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Lewis number effects on premixed flames interacting with turbulent Kármán vortex streets
Lewis Number Effects on Premixed Flames Interacting with Turbulent Kfirmfin Vortex Streets J. G. LEE, T.-W. LEE,* D. A. NYEt and D. A. SANTAVICCA:~ Turbulent Combustion Laboratory, Department of Mechanical Engineering, Propulsion Engineering Research Center, Penn State University, University Park, PA The effects of Lewis number on the global and local structure of premixed flames interacting with turbulent Kfirmfin vortex streets are experimentally investigated using OH planar-laser-induced fluorescence (PLIF). The OH PLIF results show that over the range of Lewis numbers studied, i.e., Le = 0.21, 0.94 and 1.79, the flame area increases and the flame front is oriented more randomly as Lewis number decreases, while the flame curvature pdfs are unchanged. The relationship between the local flame structure and the local flame curvature is found to be consistent with the results of stretched laminar flame theory. The correlation between the local maximum OH fluorescence intensity and the local curvature tends to level off for large positive curvature (H > 0.5 mm i) as Uo/S L increases, indicating that the response of the flame to large flame stretch may be non-linear at high Uo/SL. The pdfs of peak OH LIF intensity suggest that the mean burning rate of the H 2 / H e / a i r flame at Uo/Sc = 3.3 is increased approximately by 10% in comparison to the undisturbed laminar flame. The present results imply that even though the local flame curvature may strongly influence the local structure and burning rate of nonunity Lewis number flames through the effect of flame stretch on the local burning rate, these variations tend to cancel in the mean due to the linear relationship between local burning rate and curvature for the most probable values of curvature ( - 0 . 5 mm- ~ < H < 0.5 m m - 1) and due to the symmetry and zero mean of the curvature distribution. Therefore, the main effect of turbulence and Lewis number is to wrinkle the flame and produce flame area, while increasing the mean burning rate per unit surface area by relatively small amount through flow strain effects.
INTRODUCTION The structure of premixed flames in turbulence is an important problem in combustion fluid mechanics, which has significant implications related to the performance of practical combustion devices. Experimental evidence indicates that combustion in most practical devices takes place in the so-called thin laminar flamelet regime [1-3]. Of primary importance in understanding and modelling turbulent premixed combustion in this regime are (1) surface properties, such as the wrinkled flame area, flame curvature and orientation statistics; (2) local flame structure and flame speed; and (3) changes in turbulence properties across the
* Current address: Dept. of Mechanical and Aerospace Engr., Arizona State University, Tempe, AZ 85287-6106. t Current address: Allison Engine Co., P.O. Box 420, Indianapolis, IN 46206-0420. :~Corresponding author: Professor D. A. Santavicca, 132 Research Building East, Bigler Road, University Park, PA 16802. Presented at the Twenty-Fifth Symposium (International) on Combustion, Irvine, California, 31 July-5 August 1994.
flame. In order to arrive at a fundamental understanding of these various aspects of turbulent premixed combustion, laminar flames interacting with organized vortex structures, such as a toroidal vortex [4-6], an isolated line vortex pair [7,8], a single vortex (9), and K~irmfin vortex streets [10-12], have been investigated both numerically and experimentally. These studies attempt to isolate effects of a known vortex scale on premixed laminar flames and have provided insight into the nature of flame-vortex interactions, such as the alteration of the vortex structure by heat release, the convection of the flame surface by the vortex and flame-generated vorticity due to the simultaneous evolution of the flame and vortices. Recent work, both experimental [13-15] and numerical [16-18], suggests that not only the turbulence properties, i.e., turbulence intensity and length scale, but also flame stretch and differential thermal and species diffusion, which is represented by the Lewis number of the reactant mixture, have important effects on the overall surface properties and the local response of premixed flames.
COMBUSTIONAND FLAME 100:161-168 (1995) Copyright © 1995 by The Combustion Institute Published by Elsevier Science Inc.
0010-2180/95/$9.50 SSD10010-2180(94)00079-8
162
J.G. LEE ET AL.
The objective of the present study is to investigate the effect of flame stretch at various Lewis numbers on the local and global structure of premixed flames interacting with turbulent Karm~n vortex streets. This is an extension of a previous study of the interaction between laminar vortices and premixed flames [12], where now the use of a turbulent Kfirm~in vortex street allows for a larger variation of the vortex rotational velocity and introduces a multiplicity of vortex scales.
EXPERIMENTAL METHODS A schematic of a flame-vortex interaction device is shown in Fig. 1. The test section has a square cross section measuring 96 × 96 mm and includes two opposing uv-transmitting fused silica windows (60 × 100 mm) mounted in the side walls, which provide optical access for flame visualization. The other two test section walls have a slot to permit passage of a laser sheet. Premixed fuel-air mixtures are prepared in a continuous flow system and introduced through four opposing ports at the bottom of the test section. The flow is laminarized by passing it through a sintered porous plate and a honeycomb flow straightener. A premixed V-flame is stabilized on a flame holder (stainless steel rod with a diameter of 1 mm) located at the mid-section of the test section, while a K~rmfin vortex street is produced in the wake of a cylindrical rod (diameter D) placed upstream of the flame holder
~
uv transmitting fused silica window Flame holder
Vortex generating rod Honeycomb flow straightener
I
Sintered porous plate
J--
Premixed fuel/air mixture Fig. 1. Schematicdiagramof experimentalapparatus.
