air mixtures in the stagnation-point flow

Eighteenth Symposium (International) on Combustion

The Combustion Institute, 1981

LEAN-LIMIT EXTINCTION OF PROPANE/AIR MIXTURES IN THE STAGNATION-POINT FLOW CHUNG K. LAW, SATORU ISHIZUKA, AND MASAH1KO M I Z O M O T O Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60201

The extinction limits of lean propane/air mixtures in the stagnation-point flow of a flat surface were mapped as functions of the surface temperature and the mixture concentration, velocity, and temperature. The maximum flame temperatures and the flame locations were also measured. The results show that the extinction limits are extremely insensitive to the nature of the surface, which can be heated to 1000~ On the other hand preheating the gas mixture increases the flame temperature by an almost equal amount and therefore significantly extends the extinction limits. It is also found that at extinction the maximum flame temperatures and the flame locations, which when scaled with the velocity gradient, assume almost constant values independent of the other system variables investigated. The present results provide useful insights on the flame location relative to the boundary layer, the importance of flame stretch relative to downstream heat loss in causing extinction, and the viability of the concept of limit temperature.

Introduction Lean combustion offers the potential of enhanced combustion efficiency and reduced NO x formation, and therefore is at least partly responsible for such recent technological interests as stratified charge combustion, lean premixed prevaporized combustion, and the utilization of low-Btu gases. These lean mixtures, however, are generally prone to extinction and hence may severely limit operational reliability. Thus it is of practical interest to quantify and possibly extend these lean limits of operation. From the fundamental viewpoint a major effort in combustion research over the years has been the attempt to identify the basic mechanism(s) responsible for flame extinction, ~ whether it is heat loss from the flame, 2 wall quenching and deactivation, 3 flame stretch, 4'~'~4'25 buoyancyf '7 chain mechanisms, 8 flame-front instability from processes such as preferential diffusion, 9a~ or combinations of the above factors. Based on this knowledge it is hoped that absolute flammability limits depending only on the physico-chemical properties of a given mixture can be established) 1 Previous experimental investigations on flammability limits have employed the flow tube, 12'~3 the flat-flame burner, 14 the tent flame burner, '~ and the so-called Tsuji-Yamaoka burner H which uses

a diffusion flame to stabilize a premixed flame in the stagnation flow of a porous cylinder. The "flammability limits" determined by these methods, however, differ from each other, indicating the difficulty in, or even the possibility of, experimentally establishing unique, system-independent, flammability limits. Progress in identifying extinction mechanisms has also been quite limited. In the present experiment we investigated lean limit extinction of a premixed propane/air flame in the stagnation-point flow of a flat surface. This flow configuration, which was first adopted by Fang et al. 16 to determine the overall kinetics of CO oxidation, offers the following advantages in the study of limit phenomena: (1) The flow is steady, hence allowing detailed probing; (2) Upstream disturbances and heat losses are minimized; (3) Downstream heat loss and wall effects can be investigated by varying the nature of the stagnation surface; (4) Effects of flame stretch can be well characterized because the flow is controlled, two-dimensional, and has a high rate of blowing; the last factor is also of practical interest; and (5) The flow within the boundary layer is self-similar. It is also of interest to note the equivalence between the present configuration and the flow tube method in studying flame stretch effects. That is for flame propagating in the flow tube the approach

1791

1792

IGNITION

flow is one-dimensional and the flame is curved, whereas for the stagnation flow the flame is planar but the approach flow is divergent. Thus the flames suffer stretch in both cases, except for the stagnation flow the stretch is well-defined, controllable, and can have high rates. The experimental apparatus and procedure are discussed in the next section. Then the experimental results are presented and discussed.

Apparatus and Procedure

The experiment (Fig. 1) involves passing propane (99.0% minimum purity in the liquid phase) and air through flowmeters, a mixing chamber, an electric preheater, a diffuser packed with glass beads, a settling chamber with damping screens, and a water-cooled nozzle with a contraction ratio of eight and an inner diameter of 3.81 cm. The mixture then impinges onto a flat stagnation surface located 3.81 cm above the nozzle exit. The exit velocity profile is very fiat with low turbulence. Two kinds of stagnation walls were used to produce isothermal surfaces of up to 1000~ The first is a water-cooled bronze block with a shielded thermocouple welded close to the surface. The surface temperature is between 150~ to 200~ For high-temperature surfaces we used an inconel block heated at the back by a torch flame of propane/oxygen/air mixture. Surface temperature is determined by linear extrapolation of readings from three thermocouples located at different depths from the surface. Uniformity in surface temperature was established by measuring both the center and halfradial values. In the experimental procedure extinction was achieved by first establishing a flat flame in the flow, Then the propane flow rate was gradually reduced, while maintaining the total flow rate and

