A study of flat flames on porous plug burners: Structure, standoff distance, and oscillation

COMBUSTION A N D F L A M E 6 9 : 3 7 - 4 8 (1987)

37

A Study of Flat Flames on Porous Plug Burners: Structure, Standoff Distance, and Oscillation A K I M A S A Y U U K I and Y A S U J I M A T S U I Central Research Laboratory, Mitsubishi Electric Corp., Amagasaki, Hyogo, Japan

The stable structure and the time-varying behavior of stoichiometric methane-air flames on a porous metal burner at atmospheric pressure were studied using a numerical model which includes detailed chemical reactions. It has been confirmed that the model gives quantitative agreement with experiment for stable flame structures such as flame temperature, radical concentrations, and standoff distance, and also flame oscillation. It was shown that the overall activation energy and the standoff distance increase rapidly in the region of flame temperature < 1550K. Furthermore, it was also confirmed that the flame intrinsically oscillates due to the propagating time lag of the temperature disturbance from the burner surface to the reaction zone, and its instability is enhanced by a large standoff distance. On the basis of these results, it is asserted that the critical flame temperature for the stability of stoichiometric methane-air flames on porous plug burner is near 1550K.

INTRODUCTION The recent requirement for low NOx emission has stimulated interest in surface combustion, resulting in the wide use of low temperature flames stabilized on wire meshes for domestic heaters in Japan. The mechanisms of flashback and NOx emission for mesh burners have been discussed in previous papers [1, 2]. The experiments in those papers showed that the flame became unstable and extinguished when the mixture velocity was decreased excessively. Kaskan [3] and Ishizuka and Law [4] also reported the observation of a vibrating flame on porous metal burners at low mixture flow velocity. The extinction mechanism is usually explained by a heat loss and/or a flame stretch, and has been studied theoretically by many authors assuming a one-step reaction model [5-8]. Some have succeeded in describing qualitatively the flame quenching behavior. Near the extinction limit, however, the flame temperature is so low that the combustion mechanism may be different from that of normal high temperature flames. One Copyright © 1987 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017

of the main purposes of this study is to determine quantitatively flame behavior near the extinction region. The flame near the extinction limit is so sensitive to flame stretch and heat loss that it is difficult to study by experimental techniques. Therefore, a numerical approach is tried in this paper. The detailed chemical kinetic mechanism for hydrocarbon-air flames has been studied for more than a decade. Recently some sets of reactions have been proposed [9-11], and shown to be applicable for the burning velocity and species concentrations. In this paper, the reaction mechanism proposed by Warnatz [10] is used for stoichiometric (4~ = 1.0) methane-air flames. First, the structures of the steady-state flames at atmospheric pressure are calculated for a wide range of mixture flow rates. Second, the dynamic behavior of the flames is simulated, and results are confirmed by the experimental evidence. The fundamental extinction condition of the flame on the porous plug burner is then discussed.

0010-2180/87/$03.50

38

AKIMASA YUUKI and YASUJI MATSUI

NUMERICAL

burner surface:

PROCEDURE

A time varing one-dimensional laminar flame stabilized on a porous plug burner is considered, as schematically shown in Fig. 1. The flame is at a constant pressure and locally follows an equation of state. The behavior of such a flame is controlled by conservation of mass, enthalpy, and species,

O0 aG

A --+--=0, at a X

(1)

Oh Oh A2O ~-~+G ff-X

at X = 0:

Yi = Y/o

and

T = Tm.

(7)

Since the burner has a large heat capacity and a high heat conductivity, it is reasonable to assume T = Tin. But it seems unreasonable to keep stable species concentrations at constant values. For radicals, even though there is little knowledge about the influence of the solid wall on radical behavior, it has been experimentally observed that the catalytic effect of the cooled wall is not significant for gaseous reactions [14]. Therefore, in this paper the solid wall is assumed to be inert for chemical reactions. Thus the boundary condition at the burner surface is modified as follows: at X = 0:

T= Tm,

x t ~ ( h M ~

) Cp a x j ]

'

OX

_ O (Dio OYiMm']

ax

ax

/

+ A 2m T Mi,

(3)

where X is the new coordinate related to the normal distance x by the following equation,

X =x/A,

(4)

and A is the opening area ratio of the burner and represents the net part through which the mixture flows. The burned and unburned side boundary conditions are the same as usual adiabatic flames: at X =

