CHARACTERISTICS OF PRESSURIZED OXY-COAL COMBUSTION UNDE

R INCREASING SWIRL NUMBER

1OC

, Ahmed

AAKoPT

Nomenclature a emissivity weighting factor A pre-exponential factor in Arrhenius law, 2

ß( )k g m P a s K · · ·

T temperature, K U axial velocity, ms

m W tangential velocity, ms and a κ absorption coefficient, 1/m

p2c specific heat, ( ) J/ kg K· , or ( ) J/ kmol K· D binary diffusion coefficient, m s

V volume, 3

ß order of temperature dependent in Arrhenius law

axial flux of angular momentum, ( )h mass transfer coefficient, ms h enthalpy, J/kg L length of the combustor, m MW molecular weight, kg kmol P and p total and partial pressure, Pa

2

2

ρ density, 3kg m ( )W/ m K  

R overall char reaction rate, c2( )kg m s f flame

R , diff

u

kin

2( )k g m P a s · ·

g bulk gas i species i p particle rec recirculation rev reverse

of the combustor. The refractory lined cylindrical combustor is mounted horizontally with a small degrees slope. Results are plotted in dimensionless manners normalized with the length (L) and the radius (R) of the combustor in axial and radial directions respectively. Bituminous coal was used in this study, and its properties including approximate and ultimate analysis are shown in Table 1. The operating conditions were optimized through system analysis study in [8, 9] and scaled down to a 3 MWth operating condition in this simulation as

shown in Table 2. 3. Numeric

al Method FLUENT 12.0.16 was used in this study, with modified char combustion sub-models. The modeling was based on Eulerian-Lagrangian

approach to the gas-discrete phase coupling. The flow field was modeled using the Reynolds Average Navier Stocks (RANS) equations with SIMPLE algorithm for pressure-velocity coupling. For gas phase homogenous combustion reactions, the finite rate/eddy dissipation model was adopted for turbulence-chemistry interaction. The ideal gas law was used to calculate the density at the elevated operating pressure of 4 bar.

dx

GGm

e emissivity

s Stefan-Boltzmann constant, ν stoichiometric value Subscript symbol 0 reference value

C carbon

24

Swirl flow

Recycled flue gas + Ofrom ASU: O, CO22, H2O2

Coal water slurry + Atomization steam Atomization spray

Figure 1: Geometry of the pressurized oxy-coal combustor. Figure 2. Schematic diagram of the swirl burner and

coal water slurry effervescent atomizer An axisymmetric two dimensional mesh including

~19,300 cells was constructed. The computational domain consists of the burner, the reactor, and the flue gas outlet. Since the mesh is axisymmetric, the flue gas outlet duct was modeled as annual pressure-outlet with identical area of the real geometry. The sub-models used in this numerical study are described as follows. 3.1. Modeling Turbulence The realized k-e model was used in the simulation of the cold flow and the reacting flow. A comparison study of the k-ω model shows flow field results.

modeled as single phase sphere consisting of water and an agglomerated coal particle. The water content boils and evaporates at the saturation temperature (143 ºC at the operating pressure) before devolatilization occurs. Devolatilization kinetics is calculated using the Chemical Percolation Devolatilization (CPD) model [19]. NMR chemical structure inputs were calculated based on the proximate and ultimate analysis data using the correlations in [20]. The molecule m n p q CHON (sulfur is counted as oxygen) represents the volatile matter. It decomposes into gas compounds consisting of CO, CO

3.2. Modeling Oxy-coal Combustion

, H2, N2, H2O and CHx (hydrocarbons) as follows [21]: 2

An effervescent CWS atomizer is used in the combustor, and its properties such as the spray angle, droplet velocity and Sauter Mean Diameter were calculated using the correlations from [15] and [16]. A total of 1000 atomized CWS droplets with different sizes sampled from a Rosin-Rammler distribution are injected on axis. Since experiments show that the coal particles in a CWS droplet tend to agglomerate [17, 18], each droplet is

C

TH

Atomization gas (265 ºC, 18 bar)

H O 0.01 1

experimental data from a similar ranked coal undergoing rapid pyrolysis [22-24]. Formation enthalpy of the volatile is calculated to match the high heating value (HHV) of the coal.