the stagnation surface temperature T constant, until the flame went out. Thus the extinction boundaries of propane / air mixtures were systematically mapped as functions of T, and the mixture velocity V, temperature T~, and propane concentration f~, where fl is the volume percent of propane in the propane/air mixture and the subscript e is for the state at the nozzle exit. The freestream velocity V is calculated by dividing the flow rate of the cold mixture by the exit area. The flame location p,, defined as the center of the luminous flame zone, was measured by direct photography. The temperature distribution across the flame was determined using a silica-coated Pt/Pt-13%Rh thermocouple (wire diameter; 0.10 mm); but no correction for the thermometric error due to radiation was made. Results

Appearance of Flame For lean mixtures two types of flames were observed, namely a plate-stabilized flame and a rim-

W~erOut

(HeatedWoll) Propane ~ ~ eri owe n er

FlatFlorae Con~er~lnNozzl g e

xl

5 . , , , , ~ 1 7c6

oo0.,

0i.o,,r C*mpre~sor o o,,.o~

(b] FIc. 1. Schematic of the Stagnation Flow Apparatus.

FIG. 2. Configurations of (a) plate-stabilized and (b) rim-stabilized flame.

P R O P A N E / A I R MIXTURES IN STAGNATION-POINT FLOW i

35

/

Flal F R~m- f: Fbome 30 Region ~

l

a

m

e

!,

i l l

~

Stable

~

J

1793 i , i

Flat Flame

~ "~zg--

3O

v = 3 40 m/sec 170 m/sec

Exlinction

085 m/sec 25

,

I I

I 2

, 3

I 4

V (m/see)

Extinchon 25

0

500

FIG. 3. Regions of rim-flame, flat-flame, and extinction states in the stagnation field.

I000

500

T s (~

FIG. 4. Variations of fuel concentration with surface temperature at the extinction limit. stabilized flame as shown in Figs. 2a and 2b respectively. The rim-stabilized flame occurs for lower velocities or higher fuel concentrations. By gradually increasing V or decreasing II the rim flame converts fairly abruptly to a stable, thin, laminar, fiat flame located at some distance from the surface in the stagnation flow field. Further changes in V or II cause the flat flame to move closer to the stagnation surface. Eventually extinction occurs abruptly when the flame is at a finite distance away from the surface. Because of the rapidity of extinction and the faintness of the flame at extinction, we were not able to obtain adequate time-resolved observations to indicate whether extinction occurs uniformly over the flame or is initiated at the center and propagates outward.~7 Figure 3 shows a typical mapping of the extinction limits with variations in velocities and fuel concentrations, using the water-cooled wall. The boundaries between the plate- and rim-stabilized flames are also plotted, which exhibit a hysteresis effect probably caused by the complicated flow field around the rim of the nozzle. Extinction Limits

The effects of the nature of the stagnation surface on the extinction limits were investigated for either isothermal, adiabatic, or catalytic surfaces. Figure 4 shows the variations of fuel concentration with surface temperature at the extinction limits, using V as a parameter. It is seen that whereas i'l decreases almost linearly with increasing T s, the dependence is extremely weak, being 0.014%C3H 8 for 100~ rise in Ts for the steepest case. This is an interesting result especially because T, can be as high as 1000~ which is close to the maximum flame temperature of about 1230~ to be reported later. Effects of surface adiabaticity were investigated by using various materials of low thermal diffusivities. The extinction limits obtained generally agree closely with those of isothermal surfaces. However, since these surfaces are not perfectly adiabatic as

evidenced by the result that the measured surface temperatures are even lower than the maximum isothermal surface temperature of 1000~ these results are not definitive in demonstrating the flame extinction phenomena with an adiabatic surface. We have also coated the inconel surface with a 2 Ixm layer of platinum, and mapped the extinction limits between 400~ and 800~ There was no difference, at the same surface temperature, between these results and those obtained using either the bare inconel surface or some "adiabatic" surfaces which are considered to be inert. This indicates that either there was very little reactant leakage through the flame, or even if there was substantial leakage the subsequent reaction at the catalytic surface produced no noticeable effect on flame extinction. Figure 5 shows the change in the extinction limits with preheating up to 200~ The temperature of the unburned gas was measured at the nozzle exit by a thermocouple. It is seen that preheating widens the stable flame region, and that the fuel concentration at extinction decreases almost linearly with the unburned mixture temperature T e. The variation corresponds to 0.19%C3H 8 for 100~ increase in Te,