with a transverse offset of 12 mm. In this arrangement, the vortex street interacts with only one branch of the V-flame. Three mixtures were used in order to investigate the effect of Lewis number on the structure of premixed flames interacting with vortices: hydrogen/helium/air (Le = 0.21), methane/air (Le = 0.94) and propane/air (Le = 1.79). The equivalence ratio in each case was selected so that the mixtures have the same ratio of characteristic vortex rotational velocity to flame speed (Uo/SL) as summarized in Table 1. Time-resolved LDV was used to verify the uniformity of the flow in the absence of the K~irmfin vortex street and to estimate the vortex strength. The mean velocity was uniform within + 3%, while the velocity fluctuations were negligible (less than + 5%). The shedding frequency was measured using timeresolved LDV. It is well known that in the range of 40 < Re o < 150, there exists a regular array of alternating shedding vortices for long distances downstream (which is referred to as a Kfirmfin vortex street). Periodic vortex shedding also occurs at Reynolds number up to 105 or more, but the free vortices which move downstream are quickly obliterated by turbulent diffusion and a turbulent wake is established. The predominant (shedding) frequency (f,) can be determined from the energy spectrum of the velocity fluctuations. In this experiment, the vortex-generating rod is placed 8D upstream of the location where the flame interacts with the vortices. As shown in Fig 2, as the Reynolds number (Re D) increases, the energy spectrum begins to evolve into a classical turbulent spectrum but with periodic vortex shedding still evident over the range of Reynolds numbers employed, i.e., from 320 to 570. The distinct peak at the shedding frequency indicates that the coherent vortices persist at that location. The measured shedding frequency was within _+1% of Roshko's results [19]. Uo was estimated from the measured mean axial velocity (U0) and turbulence intensity (u'/U) profiles in the wake of the cylinders. Since the velocity defect in the mean velocity and corresponding velocity fluctuations are associated with the drag of the cylinder, their magnitude increases as the mean flow velocity increases. The vortex rotational
PREMIXED FLAMES INTERACTING WITH V O R T E X STREETS
163
TABLE 1 Summary of Test Conditions and Vortex Parameter U0 (m/s)
D (mm)
Re D
q5
SLf (m/s)
3L (mm)
Uo/S c
6v/fi L
H 2/He/Air (Lc = ().21)
(}.90 1.16
5.2 5.2
320 41(}
0.09 b 0.09 b
0.18 0.18
1.6 1.6
2.2 3.3
2.8 2.4
CH4/Air (Le = 0.94)
1.10 1.4(}
5.2 5.2
39(} 500
(}.81) 0.80
(}.27 0.27
0.9 0.9
2.2 3.3
4.4 3.6
C3Hs/Air (Le = 1.79)
1.25 1.60
5.2 5.2
440 570
0.80 0.80
0.32 0.32
0.8 0.8
2.2 3.3
4.3 3.8
"Egolfopoulous et al. [22] except H 2 / H e / A i r (measured). hVol.% of H 2 / ( H 2 + He + Air) = 9 and vol.% of H e / ( H e + Air) = 43.
velocity was estimated by Uo = 2 . ( U o ) . (U'//U). . . . where ( u ' / U ) m a x is the maximum turbulence intensity. The estimated values were within _+10% of Roshko's results. The vortex parameters determined in this manner are used to define the test conditions listed in Table 1. O H planar-laser-induced fluorescence (PLIF) was used to define the flame interface and to determine the local flame structure. The OH PLIF setup included an Nd:YAG laser-pumped tunable pulsed dye laser and a double-stage, microchannel plate intensified 128 × 128 Reticon array camera. The tunable pulsed dye laser output was frequency-doubled and yielded ca. 5 m J/pulse at 283.92 nm, which was used to excite the Q~(8) and Q1(9) transiI
I
i
r
fs=58
50 IO0 150 Frequency (Hz)
200
(a) i
i
i
o
tions in the (l,0) vibrational band of the A 2 ~ - X 2 H system of OH. A spherical-cylindrical lens combination was used to generate a laser sheet of 60-mm height. A filter combination, consisting of two long pass filters (Schott WG-305) and two band pass filters (Schott UG-11) was mounted in front of the camera lens to allow only fluorescence from the (1, 1) and (0,0) transitions near 310 nm to be detected. Two different fields of view were employed in this study. A larger field of view (60 mm × 60 mm) was employed for analysis of flame surface properties, while a smaller field of view (20 mm × 20 mm) was employed to measure OH fluorescence intensity profiles normal to the flame front. The spatial resolution was about 160 # m / p i x e l and 460 ~ m / p i x e l for the 20 × 20 mm and 60 × 60 mm fields of view, respectively. The twodimensional images were normalized before being analyzed in order to correct for nonuniformity in the laser intensity across the laser sheet and shot-to-shot variation of laser power. The reference image for the normalization was obtained from images of the undisturbed Vflame by averaging the maximum pixel intensities of each horizontal line over 10 digitized images. RESULTS AND DISCUSSION
o 0 e~
0
50 1 O0 150 Frequency (Hz)
200
(b) Fig. 2. Energy spectrum of velocity fluctuation for (a) U0 = 0.7 m / s , d = 2.1 mm (Re d = 100) and (b) UII = 1.3 m / s , d = 5.2 mm (Re d = 450).
The effect of Lewis number on the global flame front structure is shown in Fig. 3, where binarized flame boundaries for hydrogen/ helium/air (Le = 0.21), m e t h a n e / a i r (Le = 0.94), and propane/air (Le = 1.79) mixtures are shown. From stretched laminar flame theory [20], when the Lewis number is less than
164
J.G. LEE ET AL. L e = 0.21
Le :
0.94
3.0
Le = 1.79
'
UO/~
V •
2.5
L
0.8 (Lee el., al., 1993) 2.2 3.3
[]
[] 2.0
(a)
1.5 V V 1.0
0.0
I
I
I
0.5
1.0
1.5
£.) Fig. 3. Binarized images of flame fronts for Le = 0.21, 0.94, and 1.79 at (a) Uo/St. = 2.2 and (b) 3.3 (Black: Burned product, White: Unburned mixture).
one, convex (toward reactants) elements of the flame surface are expected to burn faster while concave (toward reactants) elements are expected to burn slower than undisturbed planar flames. This leads to the amplification of the flame front wrinkles initially created by the vortices. This effect is clearly evidenced in Fig. 3, where the hydrogen/helium/air flame shows significant penetration of the concave regions on the flame front. In contrast, there is a substantial suppression of the flame front wrinkles in the propane/air flame, where the flame front is much less distorted compared to the hydrogen/helium/air flame. As the characteristic vortex strength (Uo/S L) increases, the flame fronts are no longer simply-connected, but form many separate and locally closed surfaces such as burned pockets and islands. The occurrence of those unconnected flame fronts are more frequent in hydrogen/ helium/air flames than methane/air flames, while propane/air flames only exhibit simplyconnected flame fronts. Changes in flame surface properties such as flame area, curvature and orientation with respect to the variation of the Lewis number and Uo/S L are shown in Figs. 4 and 5. In Fig. 4, the flame area ratio is plotted against the Lewis number for three values of Uo/SL, where the results for Uo/SL = 0.8 from previous work [12] are included for comparison. The flame area ratio is defind as the ratio of the wrinkled
2.0
Le
Fig. 4. Effect of Lewis number on the flame area ratio at various normalized vortex rotational velocity (Uo/SL).