The kinetic parameters for external surface reactions cited from the literature [7, 29, 30] are shown in Table 3. Diffusion often controls the burning rate at high temperatures. The corresponding mass transfer limited

MW

S h D P S h T h D d d P T · ⎛ ⎞ ⎛ ⎞ = = ⎜ ⎟ ⎜ ⎟

⎝ ⎠ , , 0

0 ⎝ ⎠i m i i 1.75 0 (9)

Char particle combustion characteristics are different under oxy-fuel conditions where CO concentration is much higher than that in air combustion. Shaddix et al. [25] and Bejarano et al. [26] reported lower char surface temperature and reaction rate in oxy-fuel combustion because of the slow O22 diffusion in CO. On the other hand, Rathnam et al. [27] found that the char gasification reactions (Char-CO2 and Char-H22O) become significant at the high temperature, oxygen-deficient conditions. These characteristics should be considered in the char burning sub-models under oxy-fuel conditions.

reaction rate,

R , can be expressed as: ,diff i

where ,0i

We considered three surface reactions in the fixed core model of a char particle, i.e.

D were taken from [31]. In practical pulverized coal combustion, the relative velocity

the overall char reaction rate (, c i R ) depends on the rate of oxidizer transport by external diffusion and the

surface reaction kinetics. The reaction rate is:

T

n c i diff i i g i s kin i( ) R R p p R p = - = ( 5 ) , , , , , i s ,conditions are shown in Table 3. It is notable that iC is different for air-combustion and oxy-combustion If the reaction is first order (n=1), the overall reaction rate becomes

because of different diffusivities in the nitrogen enriched or carbon dioxide enriched environment.

where kinetic rates of char surface reaction are:

2

22x

R R R p d i f f i k i n i c i ig

x0.5 2

Eq. 2( )kg m sPa i( ) kJ molK Ref

0.75

*x1 2 ⎜ ⎟⎝ ⎠ 2

2   ( 1 2 ) O t h e r i m p o r t a n t h o m o g e n e o u s r e a c t i o n s i n t h e h i g h C O 2 and HO combustion environments, such as the gas shift reaction and the burning of CO and H

2 2 2 are considered:

* 2 2 H O H O + → ( 1 4 ) 2 2 2

6. 2 2 C O O C O + → ( 1 5 ) 2 2

* C

The global kinetic rates for these reactions taken from the literatures [32, 33] are shown in Table 3. These global reactions were obtained for air-fuel hydrocarbon combustion, and might be different under the oxy-fuel combustion. Improved mechanisms for oxy-combustion [34] might be used in the future. 3.4. Modeling Radiation Heat Transfer The heat transfer characteristics of the oxy-fuel combustion flue gas are different from traditional air-fuel combustion, in part because the presence of triatomic gases (CO2 and H2O) enhance the emissivity [2]. Radiation heat transfer was simulated using the Discrete Ordinates Radiation (DO) model where the local absorption coefficient was calculated as the sum of the gas and particle absorption coefficients. The Weighted Sum of Gray Gases (WSGG) model was used to calculate the absorption coefficients of the local gas mixture. This model will be discussed later. 4. Results and Discussion In the first part of this paper, we compare the flow field, combustion temperature distribution, radiation intensity and coal burning reactions under air-fuel and oxy-fuel conditions. The effects of surrounding gas properties, such as specific heat and absorption coefficient, on the different combustion characteristics are analyzed. The effects of swirl number on the oxy-fired coal combustion are investigated in the second part.

hR

TrT-

13 rC RT f

6.8 10 e 8 RT [ ] [ ]

4.1. Comparison of Air- and Oxy-fired Combustion

13

In the following results, air-fired and oxy-fired coal combustion are compared at similar operating conditions except for the oxidizer stream compositions. The diameter of the axial guide vanes in the burner is one

8

1.

1 T e m p er at u r e: 200 400 600 800 1 000 1200 1 400 1600 1800 2 000 2200

A R

a di

a l

posi

tion

( R )

R a

dia

l pos

itio

n ( R

)

6

c is the specific heat of the species. Piecewise-polynomial correlations are used to calculate the specific heat of major gas species such as N2, CO2 and H2O. Figure 4 shows the specific heat of these three gases as function of temperature. NIST data are also shown for

The different gas absorption characteristics are considered using WSGG model in this study. WSGG model assumes that the gases are gray-gases with

different absorption coefficients

composition dependent.

i

S 1

10.2 0.4 0.6 0.8

O xy- fire d

0 0.1 0.2 0.3 0.4 0.5 0A x ia l p o s it io n ( L ) Figure 5. Comparison between specific heat (in J/kg-K) distributions under air-fired and oxy-fired combustion.

