Analysis of the structure and mechanisms of extinction of a counterflow methanol-air diffusion flame

COMBUSTION

AND FLAME

76:111-132

(1989)

111

Analysis of the Structure and Mechanisms of Extinction of a Counterfiow Methanol-Air Diffusion Flame K. SESHADRI and C. TREVINO* Department of Applied Mechanics and Engineering Sciences~Chemical Engineering, University o f California, San Diego, La Jolla, CA 92093

and M. D. SMOOKE Department of Mechanical Engineering, Yale University, New Haven, CT 06520

Numerical calculations were performed to determine the structure and to clarify the extinction mechanisms of diffusion flames stabilized between counterflowing streams of methanol and air. The calculations were performed at a value of the thermodynamic pressure equal to 1 atmosphere, with different values for the rate of strain and with two different chemical kinetic mechanisms. We will refer to these two mechanisms as "mechanism a " and "mechanism b . " Mechanism a and mechanism b have the same set of elementary reactions, but the rate constants for these elementary reactions were obtained from two different references. Temperature profiles, concentration profiles of various species, rates of production and destruction of various species, and rates of various reactions were plotted as a function of the axial coordinate using mechanism a and mechanism b. Both chemical mechanisms show that the structure can be subdivided into three regions: the fuel consumption region where the reaction proceeds via the path CH3OH--CH2OH--CH20--CO, He, the H2-CO oxidation region where the compounds H2 and CO oxidize to form I-I20 and CO2, and the radical destruction region where radicals are destroyed by three body reactions. If mechanism a is used, we conclude that at low rates of strain the concentration of CH2OH and HCO are in steady state and, ff partial equilibrium is assumed for certain reactions, there exist algebraic relations among the concentrations of the radicals OH, H, and O. As the rate of strain is increased, HCO is no longer in steady state and no solution was obtained for a strain rate greater than 521 s- L However, if mechanism b is used, the concentration of HCO alone is in steady state, and there also exist algebraic relations among the concentrations of the radicals OH, H, and O. As the rate of strain is increased, no solution was obtained for a strain rate greater than 168 s-t, and we speculate that extinction of the flame is due to a large value of the activation energy for a reaction controlling the pyrolysis of CH2OH to CH20.

INTRODUCTION D e t a i l e d studies o f t h e o x i d a t i o n o f m e t h a n o l in premixed flames and diffusion flames are of p r a c t i c a l i m p o r t a n c e b e c a u s e m e t h a n o l is c o n s i d * Visiting Professor. Permanent address: Divisidn de Ing. Mec~aica y El~ctrica, Universidad National Autonoma de Mexico, 04510, Mexico, D.F. Copyright © 1989 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 655 Avenue of the Americas, New York, NY 10010

e r e d as a n a l t e r n a t e fuel f o r u s e in i n t e r n a l combustion engines. Previous detailed experimental a n d t h e o r e t i c a l s t u d i e s o f t h e c o m b u s t i o n o f methanol have been concerned primarily with premixed flames [1-5]. Although experimental measurements of the structure and critical conditions of extinction of counterfiow diffusion flames stabilized above the surface of a burning pool of

0010-2180/89/$03.50

112 methanol have been reported [6-9], complementary theoretical studies are not available. In this paper we report results of a detailed numerical study of the structure of a laminar, stretched, counterflow methanol-air diffusion flame. We show that there are three distinct regions in the flame, and we identify key chemical reactions predominantly influencing the structure of these regions. Attempts are also made to clarify the mechanisms of flame extinction. The detailed chemical kinetic mechanism of the oxidation of methanol has been outlined by a number of investigators [1-3, 5, 10-14]. Westbrook and Dryer [1] performed numerical calculations to determine the structure of unstretched methanol-air, premixed flames. Eightyfour elementary chemical reactions, involving 26 chemical species were used in these calculations [1], and the results were used to study the dependence of the laminar flame speed and flame structure on the pressure, the equivalence ratio, a~,d the temperature of the unburned gas. Westbrook and Dryer [1] compared their predictions with available experimental data, and the results were in good agreement. It has been shown that there are roughly two paths for decomposition and oxidation of methanol [10]. One path involves the reaction of methanol with active radicals such as OH, H, and O to form the hydroxymethyl radical CH2OH. The radical CH2OH reacts further with 02, H, and M to form formaldehyde CI-I20. The reaction proceeds by subsequent oxidation of CH20 to form CO and H2, and finally to CO2 and H20. The alternate path involves formation of methyl radicals CH3 from methanol, followed by the formation of the intermediate products CH4, C2H6, C2H5, C2H4, C2H3, C2H2, C2H, CH2, and CH, and the subsequent oxidation of these compounds. Because numerical calculations show that the concentration of the C2 compounds are small, Westbrook and Dryer [1, 11] concluded that the dominant path for the oxidation of methanol proceeds by the path CH3OH-CH2OH-CH20-HCO-CO-CO2. Therefore, in the numerical calculations reported here we have excluded the chemical kinetics of the formation and destruction of C2 hydrocarbon compounds. In addition, experimental data [7] for

K. SESHADRI ET AL. profiles of stable species in counterflow diffusion flames stabilized over the surface of burning pools of methanol show that the concentration of CH20 is higher than the concentration of C2 hydrocarbon compounds, further justifying the neglect of C2 chemistry in our calculations. The configuration used for our study is the diffusion flame stabilized between counterflowing streams of methanol and air. Numerical calculations were performed for different values of the rate of strain. The chemical kinetic mechanism used in the calculations consisted of 37 reactions involving 15 species. The numerical values of the rate constants used in the calculations were those primarily proposed by Warnatz [12-15] and used by Paczko et al. [5]. To simplify the analysis, the chemical kinetic mechanism was further reduced systematically to 15 principal steps involving 13 species and the results were compared and found to be in agreement. The calculations with the 15 principal steps were repeated using numerical values of the rate constants proposed by Westbrook and Dryer [1, 2, 10, 11]. The strain rate at extinction obtained using the data proposed by Warnatz [5, 12] was much higher than that obtained using the data proposed by Westbrook [2]. We show that the differences for the value of the critical strain rate at extinction are attributed to the fact that the data for the rate constants for the path CH2OH-CH20-HCO are different iv. these two mechanisms. In this paper we outline a systematic procedure to analyze the structure and mechanisms of extinction of diffusion flames using detailed chemical kinetic schemes. Studies of this type are useful in identifying key reactions characterizing the oxidation of the fuel. Results obtained in this paper can then be used to simplify the chemical kinetic mechanism further to a smaller number of global chemical reactions. The reduced set of global reactions can be used in performing asymptotic analyses. Recently this procedure has been implemented successfully for methane-air diffusion flames [16]. If results of the final asymptotic analysis agree well with numerical results, then the reduced global set of reactions can be used for analysis of multidimensional and time-dependent engineering problems. However, asymptotic anal-

METHANOL-AIR DIFFUSION FLAME

113

Oxidizer x

pUCp 0"~ "1"pVCP OX

OX

"~X

x OT ~: + Z PYkVkxCpk~x+ Z I~kWkhk=O" k=l

(4)

k=l

The system is closed with the ideal gas law, lm

pW

r

P = RT"