flame front area to the undisturbed V-flame area within the same field of view. The results plotted in Fig. 4 are the ensemble average of the area ratios from 30 images for each condition. For fixed Uo/SL, the flame area ratio increases with decreasing Lewis number, while the effect of Lewis number of the flame area ratio is found to be greater at larger Uo/S L. Figure 5a shows the effect of Lewis number on the area-weighted flame curvature probability density function. Curvature is defined positive for a flame front convex towards the reactants. In spite of a substantial change in the 0.5
, I
i
i
/SL=2.2
i
0.4 -
i
i
Ue/SL =3'3
Le
Le V
V 0.21 • 0.94
0.21
olo4
-
0.3 0.2 0.1 0.0 I~
-1
0
1
-2
0
-I
1
H (ram-~)
H (ram -t )
(-) 0.2
i , Ue/SL:2'2
,
J
, Le ~7 0 . 2 1 • 0.94 D 1.79
0.1 ~2.. ~ ~ i 1 , ~ 7 00 ---15 --10 --5
0
5
(,*--0)/%
Ue/SL =3-3 •
Le 0.21 0.04
D 1.79
I , 10 15
-15 -10 -5
0
5
(c,-a,)/C,o
10
15
(b) Fig. 5. Probability density functions of (a) flame curvature and (b) normalized flame orientation angle.
PREMIXED FLAMES INTERACTING WITH VORTEX STREETS flame surface area with Lewis number, there is no apparent effect on the curvature pdfs. The curvature pdfs for the three different mixtures are nearly symmetric with mean value near zero, while there is a weak broadening of the pdfs when Uo/S L is increased from 2.2 to 3.3. This is in contrast to the strong asymmetry observed during interactions with laminar Kfirmfin vortex streets [12]. The flame front orientation pdfs for the three different mixtures are shown in Fig. 5b. Here the orientation angle ( a ) is measured with respect to the horizontal axis and normalized by the direction of propagation of the undisturbed flame front (a0). For propane/air flames, the pdf is peaked around the direction of flame propagation while a decrease in the Lewis number causes a broadening in the distribution and a shift towards a larger flame angle. This can be seen more clearly at higher Uo/S L. These results indicate that, a s Uo/S L increases and Lewis number decreases, the flame front is oriented more randomly, thus increasing the effective flame propagation speed, which can be approximated as the normal component of the incoming gas velocity to the flame front. The principal findings are that the flame surface area is dependent on the Lewis number in such a way that more flame area is generated for Le < 1 than for Le > 1 and that the pdfs of flame curvature are nearly symmetric about a near-zero mean and not sensitive to the Lewis number. Similar behavior has been observed in turbulent premixed flames at various Lewis numbers in both experimental [13-15] and numerical [16-18] studies. The maximum OH concentration within the flame front is a good measure of the strength of chemical activity (or burning rate) in the flame [21]. In linear fluoresence measurements, uncertainty in the collisional quenching rate and temperature dependence of the population fraction in the absorbing state are sources of error which limit the ability to determine absolute concentrations. For the excitation scheme and flame conditions used in this study, it is estimated that the maximum OH fluorescence intensity can be used to represent the relative OH concentration with an uncertainty of less than +20%.
165
The normalized average maximum OH fluorescence intensity is plotted versus the local fame curvature in Fig. 6, where the maximum OH fluorescence intensities of many samples with curvatures within a narrow range (AH = 0.25 mm -1) were averaged and normalized by the average maximum intensity at zero flame curvature. Also shown in Fig. 6 are "error bars" that represent the standard deviation of the maximum OH intensity measurements for a given curvature. All of the results show a relatively strong correlation, where as expected from stretched laminar flame theory [20], the flame response 1.5
~ 0 ,_...~ ~
1.0
uo/s L 0.8 (Lee el; ai.,1993 2.2 3.3
0.5
i o,o 2;
- 1 .!
I
I
I
1
-I .0
-0.5
0.0
0.5
1.0
H (rnnl-I)
(a) 1.5
~ 0~
1.0
~
0.5
UJS L • D I
o.o --
-1.0
.5
0.8 (Lee et al., 1993 2.2 3.3 [ [
• [
-0.5
0.0
0.5
1.0
H (ram -I)
(b) 1.5
~o
1.0
o.5
Us/S L • o
~,"4
Z"
o.o
I
-1.0
0 . 8 ( L e e eL a l . , 1 9 9 3 2.2 L
[
-0.5
0.0
0.5
H
(lrnm-1)
[ •
3.3
.0
(o) Fig. 6. N o r m a l i z e d a v e r a g e m a x i m u m O H L I F i n t e n s i t y as a f u n c t i o n o f local f l a m e c u r v a t u r e at v a r i o u s Ue/SL: (a) L e = 0.21, (b) L e = 0.94, a n d (c) L e = 1.79.
166 to flame stretch was found to be fundamentally different in the different Lewis number cases. For each Uo/S L considered, the slope of the correlation of hydrogen/helium/air flames is positive and much larger in magnitude than the negative slope for propane/air flames, while the methane/air flames shows only a very weak positive slope, indicating minimal effect of flame stretch. The effect of averaging many samples is to average over the fluctuations in the flow strain and cancel out the effects of flow strain, so that only the effect of flame curvature on the peak OH LIF intensity can be recovered. Therefore, the slope of the correlation does not show a strong dependence on Uo/S L. Also, it can be noted that for hydrogen/ helium/air flames, the normalized average maximum OH intensity is more responsive to negative curvature than positive curvature as Uo/S L increases in that the correlation is linear for negative curvature and tends to level off for positive curvature larger than 0.5 ram- 1, in contrast to the results for laminar vortex streets. Though stretched laminar flame theory has been derived under the assumption of small flame stretch, these results indicate that the response of the flame to large flame stretch may be nonlinear. Similar behavior can be found in the numerical work of Haworth and Poinsot [17] for turbulent premixed flames. They found that the local burning rate is correlated more strongly with negative than positive curvature. They argued that since self-propagating flame fronts sustain concave (towards reactants, R < 0) elements and destroy convex (R > 0) elements, curvature of a flame element can be expected to be sustained longer for concave than convex elements and therefore the concave region is more responsive to thermodiffusive effects. Figure 7 shows the area-weighted pdfs of the normalized maximum OH fluorescence intensity, which represents the distribution of the reaction rate along the flame front. It can be observed that the OH intensity pdfs for flames with nonunity Lewis numbers are broadened relative to that corresponding to methane/air flames which have a near-unity Lewis number (0.94). Furthermore, the broadening is greater for larger Uo/SL, indicating the stronger effect
J.G. LEE ET AL. 0.6
i Le v 0.21 • 0.94 [] 1 . 7 9
o.4
0.2 Z 0.0 . . . . . 0.5
1.0
1.5
Normalized maximum intensity, OH]/[0H]H=O
(a) 0.6 ¢9
Q9
Z
i
Le
0.2
v
• 0.94 [] 1 . 7 9
0.4
0.0
0.21
....
