Temperature Measurement in Flames through CO2and CO Emission: New Highly Excited Levels of CO2

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

182, 10–17 (1997)

MS967205

Temperature Measurement in Flames through CO2 and CO Emission: New Highly Excited Levels of CO2 D. Bailly,* C. Camy-Peyret,† and R. Lanquetin† Laboratoire de Physique Mole´culaire et Applications, Unite´ propre du CNRS (UPR 0136), associe´ aux: *Universite´ Paris-Sud, Baˆt. 350, 91405 Orsay Cedex, France; and †Universite´ Pierre et Marie Curie, Tour 13, Boite 76, 4 place Jussieu, 75252 Paris Cedex 05, France Received March 22, 1996; in revised form October 8, 1996

Spectra of CH4 / O2 low-pressure flames have been recorded at a resolution of 0.020 cm01 with an infrared Fourier transform spectrometer in the spectral range 1790 to 5029 cm01 . Through the use of CO2 and CO emission lines, the flame temperature has been determined with a precision of the order of 1%. Results (wavenumbers, band centers, and spectroscopic constants) concerning six new vibrational transitions D£3 Å 1 with (2£1 / £2 ) Å 5 which have not been observed earlier and which occur between highly excited vibrational states are reported. q 1997 Academic Press

dling lines leading to calibrated sonic orifices which regulate the flows and allow stoichiometry. The fuel and oxidizer are mixed at the base of the water-cooled porous burner, the surface of which is adjustable inside the combustion chamber along the vertical axis. An insulated feed-through is used for positioning a metal igniter connected to a high-voltage Tesla coil and producing an electrical discharge at the burner surface to light up the gaseous mixture. It is removed as soon as the flame is stabilized. After this initial phase, a standard UV flame detector is used as a safety device commanding an electrovalve to close the gas inlets in case of flame shutoff. The flame front is at about 1 mm above the burner surface and the exhaust gases are pumped out with a mechanical pump (40 m3 /hr) through a water-cooled contraction, with a manual valve to vary the pumping speed, and hence the pressure inside the chamber which is measured with a Bourdon gauge. The outer ring of the burner is used to inject around the cylindrical inner core of the flame a sheath of gaseous nitrogen in order to prevent recirculation of the combustion products. The nitrogen gas also controls the pressure inside the chamber but is especially useful as a flowing buffer to reduce self-absorption by the infrared active molecules (mainly CO2 and to a lesser extent H2O) as well as an insulating buffer to reduce the thermal stress on the infrared window used to collect the flame emission. The corresponding infrared radiation is injected as a parallel beam into the Fourier transform (FTIR) spectrometer through a collecting lens ( f Å 250 mm) positioned to sample the combustion gases on the axis of the flame at a given distance above the flame front. The spectra have been recorded in the region 1800–5000 cm01 with a standard DA2.01 BOMEM-type interferometer with a 0.25 1 0.25-mm liquid nitrogen-cooled InSb detector at the output optics (no optical filter has been used). The

INTRODUCTION

Spectra of CH4 / O2 flames (PCH4 /PO2 Å 0.49) under a total pressure of 20 mbar have been recorded with a Fourier transform infrared spectrometer (DA2 BOMEM) at a resolution of 0.020 cm01 in the spectral range 1790 to 5029 cm01 . Different species have been identified in this ‘‘hot medium’’ such as H2O, CO2 , CO, OH, and CH. For CO2 , we have observed rovibrational transitions with very high J values [generally J É 120 but up to 146 for the transitions 00 01 r 00 00 and 01 11 r 01 10 (ee and f f )] in the spectral range 4–5 mm (Figs. 1 and 2). Among the D£3 Å 1 rovibrational transitions, we have also assigned those with (2£1 / £2 ) Å 5 which have not been observed earlier and which occur between highly excited levels (Fig. 3). In order to confirm the identification of the associated very-low-intensity lines, it was necessary to determine the temperature of the medium. We have used a method developed for vibrationally excited media (1) to determine the value of the temperature of the present ‘‘hot medium’’ (where local thermodynamic equilibrium prevails) with a precision better than 1%. EXPERIMENTAL SETUP

The flame spectra used in the present study have been obtained with the experimental setup described below. A flat homogeneous burner (full diameter 70 mm with an inner core of 40 mm and an outer ring for optional buffer gas) produces a stable methane / oxygen flame at reduced pressure ( É20 hPa) in a combustion chamber with appropriate optical ports. The pure (U grade) CH4 and O2 gases contained in standard high-pressure vessels (at 200 bar from Air Liquide) after proper adjustment of each output pressure with a regulator/manometer are fed into stainless-steel han10 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.

AID

JMS 7205

/

6t16$$$201

01-30-97 00:03:31

mspa

11

CO2 AND CO FLAME EMISSION SPECTRA

FIG. 1.