l

Stable Flat Flame

30

V:180

m/see 26Ore/see

25

50

I00

1SO

200

T e (~

FIG. 5. Variations of fuel concentration with unburned gas temperature at the extinction limit.

1794

IGNITION

which is about 14 times as steep as the variation with increasing the surface temperature. It may be noted again that the velocities indicated in Fig. 5 are those of the cold mixture such that the mass flux remains constant for each curve, as should be.

r

15

70 4 Lu

85 m/sec

E v

Figure 6 shows a typical temperature distribution close to extinction, obtained using the water-cooled block and with ~ = 3.04% and V = 1.70 m/sec. The boundary layer variable "11 is also shown; its computation will be discussed later. The temperature near the wall could not be measured due to the thickness of the thermocouple insulation and the need to place the thermocouple parallel to the wall and hence the isothermal lines. The flame location y, and the maximum flame temperature T .... were systematically measured as functions of 11, V, To, and T,. The data in Figs. 7 to 9 were obtained with the water-cooled surface while the data in Fig. 10 were obtained with the heated surface. Figures 7 and 8 show that as f~ decreases or V increases the flame moves closer to the surface whereas the flame temperature decreases as would be expected. The flame location at extinction also decreases with increasing velocity. Since the maximum flame temperature at extinction cannot be measured, it is estimated by extrapolating the measured Tma. for states close to extinction. The values of T=~, at extinction decrease very slightly with decreasing V, varying from 1240~ to 1210~ as V decreases from 3.40 m / s e c to 0.85 m/sec. The measured T . ~ are much lower than the adiabatic flame temperatures. Again we note the finite values of y, at flame extinction. Figure 9 shows y, and T .... with various extent of preheating, keeping V = 1.80 m/sec. It is seen that with preheating the flame moves towards the

T

r

g

Flame Location and Maximum Flame Temperature

,

~

/ ~ 0

~

I0

1500 t

~

,

i

i

[

27

i

i

i

i

i

50

L

35

37

( % C3 Hs)

Fro. 7. Variations of flame location with fuel concentration and mixture velocity. nozzle, indicating an increase in the mass burning rate. This is in agreement with the flame propagation results of Dugger and Heimel L8 who showed an increase in the mass burning rate by increasing the mixture temperature. Since the mixture is now more reactive, a leaner combustion can be sustained such that at extinction the flame locations assume a near constant value, being almost independent of the extent of preheating. Figure 9 also shows that Tma• increases by almost the same amount as the increase in T,. This is reasonable because the mixture is lean such that much of the preheating is used in heating the inert. However, similar to y,, the maximum flame temperature at extinction also does not change much with preheating. The values shown in Fig. 9 are between 1225~ and 1245~ Finally, Fig. 10 shows y, and T , with variations in the wall temperature. The variations are very small, similar to those shown in Fig. 4 for the extinction limits. However, at extinction y, and Tm,x again attain almost constant values.

5

me Zone

1600

I000

2~

500

I

~500 ~

mOO

~

13oo

ExHnction

0

0

I

2

5

4

5 6 y (mm)

7

8

9

0

[0

FIG. 6. Typical temperature profile; l] = 3.04%, V = 1.70 m/sec.

IIO07

I

i

2e

29

i 30

: 51

,

32

I 33

314 5

(% C~H~)

Fro. 8. Variations of maximum flame temperature with fuel concentration and mixture velocity.

