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Nitrogen CARS thermometry for a study of temperature profiles through flame fronts
COMBUSTION AND FLAME 54: 149-154 (1983)
149
Nitrogen CARS Thermometry for a Study of Temperature Profiles through Flame Fronts SHIGEO FURUNO,* KAZUHIRO AKIHAMA, and MITSUGU HANABUSA Department of Electrical And Electronic Engineering, Toyohashi Universityof Technology, Tenpaku, Toyohashi440, Japan
and
SATOSHI IGUCHI and TOKUTA INOUE Higashifuji TechnicalCenter, ToyotaMotor Co., Susono, Shizuoka410-11, Japan
Using coherent anti-Stokes Raman spectroscopy (CARS), we have performed detailed axial and radial temperature surveys in a premixed methane-air flame at atmospheric pressure with a special emphasis on ~ u r e r a e n t s of temperature profiles through thin flame fronts. The temperature is inferred from N 2 CARS spectra. The thickness of flame fronts for flames with a stoichiometric mixture is about 700/am, while it broadens considerably in a fuel rich flame. The spatial resolution for measuring the temperature profile is about 100/am.
INTRODUCTION Coherent anti-Stokes Raman spectroscopy (CARS) has great potential as a tool for studies of such hostile gaseous states as those involved in combustion and plasmas. For the diagnostic probing of such environments, its high signal levels and coherent character become overwhelmingly advantageous over other optical techniques, such as spontaneous Raman scattering; in addition, CARS is characterized by its excellent spatial and temporal resolution [1 ]. In the present work we have applied CARS to a study of a premixed flame with a special interest in a temperature profile through its flame front. In the past, flames have been a favorable target * Present address: Higashifuji Technical Center, Toyota Motor Co., Susono, Shizuoka 410-11, Japan. Copyright ~) 1983 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
to which CARS is applied [1-6], but the temperature prof'de in the vicinity of the flame front in conventional premixed flames has not been studied in detail. Since in the flame front temperature rises rapidly across a narrow region from room temperature to high flame temperature, experimental difficulties in such a temperature study are considerable [7]. We employ BOXCARS for nitrogen and succeeded in mapping a temperature profile across the flame front in a premixed methane-air flame at atmospheric pressure. In BOXCARS, laser beams are crossed and signals are generated only at the beam intersection [8]. This gives rise to spatial resolution high enough to map temperature distributions in the flame front. The flame has been generated by a stabilized Bunsen burner. In the next section we describe an experimental arrangement used for the present work. Experi-
0010-2 ! 80/83/$03.00
150
SHIGEO FURUNO ET AL. OMA 2). The single pulse method becomes essential when good temporal resolution is required [9]. We use this method for the convenience of data acquisition. The signal-to-noise ratio can be improved by accumulating CARS spectra repeatedly. Also, a large amount of data needed to map temperature profiles can be stored in memories for later processing. In the single pulse method the Stokes beam spectra should be broad enough to cover the whole CARS spectra and yet not too broad to waste its power. Its output is adjusted to peak at 606.8 nm with a Gaussian bandwidth of 110 cm - i (FWHM) and a total power of 35 mJ per pulse. Pulse width is 7 ns. CARS signals are separated from laser beams by dichroic mirrors, dispersed by a 1.5 m monochromator (Jobin-Yabin THR-1500), and detected by OMA. The slit of the monochromator is open wide enough to pass focused CARS signals fully; spectral resolution expressed by a triangle slit function is 2.7 cm- i . A premixed flame is obtained by a Bunsen burner at atmospheric pressure with special precautions paid for stability of flames. The experimental setup is shown schematically in Fig. 2. Methane and air are premixed in a long tube with capillary tubes inserted at several locations (code 1). The inner diameter of a burning tube is made small (7 mm) to get a stable flame. Flame stability is greatly improved by a blower generated surrounding air flow. This protective air is flowing at a speed of about 1 m/s after passing through layers of glass balls and fine meshes. Temperature can be inferred by comparing the observed CARS spectra with computer generated
mental results are presented in the third section. Spatial resolution obtained with the present work is examined there. The final section presents a conclusion.