- oo:

at X =

+ o~:

i

Yi = Yio

and

T = To, (5)

The diffusion coefficients in the mixture Di and the heat conductivity k are calculated by methods V and III of Ref. [15], respectively. The kinetic scheme, reaction rates, and the molecular constants are taken from Warnatz [10], and were found in preliminary calculations to reproduce well adiabatic flame characteristics such as burning velocity and stable species profiles. The computational procedure is essentially based on that of Spalding and Stephenson [12]. In the calculation of the time dependent behavior, the mass flow rate G is kept constant and uniform along the flow direction after the stepwise change of G. Therefore, the mass of the calculational zone predetermined by making use of the relation between the burning velocity and flame thickness to be greater than that of the flame zone is kept constant during the calculation. STEADY-STATE

OYJcgX = 0

h m= ~ h* Yim/Mi .

(8)

A paY,+caY, Ot

i.e.,

(2)

and

OT/cgX = O.

(6)

One more boundary condition at the burner surface should be added; Spalding and Stephenson [12] and Dasch and Blint [13] used the following Hirschfelder type boundary conditions at the

FLAME

Calculations were made for a stoichiometric (~ = 1.0) methane-air flame at atmospheric pressure for A = 1.0. Equations (1)-(3) indicate that if the flame is steady and the reactions in the burner are sufficiently slow, the opening area ratio of the

SIMULATION OF COOLED FLAMES

39

Porous Cooling Wall

Flame

~/

i

•

Temperalure

.

. -,o . .

.

.

6

.

'

'

Nomol Disl'anoe x

'

' , 6 '

'

'

'

i 1 I 1 I i IO i i i i . 0 New Coordinote X ( A = 0 . 5 ) Fig. 1. Schematic diagram of a one-dimensional premixed flame On a porous plug burner. ii

i

i

,

i

J

-20

i

t

J

t

I

i

-IO

burner A does not influence the flame structure of the reaction zone. Figures 2a and 2b show the typical profiles of temperature and species concentrations. The mixture flow velocity at 298K, (Uo298 for short) is 8.8 cm/s and the surface temperature Tm is kept at 500K. The discontinuity point in the temperature profile represents the burner surface. The imbalance of the heat flow at the burner surface corresponds to the heat loss to the burner, which

results in reduction of the maximum flame temperature. In this case, radical concentrations at the burner surface are so small that the burner is considered to be located in the preheating zone of the flame, and not to disturb the reaction zone. To investigate the influence of the surface location on the flame structure, the relation between the burner surface temperature Tm and the flame temperature Tf is simulated. Results are shown in Fig. 3 for the mixture mass flow rate of

CI'I4-AIR I1=1.0 Go= O.OlOg/cn~s

30

-015

-0~

,¢

.,.~, ==

O2

~'0

cH4

COz

-O2

0

X

02 mm

Fig. 2a.

04

Q6

0.8

1.0

40

AKIMASA YUUKI and YASUJI MATSUI

0.3E

CHOxlO00

~

LL I~t 0.12 -0.6

-0.4

-0.2

0

02

04

06

0.8

1.0

X mm Fig. 2b. Fig. 2. Species and temperature profiles for a stoichiometric methane-air flame at atmospheric pressure, where Uo298 = 8.5 em/s and Tm= 500K.

CH4- AIR =1.0

2300 Gg=O.O45g/cmZ$ ~ ,

2200

To= 296K To =800K

To =I O00K

~," 2100 Go=0.02 g/crn2s

---,,,.

To = IO00K 1900

1800 I

tO00

.

.

1500

Tm

.

.

|

2OO0

K

Fig. 3. Dependence of the burner temperature Tm on flame temperature T~ as parameters of Go and To.