Fuel

Fig. 1. Schematic illustration of the counterflow configuration. ysis using reduced global chemical reactions is beyond the scope of this paper. The mathematical formulation of the problem is described in the following section. In subsequent sections the results are discussed, and our conclusions are summarized. MATHEMATICAL FORMULATION Figure 1 shows a schematic illustration of a counterflow diffusion flame stabilized near the stagnation plane formed by two steady, laminar, infinitely wide, axisymmetric, counterflowing reaction jets. One jet is presumed to be gaseous methanol and the other jet is presumed to be air. If we let r and x denote the independent spatial coordinates in the tangential and transverse directions, respectively, then the governing boundary layer equations for mass, momentum, chemical species and energy in cylindrical coordinates can be written as [17, 18]. 0

O-r (pur) + -Ox (pvr) = O au

0Yk

Ou #p

aYk

pU -~r + pv ax

0 // Ou~

(1) (2)

a

In these equations T denotes the temperature; Yk, the mass fraction of the kth species; p, the pressure; u and v the tangential and the transverse components of the velocity, respectively; p, the mass density; Wk, the molecular weight of the kth species; IJ/, the mean molecular weight of the mixture; R, the universal gas constant; X, the thermal conductivity of the mixture; Cp, the constant pressure heat capacity of the mixture; Cvk, the constant pressure heat capacity of the kth species; ~i'k,the molar rate of production of the kth species per unit volume; hk, the specific enthalpy of the kth species; p, the viscosity of the mixture, and Vkx,the diffusion velocity of the kth species in the x direction. The form of the chemical production rates and the diffusion velocities can be found in detail elsewhere [19, 20]. The free stream tangential and transverse velocities at the edge of the boundary layer are given by uo~ = ar and 00, = - 2 a x , where a is the strain rate. If we introduce the notationf' = u/u~,, and V = pv, where f" is related to the derivative of a modified stream function [17], then the boundary layer equations can be transformed into a system of ordinary differential equations valid along the stagnation-point streamline r = 0. Thus,

dV - - + 2apf' = 0 dx

(6)

"~X \ dx ,] V - - ~ +al'po~-p(f')2)=O

(7)

_ d (pYkVO- vaY~+ .'~wk=o,

-{--- (P Yk Vkx)-- I~k W k : O , ax

k = 1, 2, . . . , K

(5)

dx (3)

k = 1, 2 , - . . , K

dx (8)

114

K. SESHADRI ET AL.

x

-- cp V

--

p Yk Vk cpk

dT K X ~-X--- 2 l~'kWkhk = O.

(9)

k=l

Without loss of generality we will presume that the fuel flows towards the stagnation plane from x = - c o and that the oxidizer flows towards the stagnation plane from x = oo. We will assume that the flame is located near the stagnation plane and we will prescribe the product of the axial component of the velocity of the fuel stream and its density at x = - 1 cm, and the product of the axial component of the velocity of the oxidizer stream and its density at x = 1 cm. Hence, the boundary conditions are

pv=p_~.v_~., T= T_~., Y F = I , Yk=O k;eF, f' = pyre/p_®

at x =

- 1 cm

(10)

pv=p**v.,, T=T®, Yo2=0.23, YN2=0.77, Yk=Ok~O2, N 2 , f ' = l a t x = I c m

(ll)

where the subscript - o o denotes conditions at x = - 1 cm, the subscript oo denotes conditions at x = 1 cm, and the subscript F denotes the fuel. Equations 1-9 together with the boundary conditions 10 and 11 form a system of nonlinear twopoint boundary value problems. The solution procedure employs a combination of time integration and an adaptive finite difference method to obtain profdes for the dependent variables. The method has been discussed in detail elsewhere [17, 18, 21-24]. Because the mass conservation equation is first order in space, and because both mass flux boundary conditions (po,v~, and p_ ~v_~,) are given, the problem is overspecified. Consequently we calculate the strain rate as an eigenvalue by introducing the trivial differential equation da/dx = O. Because the strain rate is a fundamental quantity characterizing the flame structure [25], results will be reported for different values of a. The numerical calculations were performed on the Cray X-MP supercomputer, located at the NSF Center in La Jolla, California. Three different chemical kinetic mechanisms

were used in the calculations and they are shown in Table 1, Table 2, and Table 3. The mechanism in Table 1 will be referred to as the "long mechanism a , " and the mechanisms shown in Tables 2 and 3 will be referred to, respectively, as the "short mechanism a " and the "short mechanism b " . The rate constants for the reactions are assumed to be represented in the Arrhenius form kj = Aj TnJ e x p ( - E / ( R T ) ) , where Aj is the frequency factor, nj the temperature exponent, Ej the activation energy, and R the gas constant. The data for k, shown in Tables 1, 2, and 3 represent the forward rate of the reaction. In our calculations we allow the reaction to proceed in the forward as well as in the backward direction. The backward rate of the reaction is calculated from the equilibrium constant, which is computed internally in the computer program using modified JANAF data as contained in [26]. The data for A j, nj and Ej shown in Table 1 for reactions 3, 8-37 were obtained from [5] and [12], while the data for reactions 1, 2, 4-7 were obtained from [2]. For simplicity, in Tables 2 and 3 only the principal chemical reactions appearing in Table 1 are shown. In the reduced mechanisms shown in Tables 2 and 3 all elementary reactions involving the methyl radical CH3 and methane CH4 were neglected. Table 1 shows that CH2OH is formed from CHaOH via reactions 2-5 and 7. Numerical calculations show that the rate of consumption of CH3OH via reactions 3 and 5 is larger than the rate of consumption of CH3OH via the other reactions. In addition, numerical calculations also show that the concentration of O atoms and 02 are small in the region where CH3OH is consumed. Therefore, the reduced mechanisms shown in Tables 2, and 3 only contain the principal rate of consumption of CH3OH. Formaldehyde, CH20 is formed from CH2OH via reactions 8-10 shown in Table 1, and are retained in the reduced mechanism shown in Tables 2 and 3, although reaction 9 shown in Table 1 could have been eliminated because the concentration of 02 is small in the region where CHEOH is consumed. The reactive species HCO is formed from CH20 via reactions 18-20 shown in Table 1. Reaction 20 shown in Table 1 was eliminated in the reduced mechanism because the rate of this reaction is smaller than the rate of reactions 18 and

METHANOL-AIR DIFFUSION FLAME

115 TABLE 1 Long Mechanism a

No.