R-branch bandhead of the 00 01 r 00 00 transition at a temperature of É1850 K.

normal scanning speed (0.5 cm/sec) of the moving mirror was used, producing one scan at 0.02 cm01 apodized resolution every 50 sec (the fly-back time is not included). The scans (forward only) were coadded during a period ranging from 15 to 30 min. The interferograms were transformed (with no apodization) and the spectra displayed and plotted with the BOMEM software. The measured width of the CO line is about 0.020 cm01 (FWHM) in the unapodized spectra with a slight asymmetry of the instrumental lineshape increasing with the wavenumber (but negligible for the present analysis). Using the peakfinding routine provided with the BOMEM software, the wavenumber calibration has been performed using (2, 3) as standards. The intensities discussed below have been obtained, for selected transitions, by integration over the line with upper and lower wavenumber limits defined in an interactive manner using the instrument software. METHODOLOGY

The intensity Lsi of a rovibrational line si produced by a vibrationally excited molecular medium is theoretically, for

an optically thin medium, proportional to the product of the upper level population of the given transition £s Js r £i Ji by the corresponding effective transition dipole moment matrix element,

Lsi } É R£sr £i É2s 4i Li F(m)N£s Js ,

where É R£sr £i É2 is the pure vibrational transition moment, Li is the Ho¨nl–London factor theoretically expressed, for the vibrational transitions Dl Å 0, as Li Å

JMS 7205

/

6t16$$$202

01-30-97 00:03:31

m2 0 l 2 ÉmÉ

[2]

with m Å 0Ji for P lines and m Å Ji / 1 for R lines. F(m) is the Herman–Wallis factor, F(m) Å [1 / APRm] 2 for P (m Å 0Ji ) and R (m Å Ji / 1) branches

Copyright q 1997 by Academic Press

AID

[1]

mspa

12

BAILLY, CAMY-PEYRET, AND LANQUETIN

FIG. 2.

R-branch bandhead of the 01 11 r 01 10 ee and f f transitions at a temperature of É1850 K. Copyright q 1997 by Academic Press

AID

JMS 7205

/

6t16$$7205

01-30-97 00:03:31

mspa

13

CO2 AND CO FLAME EMISSION SPECTRA

FIG. 3. Lines observed in the spectral range 2244.5–2244.6 cm01 . All the lines are identified only by the upper vibrational level noted ( £1£ l2 £3 )n in which ( £ ) indicates a vibrational quantum number, ( l) the vibrational angular momentum quantum number, and ( n) the sequence number of a Fermi resonance group. The lines with underlined assignments belong to newly observed transitions.

F(m) Å [1 / AQm(m / 1)] 2 for Q (m Å Ji ) branches,

[3]

and N£sJs is the population of the upper rovibrational level £s Js . To express the number of molecules per unit volume in the £s Js upper state, the populations of the rotational levels are assumed to be in a Boltzmann equilibrium characterized by a rotational temperature TR and under this assumption

N£s Js g£s Js

F G

EJs 1 N£s Å exp 0 QR g£s kTR

where EJs É hcB£s m(m / 1) is the rotational energy of the level, N£s the population, and B£s the rotational constant of the vibrational level £s , respectively. TR is the rotational temperature and QR , the rotational partition function,

Js

QR É ,

JMS 7205

/

6t16$$$202

EJs

kTR

can be expressed for CO2 to a good approximation by

[4]

kTR , 2hcB£s

where h, c, and k have their usual meanings. Copyright q 1997 by Academic Press

AID

S D

QR Å ∑ (2Js / 1)exp 0

01-30-97 00:03:31

mspa

[5]

14

BAILLY, CAMY-PEYRET, AND LANQUETIN

If the vibrational transition moments as well as the quantities which depend on the line for all the transitions considered are known, the measurement of the intensities of the observed lines allows one not only to reach the populations of all the vibrational levels involved in the emission, but also to analyze the thermodynamic state of the emitting hot gas, i.e., to determine the value of TR . The intensity can be evaluated experimentally, for each well-isolated line, from the area of this line. This area, called Imes , is proportional to both the total absolute intensity coming from the source and the relative responsivity of the spectrometer in this range. If the medium can be considered as a thin medium for a given vibrational transition, and if I* mes is the intensity of a rovibrational line divided by all the known quantities (transmission, si , Li , F(m), B£s ), the expression

ln(I* mes ) Å ln(N£s ) 0

hc B£ m(m / 1) / constant, [6] kTR s

deduced from Eqs. [1] – [5], defines a straight line as a function of B£s m(m / 1) for all the transitions belonging 5 5 FIG. 5. ln(I* mes ) plotted versus B£s m(m / 1) for the 05 1 r 05 0 and 1 1 the (21 0)1 r (21 0)1 transitions.