P R O P A N E / A I R MIXTURES IN STAGNATION-POINT FLOW I0

i

/

i

i

i

i

Discussions

t

An interesting result revealed by the present investigation is that the extinction limits are very insensitive to the nature of the stagnation surface, in particular its temperature. Since surface conditions have to be important if the flame is within the boundary layer, this result then seems to indicate that the boundary layer has only small influences on the flame behavior at extinction. To explore this possibility we have estimated the flame location expressed in the boundary layer variable

s

t

ExHnchon

0 I

I

I

I

I

1795

I

1600

/~r

1500

'(30

(1)

*G

~

Z

o~~

1400

1300

Ext,nction

i,oo 2.z

I

2.6

I 2.9

I 30

I

I 32

3,

l 33

I 34

3s

where k is the geometry factor and is k = 1 for the present axisymmetric flow, v is the kinematic viscosity, ct is the velocity gradient and is taken ~9 to be ~ = V/21, p is the density, and I is the distance between the surface and the nozzle exit. For lean propane/air flames the compositional change is small such that Eq. (1) can be expressed as

C3 Hs)

.O, ( %

FIG. 9. Variations of flame location and maximum flame temperature with fuel concentration and preheat temperature.

(2) L

%

J

Jo T

Hence using v = 0.158 cm2/sec, l = 3.81 cm, and the temperature profile shown in Fig. 6, we have computed the corresponding ~l's which are also plotted in Fig. 6. From this figure we get the approximate relation

10

~'T

I

E

o

I

i

I

L

y,.

(3)

Tmax

Since from large activation energy considerations the flame temperature at extinction changes from its value just before extinction only by a small amount inversely proportional to the activation energy, it is therefore reasonable to assume that Eq. (3) also holds at extinction. Thus using Eqs. (2) and (3), the flame location at extinction can be expressed as

Extinction I

T,,

T dy = 1.25

i

1600

1500

o...

(~l,),,x =

~500

1200 ' HO0 2,7

Extinction 2.8

I 2,9

I 5.0

I

I

I

]

3 1

32

3,3

3 4

35

D. (% C3 Hs) FXG. 10. V a r i a t i o n s

of flame

location

and

maxi-

flame temperature with fuel concentration and surface temperature. mum

1.25 \ T ...... ] L ~

J

(Y*)~

(4)

Thus upon substitution, with T~ = 20~ T ..... = 1230~ V =- 1.70 m/sec, and y, = 4.1 mm, it is found that (~1,)~ = 1.70. From the numerical results of SaitohY ~q, = 1.70 places the flame at the outer boundary of the boundary layer. Further realizing that his computed boundary layer thickness will be further reduced by using lower flame temperatures such as the

1796

IGNITION

present ones, it seems to indicate that the flame, particularly when at its extinction state, is not close to the stagnation surface in the sense of the boundary layer for the present propane/air mixtures. This may explain the insensitivity of the extinction states on the nature of the stagnation surface. It is also of interest to note that whereas (Y,)~x varies with V but not with T e and T~, as shown in Figs. 7, 9, and 10, it is found that if (Y,)~x is scaled with the velocity gradient a through = ~

( Y,),,

(5)

then a constant value of ~ = 1.87 cm-sec -~/2, with scatters of _+7%, is obtained for all of the present experimental data. The correlation is especially good for the cold flow case, ~_tth scatters of _+2%. The scaling factor V a used in g is anticipated from nondimensional considerations in stagnation flow analysis. The result that g is almost constant indicates, at least for incompressible flows, that the flames suffer the same amount of stretch at extinction. With compressibility effects the scaling factor needs to be modified and the extent to which the above observation is influenced is unclear. The present result that extinction is insensitive to the surface temperature indicates the possibility that flame extinction can be achieved in the absence of downstream heat loss. Whereas the present results are short of being conclusive because the maximum stagnation surface temperature is still below the maximum flame temperature and therefore the surface is not perfectly adiabatic, the possibility of such an extinction mechanism is in agreement with either one of the following two viewpoints. First, the numerical results of Saitoh 2~ and Takeno 2~ predict that extinction in the adiabatic stagnation point flow can occur by simply considering effects of the Damk6hler number, which varies inversely with the velocity gradient a. The second viewpoint is that of Sivashinskyf 4 who showed that extinction through flame stretch can occur because of preferential diffusion, which is represented by the relevant Lewis number Le, defined as the ratio of the thermal diffusivity of the mixture to the mass diffusivity of the deficient species. In particular, extinction is possible for Le >1 as is the case with the present lean propane/air mixture; for Le <1 increasing velocity raises the temperature of the reaction zone and causes the flame front to approach the surface. Further experiments are being conducted to resolve the questions of surface adiabaticity as well as the Damk6hler number effect versus Lewis number effect. We have also shown that the maximum flame temperatures at extinction are almost constant, being around 1210 - 1240~ for the data in Fig. 8 and about 1230~ with the preheating and heated surface cases. This agrees with those determined from flam-