EXPERIMENTAL For the measurements to be described here, we employ a single pulse BOXCARS with an arrangement shown schematically in Fig. 1. A frequency doubled, 15 ns pulsed Nd:YAG laser (Quantel Model YG 481A) is used to provide a pump frequency as well as to drive a Stokes shifted dye laser (Quantel Model TDL III) at a repetition rate of 10 pps. The 532 nm, 100 mJ CARS pump beams are split into two, and they are crossed by a 300 mm focal length lens at a full angle of 11 °. The Stokes beam is added at an angle that satisfies the phase matching condition [8]. The pump beam has a bandwidth of 0.13 cm- 1 (FWHM). The spot size of focused beams is made identical for both pump and Stokes beams with the aid of a set of telescopes. The full width of 1/e maximum is approximately 80 /am at the crossed points, as measured by a combination of a narrow slit and a phototube. A large crossing angle is desirable for high spatial resolution, whereas the signal strength is reduced accordingly. The crossing angle of 11" used in the present experiment turns out to be adequate to explore temperature profiles even through flame fronts in premixed flames at atmospheric pressure, as shown later. We employ a single pulse method based on a broadband Stokes laser beam and an optical multichannel analyzer (Princeton Applied Research
Monochromator OMA / ~ L _ / h I Lens
l___l ....
TeleScope ~
Beam Trap 71'/4' / /
-
Dichroic Mirror
=
',
" ',
. . . . . . . . . . . . . . Di c Mirror
Lens
~ P r isrn Lens Beams olitter
Fig. 1. Schematic illustration of BOXCARS experimental arrangement used for N 2 thermometry.
FLAME TEMPERATURE PROFILES BY CARS
gave essentially identical inferred temperatures [11]. Theoretical curves thus generated agree
Stabilized Flame CH4 TANK
GLASS,
Air TANK
Mesh --...
V~kVE Glc~ss Btalls
BLOWER
151
F'L(:~ METER
Air --,~__
y VALVE
(:]:)
Air
Air Fig. 2. Experimental setup for stabilized, premixed Bunsen burner. Methane-air mixture is burned at atmospheric pressure. Code 1 shows capillary tubes. Protective air is provided by a blower.
patterns. A description of the computer code needed for producing theoretical spectra is summarized by Hall [10], and we follow his method closely except for changes in parameters associated with experimental details and molecular constants expressing vibrational and rotational energies of nitrogen. For the latter we use the values of Rahn and Owyoung, supplied through Hall. Also following Hall, we use a constant Raman line width of 0.1 cm - 1 ; more complicated calculations based on temperature and Q-branch dependent line widths
with experimental ones fairly well, as shown in Fig. 3 as an example at 1750K. Although this precise comparison between the experimental and theoretical curves was used to deduce temperature occasionally, we relied often on a simple method to handle a large amount of data needed to determine the temperature profile in the flame: namely, the widths in the main v = 0-1 band were measured at half- and one-third maximum, and then the values thus obtained were compared with those predicted from the computer simulation. The reason why we measured the widths at both half- and one-third maximum was to detect any distortion of the observed CARS spectra; if the spectra are distorted, different temperatures should be obtained from these two measurements. In addition to the width measurements, the heights of the 1-2 hot bands were compared with those for the 0-1 main bands, when the hot bands were observed at high temperatures. Again comparing this ratio with the theoretical one, we deduced temperatures. All of these temperatures were averaged to yield final values. Note that the width measurements yield an effective rotational temperature, while the height measurements give an effective vibrational temperature. For chemically inert gases like nitrogen, however, these two temperatures are expected to be in close equilibrium with translational temperature [7], and in
1.0
M
0.S
Z hi
z~- 0.6 0.4 _d
~r
~" 0,2
0 Z
0
21080
21100 WAVENUMBER
21120 ( c m -t )
I,
21140
Fig. 3. N2 CARS spectrum at 1750K. The solid line is experimental trace; dotted line is computer code prediction.
152
SHIGEO FURUNO ET AL. (K)
fact we observed no discrepancy between them throughout the flame. RESULTS
(ram) 11,5
_
ee3o
/J
~1.0
•
Y •~,,
s. 10.5 1000
v i-
2000 ( K )
\
~2o
I
LIJ "r-
10
b
,P II
!