to the same vibrational band. The slope of this line gives the corresponding value of TR . For CO2 , previous work in our group, for vibrationally excited media (1) (mixtures of CO2 / N2 / He excited by dc discharge), has shown that: (a) the vibrational transition moment for all the observed transitions ( D£3 Å 1) is given (with an error smaller than 2%) by the harmonic approximation l

l

É R£1£ 2£3r£1£ 2( £301 ) É2 Å £3É R00 01r00 00 É2 ,

where É R00 01r00 00 É2 is known with very good precision thanks to recent results of Johns (4), É R00 01r00 00 É2 Å 0.1032 { 0.0001 (D 2 )

for 12C 16O2

É R00 01r00 00 É2 Å 0.1008 { 0.0002 (D 2 )

for 13C 16O2 ;

(b) the value for the Herman–Wallis factor given by Johns (4) for the fundamental band can be used for all the transitions observed (this coefficient can be taken equal to 1 for J õ 40 with a precision better than 1%), namely, FIG. 4. ln(I* mes ) plotted versus B£s m(m / 1) for several transitions of C 16O, 12C 16O2 , and 13C 16O2 . The slope of the lines gives the corresponding value of TR . 12

F(m) Å (1 0 0.000143 m) 2

for 12C 16O2

F(m) Å (1 0 0.000135 m) 2

for 13C 16O2 .

Copyright q 1997 by Academic Press

AID

JMS 7205

/

6t16$$$202

01-30-97 00:03:31

mspa

15

CO2 AND CO FLAME EMISSION SPECTRA

For CO, having observed only the transitions occurring between the lowest levels, we have also used the harmonic approximation for the vibrational transition moment and adopted for É R1r0É2 the value given by Chackerian and Tipping (5): É R1r0É2 Å 0.0108 (D 2 ).

In our calculation, the value for the Herman–Wallis factor is the theoretical value given by Bouanich (6), a value which has been confirmed experimentally by Bailly et al. (7). RESULTS

(1) Temperature of the Medium For each molecular species, 12C 16O, 12C 16O2 , and 13C 16O2 , we have analyzed all the vibrational transitions for which self-absorption is negligible. From the intensities of all the measured lines belonging to a given band, we have performed, using Eq. [6], a least-squares fit from which we have deduced the rotational temperature TR . For CO, we have used only three transitions: 2 r 1, 3 r 2, and 4 r 3; the values of TR obtained for each transition are respectively 1849 (12), 1862 (21), and 2007 (97) K. The standard deviation for this last transition is higher because the lines are very weak (the precision is still better than 5%). The three rotational temperatures being the same within two times the standard deviation, we have performed

a least-squares fit including the three transitions and assuming for each one the same temperature; the result is TR Å 1866 (17) K. For CO2 , only seven transitions are usable because they are not self-absorbed: 00 02 r 00 01, 01 12 r 01 11, 02 21 r 02 20, 03 31 r 03 30, 04 41 r 04 40, and (11 11)I,II r (11 10)I,II . The global fit including all the CO2 transitions gives for TR the value TR Å 1835 (26) K. For all the transitions belonging to the three molecular species, the temperature being the same within one standard deviation, we have performed a weighted least-squares fit of all the data in order to determine a unique TR that we can consider to be the real rotational temperature of the medium. This temperature is obtained with a precision of the order of 1%: 1854 (8) K (Fig. 4). (2) Newly Observed Transitions Knowing the rotational temperature of 12C 16O2 and using the method described above, it has been possible to confirm the identification of the very-low-intensity lines belonging to the D£3 Å 1 rovibrational transitions with (2£1 / £2 ) Å 5 which have not been observed earlier (Fig. 5). The following rovibrational transitions have been observed: 05 51 r 05 50 (13 31)1,2 r (13 30)1,2 (21 11)1,2,3 r (21 10)1,2,3 .

TABLE 1 Spectroscopic Constants and RMS (cm01 )

Note. The uncertainties given in units of the last digit correspond to one standard deviation. The spectroscopic constants are given with the appropriate number of decimals to generate the calculated values given in Table 2.

Copyright q 1997 by Academic Press

AID

JMS 7205

/

6t16$$$202

01-30-97 00:03:31

mspa

16

BAILLY, CAMY-PEYRET, AND LANQUETIN

Spectroscopic constants. Our purpose was to calculate, for the relevant vibrational levels £, the effective constants B£ , D£ , and H£ and the band centers s0 for each vibrational transition. The wavenumber of a particular rovibrational line belonging to the vibrational transition £*1 £*2 l = £*3 r £1£ l2 £3 can be expressed by