Go = 0.045 g/cm2s and 0.020 g/cm 2 s, where Tf is the equilibrium temperature calculated with the burned gas composition and enthalpy. The former Go value corresponds to Uo298 = 40.0 cm/s, i.e., the burning velocity of the adiabatic flame at To = 298K. In the region of Tm < 1200K, Te is independent of both Tm and To. This fact is in good agreement with the previous experimental observation [1], where the flame temperature on a wire mesh was found to be determined only by the mixture composition and the flow rate, independently of To and the mesh temperature. However,

when Tm increases beyond ca. 1200K, Tf decreases gradually, and the decay rate increases as To increases. This decrease in Tf is due to reactions inside the porous plug burner. Therefore, the point of critical temperature T*m' beyond which Te becomes dependent on To and Tm, corresponds to the boundary between the preheating and the reaction zones. Figure 3 shows that T* is almost independent of To and decreases somewhat with decreasing Go. In other words, the porous plug burner of Tm < ca. 1000K is located in the preheating zone of the flame and does not influence the profiles in the reaction zone. The flames on the porous plug burner for mixture flow velocity Uo298 = 0.80-40.0 cm/s are stimulated at Tm = 500K. The solid line in Fig. 4 shows the simulated relation between the flame t e m p e r a t u r e Tf and Uo298 , together with that of the preheated adiabatic flames. The almost linear relation Tf-1 versus log(Vo298) in the region of Tf > 1550K is in agreement with the theoretical predictions [16, 17]. The experimental data by Kaskan [3] and Yuuki and Matsui [1] for flames on porous plug burners and by Andrews and Bradley [18] for adiabatic flames are also plotted in Fig. 4. Here, it should be noted that the measured temperatures were not the adiabatic values because of the heat loss to the surroundings. Therefore, those data should be compared based on the corrected flame temperature T f , where the calculated temperature-increasing rate in the postflame region is equal to the measured temperature-decay rate [1], and shown by a dotted line in Fig. 4. The

SIMULATION OF COOLED FLAMES

41

10(3 ~

~

CH4-AIR

CH4-AIR It=

~= 1.0

1.0

P = I.Ootm

O0 1.0

5 1(3 LL

E

u

I.=J 0.1

m

oJ o

1.0

4.0

x o

KASKAN YUUKI 8t MATSUI

~k \-

•

ANDREWS ~ BRADLEY

5.0 I/T

X

1600K ~

6.0

x 10-4

•

T CATTOLICA

001

IO

K

MATSUI ~ NOMAGUCHI

IO

Oo-zge

I00

cm/s

Fig. 4. Arrhenius plot of the burning velocity of a stoichiometric methane-air flame at atmospheric pressure. Solid and dotted lines are the simulated results versus Tf and T ( , and the dashed line is the result with the boundary condition (7). Points are measurements by Andrews and Bradley [18], Kaskan [3], and Yuuki and Matsui [1].

Fig. 5. Calculated peak concentrations of H, OH, and 0 radicals in stoichiometric methane-air flames at atmospheric pressure as a function of mixture flow velocity Uo29s. Points are measurements by Matsui and Nomaguchi [19] and Cattolica

dependence of the flame temperature on Uo298 is quantitatively well simulated by this model. The relation Tf-I-log(1,'o298) simulated with a Hirschfelder type boundary condition (7) at Tm = 298K is also represented by a dashed line in Fig. 4, which is almost straight but fails to continue smoothly to the preheated adiabatic region. The higher flame temperatures of relatively low mass flow velocity is due to the unreal diffusional transports of CH4, 02, CO2, and H 2 0 at the burner surface. This fact disputes the Hirschfelder type boundary condition. Figure 5 shows calculated maximum O, H, and OH concentrations versus the mixture flow velocity Uo298, together with the measured OH concentrations in flames stabilized on porous metal burners [19, 20]. Here, good agreement between the simulated and measured OH values is also obtained. Figure 6 shows the dependence of standoff distance DX on Tf for T m = 500K, where DX is

the distance between the burner surface and the peak position of H atom concentration. The curve is similar to the relation obtained by Ferguson and Keck [17], who theoretically derived the relation by making use of the linear relation Tf-1-Uo298 obtained by Kaskan [3]. The open circles in Fig. 6 'are experimental results measured by Yamasaki [21], who took pictures of the flames stabilized on a water cooled porous metal burner and obtained the standoff distance from the end of the luminous zone. The calculated curves are quantitatively in good agreement with the experimental data, especially in the low temperature region where experimental error seems relatively small. The standoff distance is affected by the burner surface temperature Tin. Figure 6 also presents the distance between the burner surface and the point where the gas temperatures are 600, 700, and 800K, respectively. Since the burner of Tm < 1000K does not disturb the flame structure, the standoff distance DX for Tm = 600, 700, and

[201.