mability experiments. For example Edgerton and Thabet ~4 determined the lean-limit flame temperatures using the flat flame burner, and it is found 22 that these temperatures are almost always around 1200~ for the hydrocarbon-air mixtures considered. Furthermore, Zabetakis ~a modified the BurgessWheeler Law z3 to show that the flame temperature of lean mixtures is increased by almost the same amount as preheating, and extinction occurs at a constant limit temperature. Thus it is seen that even though the present fuel concentrations at extinction are higher than those from experiments specially designed for "flammability limit" studies, our maximum temperature at extinction is very close to the lean limit temperatures. This observation substantiates the concept of limit temperature for flames, whether it is stabilized over a one-dimensional fiat flame burner, or propagating in a flow tube, or stabilized in the present highly-sheared two-dimensional stagnation flow field.

Conclusions The present results show that the extinction limits are sensitive to the preheat but not the surface temperatures, and that at extinction the maximum flame temperature, and the flame location scaled with the velocity gradient, are almost independent of the system variables investigated. These results seem to imply that the flame is not close to the stagnation surface in the sense of the boundary layer, that flame stretch can cause extinction with minimal or no downstream heat loss, and that extinction of lean hydrocarbon/air mixtures occur at an almost constant limit temperature.

Acknowledgement We appreciate the stimulating discussions with Professors R. A. Strehlow and F. A. Williams on this work, which was supported by NASA-Lewis under Grant No. NAG3-53. R. O. Buckius, D. Cocke, and R. O. Matthews generously helped us to coat some of the surfaces.

REFERENCES 1. LEWIS,B. ANDVONELRE, G.: Combustion, Flames and Explosions of Gases, 2nd Ed., Academic Press, New York, 1961. 2. WILLIAMS, F. A.: Combustion Theory, The Fundamental Theory of Chemically Reacting Flow Systems, Addison-Wesley, Palo Alto, 1965. 3. ANDREWS, G. E. AND BRADLEY, B.: Fourteenth Symposium (International) on Combustion, p. 1119, The Combustion Institute, 1973.

PROPANE/AIR

MIXTURES IN STAGNATION-POINT FLOW

4. KARLOV1TZ,B., DENNISTON, D. W., KNAPSCHAEFER, D. H. AND WELLS, F. E.: F o u r t h S y m p o s i u m (International) on C o m b u s t i o n , p. 613, W i l l i a m s a n d Wilkins, 1953. 5. STREHLOW,R. A. AND SAVAGE, L. D.: C o m b u s t i o n a n d F l a m e 31, 209 (1978). 6. LOVACHEV, L. A.: C o m b u s t i o n a n d F l a m e 17, 275 (1971). 7. LOVACHEV, L. A., BABKIN, V. S., BUNEV, V. A., V'YUN, A. V., KRIVULIN, V. N. AND BARATOV, A. N.: C o m b u s t i o n a n d F l a m e 20, 259 (1973). 8. WEINBERG, F. J.: Proc. Roy. Soc. (London) A230, 331 (1955). 9. MARKSTEIN,G. H.: F o u r t h S y m p o s i u m (International) on C o m b u s t i o n , p. 44, W i l l i a m s a n d Wilkins, 1953. 10. BREGEON, B., GORDON, A. S. AND WILLIAMS, F. A.: C o m b u s t i o n a n d F l a m e 33, 33 (1978). 11. YAMAOKA,I. AND TSUJI, n . : S e v e n t e e n t h S y m p o s i u m (International) on C o m b u s t i o n , p. 843, T h e C o m b u s t i o n Institute, 1979. 12. COWARD, H. F. AND JONES, G. W.: L i m i t s of F l a m m a b i l i t y of G a s e s a n d Vapours. US B u r e a u of Mines, Bulletin 503, 1952. 13. ZABETAKIS,M. G.: F l a m m a b i l i t y Characteristics of C o m b u s t i b l e G a s e s a n d Vapours. US B u r e a u of Mines, Bulletin 627, 1965. 14. EGERTON, A. C. AnD THARET, S. K.: Proc. Roy. Soc. (London) A221, 445 (1952).