TABLE 2 Experimental and Calculated Wavenumbers (cm01 ) for the 05 51 r 05 50 Transition

s£ =J =r£J Å s0 / [B£ =m(m / 1) 0 D£ =m2 (m / 1) 2 / H£ =m3 (m / 1) 3 ] 0 [B£ m(m 0 1) 0 D£ m2 (m 0 1) 2 / H£ m3 (m 0 1) 3 ]

with m Å 0J for the P branch and m Å J / 1 for the R branch. However, for all the transitions observed, it was not necessary to introduce the H constant to reproduce adequately the experimental wavenumbers within the experimental accuracy. The H value, being not significant, 1 has been constrained to zero. For transitions involving 05 5£3 and (13 3£3 )1,2 sublevels of type ef, the degeneracy is not removed for the sublevels e and f. For transitions involving (21 1£3 )1,2,3 sublevels of type ef, we have assumed the same band center for ee and f f transitions (B e x B f and D e x D f ) Table 1 gives the values obtained for all the spectroscopic constants of all the vibrational levels involved and the RMS obtained for each transition. We give in Table 2 the experimental and the calculated wavenumbers corresponding to the 05 51 r 05 50 transition as an example. All the experimental wavenumbers are available on request.2 Comparison with other studies. We can compare our results to two previous studies by Arcas et al. (9) and Esplin and Hoke (10). The first one reports transitions in the 2mm region and the second one in the spectral range 580 to 940 cm01 . Arcas et al. provide spectroscopic constants for the (21 11)1,2,3-type ef sublevels from (21 11)1,2,3 r 01 10 transitions; our new constants are in good agreement, within the standard deviation, but have a lower precision. For the transition (21 11)3 e r (21 10)3 e, the Coriolis perturbation, first discussed in (9) for (21 11)3 e sublevels and involving mainly low J values, does not affect our effective constants because only J § 17 lines have been identified and used in the fit. 1 In this work, unless stated otherwise, a parameter will be considered significant if: (i) its introduction reduces the residuals without increasing the uncertainty on the other coefficients; and (ii) the value of this parameter is greater than three times the standard deviation (i.e., the 99.7% confidence interval) (8). 2 A copy of the different tables is on deposit in the Editorial Office of this journal.

In Ref. (10) the spectroscopic constants of the states 05 50, (13 30)1,2 , and (21 10)1,2,3 were not determined from a global analysis of all the bands involved. We thus decided to com-

Copyright q 1997 by Academic Press

AID

JMS 7205

/

6t16$$$203

01-30-97 00:03:31

mspa

17

CO2 AND CO FLAME EMISSION SPECTRA

pare our values with the averages of the different determinations (B, D, and H of Table 1 of (10)). The agreement between our values (reported in Table 1 of the present work) and the values of Esplin et al. is generally within the uncertainties of each determination.

ACKNOWLEDGMENTS We are very grateful to A. Coppalle for his help with the low-pressure combustion chamber and to I. Pe´pin for her participation in the processing of the intensity data.

CONCLUSION

REFERENCES

For three molecular species, 12C 16O, 12C 16O2 , and 13C 16O2 , and from the intensities of all the measured lines belonging to each observed band, we have performed a weighted leastsquares fit of all the data in order to determine a unique TR that we can consider to be the real rotational temperature of the medium. This temperature is obtained with a precision of the order of 1%. This temperature being known precisely, it has been possible to confirm the identification of the very-low-intensity lines belonging to the D£3 Å 1 rovibrational transitions with (2£1 / £2 ) Å 5 which have not been observed earlier. The band centers of six new transitions and the corresponding effective spectroscopic constants have been determined. These constants are in good agreement with recent studies performed in other spectral regions.

1. D. Bailly, C. Rossetti, and G. Guelachvili, Chem. Phys. 100, 101–118 (1985). 2. A. G. Maki, J. S. Wells, and D. A. Jennings, J. Mol. Spectrosc. 144, 224–229 (1990). 3. D. Bailly, J. Mol. Spectrosc. 166, 383–394 (1994). 4. J. W. C. Johns, J. Mol. Spectrosc. 134, 433–439 (1989). 5. C. Chackerian, Jr., and R. H. Tipping, J. Mol. Spectrosc. 99, 431–449 (1983). 6. J. P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 37, 17–46 (1987). 7. D. Bailly, C. Rossetti, F. Thibault, and R. Le Doucen, J. Mol. Spectrosc. 148, 329–337 (1991). 8. A. H. Bowker and G. J. Lieberman, ‘‘Me´thodes statistiques de l’inge´nieur,’’ p. 499, Dunod, Paris, 1965. 9. Ph. Arcas, E. Arie´, M. Cuisinier, and J. P. Maillard, Canad. J. Phys. 61(6) (1983). 10. M. P. Esplin and M. L. Hoke, J. Quant. Spectrosc. Radiat. Transfer 48(5/6), 573–580 ( 1992).

Copyright q 1997 by Academic Press

AID

JMS 7205

/

6t16$$$203

01-30-97 00:03:31

mspa