0,5
1.0
1.5
Normalized maximum intensity, [0H]/[0H]It__ 0
(b) Fig. 7. P r o b a b i l i t y density functions of n o r m a l i z e d maxim u m intensity [ O H ] / [ O H ] H = 0 at Uo/S L = (a) 2.1 and
(b) 3.3. of flow strain at higher Uo/S L. There is also a tendency for the pdfs to be positively shifted for hydrogen/helium/air flames, which corresponds to an increase in the mean burning rate. The increase is about 10% over the undisturbed laminar flame case. This is consistent with DNS calculations for nonunity Lewis number turbulent premixed flames by Trouv6 and Poinsot [18]. CONCLUSIONS The major conclusions of the study can be summarized as follows: 1. Effect of Lewis number on the global flame surface properties: a. For fixed Uo/S L, the flame area increase in H 2 / H e / a i r flames (Le = 0.21) is promoted compared with CH4/air flames
P R E M I X E D FLAMES I N T E R A C T I N G W I T H V O R T E X STREETS which have a Lewis number near unity, while the flame area increase in C 3 H J a i r (Le = 1.79) flames is inhibited compared with C H 4 / a i r flames. In addition, flame area increases more rapidly with Uo/S L for H 2 / H e / a i r flame than for C H 4 / a i r or C 3 H s / a i r flames, indicating that the effect of Lewis number on flame area increases with Uo/S c. b. Flame curvature pdfs are nearly symmetric with respect to a zero mean and are insensitive to Lewis number. c. The flame front is oriented more randomly as Lewis number decreases and Uo/S c increases. 2. Effect of Lewis number on the local flame response: a. Local flame response to flame curvature is qualitatively consistent with the results of stretched laminar flame theory. b. The correlation between the peak O H LIF intensity and curvature tends to level off for positive curvature larger than 0.5 mm i as Uo/S L increases, indicating that the response of the flame to large flame stretch may be nonlinear at high Uo/S L. c. The pdfs of peak O H LIF intensity suggests that the mean burning rate of the H z / H e / a i r flame at Uo/S L = 3.3 increases by only about 10% compared with the undistributed laminar flame. 3. The present results imply that even though the local flame curvature may strongly influence the local structure of nonunity Lewis number flames through the effect of flame stretch on the local burning rate, these variations tend to cancel in the mean due to the linear relationship between local burning rate and curvature for the most probable values of curvature, i.e., - 0 . 5 m m - ~ < H < 0.5 mm -1 and due to the symmetry and zero mean of the curvature distribution. Therefore, the main effect of turbulence and Lewis number is to wrinkle the flame and produce flame surface area, while increasing the mean burning rate per unit surface area by only approximately of 10% through flow strain effects. This research was supported by the Air Force Office of Scientific Research under Grant
167
AFOSR-87-O037, with Dr. Julian Tishkoff as program manager.
REFERENCES 1. Gouldin, F. C., Hilton, S. M., and Lamb, T, TwentySecond Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 541-550. 2. North, G. L., and Santavicca, D. A., Combust. Sci. Technol. 72:215-232 (1991). 3. Mantzaras, J., Felton, P. G., and Bracco, F. V.. Cornbust. Flame 77:295-310 (1989). 4. Cattolica, R. J., and Vosen, S. R., Combust. Sci. Technol. 48:77-87 (1986). 5. Roberts, W, L., and Driscoll J. F., Combust. Flame 87:245-256 (1991). 6. Roberts, W. L, Dris¢oll J. F., Drake M. C., and Goss L. P., Combust. Flame 94:58-69 (1993). 7. Poinsot, T., Veynante, D., and Candel, S., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 613-619. 8. Poinsot, T., Veynante, D., and Candel, S., J. Fluid Mech. 228:561-606 (1991). 9. Rutland, C. J., and Ferziger, J. H., Combust. Flame 84:343-360 (1991). 10. Hertzberg, J. R., Namazian, M., and Talbot, L., Cornbust. Sci. TechnoL 38:205-216 (1984). 11. Escudi~, D., Prog. Astronaut. Aeronaut. 113:215 239
(1988). 12. Lee, T.-W., Lee, J. G., Nye, D. A., and Santavicca, D. A., Combust. Flame 94:146-160 (1993). 13. Lee, T.-W., North, G. L., and Santavicca, D. A., Combust. Flame 93:445-456 (1993). 14. Wu, M. S., Kwon, S., Driscoll, J. F., and Faeth, G. M., Combust. Sci. Technol. 78:69-96 (1991). 15. Goix, P. J., and Shepherd, I. G., Combust. Sci. Technol. 91:191-206 (1993). 16. Ashurst, Win. T., and Smooke, M. D., Combust. Sci. Technol. 53:339-375 (1987). 17. Haworth, D. C., and Poinsot, T. J., J. Fluid Mech. 244:405-436 (1992). 18. Trouvd, A., and Poinsot, T., Western States Section/The Combustion Institute 1992 Fall Meeting. 19. Roshko, A., NACA TN 2913, 1953. 20. Law, C. K., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 1381-1402. 21. Becker, H., Monkhouse, P. B., Wolfrum, J., Cant, R. S., Bray, K. N. C., Maly, R., Pfister, W., Stahl, G., and Warnatz, J., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 817-823. 22. Egolfopoulos, F. N., Zhu, D. L., and Law, C. K., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 471-478. Received 1 December 1993; revised 20 April 1994
168
J.G. LEE ET AL.