42

AKIMASA YUUKI and YASUJI MATSUI

1.5

..~1.0

~

0.5

24.00 2200 2000 1800 1600 Tf K Fig. 6. Calculateddistances from burner surface (Tin = 500K) to the peak points of H atom concentration and to the points at T = 800, 700, and 600 K, respectively,as a function of Tf for a stoichiometric methane-air, atmospheric pressure flame. Points are measurements by Yamasaki [21] and from the present experiment. 800K can be estimated by deducting the distance from the burner to those temperature points from DX of Tm -- 500K. The burning velocity in Fig. 4 decreases rapidly in the region of Tf < 1550K. This tendency was also observed by Kaskan in rich hydrogen-air and acetylene-air flames [3]. Therefore, in the low temperature region, the standoff distance in Fig. 6 increases more rapidly than predicted by Ferguson and Keck [17]. TIME-DEPENDENT BEHAVIOR

The vibration of a flame on a porous plug burner has been observed by many authors [3, 4, 21], and studied theoretically in recent years [22-24]. As the vibration always appears near flame extinction conditions, it is considered to have a close relation with the extinction limit. Therefore the response of a flame to a stepwise change of mixture flow rate

was simulated in studying the dynamic behavior of the flame on the porous plug burner. Here, the mixture mass flow rate Go is kept constant at the burner surface, and the opening area ratio A is 1.0. Figure 7a shows the simulated flame vibration that occurred when Go is decreased stepwise from 0.045 g/cm 2 s to 0.020 g/cm 2 s. The abscissa is the time after Go was changed, and the longitudinal axis is the instantaneous burning rate Gs calculated from the oxygen consumption rate. The mass burning velocity Gs may approach the stable value Go after a damping oscillation. The frequency of the flame oscillation increases only 7 % as the calculational time step width decreases from 7 x 10-6 s to 3.5 × 10-6 s. Therefore, the flame oscillation is not considered to be caused mainly by the failure of the numerical procedure. Figure 7b shows the influence of the burner surface temperature Tm on the flame oscillation, where Go is changed stepwise from 0.010 g/cm 2 s to 0.011 g/cm 2 s and Tm is fixed at 500, 700, and 1000K, respectively. The oscillation frequency and the damping rate increase as Tm increases and these tendencies are in good agreement with the prediction of Margolis [22]. He made a theoretical study of the oscillation of flames stabilized on a porous plug burner and predicted that the instability of the steady-state solution is always enhanced by a low burner surface temperature and a slow mixture flow velocity. The frequencies of flame oscillation fn versus Go or Tm are shown by solid lines in Figs. 8a and 8b, respectively. Joulin [23] has shown with the thermal theory that the oscillation is generated by the time lag of temperature disturbances propagating from the burner surface to the reaction zone. A modified calculation has been performed to confirm the influence of the temperature disturbance on the flame oscillation. Here p h ' is added to the right side of the enthalpy conservation equation (2) to compensate for the time lag, and is defined as follows:

dhm/dt,

at X > 0:

h' =

at X < 0 :

h' =0.

The result of the modified simulation is shown

SIMULATION OF COOLED FLAMES

43

0.02~

q/)

CH4-AIR

II-I.0 Go-O.O 20glcn'Fs Tm- 500K

oO°°O0 o

o

C~

o• •

o o

0-o20

.co

• O O

•e

° °

e

O

•

•

0

o

QO 0 0 0 0

° Q o o o °

°°

• •coo• •o•

QOI! 4

i

|

i

i

6

8

I0

12

14 x I0 -3

TIME SEC Fig. 7a.

0

12

0

E

CH4-AIR J " 1.0

0 0

0

N

00

0

0

0

Go-O.O I I g/cmZs 0

0

0 0

0

o

0

~II

Q

(3

•

o

X x x z X

o

K x x x I x x x "

X •

x

Tm-5OOK

,

O

Tm- IO00K 0 0

0

0

o

0

0 o o °o

I00

0

o

0

I0

0

Tm • 7 0 0 K

• 0

0oo0O

o°

."

o

TIME SEC

xlO -s

Fig. 7b. Fig. 7. Simulated oscillation of mass burning vet•city Gs in a stoichiometric methane-air flame at atmospheric pressure (a) for Go = 0.02 g/cm 2 s and T m = 500K, and Co) for Go = 0.001 g/cm z s and Tm = 500, 700, and 100OK, respectively.