iY is the mass fraction of the species i , and

,p i

κ

R a

dia

l pos

itio

n ( R

)R

a di

a l p

ositi

on

( R )

Spe

cific

hea

t (J/

kmol

-K)

The absorption coefficient of the gas mixture, a , is calculated as:

( ) l n 1 s a e = - -   ( 1 9 ) w h e r e e i s t h e g a s e m i s s i v i t y , a n d s i s t h e r a d i a t i o n

concentrations are higher near the burner, secondly the gas absorption is stronger at lower temperature because of the higher emissivity weighting factor [37].

b

=

where pn

pn

pn Figure 8 shows the area average volatile and

carbon monoxide mole fraction under these two combustion conditions. Devolatilization starts 0.25L downstream of the burner under the oxy-fired case, compared to 0.2L under the air-fired case. This is because of the lower combustion temperature near the burner (see also Figure 3 and Figure 7). Similar trend is observed for the CO mole fraction. It is notable that the CO mole fraction under oxy-fired condition is higher than the air-fired condition. This might be because of the lower combustion temperature and hence lower reaction rate of CO oxidation. The longer distance of combustion intermediate species indicates delayed ignition in the oxy-fired condition.

T are the emissivity, projected area and temperature of particle n, respectively. Summation over all the particles in volume V gives the equivalent particle absorption coefficient. Figure 6 shows the average incident radiation in the combustor under both air-fired and oxy-fired cases. The radiation intensity in the air-fired condition is almost 2 times higher than that in the oxy-fired condition. Figure 7 shows the two factors that affect the radiation intensity in Figure 6: the area average temperature, and the area average absorption coefficient under air-fired and oxy-fired conditions. It is notable that the equivalent absorption coefficient is higher near the burner in both cases, because firstly the CWS droplets and char particle

Figure 6. Area average incident radiation with normalized axial position under air- and oxy-fired combustion.

Normalized axial position (L)

4 3 2 1

1800 1900 2000 21

00 2200

Air-fired Oxy-fired

Average T Air-fired Oxy-firedAverage a

Air-fired Oxy-fired

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.

e , A , Figure 7. Area average temperature and

absorption coefficient with normalized axial positi

on under air- and oxy-fired combustion. )2Average incident radiation (MW/mAverage temperature (K)Average absorption coefficient (1/m)

0.006

0.005

0.004

0.003

CO Air-fired Oxy-fired

Volatile Air-fired Oxy-fired

3.0

2.5

2.0

0.002

0.001

1.5

1.0

0.5

Air-fired Oxy-fired

Figure 9 shows the area integrated sensible enthalpy flow rate under air-fired and oxy-fired conditions. Although the combustion temperatures are different, identical sensible enthalpy increase is observed in both cases because of the same fuel flow rate and complete combustion. The sensible enthalpy increase delays about 0.1L in the oxy-fired case because of the delayed ignition and coal combustion as discussed in Figure 8. Results shown in Figure 3 - Figure 9 indicate that a similar flow field is observed in oxy-fired combustion compared to the traditional air-fired combustion. However the combustion temperature is distinctly lower in the oxy-fired case because of the higher specific heat of CO2 and H2O. Although having higher absorption coefficient and emissivity, the radiation intensity in oxy-fired condition is still lower because of the lower combustion temperature. Devolatilization and char burning are delayed in the oxy-fired case as a result of lower temperature and radiation intensity. This may be further improved by increasing the oxygen concentration in the oxidizer stream. Combustion temperature is one of the most critical factors affecting combustion characteristics, and it can be controlled by varying the flue gas recirculation ratio.

However changing the recirculation ratio may also affect the linear and tangential momentum fluxes if they are dependent as discussed in [6]. In this specific study, the burner flow S’ is only controlled by the guide vane operating, and its affect on the flow patterns will be discussed in section 4.2. 4.2. Swirl Number Effect Parametric Study 4.2.1. Cold Flow Field Varying the swirl number may improve the combustion

stability in oxy-fired condition. A parametric study of the swirl effect on cold and reacting flow was carried out by varying the guide vane angles and diameters for different swirl numbers. The guide vane diameter and angles with its corresponding S’ are summarized in Table 5. Case 3 to 8 applied full height guide vanes to obtain higher S’ up to 0.78. All the other operating conditions remain the same as shown in Table 2 except that the cold flow simulations are without CWS and atomization steam injection. As shown in Figure 10, the flow pattern changes progressively with increasing S’. At small swirl number (S’<0.36), a confined jet flow dominates the flow downstream the burner, with external

entrainment which suppresses the axial velocity component. At high swirl number (S’>0.45), the centrifugal force formed by the swirling flow becomes significant, and the resulting radial pressure gradient forces a reverse flow or internal recirculation zone near the axis. The fuel and oxidizer mixing and flame stabilization mechanisms might be different under low and high swirl number flows, which will be discussed in the following section. Table 5. Parametric study of the swirl number effects Case Guide vane diameter Guide vane angle S’