Reaction

Ai

ni

Ei

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

CH3OH + M = CH3 + OH + M CH3OH + 02 = CH2OH + HO2 CH3OH + OH = CH2OH + H20 CH3OH + O = CH2OH + OH CH3OH + H = CH2OH + H2 CH3OH + H = CH3 + H20 CH3OH + CH3 = CH2OH + CI-L CH2OH + M = CH20 + H + M CH2OH + 02 = CH20 + HO2 CH2OH + H = CH20 + H2 CH3 + H + M = CI'L + M CH4 + H = CH3 + H2 CI.L, + OH = CH3 + H20 CI-L + O = CH3 + OH CH3 + OH = CH20 + H2 CH3 + O = CH20 + H CH3 + OH -- CH20 + H + H CH20 + OH = HCO + H20 CH20 + H = HCO + H2 CH20 + O = HCO + OH HCO + OH = CO + H20 HCO + M = H + CO + M HCO + H = CO + H2 HCO + O = CO + OH HCO + 02 = CO + HO2 CO + OH = CO2 + H H + 02 = O + OH H2 + O = OH + H H20 + O = OH + OH H2 + OH = H20 + H H + 02 + M = HO2 + M HO2 + O = OH + 02 HO2 + H = OH + OH HO2 + H = I-I2 + 02 HO2 + OH = H20 + 02 H + H + M = I"I2 + M H + OH + M = H20 + M

3.02 1018 3.98 101° 1.00 1013 1.69 1012 3.02 1013 5.25 1012 1.82 1011 1.00 1014 1.00 1013 2.00 1013 2.00 1034 2.20 104 1.60 106 1.20 107 8.00 1012 7.00 1013 5.00 1014 8.00 1013 2.50 1013 3.00 1013 1.00 1014 8.00 1014 3.00 1014 3.00 1013 3.00 1012 4.40 106 2.20 1014 1.80 101° 1.50 101° 1.20 109 2.30 1018 2.00 1013 1.50 1014 2.50 1013 1.50 1013 9.00 1016 2.20 1022

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -5.00 3.00 2.1 2.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.50 0.00 1.00 1.14 1.30 -0.80 0,00 0.00 0.00 0.00 -0.600 -2.00

80.00 50.910 1.697 2.290 7.000 5.340 9.800 25.118 7.193 0.00 3.394 8.747 2,462 7.648 0,00 0.00 15.487 1.505 4.110 3.394 0.0 15.009 0.00 0.00 0.00 -0.741 16.825 8.914 17.002 8.914 0.00 0.00 1.004 0.693 0.00 0.00 0.00

Here cm, tool, kcal, and K are the units, with kj = AjTnJ

exp[-E/(RT)].

19. The compounds H2 and CO are formed from HCO via reactions 21-25 shown in Table 1. Because numerical calculations show that the rates of reactions 22 and 23 are larger than the rates of reactions 21, 24, and 25, only reactions 22 and 23 were retained in the reduced mechanisms shown in Tables 2 and 3. Reactions 26-37 shown in Table 1 involve the oxidation of H2 and CO to form H20

and CO2. Reactions 26, 27, 28, and 30 were retained in the reduced mechanism shown in Tables 2 and 3. For the three-body reactions 31, 36, and 37 shown in Table 1, numerical calculations show that the rate of reaction 31 is much larger than the rates of reactions 36 and 37. Therefore, only reaction 31 shown in Table 1 is retained in the reduced mechanisms. The species

116

K. SESHADRI ET AL. TABLE 2 Short Mechanism a No.

Reaction

Aj

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

CH3OH + OH = CH2OH + H20 CH3OH + H = CH2OH + H2 CH2OH + H = CH20 + H2 CH2OH + M = CH20 + H + M CH2OH + 02 = CH20 + H02 CH20 + OH = HCO + H20 CH20 + H = HCO + H2 HCO + M = H + CO + M HCO + H = CO + H2 CO + OH = C02 + H H + 02 = O + OH H2 + O = H + OH H2 + OH = H20 + H H + 02 + M = HO2 + M HO2 + OH = H20 + 02

1.0 1013 3.02 1013 2.00 1013 1.00 1014 1.130 1013 8.00 l013 2.50 1013 8.00 1014 3.00 1014 4.40 1016 2.20 10 TM 1.80 101° 1.20 109 2.30 1018 1.50 1013

nj 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.50 0.00 1.00 1.300 -0.80 0.00

Ej 1.697 7.000 0.00 25.118 7.193 1.505 4.110 15.009 0.00 -0.741 16.825 8.914 3.633 0.00 0.00

Here cm, tool, kcal, and K are the units, with kj = AjTnJ exp[-Ej/(RT)].

HO2 is consumed via reactions 32-35 shown in Table 1. Numerical calculations show that the rate of reaction 35 is larger than the rates of reactiom 32, 33, and 34 because the concentration of the radical OH is larger than the concentrations of the radicals H and O in the region where HO2 is

consumed. Therefore, only reaction 35 is retained in the reduced mechanism. The data for the rate constants in Table 2 are the same as those in Table 1. However, the data for the rate constants shown in Table 3 were obtained from Ref. [2]. The principal differences in the values of the rate

TABLE 3 Short Mechanism b No.

Reaction

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ll. 12. 13. 14. 15.

CH3OH + OH = CH2OH + H20 CH3OH + H = CH2OH -4- H2 CH2OH + H = CH20 + H2 CH2OH + M = CH20 + H + M CH2OH + 02 = CH20 + HO2 CH20 + OH = HCO + H20 CH20 + H = HCO + H2 HCO + M = H + CO + M HCO + H = CO + H2 CO + OH = CO2 + H H + 02 = O + OH H2 + O = H + OH H2 + OH = H 2 0 + H H + 02 + M = HO2 + M H02 + OH = H20 + 0 2

Aj 4.00 3.02 3.02 2.51 1.00 7.58 3.31 1.44 2.00 1.51 5.13 1.80 2.19 1.51

1012 1013 1012 I0 ~3 1012 1012 1014 1014 1014 l07 1016 10 l° 1013 1015

5.01 1013

Here cm, tool, kcal, and K are units, with kj = AjTnj exp[-Ei/(RT)].

nj 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.30 -0.816 1.00 0.00 0.00 0.00

Ej 2.00 7.00 0.00 29.000 6.00 0.170 10.50 19.00 0.00 -0.770 16.510 8.900 5.150 -1.00 1.00

METHANOL-AIR DIFFUSION FLAME

117

2a -1 a=-~-~H 3 ON 0 : C02 ,~ : H 2 0 O : 02 • : Temperature

2000 1800 0.8

1600 14OO

•~- 0.6 2a -2 a:CO O:

12O03

£ u_ 0.4

H2

A: CH20 • : Temperature

Q.

~J

ecoE

~- 0.2

6oo ~ 4OO

2a -3 o:H

0 -0.5

o : OH ~,:O O: HCO x l O 0 0

-o13

-o.i

• : Temperature

.2000

2O00

.010 -

18OO

1800 0.10

160)

• 1600~.

1,~o}

•1400 :~

o.o8

~

2(?0

2a -1

V: CH20H

0.12

o'.1

X (cm)

.1200 0.06

~ .006-

-1000

.~o~ ~

~0.04

,12oo 3

.O04-

.800

&l

6OO

~002-

E

6oo~

_ .002.