44

A K I M A S A Y U U K I and Y A S U J I M A T S U I in Fig. 9 and compared with the the original one, where flame oscillation is expressed by CH radical concentration. The fact that the damping rate o f the modified calculation is much greater than that o f nomal flame oscillation supports the conclusion o f Joulin [23]. The steady-state flame structure presented in the previous section was calculated with this modified method.

402 N

-r

lOG

J

o ME/I~URED -- ~'IEO

CH4-AIR P, 1.0 • Tm,5OOK

o.b3

EXPERIMENT

Go g / c n ~ Fig. 8a.

In this section, the flame response against the perturbation o f the mixture flow velocity was measured to confirm the adequateness o f the simulated results. The experimental apparatus is shown in Fig. 10. The porous metal burner is a 45 m m diameter disk made from 0.050 m m diameter bronze balls. The opening area ratio A o f the burner is about 0.2, and the burner is not cooled. The mixture o f methane and air burns on the porous metal burner. In the passage o f the mixture, an injector and a loudspeaker are equipped to study the step response and the frequency transfer function of the flame, respectively. The disturbance in the mixture flow rate and the flame front movement are detected by hot wire and flame ion current measurements, respectively, and analyzed by an F F T analyzer. The flame-rod is a water cooled stainless steel pipe and is charged at 200 V. The standoff distance DX is measured by making

I I - 1.0 G=O.OI I g / m a s

CH4-Air

IOOC

400 N

-I200

J

I0(

~C/¢CtI.ATEE o MEASURED

Tm

K

Fig. 8b. Fig. 8. Frequencyfn of damping oscillation versus (a) Go for Tm= 500K, and (b) Tm for Go = 0.011 g/cm 2 s. Points are from the present experimental result.

I(~1 ~-0.02 g/cn~ CH, I - A I R

0

E z

o

x

o x o

]( o

w xx

g¢j Iu

x

x

ORIGINAL

x x

x

oooOOOO~OOOOooOO

°oX

F.- i0 e z LnJ

I-l.O

Tm = 5 0 0 K

oo

x

x

MOOIRED

x x

x x

x

x

x

i

!

4 TIME

x I0 -3

SEC

Fig. 9, Simulated oscillation of the CH radical concentration for a stoichiometric methane-air flame at atmospheric pressure simulated by the modified and original models, where Tm = 500K and Go = 0.02 g/cm 2 s.

SIMULATION OF COOLED FLAMES

45

HIGH VIDLTAGE POWERSUPPLY

WATER-COOLED FLAME-RO0 RESISTANCE ~_~

Pt-Rh

iFFT ANALYZER L~

READING MICROSCOPE

INJECTOR

FUEL AIR

I-:.1.: -::..'.'i' :' 1":~:::'.":,:.'-.'," ?'.": I

THERMO

COUPLE

IIIIIllllllllll

HONEYCOMB I

~

FUNCTION

SPEAKER

Fig. 10. Experimentalapparatus; porous metal burner. use of 0.1 mm diameter 10% Rh-Pt thermocouple and a reading microscope. Here DX is defined as a distance between the burner surface and the point where the thermocouple shows the maximum voltage. A chromel-alumel thermocouple buried in the burner is used to measure the surface temperature. Figure 1 la shows the typical step response of the flame, where the equivalence ratio ~b is 0.7 and mixture flow velocity Uo298 ~- 12 cm/s. It is

interesting to note that the f l a m e current If shows a damping oscillation similar to the simulated oscillation in Fig. 7a. The most probable frequency of such an oscillation f n can be obtained from the Bode diagram. Figure l lb shows the Bode diagram of the flame under the same conditions as in Fig. l la. The Bode diagram resembles in shape that of the 2nd order lag system, and indicates that the natural frequency f n of this flame is about 50 Hz. The frequency f n and the standoff distance DX were measured for the wide ranges ofq~ = 0.5-1.0 and U o 2 9 8 = 3.6-24.0 cm/s, and compared with the simulated ones. The present measurement of DX for stoichiometric

flames in Fig. 6 is in good agreement with the simulated result. The measured natural frequencies f n for ¢ = 1.0, though comparable measurements are few, are in good agreement with simulated ones in Figs. 8a and 8b. Another comparison is also shown in Fig. 12, w h e r e f n decreases as DX increases. The good agreement between the measured and simu2 CH4 - AIR ¢ =0.7