Comments T. Tsuruda, University of Tokyo, Japan. Your images show a larger OH emission zone width than the expected flame zone width. Why do you have such a thick reaction zone? Authors' Reply. The OH concentration in the premixed flame rises sharply through the flame front from its unburned value to its maximum nonequilibrium concentration [1, 2]. The previous OH LIF measurement in our laboratory [3] shows that the steepest gradients in the OH LIF intensities are confined to a region of approximately 1 mm, which is the order of reaction zone thickness. In the post flame re-
gions, however, the OH LIF intensity decreases gradually due to recombination reactions to its equilibrium value, which is the reason why the LIF image shows relatively thick high OH LIF intensity region around the reaction zone. REFERENCES 1. Smoot, L. D., Hecker, W. C., and Williams, G. A., Combust. Flame 26:323-342 (1976). 2. Bethtel, J. H., and Teets, R. C., Applied Optics 18:4138-4144 (1979). 3. Lee, T. W., Lee, J. G., Nye, D. A., and Santavicca, D. A., Combust. Flame 94:146-160 (1994).
INTRODUCTION The structure of premixed flames in turbulence is an important problem in combustion fluid mechanics, which has significant implications related to the performance of practical combustion devices. Experimental evidence indicates that combustion in most practical devices takes place in the so-called thin laminar flamelet regime [1-3]. Of primary importance in understanding and modelling turbulent premixed combustion in this regime are (1) surface properties, such as the wrinkled flame area, flame curvature and orientation statistics; (2) local flame structure and flame speed; and (3) changes in turbulence properties across the
* Current address: Dept. of Mechanical and Aerospace Engr., Arizona State University, Tempe, AZ 85287-6106. t Current address: Allison Engine Co., P.O. Box 420, Indianapolis, IN 46206-0420. :~Corresponding author: Professor D. A. Santavicca, 132 Research Building East, Bigler Road, University Park, PA 16802. Presented at the Twenty-Fifth Symposium (International) on Combustion, Irvine, California, 31 July-5 August 1994.
flame. In order to arrive at a fundamental understanding of these various aspects of turbulent premixed combustion, laminar flames interacting with organized vortex structures, such as a toroidal vortex [4-6], an isolated line vortex pair [7,8], a single vortex (9), and K~irmfin vortex streets [10-12], have been investigated both numerically and experimentally. These studies attempt to isolate effects of a known vortex scale on premixed laminar flames and have provided insight into the nature of flame-vortex interactions, such as the alteration of the vortex structure by heat release, the convection of the flame surface by the vortex and flame-generated vorticity due to the simultaneous evolution of the flame and vortices. Recent work, both experimental [13-15] and numerical [16-18], suggests that not only the turbulence properties, i.e., turbulence intensity and length scale, but also flame stretch and differential thermal and species diffusion, which is represented by the Lewis number of the reactant mixture, have important effects on the overall surface properties and the local response of premixed flames.
COMBUSTIONAND FLAME 100:161-168 (1995) Copyright © 1995 by The Combustion Institute Published by Elsevier Science Inc.
0010-2180/95/$9.50 SSD10010-2180(94)00079-8
162
J.G. LEE ET AL.
The objective of the present study is to investigate the effect of flame stretch at various Lewis numbers on the local and global structure of premixed flames interacting with turbulent Karm~n vortex streets. This is an extension of a previous study of the interaction between laminar vortices and premixed flames [12], where now the use of a turbulent Kfirm~in vortex street allows for a larger variation of the vortex rotational velocity and introduces a multiplicity of vortex scales.
EXPERIMENTAL METHODS A schematic of a flame-vortex interaction device is shown in Fig. 1. The test section has a square cross section measuring 96 × 96 mm and includes two opposing uv-transmitting fused silica windows (60 × 100 mm) mounted in the side walls, which provide optical access for flame visualization. The other two test section walls have a slot to permit passage of a laser sheet. Premixed fuel-air mixtures are prepared in a continuous flow system and introduced through four opposing ports at the bottom of the test section. The flow is laminarized by passing it through a sintered porous plate and a honeycomb flow straightener. A premixed V-flame is stabilized on a flame holder (stainless steel rod with a diameter of 1 mm) located at the mid-section of the test section, while a K~rmfin vortex street is produced in the wake of a cylindrical rod (diameter D) placed upstream of the flame holder
~
uv transmitting fused silica window Flame holder
Vortex generating rod Honeycomb flow straightener
I
Sintered porous plate
J--
Premixed fuel/air mixture Fig. 1. Schematicdiagramof experimentalapparatus.
with a transverse offset of 12 mm. In this arrangement, the vortex street interacts with only one branch of the V-flame. Three mixtures were used in order to investigate the effect of Lewis number on the structure of premixed flames interacting with vortices: hydrogen/helium/air (Le = 0.21), methane/air (Le = 0.94) and propane/air (Le = 1.79). The equivalence ratio in each case was selected so that the mixtures have the same ratio of characteristic vortex rotational velocity to flame speed (Uo/SL) as summarized in Table 1. Time-resolved LDV was used to verify the uniformity of the flow in the absence of the K~irmfin vortex street and to estimate the vortex strength. The mean velocity was uniform within + 3%, while the velocity fluctuations were negligible (less than + 5%). The shedding frequency was measured using timeresolved LDV. It is well known that in the range of 40 < Re o < 150, there exists a regular array of alternating shedding vortices for long distances downstream (which is referred to as a Kfirmfin vortex street). Periodic vortex shedding also occurs at Reynolds number up to 105 or more, but the free vortices which move downstream are quickly obliterated by turbulent diffusion and a turbulent wake is established. The predominant (shedding) frequency (f,) can be determined from the energy spectrum of the velocity fluctuations. In this experiment, the vortex-generating rod is placed 8D upstream of the location where the flame interacts with the vortices. As shown in Fig 2, as the Reynolds number (Re D) increases, the energy spectrum begins to evolve into a classical turbulent spectrum but with periodic vortex shedding still evident over the range of Reynolds numbers employed, i.e., from 320 to 570. The distinct peak at the shedding frequency indicates that the coherent vortices persist at that location. The measured shedding frequency was within _+1% of Roshko's results [19]. Uo was estimated from the measured mean axial velocity (U0) and turbulence intensity (u'/U) profiles in the wake of the cylinders. Since the velocity defect in the mean velocity and corresponding velocity fluctuations are associated with the drag of the cylinder, their magnitude increases as the mean flow velocity increases. The vortex rotational
PREMIXED FLAMES INTERACTING WITH V O R T E X STREETS
163
TABLE 1 Summary of Test Conditions and Vortex Parameter U0 (m/s)
D (mm)
Re D
q5
SLf (m/s)
3L (mm)
Uo/S c
6v/fi L
H 2/He/Air (Lc = ().21)
(}.90 1.16
5.2 5.2
320 41(}
0.09 b 0.09 b
0.18 0.18
1.6 1.6
2.2 3.3
2.8 2.4
CH4/Air (Le = 0.94)
1.10 1.4(}
5.2 5.2
39(} 500
(}.81) 0.80
(}.27 0.27
0.9 0.9
2.2 3.3
4.4 3.6
C3Hs/Air (Le = 1.79)
1.25 1.60
5.2 5.2
440 570
0.80 0.80
0.32 0.32
0.8 0.8
2.2 3.3
4.3 3.8
"Egolfopoulous et al. [22] except H 2 / H e / A i r (measured). hVol.% of H 2 / ( H 2 + He + Air) = 9 and vol.% of H e / ( H e + Air) = 43.