J
I
tqcmeOee'"
/
AND DISCUSSIONS
To obtain temperature profiles in the premixed flame we change the position of the flame relative to the laser beam intersection horizontally and vertically. The displacement is as small as 50 tam in the vicinity of flame fronts. The CARS spectra are accumulated in the OMA for 20 to 180 times depending on the signal strength. Temperatures are inferred from these averaged spectra according to the method described above. At each location, the measurement is repeated 2-4 times. Judging from reproducibility of inferred temperatures and taking into consideration such unresolved uncertainties in computer simulation as the estimate of nonresonant third order susceptibility [10], the measured flame temperatures are thought to be accurate to within 50K. The axial variation of temperature in the premixed flame with height above the tube burner is shown in Fig. 4. A stoichiometric mixture of air and methane with flow rates of 2.3 and 0.23 1/min, respectively, is employed. The height of its inner core is seen to be about 11 mm, and the temperature rises to 2100K in a narrow flame front. The maximum temperature in flames should
,~0
2000
i
1000
I 2000
TEMPERATURE (K)
Fig. 4. Axial temperature profile in premixed flame with stoichiomettic m e t h a n e - a i r mixture. The insert is a blowup for flame front.
I000
/
r
~2000 v W
__e.Jm-~/~
~I000
(rnm)
! !
\
/
I
W
I 2
1.5
I
<
/
\
z
\ I
,
I
0
5 10 RADIAL POSITION (ram) Fig. 5. Radial temperature profile in stoichiometrically premixed flame. The insert is a blowup for flame front.
be close to but somewhat lower than theoretical adiabatic temperature, which is 2222K for the present mixture [12]. The observed maximum temperature is about 100K low, which is quite reasonable. A detailed temperature profile across the flame front is shown in the upper part of Fig. 4. Its thickness is about 750/am, if the flame front is defined as a region where temperature is between 400 and 2000K. The radial profile of temperature measured in the same flame at 5.4 mm above the burner is shown in Fig. 5. The position is measured from the center of the flame. The observed profile shows a rapid rise in temperature in the flame front and a gradual decline in the outer diffusion zone. Again the insert is a blowup of the temperature profile across the flame front. Its thickness, as defined above, is 650/am. The flame front is not perpendicular to the radial transverse direction in this case, but since the angle is only 16 ° apart from the perpendicular direction, its effect on the reaction thickness can be ignored. To see how an air/fuel ratio influences the flame structure, we measured a radial temperature profile in a fuel rich flame. The results are shown in Fig. 6. The flow rates are 2.2 and 0.371/min for air and methane, respectively. The measurement is
FLAME TEMPERATURE PROFILES BY CARS
f ;,¢'.-'~"~,
2000
L
v w
iooo w w
I
5
[
I
10
RADIAL POSITION (mm)
Fig. 6. Radial variation of temperature in fuel rich flame.
made at 12.3 mm above the tube, about halfway in the inner core. The temperature prof'de for this flame is characterized by a broad flame front. It is so thick (about 1.3 mm) that the blowup is not shown. A similar measurement has been attempted with an air rich flame, but since the flame is blown off easily with the secondary air, the data taken are not reliable and therefore not reproduced here. We now compare the observed thickness of flame fronts with a theory. It is to be pointed out that the flame front consists of a preheating zone and a reaction zone. In the preheating zone gases are heated by thermal conduction to an ignition point To. Its thickness/)i,r is defined as the region between the ignition temperature and the position where the temperature has risen by 10% of the rise in the zone; the latter temperature is designated as Ti. The reaction zone is the region where heat is released as the result of reactions; its thickness 8r is defined as a distance between the ignition point and the end of the reaction zone, where the temperature is given by Te. The thickness of these zones is given approximately by [13] ~p~ = 2.3kNoS and ko(T~ - To)
(pS(To- Ti) where k and ? are the average thermal conductivity and specific heat in the preheating zone, respectively, p is the initial density of unburnt gases, S is the burning velocity, and k o is the thermal