400

0.0 -0.5

2OO

-0.3

-0.1

01

x(cm)

0.0' -0.5

2(3O

-0.3

-0.1

0.1

x(cm) 2a -2

Fig. 2a. Structure o f a counterflow methanol diffusion flame calculaW, d for a the long mechanism a (dotted line), and the short mechanism a (solid line).

constants shown in Tables 2 and 3 relate to the path CH2OH-CH20-HCO. Because some uncertainty exists concerning the true value of the rate constants, we will consider both sets separately. Numerical calculations were performed for different sets of values of the quantities p~.v** and p_ ®v_ **, and each set represents a particular value of a. The value of the absolute pressure was 1 atmosphere in these calculations. The results are discussed in the following section. RESULTS A N D DISCUSSIONS In Figs. 2a-l, 2a-2, 2a-3 we compare the structure of the flame calculated using the long mechanism shown in Table 1 (broken line) with that calculated using the short mechanism shown in Table 2 (solid line). The calculations were performed with p**v® = - 0 . 1 5 gm/cm2/s, and Yo2® = 0.23, Ys2o, = 0.77 at x = lcm, and p_~.o_® = 0.1 gm/cm2/s, Yk = O, k :/: F a t x = - 1 cm. A t a = 60 s-I the flame is far from the critical conditions of extinction, and the stagnation plane is located at x =

2a-3 = 60 s - J using

- 0 . 2 6 cm. Figure 2a-1 shows excellent qualitative and quantitative agreement between the two sets of profiles for CH3OH, 02, H20, and CO2. The temperature profile calculated using the short mechanism a is slightly lower and slightly shifted towards the oxidizer side as compared to the profde obtained by using the long mechanism a. In Fig. 2a-2 the profiles for the major intermediate species H2, CO, and CH20 are plotted. There is qualitative agreement between the sets of profdes, but the peak values of the concentration of H2 and CO are much lower for the results obtained using the long mechanism when compared with the results obtained using the short mechanism. The differences can be attributed to the pyrolysis of CHaOH to form CH3 and CH4 in the long mechanism and to the formation of CH20 from CH2OH. In Fig. 2a-3 we have plotted profdes for the reactive species and radicals. The profiles again show excellent qualitative agreement, however, from Fig. 2a-3 we observe that the peak values of the concentration of the H radical are different. Because CI-I4 reacts with H, the peak

118

K. SESHADRI ET AL. 2 b -1 o=--~--CH3 OH o = CO2

16oo ~ 1400 1200 2

0.8

= H20 O = O2

~

• : Temperature

2b-2 o = CO O: A:

2OOO 1800

1

o.6

iooo ~o.4

H2

CH20 • = Temperature

~ 0.2

2b-3 o:H o : OH ~:O O: HCO x l O 0 V : CH2OH = Tempercrture O.12.

0

-0.5

-0.3

-0.1 X (cm)

O.1 2b-1

2000 18OO

.18OO O.10-

•1 6 0 0 ~

16oo

•

140o "~

~ 12oo~ 8 .006. .lOOO g ~ .a00~ ~ .004. .14oo

= 0.08" ._O

"~ O.06i.a.

o 0.04.

1200 10OO

~ 800 E 600 ~ 400 2OO

Q)

600 400

~- 0.020.O -0.5

200 -0.3

~

800E 6OO ~ 4OO 200

-0.1

01

~ .002, 0.0 -0.5

-0.3

-O.1

O.1

x(cm)

x(cm) 2b-2

2b-3

Fig. 2b. Structure of a counterflow methanol diffusion flame calculated for a = 60 s- l using the short meehartism b.

value of the concentration of the H radical is lower when the long mechanism is used. Both sets of profiles show that the peak values of H, OH, and O occur on the oxidizer side of the flame. Because the radicals H, OH, and O react rapidly with CH3OH, CH2OH, CH20, and CI-I4, their concentration is small in the regions where the concentration of CH3OH, CH2OH, CH20, and CI-I4 are not negligible. However, the concentration of these radicals rise rapidly after the concentration of CH3OH, CH2OH, CH20, and CI-I4 have attained negligibly small values. A similar observation has been made previously for methane-air diffusion flames [2, 5, 16-18, 27]. Figs. 2-a2 and 2a-3 also show that the concentration of the radical HCO is small, and that the concentration of CH2OH and CH20 are nonzero over a broad range. From Tables 1 and 2 we observe that the decomposition of CH2OH by active radicals and the third body M leads to CH20. However, the concentration of the active radicals are negligibly small on the fuel rich region of the flame, and in this region decomposition of CH2OH occurs only by collision with an

energetic third body M, whereas in the fuel lean region, CH2OH is attacked by the third body M as well as by radicals. Consequently, the profile of CH2OH is steeper on the fuel lean region. Because CH20 is formed from CH2OH, the profile of CH20 is qualitatively similar to CH2OH. In Figs. 2b-l, 2b-2, and 2b-3 we have plotted profiles similar to those in Figs. 2a-l, 2a-2, and 2a-3 at identical ambient conditions but using the data shown in Table 3. With the strainrate a again set equal to 60 s- 1, the stagnation plane is located at x = - 0.26 cm. The profiles for CH3OH, 02, H20, and CO2 are remarkably similar in Figs. 2a-1 and 2b-1, and the peak values of the temperature are nearly the same although they occur at different locations in the flame. The peak values of the concentrations of H2, CO, and CH20 in Fig. 2b-2 are much lower than those in Fig. 2a-2 and are attributed to the higher reaction rates for the path CH2OH-CH20-H2, CO if the data shown in Table 2 is used. Comparing Figs. 2a-3 and 2b-3 we observe that the peak values of O are nearly the same, the peak values of OH and H in Fig. 2b-3

METHANOL-AIR DIFFUSION FLAME

119

3 a -1 e:CH20 0 : C H2OH •", : H C O

4.0

o : 0 : zx: O=

30t

%

2.0

x

~ 1.o

3a - 2 H20 CO2 CO H2

/ Y

S -2.0 _1.1o

~

#-°°1

3a -3

oc - 3 0

I3:H

-40 -0.5

O= O H z~:O

-63

-61 x(cm)

61 3a-1

7.O

7.05.0× o

1.0-

c

-1.O.

n," O

~× 5o 3.0 t

3.0-

c3 1.0

CC

o -3.o

-3.0.

-1° 1

rr -5.0

:," - 5 . 0 -7.0 -0.5

-(5.3

-0.1 X (cm)

6.1

-7.0

-0.5

-0'.3

-(5.1

o~1

X(cm) 3a-2

3 a -3

Fig. 3a. Net rate of production of various species calculated for a = 60 s - ' using the short mechanism a.