velocity was estimated by Uo = 2 . ( U o ) . (U'//U). . . . where ( u ' / U ) m a x is the maximum turbulence intensity. The estimated values were within _+10% of Roshko's results. The vortex parameters determined in this manner are used to define the test conditions listed in Table 1. O H planar-laser-induced fluorescence (PLIF) was used to define the flame interface and to determine the local flame structure. The OH PLIF setup included an Nd:YAG laser-pumped tunable pulsed dye laser and a double-stage, microchannel plate intensified 128 × 128 Reticon array camera. The tunable pulsed dye laser output was frequency-doubled and yielded ca. 5 m J/pulse at 283.92 nm, which was used to excite the Q~(8) and Q1(9) transiI
I
i
r
fs=58
50 IO0 150 Frequency (Hz)
200
(a) i
i
i
o
tions in the (l,0) vibrational band of the A 2 ~ - X 2 H system of OH. A spherical-cylindrical lens combination was used to generate a laser sheet of 60-mm height. A filter combination, consisting of two long pass filters (Schott WG-305) and two band pass filters (Schott UG-11) was mounted in front of the camera lens to allow only fluorescence from the (1, 1) and (0,0) transitions near 310 nm to be detected. Two different fields of view were employed in this study. A larger field of view (60 mm × 60 mm) was employed for analysis of flame surface properties, while a smaller field of view (20 mm × 20 mm) was employed to measure OH fluorescence intensity profiles normal to the flame front. The spatial resolution was about 160 # m / p i x e l and 460 ~ m / p i x e l for the 20 × 20 mm and 60 × 60 mm fields of view, respectively. The twodimensional images were normalized before being analyzed in order to correct for nonuniformity in the laser intensity across the laser sheet and shot-to-shot variation of laser power. The reference image for the normalization was obtained from images of the undisturbed Vflame by averaging the maximum pixel intensities of each horizontal line over 10 digitized images. RESULTS AND DISCUSSION
o 0 e~
0
50 1 O0 150 Frequency (Hz)
200
(b) Fig. 2. Energy spectrum of velocity fluctuation for (a) U0 = 0.7 m / s , d = 2.1 mm (Re d = 100) and (b) UII = 1.3 m / s , d = 5.2 mm (Re d = 450).
The effect of Lewis number on the global flame front structure is shown in Fig. 3, where binarized flame boundaries for hydrogen/ helium/air (Le = 0.21), m e t h a n e / a i r (Le = 0.94), and propane/air (Le = 1.79) mixtures are shown. From stretched laminar flame theory [20], when the Lewis number is less than
164
J.G. LEE ET AL. L e = 0.21
Le :
0.94
3.0
Le = 1.79
'
UO/~
V •
2.5
L
0.8 (Lee el., al., 1993) 2.2 3.3
[]
[] 2.0
(a)
1.5 V V 1.0
0.0
I
I
I
0.5
1.0
1.5
£.) Fig. 3. Binarized images of flame fronts for Le = 0.21, 0.94, and 1.79 at (a) Uo/St. = 2.2 and (b) 3.3 (Black: Burned product, White: Unburned mixture).
one, convex (toward reactants) elements of the flame surface are expected to burn faster while concave (toward reactants) elements are expected to burn slower than undisturbed planar flames. This leads to the amplification of the flame front wrinkles initially created by the vortices. This effect is clearly evidenced in Fig. 3, where the hydrogen/helium/air flame shows significant penetration of the concave regions on the flame front. In contrast, there is a substantial suppression of the flame front wrinkles in the propane/air flame, where the flame front is much less distorted compared to the hydrogen/helium/air flame. As the characteristic vortex strength (Uo/S L) increases, the flame fronts are no longer simply-connected, but form many separate and locally closed surfaces such as burned pockets and islands. The occurrence of those unconnected flame fronts are more frequent in hydrogen/ helium/air flames than methane/air flames, while propane/air flames only exhibit simplyconnected flame fronts. Changes in flame surface properties such as flame area, curvature and orientation with respect to the variation of the Lewis number and Uo/S L are shown in Figs. 4 and 5. In Fig. 4, the flame area ratio is plotted against the Lewis number for three values of Uo/SL, where the results for Uo/SL = 0.8 from previous work [12] are included for comparison. The flame area ratio is defind as the ratio of the wrinkled
2.0
Le
Fig. 4. Effect of Lewis number on the flame area ratio at various normalized vortex rotational velocity (Uo/SL).
flame front area to the undisturbed V-flame area within the same field of view. The results plotted in Fig. 4 are the ensemble average of the area ratios from 30 images for each condition. For fixed Uo/SL, the flame area ratio increases with decreasing Lewis number, while the effect of Lewis number of the flame area ratio is found to be greater at larger Uo/S L. Figure 5a shows the effect of Lewis number on the area-weighted flame curvature probability density function. Curvature is defined positive for a flame front convex towards the reactants. In spite of a substantial change in the 0.5
, I
i
i
/SL=2.2
i
0.4 -
i
i
Ue/SL =3'3
Le
Le V
V 0.21 • 0.94
0.21
olo4
-
0.3 0.2 0.1 0.0 I~
-1
0
1
-2
0
-I
1
H (ram-~)
H (ram -t )
(-) 0.2
i , Ue/SL:2'2
,
J
, Le ~7 0 . 2 1 • 0.94 D 1.79
0.1 ~2.. ~ ~ i 1 , ~ 7 00 ---15 --10 --5
0
5
(,*--0)/%
Ue/SL =3-3 •
Le 0.21 0.04
D 1.79
I , 10 15
-15 -10 -5
0
5
(c,-a,)/C,o
10
15
(b) Fig. 5. Probability density functions of (a) flame curvature and (b) normalized flame orientation angle.