153 conductivity at To. Using Tl = 400, To = 1300, and ire = 2000K, we obtain 8pr ~, 6r "~"340/am [13], which corresponds to the total thickness of about 680 /am. Considering various approximations used to derive these expressions, we can conclude that the agreement obtained between the predicted value of 680 /am and the observed average value of 7 0 0 / a n is fortuitous. Note that on the basis of the above equations we can again explain qualitatively the increased thickness of the flame front for a fuel rich flame as the consequence of the decreased burning velocity. Spatial resolution can be estimated as follows: The laser beams have about an equal spot size, 80 /am, in a focal region. Since the beams are crossed at about 11°, an overlapped region is about 840/am long and 80 /am wide. Suppose that there is a boundary across which temperature changes abruptly. If the average direction of crossed beams is parallel to this boundary layer, spatial resolution for the temperature measurement is determined approximately by the width of the crossed region, 80/am. On the other hand, if the average direction is perpendicular to the layer, the resolution is roughly given by its length, 840/am. In the flame of interest, the boundary has a curvature and resolution is given by a value between these two extreme cases. In the flame depicted in Fig. 5, the curvature has a 1.6 mm radius and we can calculate that resolution should be about 100/am. It is concluded that the present measurement has enough spatial resolution to survey sharp temperature gradients across flame fronts even in atmospheric pressure flames. Note that resolution would be improved only by less than two even if the beams were crossed near 90 ° for the best resolution; besides, this is done only at the expense of the signal strength. In this regard, it would be more advantageous to use tightly focused beams rather than to use a large crossing angle. However, the spot size at focus is determined by input beam quality and cannot be made arbitrarily small; besides, high power densities may cause gas breakdown in flames. Flame stability is a serious concern in the present experiment. If single pulse CARS spectra were taken without accumulation, any fluctuation of the flame structure could be detected easily.
154 This was not done because the signal-to-noise ratio was poor without accumulation. We believe that the flame is reasonably stable from the observation that the CARS spectra observed in flame fronts can be matched with the theoretical ones. Since the CARS spectra change their shapes greatly with temperature, any serious movement of the flame front would result in a distorted line shape for the accumulated spectra. Therefore, if the flame front moves by 0.1 mm irregularly during the data acquisition, temperature fluctuation is as large as 500K, according to the results obtained from Figs. 4 and 5. We then have to add the spectra that are greatly different, and a noticeably distorted line should be observed. Since this is not the case, we conclude that the flame is stable to well within 0.1 mm. CONCLUSION We have demonstrated that the temperature profile across a narrow flame front in a premixed flame at atmospheric pressure can be explored with a conventional N2 BOXCARS. Spatial resolution is estimated to be 100/am, while the flame front of main interest is about 700/am thick in a stoichiometric methane flame and thicker in a fuel rich flame.
SHIGEO FURUNO ET AL. ICe are indebted to Dr. N. Yoshikawa and Mr. T. Fu/ikawa for their helpful advice in constructing a stabilized burner. ICe thank Drs. L. Ritual and R. J. Hall for valuable discussions on CARS computer coding.
REFERENCES i. Nibler, J. W., and Knighten, G. V., in Raman Spectroscopy of Gases and Liquids (A. Weber, Ed.), Springer-Verlag, Berlin, 1979, Chapter 7. 2. Moya, F., Druet, S. A. J., and Tatan, J. P. E., Opt. Commun. 13:169 (1975). 3. Eckbreth, A. C., and Hall, R. J., Combust. Flame 36:87 (1979). 4. Hall, R. J., Shirley, J. A., and Eckbreth, A. C., Opt. Lett. 4:87 (1979). 5. Marko,K. A., and Ritual, L., Opt. Lett. 4:211 (1979). 6. Teets, R. E., and Bechtel, J. H., Opt. Lett. 6:458 (1981). 7. Gaydon, A. G., and Wolfhard, H. G., Flames, 4th Ed., Chapman and Hall, London, 1979, Chapters 2, 5, 10, and 11. 8. Eekbreth, A. C.,AppL Phys. Lett. 32:421 (1978). 9. Roh, W. B., Schreiber, P. W., and Tatan, J. P. E., AppL Phys. Lett. 29:174 (1976). 10. Hall,R. J., Combust. Flame 35:47 (1979). 11. Hall, R. J.,AppL Spectrosc. 34:700 (1980). 12. Ref. [7], Chapter 12. 13. Ref. [7],Chapter 5. Received 26 October 1982; revised 13 May 1983
149
Nitrogen CARS Thermometry for a Study of Temperature Profiles through Flame Fronts SHIGEO FURUNO,* KAZUHIRO AKIHAMA, and MITSUGU HANABUSA Department of Electrical And Electronic Engineering, Toyohashi Universityof Technology, Tenpaku, Toyohashi440, Japan
and
SATOSHI IGUCHI and TOKUTA INOUE Higashifuji TechnicalCenter, ToyotaMotor Co., Susono, Shizuoka410-11, Japan
Using coherent anti-Stokes Raman spectroscopy (CARS), we have performed detailed axial and radial temperature surveys in a premixed methane-air flame at atmospheric pressure with a special emphasis on ~ u r e r a e n t s of temperature profiles through thin flame fronts. The temperature is inferred from N 2 CARS spectra. The thickness of flame fronts for flames with a stoichiometric mixture is about 700/am, while it broadens considerably in a fuel rich flame. The spatial resolution for measuring the temperature profile is about 100/am.