are lower than those in Fig. 2a-3, while the peak value of CH2OH in Fig. 2b-3 is considerably higher than that in Fig. 2a-3. This is attributed again to the higher reaction rates for the path CH2OH-CH20-H2, CO if the data shown in Table 2 is used. In Figs. 3a-l, 3a-2 and 3a-3 we have plotted the chemical rates of production or destruction for the various chemical species for a = 60 s- 1 using the data shown in Table 2. The profiles represent the term WkWk in the species balance Eq. 3. Figure 3a-1 shows that in the region - 1 cm < x < - 0 . 1 6 cm the dominant reactions 1-9 are shown in Tables 2 and 3. In this region CH3OH forms CH2OH, and CH20 which subsequently form CO and H2. Hence, this region can be identified as the fuel consumption region. The region between - 0 . 1 6 cm < x < 0.00 cm will be identified as the H2-CO oxidation region, because in this region 1-12and CO oxidize to form 1-120 and CO2, and Fig. 3a-2 clearly shows that while CO and 1-12 are destroyed, 1-120 and CO2 are formed in this region. Figure 3a-3 shows production and destruc-

tion rates for the radicals H, O and OH. These quantifies are produced primarily in the H2-CO oxidation region and diffuse to both sides. On the left-hand side they react with CH3OH, CH2OH, CH20, and HCO to form CO and H2. On the righthand side near x = 0.00 cm where the temperature is around 1000 K we will show that there exists a thin radical destruction layer where radicals are rapidly destroyed by the three-body reaction 14 shown in Tables 2 and 3. In Figs. 3b1, 3b-2, and 3b-3 we have plotted profiles similar to those in Figs. 3a-l, 3a-2, and 3a-3 but using the data shown in Table 3. The profiles shown in Fig. 3b-2 are qualitatively similar to those shown in Fig. 3a-2, although the rates of H2 and CO oxidation are much lower in Fig. 3b-2. Figures 3a1 and 3b-1 show some qualitative differences in the profiles. The rates of destruction of CH2OH via reactions 3, 4, and 5 to form CH20 are much faster if the data shown in Table 2 is used. Consequently, the concentration of CHzOH in Fig. 2a-3 is lower than the concentration of CH2OH in Fig. 2b-3. However, both Figs. 3a-1 and 3b-1

120

K. SESHADRI ET AL. 3b-1 o=CH20 O = C H2OH = HCO

4.0 3.0 o x

3b o : O: z~: O=

-2 H20 CO2 CO H2

1.0 ,Y

-2.0n," -3.0.

×

3.0

~o

1.o!

-0'.3

-0.1

O.1

X(cm)

3b-1

4.0.

c -1.01 o

oh o ×

2.0

c~

0.0

5

-30-

g _2.o

o

0c

,v - 5 . 0 -7.0-0.5

-4

-4.0 -0.5

7.O 5.0

0.0

8 -1.0-

3b -3 O:H O= O H z~:O

m O

2.0

-O.3

-O.1 X(cm)

O.1

-4.0 -0.5

-0.'3

-5.1

o.I

×(cm) 3b -3

3b-2

Fig. 3b. Net rate of production of various species calculated for a = 60 s- ' using the short mechanism b.

show that CH20 is produced in a broad zone while it is consumed in a narrow zone. Figures 3a-3, and 3b-3 show that in the region where H is produced OH is destroyed, and in the region where H is destroyed OH is produced. In Fig. 4a the reaction rate of reactions 1-9 shown in Table 2 are plotted as a function of x for a = 60 s- 1. These reactions occur predominantly in the fuel consumption region. Figure 4a shows that CH3OH is consumed primarily by reaction 2, and CH2OH is consumed primarily by reactions 3 and 4, while the rate of reaction 5 is very small. The consumption of CH20 via reaction 7 is comparable to the consumption of CH20 via reaction 6, however, the consumption of HCO via reaction 9 is much smaller than the consumption of HCO via reaction 8. Similar profiles using data shown in Table 3 are plotted in Fig. 4b, for a = 60 s-l. The qualitative behaviour of the profiles in Figs. 4a, 4b are similar with the exception that in Fig. 4b the rate of reaction 8 is comparable to the rate of reaction 9. To determine which species are in steady state in the fuel consumption region, we

have plotted in Figs. 5a and 5b the net production and destruction rates of CH2OH, CH20, and HCO using the data shown in Tables 2 and 3 for a = 60 s -1, respectively. Fig. 5a shows that the net production rate of CH2OH represented by the sum of the rates of reactions 1 and 2 is nearly equal to its net destruction rate represented by the sum of reactions 3, 4, and 5. Consequently we conclude that the concentration of CH2OH is approximately in steady state. However, because the sum of the rates of reactions 6 and 7 is larger than the sum of the rates of reactions 3, 4, and 5 we conclude that the concentration of CH20 is not in steady state, but the concentration of the species HCO is in steady state because the sum of the rates of reactions 8 and 9 is approximately equal to the sum of the rates of reactions 6 and 7. However, these results may change for different values of the strain rate a. The results in Fig. 5b, however, show that the concentration of the species CH2OH and CH20 are not in steady state, whereas the concentration of the species HCO is in steady state. Some additional important conclusions can

METHANOL-AIR DIFFUSION FLAME

121 20.0

20.0. ~t o

0 x

o = Reaction 1 0 = Reaction 2

15.0-

x

0

1Q0-

""

a : Reaction 3 O: Reaction 4 /',: Reaction 5 xlO0

15.0 10.0

8

~ 5.0

5.0n-

0.0 -0.5

-0.3

-6.1 X(cm)

C).1

O.C -0.5

. ' ~ -0.3 -0.1 X(cm)

4a -1

4a-2

20.00 )<

6.1

20.0, u : Reaction 6 0 : Reaction 7

15.0-

o

a : Reaction 8 0 : Reaction 9

15.o

x

9 rr

a

10.0-

10.0-

.~_ ~ 5.0-

5.0-

rY 0,0. -0.5

-8.3

-5.~

6.1

o.o-0.5

-o'.3

-o.1

4.1

X(cm )

X(c m ) 4a -3

4a-4

Fig. 4a. Rates of various reactions for a = 60 s - ~ calculated using the short mechanism a.

20.0

20.0

o : Readion 3 O: Reaction 4 ~= Reaction 5 x 1 0

xt

o

[] = Reaction 1 0 : Reaction 2

15.0,

0 x

15.0

x o ¢r

1QO.

.8_

5.0

5.0

0.0 -0.5

0c

-6.3

-4D.1 X(cm)

0.£ -0.5

().I

0 r,-

-6.1

51 4b-2

4b -1 20.0

~t

x

A

-0.3

X(cm)

20.0

o

10.0

8

o : Reaction 6 0 = Reaction 7

15.0-

o

15.0.

x

o

10.0.

o : Reaction 8 0 = Reaction 9

~t

10.0.

8 5.0'

5.0' n~

0,0 -0.5

-()3

-6.1

(~.1

X(c m )

0.0 -0.5

-(~3 X(cm )

4b -3

-6.1

0.1 4b-4

Fig. 4b. Rates o f varioas reactions for a = 60 s - 1 calculated using the short mechanism b.

122

K. SESHADRI ET AL

20.0

15.0

~

0 Reaction

x

-g

Reaction 3 ~ 4 ~ 5 ReGction 1 ~2

10.0-

n~ co

Q~

5.0.

0.0 0.5

0.1

0.3

().1

X(cm)

Fig. 5a. Sum of the rates of selected reactions for a = 60 s-J calculated using the short mcchaulsm a.

20.0-

15.0R e a c t i o n 14 2 - ~ 0 Reaction 3 ~ 4 1 5 ,

x

~-Reaction 6 (, 7 a nd Reac[ion 81, 9

10.0cr to

*g 0 o ¢Y

5.00.0 0.5

/ o'.3

o'.~

6.1

X(cm) Fig. 5b. Sum of the rates of selected reactions for a = 60 s-1 calculated using the short mechanism b.

