration (mg/Nm3).
condition in the original coal inlets because of fuel staging, which is benefit for the complete combustion of coal and supplies sufficient heat to the succeeding reaction. The strongly reducing atmosphere reduces the NO from the rotary kiln, so the NO concentration apparently decreases (to ∼573 mg/Nm3). For case 2 of air staging, the NO concentration (∼567 mg/ Nm3) of the outlet is lower than that of case 1. It is the reason why the domain of the slightly reducing region is larger than that of the strongly reducing region in case 1, and the reducing reaction time is longer and the reducing domain is larger relatively; however, the burnout ratio of coal is lower than that observed in case 1. In optimum case 3, the NO concentration of the outlet is the lowest (∼555 mg/Nm3) among the original condition and the three optimum cases, because of the reducing interaction of air staging and fuel staging. 6. Conclusions The 2500 t/d in-line dual combustion and denitrator process precalciner (DD-PRC) is modeled in full-scale and the NO release is predicted in detail in this paper. The comparisons between predicted results and measurements validate the models used in this article. The structure of the 2500 t/d in-line DD-
PRC is reformed to solve the departure flow existing in the practice operation. The optimum cases predict the outlet temperature, burnout ratio, decomposition ratio, and NO concentration, and they show that the applications of air staging and fuel staging are beneficial to reduce NO emissions without affecting the operation. However, in regard to economy, the air staging technique will make the system reformation to be complex and fuel staging technique is easy to perform, from an economic standpoint, so the fuel staging is the optimum method for the precalciner to reduce NO emissions. Acknowledgment. The authors are grateful for the support provided by the National High Technology Research and Development 863 Program of the People’s Republic of China (under No. 2002AA529150) and the cooperation with Tianjin Cement Industrial Design and Research Institute of the People’s Republic of China.
Nomenclature DP ) diameter of raw material particle (m) E ) activation energy (kJ/kmol) k ) turbulent kinetic energy (m2/s2) k0 ) decomposition rate constants (m/s) PCO2 ) CO2 partial pressure (MPa) Pe ) equilibrium CO2 pressure (MPa)
NO Emission in Precalciner p ) pressure of fluid (Pa) R ) molar gas constant; R ) 8.314 J/(mol K) RcoalfHCN ) release rate of HCN during coal pyrolysis and char combustion (kg/s) RHCNfNO ) react rate of HCN to NO (kg/s) RNOfN2 ) react rate of NO to N2 (kg/s) SP ) mass weakening rate during coal pyrolysis and char combustion (kg/s) SYHCN ) source term of mass fraction of HCN (kg/s) SYNO ) source term of mass fraction of NO (kg/s) SΦ ) source term of variable Φ from fluid (kg/s) SP,Φ ) source term of variable Φ from particle (kg/s) T ) raw material particle temperature (K) Tg ) gas-phase temperature (K) t ) time (s) u ) tangential velocity (m/s) V ) radial velocity (m/s)
Energy & Fuels, Vol. 20, No. 1, 2006 171 w ) axial velocity (m/s) XO2 ) oxygen concentration (mol/mol) YNcoal ) mass fraction of N in coal particle YHCN ) mass fraction of HCN in gas phase YNO ) mass fraction of NO in gas phase YO2 ) mass fraction of O2 in gas phase Greek Symbols ΓΦ ) effective viscosity of variable Φ (×10-3 N s/m2) γ ) decomposition ratio of raw material ) turbulent dissipation rate (m2/s3) µt ) turbulent viscosity (kg/(m s)) F ) density of gas (kg/m3) Φ ) variable EF0502857