INTRODUCTION Coherent anti-Stokes Raman spectroscopy (CARS) has great potential as a tool for studies of such hostile gaseous states as those involved in combustion and plasmas. For the diagnostic probing of such environments, its high signal levels and coherent character become overwhelmingly advantageous over other optical techniques, such as spontaneous Raman scattering; in addition, CARS is characterized by its excellent spatial and temporal resolution [1 ]. In the present work we have applied CARS to a study of a premixed flame with a special interest in a temperature profile through its flame front. In the past, flames have been a favorable target * Present address: Higashifuji Technical Center, Toyota Motor Co., Susono, Shizuoka 410-11, Japan. Copyright ~) 1983 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
to which CARS is applied [1-6], but the temperature prof'de in the vicinity of the flame front in conventional premixed flames has not been studied in detail. Since in the flame front temperature rises rapidly across a narrow region from room temperature to high flame temperature, experimental difficulties in such a temperature study are considerable [7]. We employ BOXCARS for nitrogen and succeeded in mapping a temperature profile across the flame front in a premixed methane-air flame at atmospheric pressure. In BOXCARS, laser beams are crossed and signals are generated only at the beam intersection [8]. This gives rise to spatial resolution high enough to map temperature distributions in the flame front. The flame has been generated by a stabilized Bunsen burner. In the next section we describe an experimental arrangement used for the present work. Experi-
0010-2 ! 80/83/$03.00
150
SHIGEO FURUNO ET AL. OMA 2). The single pulse method becomes essential when good temporal resolution is required [9]. We use this method for the convenience of data acquisition. The signal-to-noise ratio can be improved by accumulating CARS spectra repeatedly. Also, a large amount of data needed to map temperature profiles can be stored in memories for later processing. In the single pulse method the Stokes beam spectra should be broad enough to cover the whole CARS spectra and yet not too broad to waste its power. Its output is adjusted to peak at 606.8 nm with a Gaussian bandwidth of 110 cm - i (FWHM) and a total power of 35 mJ per pulse. Pulse width is 7 ns. CARS signals are separated from laser beams by dichroic mirrors, dispersed by a 1.5 m monochromator (Jobin-Yabin THR-1500), and detected by OMA. The slit of the monochromator is open wide enough to pass focused CARS signals fully; spectral resolution expressed by a triangle slit function is 2.7 cm- i . A premixed flame is obtained by a Bunsen burner at atmospheric pressure with special precautions paid for stability of flames. The experimental setup is shown schematically in Fig. 2. Methane and air are premixed in a long tube with capillary tubes inserted at several locations (code 1). The inner diameter of a burning tube is made small (7 mm) to get a stable flame. Flame stability is greatly improved by a blower generated surrounding air flow. This protective air is flowing at a speed of about 1 m/s after passing through layers of glass balls and fine meshes. Temperature can be inferred by comparing the observed CARS spectra with computer generated
mental results are presented in the third section. Spatial resolution obtained with the present work is examined there. The final section presents a conclusion.