1 Half 0 0 2 Half 45 0.18 3 Full 20 0.28 4 Full 25 0.36 5 Full 30 0.45 6 Full 35 0.55 7 Full 40 0.66 8 Full 45 0.78

0. 0.0 0.2 0.4 0.6 0.8 1.0 0.0

Normalized axial position (L)

Figure 9. Sensible enthalpy flow rate (in MW) as function of normalized axial position under air-fired and oxy-fired combustion conditions.

Ent

halp

hy fl

ow ra

te (M

W)

Spe

cies

mol

e fra

ctio

n

4.2.2. Reacting Flow Field and Temperature Distribution Oxy-fired coal combustion simulations at high swirl number (S’=0.78) was carried out in the same geometry, while fuel and streams mass flow rates are the same as those used in the low S’ case in section 4.1. The operating conditions of the swirl burner are corresponding to the cold flow cases 8 in Table 5. Figure 11 shows radial distribution of the axial velocity 0.09-0.57L downstream of the swirl burner outlet for low swirl number (S’=0.18) and high swirl number (S’=0.78) oxy-fired combustion flow. The axial velocity distribution at low swirl number (S’=0.18) is similar to that of the cold flow. At high swirl number (S’=0.78), the internal recirculation zone surrounding the CWS jet flow becomes smaller compared to the cold flow. The axial velocity magnitude is much lower and uniform (almost plug flow beyond 0.38L) than the low S’ case. Figure 12 shows the radial distribution of the tangential velocity in the reactor at low and high S’ reacting flows. For the S’=0.18 case, the tangential velocity decays fast

along the axis direction. For the S’=0.78 case as shown in the right hand side, the radial distribution of the tangential velocity is almost linear beyond 0.19L away from the burner, besides it doesn’t show decay. The reacting flows at increasing swirl numbers show different temperature distribution and recirculation zones. Figure 13 shows the streamlines at low and high S’, as well as temperature distributions. At low S’ (0.18) as discussed in section 4.1, a large external recirculation dominates the reacting flow, a relatively cold, high axial momentum core persists for over 0.38L, with the main combustion zone confined to the envelope between the cold central core and the surrounding mixture of outer recirculated hot gas and unburned stream [38]. This cone-shape combustion zone is stabilized by the mixing of the unburned stream and the burned gas. At high S’ (0.78), the high swirling flow slows down the fuel jet (see also the axial velocity distribution in Figure 11), and mixes the reversed oxidizer stream and fuel jet in counter directions within the internal recirculation zone. Hot gas is recirculated by the internal recirculation and heats up the unburned stream.

1.0

0.8

x=0.09 L x=0.19 L x=0.38 L x=0.57 L

1.0

0.8

1.0

0.8

1.0

0.8

0.6

0.4

0.2

0.0

S'=0 S'=0.180.6

0.4

0.2

0.0

0.6

0.4

0.2

0.0

S'=0.28 0.6

0.4

0.2

0.0

S'=0.36

- 2 0 2 4 6 8 1 0 1 2 1 4 1 6 -2 0 2 4 6 8 10 12 -2 0 2 4 6 8 10 12 14 -2 0 2 4 6 8 10 12

1.0

0.8

0.6

V-

axia l

0.4

0.2

0.0

-4 -2 0 2 4

0.

-

1.0

0.8

0.6

0.4

x=0.09 L x=0.19 L x=0.38 L x=0.57 L

1.0

0.8

0.6

0.4

x=0.09 L x=0.19 L x=0.38 L x=0.57 L

0.2

0.0

S'=0.18 S'=0.78

0.2

0.0

S'=0.18 S'=0.78

0 5 1 0 1 5 2 0 0 5 1 0

0 1 2 3 4 5 0 1 2 3 4

Axial velocity (m/s) Axial velocity (m/s) Tangential velocity (m/s) Tangential velocity (m/s)

Figure 11. Comparison of radial distribution of the axial velocity at different swirl numbers in the reactive case.