~ "

12 cm,/s

o

-2

i

i

i

i

i

i

4O

o

TIME

Fig. 1la.

i

i

8O mSEC

46

AKIMASA YUUKI and YASUJI MATSUI 66

CH4-AIR ~=0.7 m "cJ

12 c m / s

40

0 -14

I

II

i

i

3

I0

i

ii

i

0I00

3 0 0 50O

180 CH4-AIR je = 0 . 7 t . ~ : i i = 12 c m / s 0 G)

-180

I0

30

f

I00

300

Hz

Fig. 1 lb. Fig. 11. Measured oscillation of flame current in a methane-air flame for Uo298= 12 cm/s and (~ = 0.7: (a) time varying behavior; (b) Bode diagram.

8O0 CH4-AIR AUoeu,24¢m4 • =12 x ',6

e A

o

A

V N

"I-

=3.6

O V

XxX•

eCALOJ_ATED

V •X

I(30

X

eill--

0

0

•

0 x 0

I0

i

,

0.8

i

,

1.0

i

i

12

l

,

1.4

,

,

,

,

,

,

,

1.6 1.8 2.0

,

. . . .

2.4

DX mm Fig. 12. Natural frequency fn of a methane-air flame at atmospheric pressure as a function of the standoff distance DX.

SIMULATION OF COOLED FLAMES

47

latedfn plotted by making use of DX in Fig. 6 has confirmed that the present simulation model can reproduce the nature of the flame stabilized on the porous plug burner in steady-state and also timedependent behaviors. DISCUSSION The results of the simulation and the measurement have shown that flames on a porous plug burner oscillate intrinsically, and the instabilities increase with increasing standoff distance DX as predicted by Joulin [23]. He also predicted that the flame instability increases as the activation energy E increases. Mclntosh and Clarke [24] and Margolis [22], though the assumption and the method used to deduce their conclusions are different, predicted a similar effect of E on the flame stability. This effect is considered as follows; if E is sufficiently large, a little temperature rise causes a greater increase in the heat release rate than in the heat loss rate to the burner surface. Thus the relations Tf versus Uo29~ and standoff distance in Figs. 4 and 6 stimulate interest in their low temperature region, where the activation energy E and the standoff distance DX increase rapidly as Tf decreases. Therefore, the flame of Te < ca. 1550K (corresponding to Uo298 < 1.0 cm/s) is considered to be unstable for any surrounding conditions. That is, the critical flame temperature for stability of stoichiometric methane-air flames on porous plug burners is about 1550K and may be unaltered by any modifications of the burner configurations. The rapid decrease in the combustion rate in the low temperature flame is considered to be due to the increase in the relative importance of the radical recombination reactions, as mentioned by Westbrook et al. [25]. In adiabatic lean and near stoichiometric methane-air flames, the following reaction is one of the main paths of fuel oxidation: CH3 + O ~ C H 2 0 + H.

(R1)

An O atom, whose concentration controls the rate of (R1), is mainly produced by (R2): H + 0 2 -'~ OH + O.

(R2)

The most important radical recombination reac-

tion, which competes with reaction (R2), is H+O2+M~HO2+M.

(R3)

Warnatz [10] showed that the rate constant of (R2) (k2 for short) significantly affects the burning velocity and that the influence of k3 on the burning velocity is not so important in adiabatic methaneair flames. However, since the activation energy E2 ( = 70.4 KJ/mol) is much greater than E3 ( = 0 KJ/mol), the relative importance of (R3) rapidly increases in low temperature flames. The ratio of the total reaction rate of (R2) to (R3) in the reacting zone is more than 20.0 at Uo298 = 40.0 cm/s, but is about 2.0 at Uo29S = 0.88 cm/s. Baulch and Drysdale [26] estimated the uncertainty for k3 to be +50%. It was found by calculation that this uncertainty corresponds to about ___30K of the flame temperature uncertainty at Uo298 = 0.88 cm/s. It is confirmed that the radical recombination reaction (R3) has the significant relation with the rapid decrease in the burning velocity in the low temperature flame. And the uncertainty of the critical temperature is considered to be _+30K. This discussion agrees well with the fact that a stable flame of Uo29a < 1.0 cm/s has never been experimentally observed on the porous plug burner. CONCLUSION The stable structure for a wide range of mixture flow rates and the time-varying behavior of stoichiometric methane-air flames on porous metal burners at atmospheric pressure were studied using a numerical model which includes detailed chemical reactions proposed by Warnatz [10]. It has been confirmed that the model gives quantitative agreement with experiment for stable flame structures such as flame temperature, radical concentrations, and standoff distance, and also flame oscillation. It was found that the overall activation energy, as well as the flame standoff distance, increases rapidly in the region of Tf < 1550K. Furthermore, it was also confirmed that the flame intrinsically oscillates due to the time lag of the temperature disturbance and its instability is enhanced by a large flame standoff distance as