1797

15. SORENSON, S. C., SAVAGE, L. D. AND STREHLOW, R. A.: C o m b u s t i o n a n d F l a m e 24, 374 (1975). 16. FANG, M., SCHMITZ, a . A. AND LADD, R. G.: C o m b u s t i o n Science a n d T e c h n o l o g y 4, 143 (1971). 17. POTTER, JR., A. E., HEIMEL, S. AND BUTLER, J. N.: E i g h t h S y m p o s i u m (International) o n Comb u s t i o n , p. 1027, W i l l i a m s a n d Wilkins, 1962. 18. BUGGER, G. L. AND HEIMEL, S.: F l a m e Speeds of Methane-Air, Propane-Air, a n d E t h y l e n e - A i r M i x t u r e s at L o w Initial T e m p e r a t u r e s , N A C A T N 2624 (1952). 19. KENT, J. n . AND WILLIAMS, F. A.: F i f t e e n t h S y m p o s i u m (International) on C o m b u s t i o n , p. 315, T h e C o m b u s t i o n Institute, 1975. 20. SAITOH, T.: Int. J. H e a t M a s s T r a n s f e r 17, 1063 (1974). 21. TAKENO, T.: Pre-prints of 10th S y m p o s i u m on C o m b u s t i o n in Japan, 17 (1970). 22. EGERTON, A. E.: F o u r t h S y m p o s i u m (International) on C o m b u s t i o n , p. 4, W i l l i a m s a n d Wilkins, 1953. 23. BURGESS, M. J. AND WHEELER, R. V.: J. C h e m . Soc. (London) 99, 2013 (1911). 24. SIVASHINSKY, G. I.: Acta A s t r o n a u t i e a 3, 889 (1976). 25. BUCrMASTER,J. D.: S e v e n t e e n t h S y m p o s i u m (International) on C o m b u s t i o n p. 835, T h e C o m b u s t i o n Institute, 1979.

COMMENTS H. Tsufi, University of Tokyo, lapin. T h e a u t h o r s h a v e c o n c l u d e d that, a m o n g other things, at the l e a n l i m i t extinction the f l a m e is n o t close to the s t a g n a t i o n surface in the s e n s e of the b o u n d a r y layer a n d flame stretch can c a u s e extinction with m i n i m a l or n o d o w n s t r e a m heat loss, I n this c o m m e n t s o m e w o r k carried out by Mr. I. Yamaoka a n d m y s e l f on the limits of c o u n t e r f l o w p r e m i x e d f l a m e s will be briefly described. We h a v e u s e d a p o r o u s cylinder b u r n e r ; the cylinder w a s i m m e r s e d in an u n i f o r m s t r e a m of a f u e l / a i r mixture, a n d from the surface of the cylinder the mixture of the s a m e c o m p o s i t i o n w a s ejected; twin flames c o u l d be stabilized in the f o r w a r d s t a g n a t i o n region of the cylinder; the s t a g n a t i o n surface lay b e t w e e n two flame zones, a n d c h e m i c a l species as well as h e a t c o u l d not be p a s s e d t h r o u g h this surface, b e c a u s e d i s t r i b u t i o n s of a n y scalar q u a n t i t i e s are c o n s i d e r e d a l m o s t s y m m e t r i c a l w i t h respect to this surface; t h u s adiabatic flame e x t i n c t i o n s c o u l d be e x a m i n e d . T h e locations of two visible flame z o n e s vs. c o m p o s i t i o n c u r v e s h a v e b e e n m e a s u r e d near the lean limit as well as the rich limit for b o t h m e t h a n e / a i r a n d p r o p a n e / a i r mix-

tures. It w a s f o u n d that at the lean-limit extinction of p r o p a n e / a i r m i x t u r e s the two flame z o n e s were largely separated; t h u s the d i s t a n c e b e t w e e n a flame zone a n d the s t a g n a t i o n surface w a s wide as o b s e r v e d in y o u r experiment; on the contrary, at the rich-limit extinction, two f l a m e s were close to each other; t h u s the d i s t a n c e b e t w e e n a f l a m e zone a n d the s t a g n a t i o n s u r f a c e w a s very narrow. Therefore, the rich-limit f l a m e extinction of p r o p a n e / a i r m i x t u r e s s h o u l d be affected b y the c o n d i t i o n s of the s t a g n a t i o n surface, i.e., the wall. T h e reverse situation was true for m e t h a n e / a i r flames; at the lean-limit extinction the two flame z o n e s were close to each other, a n d at the rich-limit extinction t h e s e were c o n s i d e r a b l y separated. Therefore, y o u r c o n c l u s i o n is to be true o n l y for the lean-limit extinction of p r o p a n e / a i r mixtures. T h e difference of the d i f f u s i o n coefficients of fuel a n d oxygen with n i t r o g e n is c o n s i d e r e d to be r e s p o n s i b l e for t h e s e d i f f e r e n t p h e n o m e n a at extinctions.