EXPERIMENTAL For the measurements to be described here, we employ a single pulse BOXCARS with an arrangement shown schematically in Fig. 1. A frequency doubled, 15 ns pulsed Nd:YAG laser (Quantel Model YG 481A) is used to provide a pump frequency as well as to drive a Stokes shifted dye laser (Quantel Model TDL III) at a repetition rate of 10 pps. The 532 nm, 100 mJ CARS pump beams are split into two, and they are crossed by a 300 mm focal length lens at a full angle of 11 °. The Stokes beam is added at an angle that satisfies the phase matching condition [8]. The pump beam has a bandwidth of 0.13 cm- 1 (FWHM). The spot size of focused beams is made identical for both pump and Stokes beams with the aid of a set of telescopes. The full width of 1/e maximum is approximately 80 /am at the crossed points, as measured by a combination of a narrow slit and a phototube. A large crossing angle is desirable for high spatial resolution, whereas the signal strength is reduced accordingly. The crossing angle of 11" used in the present experiment turns out to be adequate to explore temperature profiles even through flame fronts in premixed flames at atmospheric pressure, as shown later. We employ a single pulse method based on a broadband Stokes laser beam and an optical multichannel analyzer (Princeton Applied Research
Monochromator OMA / ~ L _ / h I Lens
l___l ....
TeleScope ~
Beam Trap 71'/4' / /
-
Dichroic Mirror
=
',
" ',
. . . . . . . . . . . . . . Di c Mirror
Lens
~ P r isrn Lens Beams olitter
Fig. 1. Schematic illustration of BOXCARS experimental arrangement used for N 2 thermometry.
FLAME TEMPERATURE PROFILES BY CARS
gave essentially identical inferred temperatures [11]. Theoretical curves thus generated agree
Stabilized Flame CH4 TANK
GLASS,
Air TANK
Mesh --...
V~kVE Glc~ss Btalls
BLOWER
151
F'L(:~ METER
Air --,~__
y VALVE
(:]:)
Air
Air Fig. 2. Experimental setup for stabilized, premixed Bunsen burner. Methane-air mixture is burned at atmospheric pressure. Code 1 shows capillary tubes. Protective air is provided by a blower.
patterns. A description of the computer code needed for producing theoretical spectra is summarized by Hall [10], and we follow his method closely except for changes in parameters associated with experimental details and molecular constants expressing vibrational and rotational energies of nitrogen. For the latter we use the values of Rahn and Owyoung, supplied through Hall. Also following Hall, we use a constant Raman line width of 0.1 cm - 1 ; more complicated calculations based on temperature and Q-branch dependent line widths
with experimental ones fairly well, as shown in Fig. 3 as an example at 1750K. Although this precise comparison between the experimental and theoretical curves was used to deduce temperature occasionally, we relied often on a simple method to handle a large amount of data needed to determine the temperature profile in the flame: namely, the widths in the main v = 0-1 band were measured at half- and one-third maximum, and then the values thus obtained were compared with those predicted from the computer simulation. The reason why we measured the widths at both half- and one-third maximum was to detect any distortion of the observed CARS spectra; if the spectra are distorted, different temperatures should be obtained from these two measurements. In addition to the width measurements, the heights of the 1-2 hot bands were compared with those for the 0-1 main bands, when the hot bands were observed at high temperatures. Again comparing this ratio with the theoretical one, we deduced temperatures. All of these temperatures were averaged to yield final values. Note that the width measurements yield an effective rotational temperature, while the height measurements give an effective vibrational temperature. For chemically inert gases like nitrogen, however, these two temperatures are expected to be in close equilibrium with translational temperature [7], and in
1.0
M
0.S
Z hi
z~- 0.6 0.4 _d
~r
~" 0,2
0 Z
0
21080
21100 WAVENUMBER
21120 ( c m -t )
I,
21140
Fig. 3. N2 CARS spectrum at 1750K. The solid line is experimental trace; dotted line is computer code prediction.
152
SHIGEO FURUNO ET AL. (K)
fact we observed no discrepancy between them throughout the flame. RESULTS
(ram) 11,5
_
ee3o
/J
~1.0
•
Y •~,,
s. 10.5 1000
v i-
2000 ( K )
\
~2o
I
LIJ "r-
10
b
,P II
!
