Line parameter measurements and calculations of CO broadened by nitrogen at elevated temperatures

I Quam Spectrosc Radmt TransferVol 27 No 6 pp 585-591,1982

0022.-407~1821060585..078030010

PrintedmGreatBritain

PerpmonPress Ltd

LINE PARAMETER MEASUREMENTS AND CALCULATIONS OF CO BROADENED BY NITROGEN AT ELEVATED TEMPERATURESt HEARD S LOWRY, III a n d CHARLES J FISHER Calspan Field Servtces, Inc/AEDC l~vislon, Arnold Air Force Station, TN 37389, U S A (Recewed 8 October 1981)

Abstract--Measurements of the line strengths and colhslonal broadening widths of CO in a N2 atmosphero were made from 300 to 600 K The hnes studied were the P(2), P(3), P(7), P(12), P(18), and P(22) lines of the fundamental band at 2100 cm -t The absorption spectra were parametrically fit to a Voigt lineshape model The band strength was determined to be 250_+8cm-2atm -~ The broademng results are compared to Anderson-Tsao-Curnutte calculations and to other experimental studies The possibdity of using an equation of the form y(T) = T( To)(To/T)~ to extrapolate the temperature dependence of the half-widths to flame temperatures is discussed

INTRODUCTION The determination of gaseous species concentrations and temperatures in combustion exhausts usmg non-interference techniques ts an area of current interest to the combustion technology community Infrared absorption by carbon monoxide in combustion environments is currently under development as a non-interference technique for CO concentration and temperature determinations i Accurate analysis of the absorption process through regions characterized by significant temperature gradients requires precise knowledge of the temperature dependencd~of the absorption hne strengths and shapes Th,s paper describes the determination of the temperature dependences of the line strengths and colhsional halfwldths of several CO fundamental absorption lines from 300 to 600 K m a nitrogen atmosphere using high resolution tunable diode laser spectroscopy The experimentally determined hnewidths are compared to theoretmal calculations using the Anderson-Tsao-Curnutte (ATC) formalism 2

Theoretwal development The transmission of ra&ation through a sample as a function of wavenumber (~'(v)) ts r(v) = I(v)/Io(v)

(1)

where In(v) is the radiation intensity incident on the sample, and I(v) ts the intensity transmitted by the sample The absorpaon coefficient (k(v)) is 3

k(v) = ( - 1/l) In [z(v)]

(2)

where r(v) IS the und,storted transmlsston (i e , no instrument degradation) of a homogeneous sample of thickness ! The integrated absorption coefficient or line strength, S, of an isolated absorption line is4

S = f + f k(v)dv

(3)

tThe research reported herein was performed by the Arnold Engineering Development Center (AEDC), Air Force Systems Command (Sverdrup Technology, Inc, and Calspan Field Services, Inc, operating contractors of AEDC) Further reproduction is authorized to satisfy needs of the U S Government 585

586

HEARDS LOWRY,III and CHARLESJ FISHER

The hne strength temperature dependence of a given hne is s S(T0=

S( To)exp [ - EJ k (--~t- ~o) ] Q( T°) Q( T,) × [1 - exp ( [1 - e x p ( -

hcv/kTO] hcvlkTo)]'

(4)

where S(To) Is the line strength at a reference temperature To, Q ts the internal parUtmn function, and Em IS the lower state energy level In the regime of pressures and temperatures employed m this study, the hneshape near the hne center can be described by the Vo,gt profile6 k(v)

S~/(ln 2/1r) a (+~ e x, p ( y:

J~

y")dy,,

a" + (x - v)"

(5)

where x = (2(u - vo)/yo) X/0n 2), a = ~/(ln 2) 3qJ~/o, and ~0 Is the hne center The Lorentz (colhsmnal) halfwldth and the Doppler halfwidth are, respectwely, denoted yL and' ~/~ T h Q l t r i m e n t a l l y determined hneshape ~s fit to the Volgt profile using a least-squares p r o c e d ~ by parametrically varying the hne strength and the Lorentzlan halfwldth. A theoretical halfwldth, yv,~, can be calculated by means of the theory of Anderson 7 as expanded by Tsao and Curnutte 2 This theory has prevmusly been apphed to broadening p h ~ o m e n a by Blrnbaum, 8 Benedict and Herman, 9 and Varanasl and Telwani lo In this Jexn~tieal framework, the halfwldth of a rotauonal quantum numbers v and m is