Author's Reply. Yes, o u r c o n c l u s i o n s are b a s e d o n o b s e r v a t i o n s of lean p r o p a n e / a i r mixtures, as

1798

IGNITION

the title of the p a p e r emphasizes. Your recent experimental results are certainly valuable c o n t r i b u t i o n s to the u n d e r s t a n d i n g of flame extinction. Indeed, they also corroborate s o m e preliminary results we recently obtained for rich p r o p a n e / a i r extinction, in w h i c h we f o u n d that the extinction state is s o m e w h a t more sensitive to the various system parameters. For example, contrary to the lean case, y . X/o~n o w increases with increasing V and y . also seems to decrease with increasing

,/Ret = 103

T s9

Both your results and ours appear to be in qualitative agreement w i t h the theoretical work of Sivashinsky (Acta Astronautica 3, 889 (1976)) in w h i c h it is s h o w n that flame stretch alone can cause extinction of a premixture only if the Lewis n u m b e r of the deficient species (e.g. propane in lean prop a n e / a i r mixture) exceeds a critical value.

0

02

04

06

O.B

tO

1.2

14

16

IB

Author's Reply. The following is a r o u g h estimate of the heat loss rate to the wall. First a s s u m e flame-sheet c o m b u s t i o n w i t h the flame temperature b e i n g T . = T ..... and its location being~q. ; T . and g . are k n o w n from the experiment. T h u s heat c o n d u c t i o n in the non-reactive region d o w n s t r e a m of the flame is governed by T" + f('q)T' = 0

(i)

where f('q) is the n o n - d i m e n s i o n a l stream function and superscript " p r i m e " denotes (d/d~l). The solution of Eq. (i) subject to the b o u n d a r y conditions T(0) = T s and T ( ' q . ) = T . is T('q) = T s + (T. - Ts)F('q)/F(xI . )

(ii)

where

(iii)

T h u s the heat flux to the wall is 0T

.--?--J

FT ;.T (iv)

F u r t h e r m o r e the heat release rate at the flame is

22

Fl(;. (i). Heat loss ratio as a function of the flame location.

Q . = pVCp (T. - T~) T. T. Ng, Lawrence Berkeley Lab, USA. Have you estimated the heat loss rate to the wall in various cases? Is it p o s s i b l e that flame extinction is due mainly to the heat loss to the wall in the cases you are studying?

20

(v)

Therefore the extent of heat loss to the wall can be assessed by examining the ratio

~t' .

Qs . . Q.

Pr ( T . / T s - 1) 1 . Re, '/2 ( T . / T 1) F ( ' q . )

(vi)

where Pr is the Prandtl n u m b e r and Ret = lV/v is the Reynolds n u m b e r for the present flow. To evaluate ~ , the streamfunction is a s s u m e d to have the form f = ~1 -- [1 - e =e'/~ ]/f"(O)

(vii)

w h i c h satisfies the b o u n d a r y conditions f(0) = f ' (0) = 0, f ' ( ~ ) = I, and the given shear stress at the wall, f"(0). I f we further assume incompressible axisymmetric b o u n d a r y layer flows, then f"(O)= 0.928 from the tabulated exact numerical solutions. It is f o u n d that Eq. (vii) underestimates the exact f by at most 10%. Figure (i) s h o w s ~ ( ' q . ) for different R%, and with Pr = 1 and T~ = T . F o r the case of V = 1.70 m / s e c , studied in our experiments, Re, = 4000. T h e n Fig. (i) s h o w s that ~(2) ~ 0.01, ~(1) = 0.018, and 9 (0.5) = 0.034. Since we have estimated ('q*),x = 1.70, therefore the heat loss to the wall is about 1%. Note that this estimate is further reduced for a smaller Prandtl n u m b e r and also for a higher wall temperature. The above estimates seem to further substantiate our suggestion that extinction for lean p r o p a n e / a i r flames can occur in the absence od d o w n s t r e a m heat loss. However, as emphasized in the paper, our results are short of being conclusive because of the lack of perfect adiabaticity.