As shown in Figure 13, different flow patterns were observed when increasing S’ in the oxy-fired coal combustion, especially for the different recirculation zones. As a result, the recirculated mass and heat are also different. The recirculated mass flow rate is defined as:

∫m v d A ρ =&       ( 2 2 ) rec rev A

where revv is the reversed velocity (negative axial velocity). And the recirculated enthalpy flow rate is likewise: H v hd A ρ= rec rev A

1

0

1

0

colored by gas temperature (K).

Figure 12. Comparison of radial distribution of the tangential velocity at different swirl numbers in the reactive case. where h is the enthalpy of the stream. These integrations are calculated for cross sections at different axial positions. Figure 14 shows different mass and heat recirculations at increasing S’. At low S’, the recirculated mass flow occurs across the first half of the reactor because of the large external recirculation. At high S’, the recirculated mass and heat flow take place only within 0.2L downstream of the burner. Although higher mass flow rate is observed at high S’ combustion (1.3 vs. 1 kg/s),

the recirculated heat at hig

h S’ is much less (0.4 MW vs. 1.7 MW).

S’=0.1 8

0.57 L

S’=0 .7 8

0.57 L& ∫

s it io n ( L )

(23)

T e m p er at u r e: 300 500 700 900 1100 1300 1500 1700 1900

Figure 13. Comparison of oxy-coal combustion flow streamline maps at different swirl numbers (S’=0.18, and 0.78),

R a

dia

l po

sitio

n ( R

)R

a di

a l p

ositi

o n

( R )

Nor

mal

ized

radi

al p

ositi

on (R

)

Nor

mal

ized

radi

al p

ositi

on (R

)

S1 S8Recirculated heat S1 S80.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Recirculated mass

2.0

1.5

1.0

0.5

0.0

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

CO S1 S8Volatile S1 S8

0.005

0.004

0.003

0.002

0.001

0.000

Figure 14. Recirculated mass and heat by external and internal recirculations at different swirl numbers in the oxy-fired combustion. The temperature distribution in Figure 13 shows that combustion is stabilized at different distance from the burner in the two cases. This can also be seen from the average volatile and carbon monoxide mole fraction shown in Figure 15. The volatile and CO concentration reaches its peak at 0.3-0.4L away from the burner at high S’, compared to 0.4-0.5L at low S’. The shorter distance at high S’ indicates that operating the burner at high S’ changes the ignition delay.

5. Conclusions

0.0 0.2 0.4 0.6 0.8 1.0 -0.0050.0 0.2 0.4 0.6 0.8 1.0Normalized axial position (L)

Figure 15. Average volatile and CO mole fraction with normalized axial position at different swirl numbers in the oxy-fired combustion. swirl number. At high swirl number, the distance of combustion zone from the burner is shorter, and it is stabilized by an internal recirculation zone. Acknowledgement The authors acknowledge ENEL for the research grant supporting this study, and appreciate Mr. Nicola Rossi of ENEL Ingegneria e Innovazione S.p.A. for discussions on the results.

A123

Reference 1. B. J. P. Buhre; L. K. Elliott; C. D. Sheng; R. P. Gupta; T. F. Wall, Progress in Energy and Combustion Science 31 (4) (2005) 283-307. 2. T. Wall; Y. Liu; C. Spero; L. Elliott; S. Khare; R. Rathnam; F. Zeenathal; B. Moghtaderi; B. Buhre; C. Sheng; R. Gupta; T. Yamada; K. Makino; J. Yu, Chemical Engineering Research and Design 87 (8) (2009) 1003-1016. 3. T. Suda; K. Masuko; J. i. Sato; A. Yamamoto; K. Okazaki, Fuel 86 (12-13) (2007) 2008-2015. 4. A. Molina; C. R. Shaddix, Proceedings of the Combustion Institute 31 (2) (2007) 1905-1912. 5. N. Kimura; K. Omata; T. Kiga; S. Takano; S. Shikisima, Energy Conversion and Management 36 (6-9) (1995) 805-808. 6. S. P. Khare; T. F. Wall; A. Z. Farida; Y. Liu; B. Moghtaderi; R. P. Gupta, Fuel 87 (7) (2008) 1042-1049. 7. D. Toporov; P. Bocian; P. Heil; A. Kellermann; H. Stadler; S. Tschunko; M. Forster; R. Kneer, Combustion and Flame 155 (4) (2008) 605-

61

Vola

tile

mol

e fra

ctio

n

CO

mol

e fra

ctio

n

Rec

ircul

ated

hea

t (M

W)

Rec

ircul

ated

mas

s (k

g/s)