METHANOL-AIR DIFFUSION FLAME 4.0'

123 0.020

R~cLion 10 D : Forward Rote 0 : BaEl~vord Rote

tv~

o × 3.0'

Reoction 11 n : Forward Rote . kword,Rote

0.015 rY

o

2.0

8 0.010'

~, 1.o

$ 0.005

.~_ ..J

O.C -0.5

-6.3

7.0

().1 6a-1

Reaction 12 n : Forx,vard Rate 0 : Backward Rate

o 6.0

;l

5.0 4.0" _8 3.0" o 2.0o

t'r

1.00.0 -0.5

-0.1 X(cm)

-6.3

-.0.1

X(cm)

O.OOC -0.5

0.040 0.035 0.030

-o.3

-o.1 X(cm )

o.1 6a-2

Reaction 13 0: For~vorclRote O: Backward R a t ~ .

o.o25! 0.020-

0.1

6a-3

0.0150.010. 0.0050.000 -0.5

-b.3

~.i

X(c m )

0.1

6a-4

Fig. 6a. Comparison of the forward and backward rates of selected reactions calculated for a = 60 s-1 using the short mechanism a.

be deduced from Figs. 4a, 4b, 5a, and 5b. Because the activation energies of reactions 1 and 2 are not large, these reactions, and consequently the fuel consumption reactions, are not the limiting reactions in the fuel consumption region. They are not strongly influenced by increasing values of a. Figures 4b and 5b show that the rate of consumption of CH20 is greater than the rate of consumption of CH2OH. Hence, the consumption of CH2OH is the limiting reaction. In addition, Fig. 4b shows that the rate of consumption of CH2OH via reaction 4 which has a high activation energy is larger than the rates of consumption of CH2OH via reactions 3 and 5. Consequently, if the data shown in Table 3 is used, the key limiting reaction in the fuel consumption region is reaction 4, and the rate of this reaction can be strongly influenced by increasing rates of strain. However, Figs. 4a and 5a show that CH2OH and HCO are in steady-state, while CH20 is not. Consequently, if the data shown in Table 2 is used, consumption of CH20 via reactions 6 and 7 are the key limiting reactions in the fuel consumption region. Consequently,

there is a fundamental difference in the structure of the fuel consumption region as illustrated by Figs. 4a and 5a when compared to 4b and 5b. In Fig. 6a the forward and backward rates of reactions 10, 11, 12, and 13, which occur predominantly in the H2-CO oxidation region layer, are plotted using the data shown in Table 2 for a = 60 s -1. Reaction 10 is the major path for the oxidation of CO to CO2, and reaction 11 is the principal chain branching reaction. ~ Figure 6a shows that the rate of reaction 11 is much larger than the rate of reaction 10. In addition, Fig. 6a shows that reaction 13 is extremely fast in both directions, and it can be verified that the ratio of the difference between the forward and backward rate of reaction 13 to the forward rate is a small quantity. Therefore, it is reasonable to assume that reaction 13 is in partial equilibrium. Consequently, there exists an algebraic relation among the concentrations of the species H2, OH, H20, and H. Using similar arguments it is reasonable to assume that reaction 12 is in partial equilibrium, and consequently there exists an algebraic rela-

124

K. SESHADRI ET AL. 4.0

0.020

Reaction 10 13 = F o r w a r d Rate O : Bock~vQrd Rote

% >( 3.0

ReQction 11 a = Forward Rate O : Backward Rate

0.015 o

#_

,"lr"

8 O.OLO

2.0 ~

0.005

1.00c

0.0 -0.5

-0.3

7.0.

o

6.0"

x ¢J

5.0.

o

8_

-0.1 X(cm)

-().3

6b-1

-0.I X(cm )

C).I 6b

-2

0"040 I Reaction 13 0.025. o=Fctw~rd Rote O: B a d ~ a r d Rote

Reaction 12 o : Far, rand Rate o : Backward Rate rY

4.0"

0.o20

8 o.o15

3.0-

13 o 2.0tY

0.010 0.005

1.00.0 -0.5

0.000 -0.5

().1

-{i3

-011

0.000 0.1

X(cm) 6b-3

-0.5

-o.3

~0.1 x(crn )

6.1 6b-4

Fig. 6b. Comparison of the forward and backward rates of selected reactions calculated f o r a = 6 0 s - t using the short mechanism b.

tionship among the concentrations of the species H2, O, H, and OH. From reactions 12 and 13 it can be shown that the concentration of the radical O is proportional to the square of the concentration of the OH radical. In Fig. 6b we have plotted profiles similar to Fig. 6a but using the data shown in Table 3 with a = 60 s - 1. The profiles in Fig. 6b are qualitatively similar to profiles in Fig. 6a and we deduce the same conclusions. In Figs. 7a and 7b the rates of the chain breaking reactions 14 and 15 are plotted using the data shown in Tables 2 and 3 for a = 60 s-1, respectively. Comparing the forward rate of reaction 11 shown in Figs. 6a and 6b with the rates of reactions 14 and 15, we observe that the rate of the chain branching reaction is much greater than the rate of the chain breaking reactions over a major part of the reaction zone. However, the rate of reaction 11 is approximately equal to the rate of reaction 14 atx¢ = 0.015 cm if Figs. 6a and 7a are compared, and at Xc = 0.09 cm if Figs. 6b and 7b are compared, and the temperatures at these locations are respectively T¢ = 1091 K and T~ =

853 K. At values o f x greater than xc the rate of the chain breaking reaction is greater than the rate of the chain branching reaction. Around x = xc a thin radical consumption region exists. Because the rate of reaction 14 depends on the concentration of the third body, it is a function of total pressure. To examine the change in the structure of the flame as extinction is approached, numerical calculations were performed at a value of a = 521 s-1 using the data shown in Table 2. The profiles for the temperature, the major species, the intermediate stable species and the radicals were similar to those shown in Figs. 2a-l, 2a-2, and 2a3. However, the reaction zone for a = 521 s-1 was spread over a smaller range of values of x when compared to the reaction zone for a = 60 s- 1. In Fig. 8a reactions 1-9 which occur predominantly in the fuel consumption region are plotted. Comparing Figs. 4a and 8a we observe that the reaction rates increase with increasing rate of strain. Figure 8a shows that the consumption of CH2OH by reaction 3 is comparable to that by reaction 4, whereas in Fig. 4a the rate of reaction 4

METHANOL-AIR DIFFUSION FLAME

125

5.0-

4.0-

"~ C)

0 : ReOCtlOn 14 0 : ReOctlon 15

3.0-

X

Or"

2.0-

C

o

~

1.0

0.O 0.5

0'.3

o.1

0".I

X (cm)

Fig. 7a. Rates of selected reactions calculated for a = 60 s- ~ using the short mechanism a.

5.0 ~

4.0,

"¢ 0

o : ReactLon 14 0 : R e a c t i o n 15

3.0

X

Or"

2.0

C

,£

0.0

0.5

.

63

o.t

o".1

X(cm) F i g . 7b. R a t e s o f selected reactions calculated for a = 6 0 s - ~ using the short mechanism b .

126

K. SESHADRI ET AL.

x

o

4.0-

o Reaction 1 0 Reection 2

x

n Reoction 3 0 Reaction 4 ~7React ion 5

2.0

3.0.