PREMIXED FLAMES INTERACTING WITH VORTEX STREETS flame surface area with Lewis number, there is no apparent effect on the curvature pdfs. The curvature pdfs for the three different mixtures are nearly symmetric with mean value near zero, while there is a weak broadening of the pdfs when Uo/S L is increased from 2.2 to 3.3. This is in contrast to the strong asymmetry observed during interactions with laminar Kfirmfin vortex streets [12]. The flame front orientation pdfs for the three different mixtures are shown in Fig. 5b. Here the orientation angle ( a ) is measured with respect to the horizontal axis and normalized by the direction of propagation of the undisturbed flame front (a0). For propane/air flames, the pdf is peaked around the direction of flame propagation while a decrease in the Lewis number causes a broadening in the distribution and a shift towards a larger flame angle. This can be seen more clearly at higher Uo/S L. These results indicate that, a s Uo/S L increases and Lewis number decreases, the flame front is oriented more randomly, thus increasing the effective flame propagation speed, which can be approximated as the normal component of the incoming gas velocity to the flame front. The principal findings are that the flame surface area is dependent on the Lewis number in such a way that more flame area is generated for Le < 1 than for Le > 1 and that the pdfs of flame curvature are nearly symmetric about a near-zero mean and not sensitive to the Lewis number. Similar behavior has been observed in turbulent premixed flames at various Lewis numbers in both experimental [13-15] and numerical [16-18] studies. The maximum OH concentration within the flame front is a good measure of the strength of chemical activity (or burning rate) in the flame [21]. In linear fluoresence measurements, uncertainty in the collisional quenching rate and temperature dependence of the population fraction in the absorbing state are sources of error which limit the ability to determine absolute concentrations. For the excitation scheme and flame conditions used in this study, it is estimated that the maximum OH fluorescence intensity can be used to represent the relative OH concentration with an uncertainty of less than +20%.
165
The normalized average maximum OH fluorescence intensity is plotted versus the local fame curvature in Fig. 6, where the maximum OH fluorescence intensities of many samples with curvatures within a narrow range (AH = 0.25 mm -1) were averaged and normalized by the average maximum intensity at zero flame curvature. Also shown in Fig. 6 are "error bars" that represent the standard deviation of the maximum OH intensity measurements for a given curvature. All of the results show a relatively strong correlation, where as expected from stretched laminar flame theory [20], the flame response 1.5
~ 0 ,_...~ ~
1.0
uo/s L 0.8 (Lee el; ai.,1993 2.2 3.3
0.5
i o,o 2;
- 1 .!
I
I
I
1
-I .0
-0.5
0.0
0.5
1.0
H (rnnl-I)
(a) 1.5
~ 0~
1.0
~
0.5
UJS L • D I
o.o --
-1.0
.5
0.8 (Lee et al., 1993 2.2 3.3 [ [
• [
-0.5
0.0
0.5
1.0
H (ram -I)
(b) 1.5
~o
1.0
o.5
Us/S L • o
~,"4
Z"
o.o
I
-1.0
0 . 8 ( L e e eL a l . , 1 9 9 3 2.2 L
[
-0.5
0.0
0.5
H
(lrnm-1)
[ •
3.3
.0
(o) Fig. 6. N o r m a l i z e d a v e r a g e m a x i m u m O H L I F i n t e n s i t y as a f u n c t i o n o f local f l a m e c u r v a t u r e at v a r i o u s Ue/SL: (a) L e = 0.21, (b) L e = 0.94, a n d (c) L e = 1.79.
166 to flame stretch was found to be fundamentally different in the different Lewis number cases. For each Uo/S L considered, the slope of the correlation of hydrogen/helium/air flames is positive and much larger in magnitude than the negative slope for propane/air flames, while the methane/air flames shows only a very weak positive slope, indicating minimal effect of flame stretch. The effect of averaging many samples is to average over the fluctuations in the flow strain and cancel out the effects of flow strain, so that only the effect of flame curvature on the peak OH LIF intensity can be recovered. Therefore, the slope of the correlation does not show a strong dependence on Uo/S L. Also, it can be noted that for hydrogen/ helium/air flames, the normalized average maximum OH intensity is more responsive to negative curvature than positive curvature as Uo/S L increases in that the correlation is linear for negative curvature and tends to level off for positive curvature larger than 0.5 ram- 1, in contrast to the results for laminar vortex streets. Though stretched laminar flame theory has been derived under the assumption of small flame stretch, these results indicate that the response of the flame to large flame stretch may be nonlinear. Similar behavior can be found in the numerical work of Haworth and Poinsot [17] for turbulent premixed flames. They found that the local burning rate is correlated more strongly with negative than positive curvature. They argued that since self-propagating flame fronts sustain concave (towards reactants, R < 0) elements and destroy convex (R > 0) elements, curvature of a flame element can be expected to be sustained longer for concave than convex elements and therefore the concave region is more responsive to thermodiffusive effects. Figure 7 shows the area-weighted pdfs of the normalized maximum OH fluorescence intensity, which represents the distribution of the reaction rate along the flame front. It can be observed that the OH intensity pdfs for flames with nonunity Lewis numbers are broadened relative to that corresponding to methane/air flames which have a near-unity Lewis number (0.94). Furthermore, the broadening is greater for larger Uo/SL, indicating the stronger effect
J.G. LEE ET AL. 0.6
i Le v 0.21 • 0.94 [] 1 . 7 9
o.4
0.2 Z 0.0 . . . . . 0.5
1.0
1.5
Normalized maximum intensity, OH]/[0H]H=O
(a) 0.6 ¢9
Q9
Z
i
Le
0.2
v
• 0.94 [] 1 . 7 9
0.4
0.0
0.21
....