J
I
tqcmeOee'"
/
AND DISCUSSIONS
To obtain temperature profiles in the premixed flame we change the position of the flame relative to the laser beam intersection horizontally and vertically. The displacement is as small as 50 tam in the vicinity of flame fronts. The CARS spectra are accumulated in the OMA for 20 to 180 times depending on the signal strength. Temperatures are inferred from these averaged spectra according to the method described above. At each location, the measurement is repeated 2-4 times. Judging from reproducibility of inferred temperatures and taking into consideration such unresolved uncertainties in computer simulation as the estimate of nonresonant third order susceptibility [10], the measured flame temperatures are thought to be accurate to within 50K. The axial variation of temperature in the premixed flame with height above the tube burner is shown in Fig. 4. A stoichiometric mixture of air and methane with flow rates of 2.3 and 0.23 1/min, respectively, is employed. The height of its inner core is seen to be about 11 mm, and the temperature rises to 2100K in a narrow flame front. The maximum temperature in flames should
,~0
2000
i
1000
I 2000
TEMPERATURE (K)
Fig. 4. Axial temperature profile in premixed flame with stoichiomettic m e t h a n e - a i r mixture. The insert is a blowup for flame front.
I000
/
r
~2000 v W
__e.Jm-~/~
~I000
(rnm)
! !
\
/
I
W
I 2
1.5
I
<
/
\
z
\ I
,
I
0
5 10 RADIAL POSITION (ram) Fig. 5. Radial temperature profile in stoichiometrically premixed flame. The insert is a blowup for flame front.
be close to but somewhat lower than theoretical adiabatic temperature, which is 2222K for the present mixture [12]. The observed maximum temperature is about 100K low, which is quite reasonable. A detailed temperature profile across the flame front is shown in the upper part of Fig. 4. Its thickness is about 750/am, if the flame front is defined as a region where temperature is between 400 and 2000K. The radial profile of temperature measured in the same flame at 5.4 mm above the burner is shown in Fig. 5. The position is measured from the center of the flame. The observed profile shows a rapid rise in temperature in the flame front and a gradual decline in the outer diffusion zone. Again the insert is a blowup of the temperature profile across the flame front. Its thickness, as defined above, is 650/am. The flame front is not perpendicular to the radial transverse direction in this case, but since the angle is only 16 ° apart from the perpendicular direction, its effect on the reaction thickness can be ignored. To see how an air/fuel ratio influences the flame structure, we measured a radial temperature profile in a fuel rich flame. The results are shown in Fig. 6. The flow rates are 2.2 and 0.371/min for air and methane, respectively. The measurement is
FLAME TEMPERATURE PROFILES BY CARS
f ;,¢'.-'~"~,
2000
L
v w
iooo w w
I
5
[
I
10
RADIAL POSITION (mm)
Fig. 6. Radial variation of temperature in fuel rich flame.
made at 12.3 mm above the tube, about halfway in the inner core. The temperature prof'de for this flame is characterized by a broad flame front. It is so thick (about 1.3 mm) that the blowup is not shown. A similar measurement has been attempted with an air rich flame, but since the flame is blown off easily with the secondary air, the data taken are not reliable and therefore not reproduced here. We now compare the observed thickness of flame fronts with a theory. It is to be pointed out that the flame front consists of a preheating zone and a reaction zone. In the preheating zone gases are heated by thermal conduction to an ignition point To. Its thickness/)i,r is defined as the region between the ignition temperature and the position where the temperature has risen by 10% of the rise in the zone; the latter temperature is designated as Ti. The reaction zone is the region where heat is released as the result of reactions; its thickness 8r is defined as a distance between the ignition point and the end of the reaction zone, where the temperature is given by Te. The thickness of these zones is given approximately by [13] ~p~ = 2.3kNoS and ko(T~ - To)
(pS(To- Ti) where k and ? are the average thermal conductivity and specific heat in the preheating zone, respectively, p is the initial density of unburnt gases, S is the burning velocity, and k o is the thermal