8

g

.7 2.0. cr

,I

3.0

5.0.

.~ 1.0

100.0 -0.5

-63

-6.1 x (cm)

-0.3

6.1

-0.1 X (c m)

8,3-2

Ba-1

$

6.0 ¸

4.0.

×

o ReoctLon 6 0 Reaction 7

o 3.0-

)< 13 12:

5.0

c

~d

0

I)

"~ 2.0

3.0.

o

n- 1.0-

rr

-0.5

o Reection 8 0 Reacbon 9

4.0

~_ 2.0-

O,0

0.1

-(5.3

-(5.1

X (cm)

(5.1 8a-3

1.0 O.C -0.5

-O.3

-6.1

X (cm)

6.1 Ba-4

Fig. 8a. Rates of various reactions calculated for a = 521 s-~ using the short mechanism a.

is greater than the rate of reaction 3. This causes a fundamental change in the structure of the fuel consumption region with increasing rates of strain. Reaction 4 has a large activation energy while reaction 3 has a small activation energy. In addition, the consumption of CH20 via reaction 6 is larger than that via reaction 7 in Fig. 8a, while it is reversed in Fig. 4a. This causes no fundamental change in the structure of the fuel consumption region because the activation energies of reactions 6 and 7 are comparable. In Fig. 9a the sum of reactions 1 and 2; 3, 4, and 5; 6 and 7; and 8 and 9 are plotted. Examining the profiles in Fig. 9a we can again conclude that the concentrations of CH2OH and HCO are in steady state whereas the concentration of CH20 is not in steady state. In Fig. 10 we have plotted the forward and backward rates of reactions 10, 11, 12, and 13, which are predominant in the H2-CO oxidation layer for a = 521 s-~. Examining the profiles in Fig. 10a, we observe that the qualitative behaviour of the rates of reaction 10, 11, and 13 are similar to those in Fig. 6a. However, Fig. 10 shows that the backward rate of reaction 12 is much smaller

than its forward rate, consequently reaction 12 is not in partial equilibrium. Finally in Fig. 1 la we have plotted the rates of the chain breaking reactions 14 and 15 for a = 521 s- ~using the data shown in Table 2. Comparing Fig. 7a, and Fig. 11 we observe that the rates of the chain breaking reactions also increase with increasing rates of strain. To clarify the mechanisms of extinction of methanol-air diffusion flames, calculations were performed at a number of values of the strain rate until no numerical solution was obtained for the set of equations. Figures 12a, and 13a show the peak values of the temperature and the peak values for the concentrations of CO, CO2, H2, CH20, H, OH, and CH2OH. The dotted lines represent calculations using the data shown in the long mechanism, Table 1, and the solid lines represent calculations using data shown in the short mechanism, Table 2. If the data shown in Table 1 is used, then no solution was obtained for a > 540 s -~, whereas if the data shown in Table 2 is used, then no solution was obtained for a > 521 s-~. However, the qualitative features of the profiles

METHANOL-AIR DIFFUSION FLAME

127

60.055.0" 50.0Mr

o

45,0"

X

40.0"

o rY

35.0-

co

3QO.

U

25.0'

(11 rY

20.0. 15.0.

Reaction 1 ~ 2 and Reaction 3,4 ~ 5

Reaction

6 t 7

and

10.0

React ion 8 t 9

5.0 0.0. -Q5

-0.3

d.1

-0.1

X (cm) Fig. 9a. S u m of the rates of selected reactions calculated for a = 521 s - ~ using the short

mechanism a.

4.0

0.020.

Reaction 10 o : Forward Rate 0 : Backward Rote

× 3.0

Reaction 11 O : Forward Rate O : Backward Rate

0.015(D rY

a

8 o.oio-

2.0

8 1.o.

o.oo~-

CI:

O.C -0.5

-0:1

-o. 3

0.ooo

d.1

X(cm)

-o.5

12

[] : Forward Rate 0 = Backward Rate

5.0.

o

Reaction 13 o : Forward Rate 0 : Bocl~vard Rate

0.035ej

O.030-

._~ 0.020-

._~ 3.0.

"~ 0.015a

2.0.

OOLO-

/

I:E

1.0. 0.0 -0.5

I0a-2

~ 0.025n,"

n,- 4 . 0

o

d,1

0.040 Reoqtion

6.o,

x

e

-d.1 X(cm )

I0a-I

7.0

o

/, -d,3

-O.3

0.005 -0'.1

C).1

X(cm)

0.oooi -0.5

-C).3

-O11

6.1

X(cm) 10a- 3

IC~-4

Fig. lOa. Comparison of the forward and backward rates of selected reactions calculated for a = 521 s- ~ using the short mechanism a.

128

K. SESHADRI ET AL

3.0.

o = Reaction 14 o = Reaction 15

0 X

2.0

n-

cO

"5 o

13~ 1.0.

0.0

-0.5

-0'.3

-d.1

o'.1

X (cm) Fig. 1 la. Rates of selected reactions calculated for a = 521 s - i using the short mechanism a

.1850

o= CO 0 = C02 ~, = H 2

Q32

• = Temperature

4800

cO

:'o-~0.22I,.,. LL 0

P

\ ~

\\\\

1750 e~

E

\

0.12-

Q.O 2

60

I-...-

1700

1~0

160

2~,0 360 :~60 4~0 Strain Rote (s 4 )

4ko

~0

1650

600

Fig. 12a. Maximum values of temperatures and mole fractions of certain species as a function of the strain rate calculated using the long mechanism a (dotted line), and the short mechanism a (solid line).

METHANOL-AIR DIFFUSION FLAME

129

0.20

-1850 o =CO

0 = C02 zx= H2 0.15

• =

Temperature

1825 A

tO

\

0,10LL

I

1800 o_,

E

o----.._.

1---

z

1775

0.05-

0.01

60

~

I(X)

I~

140

I~

I~0

1750

2(]0

Strain Rate (s-l) Fig. 12b. Maximum values of temperature and mole fractions of certain species as a function of strain rate calculated using the short mechanism b.

.1850 o = CH20 o=H o : CH20H

0.0306.

~=

OH

• =

Temperature

-1800

\\\

t°O ~

~ 0.0206.

-1750 -,-'

IJ_

(D ~L

~u o

E

\

(3; I--

1700

Q0106 r

0.0006

~

60

120

180

240

3()0

Strain Rate

360

4,9.0

480

,~

1650

600

(s-I)

Fig. 13a. Maximum values of temperature and mole fractions of certain species as a function of the strain rate calculated using the long mechanism a (dotted line), and the short mechanism a (solid line).

130

K. SESHADRI ET AL. 1850 .019-

a = CH20 o=H z~= OH O= CH20H • = Tempero tu re

.017

.015

tO

'5 0

.1~25

,,c-

.013

moo P .011

E I--

.00£

.1775

.007.