48

AKIMASA YUUKI and YASUJI MATSUI

predicted by Joulin [23]. On the basis of these results, it was determined that the premixed, laminar methane-air flame on the porous plug burner of Tf < 1550K (corresponding to Uo298 < 1.0 cm/s) is unstable on the burner at any surrounding conditions.

2. 3. 4.

5.

NOMENCLATURE A x X h h* Y Cp D

area ratio of porous plug burner normal distance new coordinate enthalpy per mass enthalpy of species per mole mass fraction specific heat capacity at constant pressure effective diffusion coefficient of species in a mixture M molecular weight Mm averaged molecular weight of a mixture rn" net rate of formation of species k heat conductivity P pressure p density G mass flow rate per unit cross section U flow velocity T gas temperature Tf flame temperature E apparent overall activation energy of a combustion reaction fn natural frequency of flame oscillations

6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Subscripts o 298 m i

initial at 298K at burner surface ith species

23. 24. 25. 26.

REFERENCES Yuuki, A., and Matsui, Y., Combust. Sci. Technol. 43:301 (1985).

Matsui, Y., and Yuuki, A., Jpn. J. Appl. Phys. 24:5, 598 (1985). Kaskan, W. E., Sixth Symposium (International) on Combustion The Combustion Institute, 1967, p. 134. Ishizuka, S., and Law, C. K., Nineteenth Symposium (International) on Combustion, The Combustion Institute, 1982, p. 327. Gerstein, M., and Stine, W. B., Fourteenth Symposium (International) on Combustion, The Combustion Institute, 1972, p. 1109. Vonlavante, E., and Strehlow, R. A., Combust. Flame 49:123 (1983). Buckmaster, J. Combust. Flame 26:151 (1976). Buckmaster, J., and Mikolaitis, D., Combust. Flame 45:109 (1982). Tsatsaronis, G., Combust. Flame 33:217 (1978). Warnatz, J., Eighteenth Symposium (International) on Combustion, The Combustion Institute, 1981, p. 369. Coffee, T. P., Combust. Flame 55:161 (1984). Spalding, D. B., and Stephenson, P. L., Proc. Roy. Soc. Lond. A32:315 (1971). Dasch, C. J., and Blint, R. J. Combust. Sci. Technol. 34:91 (1983). Saffman, Combust. Flame 55:141 (1984). Coffee, T. P., and Heimerl, J. M., Combust. Flame 43:273 (1981). Carrier, G. E., Fendell, F. E., and Bush, W. B., Combust. Sci. Technol. 18:33 (1978). Ferguson, C. R., and Keck, J. C., Combust. Flame 34:85 (1979). Andrews, G. E., and Bradley, D., Combust. Flame 19:275 (1972). Matsui, Y., and Nomaguchi, T., Jpn. J. Appl. Phys. 18:1, 181 (1979). Cattolica, R. J. Combust. Flame 44:43, (1982). Yamasaki, K., J. Jpn. Soc. Mech. Engng. 6:136, 465 (1957). Margolis, S. B., Eighteenth Symposium (International) on Combustion, The Combustion Institute, 1981, p. 679. Joulin, G., Combust. Flame 46:271 (1982). Mclntosh, A. C., and Clarke, J. F., Combust. Sci. Technol. 38:161 (1984). Westbrook, C. K., Adamczyk, A. A., and Lovoie, G. A., Combust. Flame 40:81 (1981). Baulch, D. L., and Drysdale, D. D., Combust. Flame 23:215 (1974).

Received 2 June 1986; revised 13 January 1987