")lYre(T)= 2-C

2

~J2 b vmJ2

(6)

where n ~s the number density of the colhdmg molecules at one atmosphere and temperature T, is the mean collmonal velocity, c is the speed of hght, OJ2 is the fractional population m the rotational level ./2 of the colhdmg molecule, and bo.a2 is the partml colhsmnal dmmeter The partml collislonal dmmeter calculation takes into account the quantum mechamcal mamfestatmns of the mtermolecular potential on the hnewldth An approximate temperature dependence of yt has been determined by Btrnbaum 8 to be

yL(T) = y°(T)(To/ T)"

(7)

where n is the temperature dependence exponent and To is the reference temperature This form has been assumed by several authors for the temperature dependence of CO hne widths Io-13

Experimental detads T I ~ hlgh-resoluhon absorption spectra were recorded using a commercial lead salt tunable dlodCIaser spectrometer The instrument is capable of 10-3 to 10-4 wavenumber resolution Optics external to the spectrometer housing were added to facthtate measurements through furnace heated sample cells The sample cell consisted of calcmm fluoride windows sealed to a copper body with sdlcon rubber sealant A schematic diagram of the optical system IS shown in Fig 1 A typical diode laser can be scanned 50-150 cm -~ at a modulation rate of 10-~-600 cm-~/sec The diodes employed m this study operated at or near 2100 cm -~ Laser emission consists of several modes characterized by hnewldths on the order of 10-4cm -1 and separations of approximately one wavenumber Individual modes can be tuned over approximately one wavenumber For spectral measurements the modes are isolated from adjacent modes by use of a grating monochromator The monochromator also provides a coarse (0 5 c m - ' ) absolute wavelength calibration

Line parameter measurements and calculatmns of CO broadened by mtrogen at elevated temperatures

Tunable Colhmatmg E Diode Lens for Wave- "~ SampleCell Laser length ~l (In Furnace) Calibration) "

587

Cell

\ ModelLS-3LaserSourceSpectrometer

\ Exit Sht

Entrance Sht I

Detector

u~

Monochromator Chooper\Shutter M

Fig 1 Block diagram of the laboratory optical system

A germanium etalon and calibration gas cell were mounted on a movable shde ~T~e etalon produces frmges spaced approx 0 047 cm -I apart at 2115 cm -~ The fringe spaclngs"~'e used to define the injection current-laser wavelength relationship for the modes used and thus provided the relattve wavelength calibration of the spectrometer. Spectral purtty of the modes used was checked by observation of the smoothness of the etalon fringe pattern and comparison of the signal level of a saturated line center w~th the shuttered beam s~gnal level. During the course of the experiments, it was found that s~gnlficant adsorption of CO On t l a cell walls was occurring To avoid changes m CO concentration due to this effect, the samiMe cell was conditioned before recording a spectra by filhng wlth I atm of the gas to be stud~d, maintaming this pressure momentarily and then pumpmg the cell down to the desired pressure. It was also found that turbulent mixing of ambient temperature air with heated atr from the furnace could significantly degrade the signal/noise To minimize this effect the optical beam was enclosed by a water cooled sleeve from near the cell windows to outside the furnace Measurements were made using commercially prepared CO-N2 gas mixtures with concentrations from approx. 3000 ppm to 5% CO In general, a 100% transmission scan (sample cell evacuated) was recorded before and after every sample transmission scan Figure 2 shows an example of raw data, mcluding the 100% transmission and etalon traces. The result of the computer fitting of these traces is shown m Ftg 3 The residual CO absorption, used to check laser stability, has been removed from the 100% transmission trace This trace was also smoothed usmg a least-squares procedure. The raw data and the best fit Voigt profile are also displayed