.005

.003

60

~,0

16o

i~o i~ Strain Rote (s-l)

leo

lao

1750 200

Fig. 13b. Maximum values of temperature and mole fractions of certain species as a function of strain rate calculated using the short mechanism b.

are nearly the same, and we can conclude that the structure of the flame determined using the short mechanism shown in Table 2 is nearly the same as that obtained using the long mechanism shown in Table 1. Figures 12a, and 13a show that the peak values of the temperature and the concentrations of CO, CO2, H2, and OH decrease with increasing values of a, while the peak concentrations of CH20, O, and CH2OH increase with increasing values of a. However, the peak value of the concentration of H increases first with increasing values of a and then decreases. Also, near extinction the peak values of these compounds decrease dramatically. The peak values of the temperature profiles in Fig. 12a initially decrease with increasing values of a, then remain at a constant value and then decrease dramatically near the value of a at extinction. We speculate that the initial decrease in the values of the peak temperatures at low rates of strain is due to the fact that the consumption of CH2OH occurs via reaction 4 which has a large activation energy (see Fig. 4a). However, with increasing rates of strain as shown in Fig. 8a, the rate of consumption of CH2OH via reaction 3

which has a small activation energy becomes comparable to the rate of consumption of CH2OH via reaction 4. Cor, sequently, the peak values of the temperature do not change dramatically with a further increase in the value of a. The sharp drop in the peak values of the temperature near extinction indicate that extinction is caused by a large value of the activation energy for a limiting reaction. Because the rates of the fuel consumption reactions 1 and 2 and the rates for consumption of CH20 via reactions 6, and 7 do not have a large activation energy, these reactions cannot be responsible for extinction. However, reaction 8 has a large activation energy. Consequently, we speculate that near extinction HCO is not in steadystate and reaction 8 causes the flame to extinguish abruptly. In Figs. 12b and 13b we have plotted profiles similar to those in 12a and 13a but using the data shown in Table 3. If the data shown in Table 3 is used, then no solution was obtained for values of a greater than 168 s-i. However, the overall qualitative features of the profiles in Figs. 12b and 13b are similar to those in Figs. 12a and 13a. The differences in these two sets of results are attrib-

METHANOL-AIR DIFFUSION FLAME uted to the differences in the rate of reaction 4, which has a large activation energy. With increasing strain, it was observed that the rate of consumption of CH2OH by reaction 4 was always greater than the rate of consumption of CHEOH by reactions 3 and 5, therefore leading to extinction at a smaller value of a. However, as before, we speculate that for values of a near extinction HCO is again not in steady state, and reaction 8 can contribute to the abrupt extinction of the flame. SUMMARY AND CONCLUSIONS Numerical calculations were performed to determine the structure and to clarify the mechanisms of extinction of diffusion flames stabilized between counterflowing streams of methanol and air. The calculations were performed at different values of the rate of strain a, with different chemical kinetic mechanisms. The detailed chemical kinetic mechanisms are identified as the long mechanism a shown in Table 1, the short mechanism a shown in Table 2, and the short mechanism b shown in Table 3. The values for the rate constants shown in Tables 1 and 2 were those proposed by Warnatz [12-14], and the values of the rate constants in Table 3 were those proposed by Westbrook and Dryer [1, 2, 10, 11]. In Fig. 2a we have compared the structure of the diffusion flame for a = 60 s-l using the long mechanism a, and the short mechanism a, and we obtained excellent agreement. Therefore, it was concluded that the short-mechanism a can be used to predict accurately the structure of methanol-air diffusion flames. In Figs. 3a and 4a, we have plotted the net rates of production and destruction for the various chemical species and various reactions for a = 60 s- 1. The profiles in Figs. 2a, 3a, and 4a suggest that the structure of the flame can be subdivided into three regions: the fuel consumption region, where reactions 1-9 shown in Tables 2 predominantly occur and follow the path CHaOH-CHEOH-CHEO-CO, HE; the HE-CO oxidation region, where reactions 10-13 shown in Table 2 predominantly occur and H2 and CO oxidize to form HEO and CO2; and the radical destruction region, where the radicals are rapidly destroyed by the three body reactions 14 and 15

131 shown in Table 2. Similar conclusions were drawn by examining the profiles plotted in Figs. 2b, 3b, and 4b calculated using the rate constants shown in Table 3. However, the concentration of CHEOH in Fig. 2a is considerably smaller than that shown in Fig. 2b, which suggests that the path CH2OH-CHEO is faster if short mechanism a is used. In Figs. 5a and 5b we have plotted the net production rates and destruction rates of CHeOH, CHEO, and HCO using the data shown in Table 2 and Table 3, respectively. Figure 5a shows that the concentrations of the compounds CHeOH and HCO are approximately in steady state, whereas Fig. 5b shows that only the concentration of HCO is in steady state. Figures 4b and 5b show that the consumption of CHEOH via reaction 4 shown in Table 3, which has a high activation energy, is the limiting reaction in the fuel consumption region, whereas Figs. 4a and 5a show that consumption of CHEO via reactions 6 and 7 shown in Table 2 are the limiting reactions in the fuel consumption region. Consequently, there is a fundamental difference in the structure of the fuel consumption region between Figs. 2a-5a and Figs. 2b-5b. In Figs. 6a and 6b the forward and backward rates of reactions 10, 11, 12, and 13 are plotted using the data shown in Table 2 and Table 3, respectively and we conclude that reactions 12 and 13 are in partial equilibrium. To clarify the changes in flame structure as extinction is approached, in Figs. 8a-1 la we have plotted profiles similar to those in Figs. 4a-7a using the data shown in Table 2 but with a -- 521 s -~. The fundamental differences are that as extinction is approached consumption of CHEOH by reaction 3 which has a low activation energy is comparable to that by reaction 4 which has a large activation energy and reaction 12 shown in Table 2 is no longer in partial equilibrium. In Figs. 12a, 13a, 12b, and 13b we have plotted the peak values of the temperature and the peak values of the concentrations of CO, CO2, H2, CHEO, H, OH, and CHEOH as a function of the rate of strain a. We observe that no solution was obtained for values of a greater than 521 s - l if the data shown in Table 2 is used, and no solution was obtained for values of a greater than 168 s- 1 if the data shown in Table 3 is used. We attribute this

132 difference to the relative rates of consumption of CH2OH via reactions 3 and 4 shown in Tables 2 and 3. If the data shown in Table 2 is used, as a is increased, the rate of consumption of CH2OH via reaction 3 becomes comparable to the rate of consumption of CH2OH via reaction 4. However, if the data shown in Table 3 is used, consumption of CH2OH via reaction 4 is always larger than consumption of CH2OH via reaction 3. Because reaction 4 has a large activation energy, abrupt extinction occurs at a comparatively low value of a. However, if the data shown in Table 2 is used, we speculate that near extinction the concentration of HCO is not in steady state and reaction 8 causes the flame to extinguish abruptly. We are currently analyzing the structure of methanol-air diffusion flames using reduced reaction mechanisms, and the results will be published later. This research was s u p p o r t e d by the US A r m y Research Office Contract n u m b e r D A A L 038G-K-O001. Dr. D a v i d M a n n is the technical m o n i t o r o f this p r o g r a m . W e t h a n k Ms. Janet B r u c k e r f o r preparing the m a n u s c r i p t f o r publication.

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Received 22 June 1987; revised 2 May 1988