153 conductivity at To. Using Tl = 400, To = 1300, and ire = 2000K, we obtain 8pr ~, 6r "~"340/am [13], which corresponds to the total thickness of about 680 /am. Considering various approximations used to derive these expressions, we can conclude that the agreement obtained between the predicted value of 680 /am and the observed average value of 7 0 0 / a n is fortuitous. Note that on the basis of the above equations we can again explain qualitatively the increased thickness of the flame front for a fuel rich flame as the consequence of the decreased burning velocity. Spatial resolution can be estimated as follows: The laser beams have about an equal spot size, 80 /am, in a focal region. Since the beams are crossed at about 11°, an overlapped region is about 840/am long and 80 /am wide. Suppose that there is a boundary across which temperature changes abruptly. If the average direction of crossed beams is parallel to this boundary layer, spatial resolution for the temperature measurement is determined approximately by the width of the crossed region, 80/am. On the other hand, if the average direction is perpendicular to the layer, the resolution is roughly given by its length, 840/am. In the flame of interest, the boundary has a curvature and resolution is given by a value between these two extreme cases. In the flame depicted in Fig. 5, the curvature has a 1.6 mm radius and we can calculate that resolution should be about 100/am. It is concluded that the present measurement has enough spatial resolution to survey sharp temperature gradients across flame fronts even in atmospheric pressure flames. Note that resolution would be improved only by less than two even if the beams were crossed near 90 ° for the best resolution; besides, this is done only at the expense of the signal strength. In this regard, it would be more advantageous to use tightly focused beams rather than to use a large crossing angle. However, the spot size at focus is determined by input beam quality and cannot be made arbitrarily small; besides, high power densities may cause gas breakdown in flames. Flame stability is a serious concern in the present experiment. If single pulse CARS spectra were taken without accumulation, any fluctuation of the flame structure could be detected easily.
154 This was not done because the signal-to-noise ratio was poor without accumulation. We believe that the flame is reasonably stable from the observation that the CARS spectra observed in flame fronts can be matched with the theoretical ones. Since the CARS spectra change their shapes greatly with temperature, any serious movement of the flame front would result in a distorted line shape for the accumulated spectra. Therefore, if the flame front moves by 0.1 mm irregularly during the data acquisition, temperature fluctuation is as large as 500K, according to the results obtained from Figs. 4 and 5. We then have to add the spectra that are greatly different, and a noticeably distorted line should be observed. Since this is not the case, we conclude that the flame is stable to well within 0.1 mm. CONCLUSION We have demonstrated that the temperature profile across a narrow flame front in a premixed flame at atmospheric pressure can be explored with a conventional N2 BOXCARS. Spatial resolution is estimated to be 100/am, while the flame front of main interest is about 700/am thick in a stoichiometric methane flame and thicker in a fuel rich flame.
SHIGEO FURUNO ET AL. ICe are indebted to Dr. N. Yoshikawa and Mr. T. Fu/ikawa for their helpful advice in constructing a stabilized burner. ICe thank Drs. L. Ritual and R. J. Hall for valuable discussions on CARS computer coding.
REFERENCES i. Nibler, J. W., and Knighten, G. V., in Raman Spectroscopy of Gases and Liquids (A. Weber, Ed.), Springer-Verlag, Berlin, 1979, Chapter 7. 2. Moya, F., Druet, S. A. J., and Tatan, J. P. E., Opt. Commun. 13:169 (1975). 3. Eckbreth, A. C., and Hall, R. J., Combust. Flame 36:87 (1979). 4. Hall, R. J., Shirley, J. A., and Eckbreth, A. C., Opt. Lett. 4:87 (1979). 5. Marko,K. A., and Ritual, L., Opt. Lett. 4:211 (1979). 6. Teets, R. E., and Bechtel, J. H., Opt. Lett. 6:458 (1981). 7. Gaydon, A. G., and Wolfhard, H. G., Flames, 4th Ed., Chapman and Hall, London, 1979, Chapters 2, 5, 10, and 11. 8. Eekbreth, A. C.,AppL Phys. Lett. 32:421 (1978). 9. Roh, W. B., Schreiber, P. W., and Tatan, J. P. E., AppL Phys. Lett. 29:174 (1976). 10. Hall,R. J., Combust. Flame 35:47 (1979). 11. Hall, R. J.,AppL Spectrosc. 34:700 (1980). 12. Ref. [7], Chapter 12. 13. Ref. [7],Chapter 5. Received 26 October 1982; revised 13 May 1983