Absorption of radiation by gases from low to high pressures. II. Measurements and calculations of CO infrared spectra

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Absorption of radiation by gases from low to high pressures. II. Measurements and calculations of CO

infrared spectra

C. Brodbeck, J. Bouanich, Nguyen-Van-Thanh, J. Hartmann, B. Khalil, R. Le Doucen

To cite this version:

C. Brodbeck, J. Bouanich, Nguyen-Van-Thanh, J. Hartmann, B. Khalil, et al.. Absorption of radiation

by gases from low to high pressures. II. Measurements and calculations of CO infrared spectra. Journal

de Physique II, EDP Sciences, 1994, 4 (12), pp.2101-2118. �10.1051/jp2:1994249�. �jpa-00248112�

Classification Physic-s Abstiacts

44.40 33.20E 33.70W

Absorption of radiation by _gases from low to high _pressures.

II. Measurements and calculations of CO infrared spectra

C. Brodbeck ('), J. P. Bouanich ('), Nguyen-Van-Thanh ('), J. M. Hartmann(', 2),

B. Khalil (3) and R. Le Doucen (3)

(') Laboratoire de Physique Moldculaire

et

Applications (*), Universitd de Paris Sud, Campus d'orsay, Bit. 350, 91405 Orsay Cedex, France

(2) Laboratoire d'Energdtique Moldculaire

et

Macroscopique-Combustion (**), Ecole Centrale Paris, 92295 Chatenay-Malabry Cedex, France

(~l D6partement de Physique Atomique

_et

Mo16culaire (***), Universitd de Rennes I, Campus de Beaulieu. 35042 Rennes Cedex. France

(Ret cried

?

./unt> /994, jet.eii,ed

iii

Iwo' li)1tli 25 Auqu.it /994, a<.<.opted 3/ Au,qu.it /994)

Rksumd. Cet article pr6sente de~ applications de~ moddles ddvelopp6s dans

_une

prem16re publication [J. Phys. II France 1(1991) 739]

_au

calcul de spectres infrarouge de CO. Des

_mesures

nouvelles h tempdrature

et

pression dlevdes

sont

aussi prdsentdes. Les rdsultats expdrimentaux

et

thdoriques confirment l'imprdcision de l'approche Lorentz ainsi que des mod61es statistiques basse densitd lorsque les effets d'interfdrence

entre

raies

_et

(es ailes lointaines contribuent notablement h

l'absorption. En revanche, [es moddles empiriques corrigds proposds dans l'article I donnent des rd~ultats satisfaisants. Des tables de parambtres adaptds pour le modble de bande g6ndralisd, qui

sont

donnde~ dans le prdsent travail, permettent, pour des applications pratiques,

_un

calcul facile

_et

rapide.

Abstract. This paper presents

tests

of the models developed in

_a

first paper [J. Phys. II Franc-e

1

(1991) 739] when applied

to

CO infrared spectra. ^New

measurements at

high ^{densities and} temperatures

are

presented. Comparisons between experimental and calculated results confirm the

inaccuracy of the Lorentz and low density statistical approaches when line-mixing and far line-

wings make significant contributions

to

absorption. On the other hand, the empirical models proposed in paper I lead

to a

satisfactory agreement ^{with the values measured.} Tabulations of data

suitable for the Generalized Narrow Band Statistical Model

_are

given, which enable easy and quick computations for practical applications.

^'

1. Introduction.

Many applications involve the need for

_accurate

computations of infrared absorptionlemission

of radiation by _gas mixtures. Since, in

most

practical _cases,

a

very large number of spectra

(*) CNRS (UPR 136).

(*±) CNRS (UPR 288).

(***) CNRS (URA 1203).

@Les Editions de Physique 1994

must

be computed, low computer

cost

models

_are

required and

_use

of line-by-line _type approaches is intractable. For this _reason, much theoretical attention has been given

to

approximate and efficient models which predict spectrally-averaged absorption properties of gases

^at

densities

_near

the ambient (reviews

_are

given in Refs. [1, 2]). Among these, the

_most

widely used

_are

the

_«

Narrow Band Statistical Models

_»

which have been proposed ^{for various}

molecules and the Voigt line-shape (including the Doppler and Lorentz limits). These

approaches

_are

limited

_to

moderate densities, when line-mixing and far wing contributions

remain negligible. In reference [3] (referred

to

hereafter

_as

I),

_we

have proposed

a

generalization of the statistical approach first suggested by Goody [4]

to

the

_case

of high

densities.

The present paper is

_a

test of the models presented in when applied

to

the computation of

CO infrared absorption. New

measurements at

high temperatures

are

also presented. The

theoretical approaches and data used

_are

described in section 2. The experimental

set

up and data used

_are

described in section 3. Measured and calculated spectra

_are

compared and

discussed in section 4.