Intensity

lO0-percentTransmitted I n

t

e

Wavenumber Fig 2 An example of the raw data

n

~

HE~,RD S LOWRY,III and CHARLE3 J FISHER

588

Smoothed 100-percent Transrn~ttocl I ntens~t~ - - ,

E

Run 57, DP 34, 15 OpsL 8OO0ppm, P(7), 0Of K

I

330

,

-0 10

-0 15

I

I

i

I

-0 05

0 Wavenumber

0 05

0 10

0 15

Fig 3 An example of the reduced data

RESULTS

Measurements were made at pressures ranging from 0 034 to 1 00 atm and temperatures ranging from 300 to 600 K for the P(2), P(3), P(7), P(12), P(18), and P(22) lines of the CO fundamental band The uncertainty of the results due to cahbraUon gas concentration uncertainties and measurement uncertamtles is estimated to be less than 10% The fundamental band strength of CI2016 was determined from the experimental line .~rengths in conjunction with calculations of the rotational quantum number dependence of the line strengths This rotational dependence was calculated using the Herman-Walhs approximation t4 as presented by Hanson i5 The average band wavenumber required for this calculation was taken to be the band center The band strength results calculated from mdwldual line strengths are shown m Fig 4 as a function of the rotational index, m The band strength, normalized to 300 K and 100% Ci20 J6, was determined to be 250 cm-2atm -), with a standard deviation of 8 cm 2 atm-) This compares with the values of Varanasl and Sarangl of 253 _+9 as determined by a curve of growth method and 257 ___6 as determined by the Wilson-WellsPenner-Weber method 16 It also compares to Varghese and Hanson's value of 256-+ 4, which we adjusted downward by approx 1 2% due to a ddference in the defimtton of the band center 17

300

! So(a~) ~ 250

2OO

E

100

I

0

J

i

i

I

2 3 4 5 6

l

I

I

7 8 9

II{i

I

..

II

I

|

i

I

I

i

|

i

i

l

i

i

I

1213 14 15 16 17 18 19 20 21 22 23 24

Fig 4 Band strength determination from Individual line strengths ( T = 298 K)

Lme parametermeasurementsand calculations of CO broadened by mtrogen at elevated temperatures

589

Table 1 Summaryof experimentalmtrogen-broadenedhalf-w~dtbs exp Vav~ x 10 3

T (K)

m

(cm-~ a r m - l )

2

3O3 399 501 601

74 61 53 49

2 2 3 5

3

300 400 500 601

69 56 48 43

6 0 7 1

7

299 360 436 525 600

60 52 46 41 37

7 3 7 0 3

12

304 401 499 600

56 46 40 35

4 2 2 2

18

302

52 5

22

301

49 8

Table 1 summarizes the experimentally determined N2 broadened CO halfwtdth results The experimental halfwidth data and some of the literature values for N2 broadenmg at 300 K are compared in Fig 5 Figure 5 also shows the comparison of the results of the theoretical model for N2 broadening to the present experimental and literature data Agreement is within 5% for the best fit to the experimental data, using as parameters a CO dipole moment (/zco) of 1 12 x 10-19esucm, a CO quadrupole moment (Qco) of 2 6 × 10 -26 esu cm 2, a N2 quadrupole moment (Q~2) of 3 3 x 10 -26 esu cm 2, and a mmtmum coihslon dmmeter (b~,.) of 4 17 × 10 -s cm The/Zco value Is that which is recommended by Stogryn and Stogryn, 24 while the quadrupole moments chosen to best fit the data are withm 10% of the values recommended by them The minimum colhslon diameter was adjusted to fit the data m the high m region at 300 K

o07

5 ~-,,, o o6

005

°

A A

~" ~ - ~ ' - A O

004--

I

I

I

I 5

I

I

I

I

I l0

I

I

i

J

lmL-

l 15

t

i

l

4-

-6

A

I .h I 20

I

J

,

,

I

25

Fig 5 A comparisonof mtrogenbroadenedexperimentaldata to hterature values and the calculated curve @, the present work, V, data from Ref 16, V, data from Ref 17, A, data from Ref 18 for the R-branch, o, data from Ref 18 for the P-branch, +, data from Ref 19, X, data from Ref 20, [~, data from Ref 21, ~, data from Ref 21 for the (3 0) band, ©, data from Ref 22, o, data from Ref 23, --, the calculated curve usmg ATC theory with/zco = 0 112 x 10-'s esu cm, Qco = 4 6 x 10-2s esu cm2, QN, = 3 3 x 10-26 esu cm:, and b,.m = 4 17 x 10-s cm

590

HEARDS LOWRY,III and CHARLESJ FISHER

Figure 6 shows the experimental temperature dependences of the halfwldths for four lines These are plotted on a log-log scale to facilitate the determination of the n exponent of Eq (7) The bars indicate one standard deviation of the data Also shown are the single exponentml approximations [Eq (7)] for the exponents of 0.75 and 0 5 corresponding to dominant quadrupole--quadrupole and hard sphere interactions, respectively In addition, the results of the calculations using the ATC theory are shown It can be seen that the experimental data fit a single exponential very well for all four lines, and that the values of the temperature dependence exponent are much closer to the dominant quadrupole-quadrupole approximation than to the hard sphere approximation It can also be seen that the temperature dependence exponent calculated from ATC theory is closer to the experimental values than either of these approximations In order to invesUgate the theoretical vahdlty of the single exponential approxLmatmnof the halfwidth temperature dependence, the ATC model was used to calculate the halfwtdth temperature dependences of four P-branch lines m the range 300-2000 K In Fig 7 the results are~own plotted on a log-log scale Plotted m this manner, straight line results correspond to agre~ent with the approximatmn As can be seen in the figure, all four lines show reasonable agreement with the approximation with the agreement improving at the higher rotational quantum numbers An interesting feature of these results IS the convergence of the halfwidths to a common value at the h i l l , temperatures, i e , typical combustion temperatures ~ e hmtted hot cell results it appears that the use of a single exponentml temperature dependence function for N2 broadened CO halfwldths from 300 to 600 K is quite justified This