10. G. Benelli; M. Malavasi; G. Girardi in: PowerGen Europe Conference and Exhibition, Madrid, Spain, 26-28 June, 2007. 11. N. Rossi; D. Cumbo; G. Benelli; M. Gazzino in: The 35th International Technical Conference on Clean Coal & Fuel Systems, Clearwater, FL, USA, June 6-10, 2010. 12. M. Malavasi; E. Rossetti High-efficiency Combustors with Reduced Environmental Impact and Processes for Power Generation Derivable Therefrom. International Patent, WO 2005/108867, 17 November, 2005. 13. E. Rossetti; M. Malavasi Method and Plant for the Treatment of Materials in Particular Waste Materials and Refuse. International Patent, WO 2004/094904, 4 November, 2004. 14. M. Malavasi; G. Di Salvia; E. Rossetti Combustion process. International Patent, WO 2009/071239, 11 June, 2009. 15. P. E. Sojka; A. H. Lefebvre, A novel method of atomizing coal-water slurry fuels: Final report for Grant No. DE-FG22-87PC79931 US DOE,in:Thermal Sciences and Propulsion Center, School of Mechanical Engineering, Purdue University: West Lafayette, IN, 1990; pp 1-116. 16. S. D. Sovani; E. Chou; P. E. Sojka; J. P. Gore; W. A. Eckerle; J. D. Crofts, Fuel 80 (3) (2001) 427-435. 17. S. F. Miller; H. H. Schobert, Energy & Fuels 7 (4) (1993) 520-531. 18. D. Dunn-Rankin; J. Hoornstra; F. A. Gruelich; D. J. Holve, Fuel 66 (8) (1987) 1139-1145. 19. T. H. Fletcher; A. R. Kerstein; R. J. Pugmire; D. M. Grant, Energy & Fuels 4 (1) (1990) 54-60. 20. D. Genetti; T. H. Fletcher; R. J. Pugmire, Energy & Fuels 13 (1) (1999) 60-68. 21. M. Kumar; C. Zhang; R. F. D. Monaghan; S. L. Singer; A. F. Ghoniem in: ASME 2009 International Mechanical Engineering Congress & Exposition, Lake Buena Vista, FL, Nov 13-19, 2009. 22. W.-C. Xu; A. Tomita, Fuel 66 (5) (1987) 627-631. 23. R. S. Jupudi; V. Zamansky; T. H. Fletcher, Energy & Fuels 23 (6) (2009) 3063-3067. 24. J. R. Bautista; W. B. Russel; D. A. Saville, Ind. Eng. Chem. Fund. 25 (4) (1986) 536-544. 25. C. R. Shaddix; A. Molina in: The 33rd International Technical Conference on Coal Utilization and Fuel Systems, Clearwater, FL, USA, June 1-5, 2008. 26. P. A. Bejarano; Y. A. Levendis, Combustion and Flame 153 (1-2) (2008) 270-287. 27. R. K. Rathnam; L. K. Elliott; T. F. Wall; Y. Liu; B. Moghtaderi, Fuel Processing Technology 90 (6) (2009) 797-802. 28. I. W. Smith, Symposium (International) on Combustion 19 (1) (1982) 1045-1065. 29. M. A. Field, Combustion and Flame 13 (3) (1969) 237-252. 30. B. W. Brown; L. D. Smoot; P. J. Smith; P. O. Hedman, AIChE Journal 34 (3) (1988) 435-446. 31. F. P. Incropera; D. P. DeWitt, Fundamentals of heat

and mass transfer, Wiley, New York, 2002, p. 981. 32. W. P. Jones; R. P. Lindstedt, Combustion and Flame 73 (3) (1988) 233-249. 33. F. L. Dryer; I. Glassman, Symposium (International) on Combustion 14 (1) (1973) 987-1003. 34. J. Andersen; C. L. Rasmussen; T. Giselsson; P. Glarborg, Energy & Fuels 23 (3) (2009) 1379-1389. 35. NIST Chemistry WebBook: Thermophysical Properties of Fluid

Systems. http://webbook.nist.gov/chemistry/ , Retrieved on (June 04, 2009),    36. S. R. Turns; F. H. Myhr, Combustion and Flame 87 (3-4) (1991) 319-335. 37. A. Soufiani; E. Djavdan, Combustion and Flame 97 (2) (1994) 240-250. 38. J. M. Beer; N. A. Chigier, Combustion aerodynamics, Krieger, Malabar, Fla., 1983, p. 264.