2. Models and data used.

2, MODELS. The models used in the present ^{work have been} presented ^{in detail} in paper1

[3] and only ^the final equations

are

thus recalled here. In the following,

_we

consider the

_case

of

a

uniform and isothermal mixture of _g

=

1, ii~ ^{gases with mole fractions} f~ ^{under total} density

D and temperature ^T (modifications, when nonuniform paths

_are

considered,

_are

described in

Appendix D of I). We

_assume

that species _g

=

is the only absorbing _gas

_at

the considered

wave

number

_«

(Appendix C of I explains how mixtures of absorbing species

are to

be

treated).

2.1,I The line-by-line lorentz (LBLL) approach. Within this well-known approach, the

absorption coefficient

_cv at _wave

number

_«

in the infrared (') is then given by (Eq. (3) ^{of I,} where line-shifts, which

_are

of negligible influence

on

medium resolution spectra, ^{have been} neglected)

_:

a~~~~(a, _{f,, f2,}

,

f,,, D, T)

=

jj ^~~ ~~'~~~ ~'~~" ~~' '~""' ^{~' ~~}

(l)

~

Jiil<nc,> lT

[(W _{W, )~}

+

y, ~fj, f2, f,,, D, T)~]

°' gJ'# ' '

where S, (T) and «,

^are

the integrated intensity and position ^of line

_r

of the absorbing species.

y, Vi, f~, f,,~, ^{D, T) is the} pressure-broadened half-width (HWHM) of line

_r

under the considered thermodynamical conditions.

2.1.2 The line-by-line cfiiiected (LBLC) apprr)ach. This approach

was

introduced in I in order

_{to correct}

for the failure of the Loreqtz model in the line-wings and

_near

band-centers

at

high density. The absorption coefficient

_cv

in the infrared I') is then given by (Eq. (6) ^of I)

:

a

~~~~(a, _{fi, f2,}

f,,~, ^{D, T)}

=

jj ^{~~ ~'~~j~ ~'~" ~~' '~"#' ~' ~~}

~

~

h~.~ yin<nc,>

^«

I(« _a, )

₊

_Y, lfi, f2, f,,,,, ^{D, T)-j}

~ ~~

~ ~~

~~' ~~

~

~~~~ ~~ ~ ~~ _{~'~ ~~~ ~~~}

~~~~ ~~ ~~ ~~~

(') For small

_wave

numbers (millimeter and microwave regions)

_a

term, similar

to

the following but

where

_«

«, is replaced by

_" +

ir, should be added

_{to a.}

The empirical line-shape correction factor _X (a _«~, f,, f~, _f,,~, ^{T) has been} introduced

in order

_to

correct for the failure of the Lorentzian shape in the line-wings.

( (« _«,, fj, f~, f,,~, ^{D, T) is}

^a

^near-wing, high-density normalization correction function whose expression is [3]

_:

~ ~

(« _{«, )2} ~~~

~ ~" ~~' '~""'

'

(« _{«, )~}

+

Y~~lfi, f2, f,i~, ^D, T)~

^~

where y~~ is

_an

average,

over

all lines, of the collisional half-width. The unknown parameter A is calculated by using equations (2), (3) and the identity

I+

m cv

(«,

j, ,, , ,,,

D, T) da

=

DS, (T). (4)

f f- f

;

~ f

~ Jii i<nc, al gJ,g

Let

_us

recall that the parameters

_y

^and x in

a

mixture of _g

=

I,

...,

ii~ gases

can

be computed

from those associated with the elementary _g collisions by using equations (C.2), (C.3) of

Appendix ^C of I. Note that correction of the Lorentzian profile through the introduction of the x and ( ^{functions is} strictly empirical and only roughly models the physical mechanisms.

2.1.3 The low density

fiario~,

band statistic-al model (LDNBSM). This approach [3, 4]

enables computation of the transmissivity averaged

over

the [« ha,

_« +

Am spectral

interval. This quantity, denoted by T~", is then given by (Eq. (18) of Ii

T~"~~~~~~

₌

_eXp K~"(T) Lfj/

₊

~~~~~ ~~~~~~ ~~~

l, ⁽⁵⁾

~ ~,, ~fj, f2'

'

f,,' l~, l~)

where L is the gas column length and the parameters

K,

r and

_are

given by

Kj"(T)

=

£ ~, (~)j ^/~~

,r e (<r 3rr + 3,r

~3,,~ _{f f} f J~j

<r 1, 2,

«~'

"

i _~< (T)

_Y<

Vi, f~,

,

f,,,, ^D, T)j /jD _Am Kj<~(T)j

,

(6)

,, ~ i,, >,, + >,,

&j"(T)

=

[D Am

²

K)"(T) r)"~fj, _f~,

,

f~, )]I(

£ US, (T) y,~fj, f~,

...,

f~, D, )j ^,

g g

«, ~ (« ~«. « + a«,

in which the summations

_{are over}

all lines

_r

centred within the [« ha,

_a +

ha interval. In

the

_case

of nonuniform _gas columns, the parameters D, &,

_K

and r should be replaced by

optical path averaged values

_as

explained in Appendix Dl of1.