E % E

ffoo4 P~3) n - 0 62~

300

I

I

~00

I

500 (00 T(K~-

~

~

\"'\-.

1 700

I 800

i

I

900 I000 3~

I

400

I

i

l

I

I

I

500 6C~ 700 8L4) 90{ ]OCJ0 [ ~K) -

006

005 E % ,'T"

7

004

P(121

003 P(71

0 02 300

"x "'.'"

06 9 ~ ~

I

I

I

400

500

600

T (K) -

I

I

I

I

700 800 900 1000 300

I

400

I

t

1

I

I

500

600 700 800 900 1000 T ~K)-

Fig 6 Temperature dependances of the experimental half-widths for the P(2), P(3), P(7), and P(12) CO hnes broadened by mtrogen --, the least-squares fit to the data, - - - - - - , a plot of the relatlonslup T(T)--I,(7"o)/(7"o/7')°75. - - - - - - , a plot of the relatmnshlp y(T)= y( To)/( To/ T) °5. - . . . . . , calculations using ATC theory

Line parameter measurements and calculations of CO broadened by nitrogen at elevated temperatures o Ol

591

p~2)

oo6 ~ J -

g o~ "7'

~

2~o~

0112

300"

I

I

400

500

I 600

I

I

i

i

i

i

i

i

i

100 800 900 lOGO 1200 1400 1600 1800 2000 T(K) -

Fig 7 Predictions using ATC theory for nitrogen broadened half widths from 300 to 2000 K

IS m agreement with the work of Sell 13 In addition, the use of this form at flame temperatures appears to be a reasonable working hypothesis consistent wRh the ATC results s h o w . F i g . ' ? To test this hypothesis a study of CO broademng in flame environments has been uaaertaken The results of this study will be presented m a subsequent paper The extension of the hot cell measurement range to 1000 K is also underway

REFERENCES 1 R K Hanson and P K Falcone, Appl Opt 17, 2477 (1978) 2 C J Tsao and B Curnutte, JQSRT 2, 41 (1962) 3 A P Thorne, Spectrophys#cs Halsted Press, New York (1974) 4 L A Young, JQSRT 8, 693 (1968) 5 H J Heaton, JQSRT 16, 801 (1976) 6 S S Penner, QuantaatweMolecularSpectroscopyand Gas Emtsstotttes Addison-Wesley,Reading,Mass (1959) 7 P W Anderson, Phys Rer 76,647 (1949) 8 G Blrnbaum,Adv Chem Phys 12, 487 (1967) 9 W S Benedict and R Herman, JQSRT 3, 265 (1963) 10 P Varanasl and G D T Tejwam, JQSRT 11,255 (1971) 11 G D T Tejwam, JQSRT 12, 123 (1972) 12 J A Sell,JQSRT 23, 595 (1980) 13 P L Vargheseand R K Hanson, JQSRT 24, 479 (1980) 14 R Herman and R F Walhs, J Chem Phys 23, 637 (1955) 15 R K Hanson, Proc 17thAerospaceSctencesMeeting,New Orleans, Lomslana, 15-17 Jan 1979 16 P Varanasl and S Sarangl, JQSRT 15,473 (1975) 17 P L Vargheseand R K Hanson, JQSRT 24, 479 (1980) 18 C Crane-Robmsonand H W Thompson, Proc R Soc (London)A272,453 (1963) 19 J Bouamchand R Farrenq, C R Acord, Scz, Pans 271,507 (1970) 20 J Bouamch and C Brodbeck, JQSRT 13, 1 (1973) 21 J Bouamch and C Haeusler, JQSRT 12, 695 (1972) 22 D A Draegert and D Wdhams,JOSA 58, 10, 1399(1968) 23 T C James and E K Plyler, JCM 40.1,221 (1964) 24 D E Stogrynand A P Stogryn, MolecularPhys 11,371 (1966)