0,5
1.0
1.5
Normalized maximum intensity, [0H]/[0H]It__ 0
(b) Fig. 7. P r o b a b i l i t y density functions of n o r m a l i z e d maxim u m intensity [ O H ] / [ O H ] H = 0 at Uo/S L = (a) 2.1 and
(b) 3.3. of flow strain at higher Uo/S L. There is also a tendency for the pdfs to be positively shifted for hydrogen/helium/air flames, which corresponds to an increase in the mean burning rate. The increase is about 10% over the undisturbed laminar flame case. This is consistent with DNS calculations for nonunity Lewis number turbulent premixed flames by Trouv6 and Poinsot [18]. CONCLUSIONS The major conclusions of the study can be summarized as follows: 1. Effect of Lewis number on the global flame surface properties: a. For fixed Uo/S L, the flame area increase in H 2 / H e / a i r flames (Le = 0.21) is promoted compared with CH4/air flames
P R E M I X E D FLAMES I N T E R A C T I N G W I T H V O R T E X STREETS which have a Lewis number near unity, while the flame area increase in C 3 H J a i r (Le = 1.79) flames is inhibited compared with C H 4 / a i r flames. In addition, flame area increases more rapidly with Uo/S L for H 2 / H e / a i r flame than for C H 4 / a i r or C 3 H s / a i r flames, indicating that the effect of Lewis number on flame area increases with Uo/S c. b. Flame curvature pdfs are nearly symmetric with respect to a zero mean and are insensitive to Lewis number. c. The flame front is oriented more randomly as Lewis number decreases and Uo/S c increases. 2. Effect of Lewis number on the local flame response: a. Local flame response to flame curvature is qualitatively consistent with the results of stretched laminar flame theory. b. The correlation between the peak O H LIF intensity and curvature tends to level off for positive curvature larger than 0.5 mm i as Uo/S L increases, indicating that the response of the flame to large flame stretch may be nonlinear at high Uo/S L. c. The pdfs of peak O H LIF intensity suggests that the mean burning rate of the H z / H e / a i r flame at Uo/S L = 3.3 increases by only about 10% compared with the undistributed laminar flame. 3. The present results imply that even though the local flame curvature may strongly influence the local structure of nonunity Lewis number flames through the effect of flame stretch on the local burning rate, these variations tend to cancel in the mean due to the linear relationship between local burning rate and curvature for the most probable values of curvature, i.e., - 0 . 5 m m - ~ < H < 0.5 mm -1 and due to the symmetry and zero mean of the curvature distribution. Therefore, the main effect of turbulence and Lewis number is to wrinkle the flame and produce flame surface area, while increasing the mean burning rate per unit surface area by only approximately of 10% through flow strain effects. This research was supported by the Air Force Office of Scientific Research under Grant
167
AFOSR-87-O037, with Dr. Julian Tishkoff as program manager.
REFERENCES 1. Gouldin, F. C., Hilton, S. M., and Lamb, T, TwentySecond Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 541-550. 2. North, G. L., and Santavicca, D. A., Combust. Sci. Technol. 72:215-232 (1991). 3. Mantzaras, J., Felton, P. G., and Bracco, F. V.. Cornbust. Flame 77:295-310 (1989). 4. Cattolica, R. J., and Vosen, S. R., Combust. Sci. Technol. 48:77-87 (1986). 5. Roberts, W, L., and Driscoll J. F., Combust. Flame 87:245-256 (1991). 6. Roberts, W. L, Dris¢oll J. F., Drake M. C., and Goss L. P., Combust. Flame 94:58-69 (1993). 7. Poinsot, T., Veynante, D., and Candel, S., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 613-619. 8. Poinsot, T., Veynante, D., and Candel, S., J. Fluid Mech. 228:561-606 (1991). 9. Rutland, C. J., and Ferziger, J. H., Combust. Flame 84:343-360 (1991). 10. Hertzberg, J. R., Namazian, M., and Talbot, L., Cornbust. Sci. TechnoL 38:205-216 (1984). 11. Escudi~, D., Prog. Astronaut. Aeronaut. 113:215 239
(1988). 12. Lee, T.-W., Lee, J. G., Nye, D. A., and Santavicca, D. A., Combust. Flame 94:146-160 (1993). 13. Lee, T.-W., North, G. L., and Santavicca, D. A., Combust. Flame 93:445-456 (1993). 14. Wu, M. S., Kwon, S., Driscoll, J. F., and Faeth, G. M., Combust. Sci. Technol. 78:69-96 (1991). 15. Goix, P. J., and Shepherd, I. G., Combust. Sci. Technol. 91:191-206 (1993). 16. Ashurst, Win. T., and Smooke, M. D., Combust. Sci. Technol. 53:339-375 (1987). 17. Haworth, D. C., and Poinsot, T. J., J. Fluid Mech. 244:405-436 (1992). 18. Trouvd, A., and Poinsot, T., Western States Section/The Combustion Institute 1992 Fall Meeting. 19. Roshko, A., NACA TN 2913, 1953. 20. Law, C. K., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 1381-1402. 21. Becker, H., Monkhouse, P. B., Wolfrum, J., Cant, R. S., Bray, K. N. C., Maly, R., Pfister, W., Stahl, G., and Warnatz, J., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 817-823. 22. Egolfopoulos, F. N., Zhu, D. L., and Law, C. K., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 471-478. Received 1 December 1993; revised 20 April 1994
168
J.G. LEE ET AL.
Comments T. Tsuruda, University of Tokyo, Japan. Your images show a larger OH emission zone width than the expected flame zone width. Why do you have such a thick reaction zone? Authors' Reply. The OH concentration in the premixed flame rises sharply through the flame front from its unburned value to its maximum nonequilibrium concentration [1, 2]. The previous OH LIF measurement in our laboratory [3] shows that the steepest gradients in the OH LIF intensities are confined to a region of approximately 1 mm, which is the order of reaction zone thickness. In the post flame re-
gions, however, the OH LIF intensity decreases gradually due to recombination reactions to its equilibrium value, which is the reason why the LIF image shows relatively thick high OH LIF intensity region around the reaction zone. REFERENCES 1. Smoot, L. D., Hecker, W. C., and Williams, G. A., Combust. Flame 26:323-342 (1976). 2. Bethtel, J. H., and Teets, R. C., Applied Optics 18:4138-4144 (1979). 3. Lee, T. W., Lee, J. G., Nye, D. A., and Santavicca, D. A., Combust. Flame 94:146-160 (1994).