2.1.4 The ~qeneialized

iiarro~>

band statistic-al model (GNBSM ). This approach, which

_was

developed in I, is valid from low

_to

high densities and extends the previous

_one.

The averaged transmissivity is given by (Eq. (29) of I)

Tj"~~~~~

=

xp1- (

"

~'~~ ^{~"~~ ~~ ~'~~}

~

~, ~

la

+

p Am ) smh («

+

p ha ) hc/2 bT]

~

~ i _P A«, f,,

,

/,,, ~,

/, DL«11,,

~,,

~T~

~,

~

«xi<~,,~~, ^{S<,< ~p) ~~>}

with

S("(p>

=

1 -~~~~ _(arctg

[6(- _p +1/2)> _arctg [6(- _p -1/2)>)

₊

2

A(D) 6(- _p -1/2) 6(- _p +1/2)

~

2 1+ 6(-p-1/2)~

₊

_{6(- p}

₊

1/2>~

^'

~~~ If> ^«l'l

p A,,

(T) &?'I,,A<,(T) ^L

" ~" ~" ~

4 rl'l,,

i,,

Vi,

,

f,,~, ^T)

and

6 p

+

1/2

=

~

~~ (

^~

^{~~' ~"}

DX,,~

,, &,,

f,,~~

,, ~,,

~/

l, ,

/,,

,

T

g

and the band model parameters

«,

r and

_are

given by equation (6). Note that equation (7>

reduces

_to

equation (5)

at

low densities (2).

2.2 DATA USEDT- The absorption line parameters _«,, S, and y,

are

involved in the line-by-

line approach (Eqs. (1), (2))

_as

well

_as

the definition of the band model parameters (Eq. (6)>. In order

to

model CO absorption _up

to

high temperatures,

we

have retained the following

:

the

energies of the rovibrational levels and line positions _«, have been computed by using

reference [5> whereas the line intensities S, have been deduced from the data of reference [6>.

This procedure is preferable

to a

direct

_use

of international databases of spectroscopic

Table I. Correction functions

_X

lo>- CO line-w>ings.

ha

ha

_<

is

_cm- I

1.70 0.0353 hoi

<Aa<10cm-1 _1. 1.

10

_cm- I_<

ha

_<

20 cm-1 3.39

20 cm-I

_<

ha 0.57 0.0331

(2) Indeed,

_X

(0, f,, f,, T) and A (D

-

0 and

9

(± ^1/2

_- ± oJ, so

that St'~>

- ar

8~_

_~,

when D

-

0.

^~

1

cm-I Am-I

o-1

0.01 P branch

~

R branch 0.001

0.0001

2000 2070 2140 2210

_a<cm-')

2280

Fig. I. Binary absorption coefficients (cm~

^'

Am~ ~) in the wings of the 1-0 CO band for pure CO.

(.) experimental results from reference [I I]

_;

) calculated from equation (2) and the data of table1.

parameters [7, _8> since the latter

_are

insufficient for high temperatures. ^References [9, 10]

provide half-widths and their temperature dependences ^for CO lines. No line-wing correction factor _X has,

to our

knowledge, been published in the

case

of CO. We have thus adjusted them

on

the experimental data of reference [I ii by using equation (2). The results

_are

given in table I. Comparisons between experimental and computed values

_are

plotted (3) in figure in the

_case

of pure CO (the _agreement is similar in the

_case

of CO-N~). Note that the values in table I

_are

for 292 K

_;

nevertheless,

_as

is shown in section 4, neglecting the temperature dependence of _X leads

_to

results

_accurate

enough ^for

most

practical applications.

The band model parameters

«,

and r have been computed by using equation ^{(6) and} the

above mentioned data. In the following comparisons with measurement, ^ha

=

5 cm~'

was

retained. For tabulations, ha

=

25 cm~' (which is

_a

widely used value, sufficient (or heat transfer applications)

_was

retained and the 150-3 000 K temperature range

was

considered. In

doing this, only ^the broadening of CO lines by _N~

_was

considered, leading

_to

the values of table IIa-IIC. The Appendix

at

the end of this paper gives practical information

_on

how

to use

the band model data.

3. Experimental.

Relatively few

_recent

experimental studies deal with medium resolution

measurements

of CO infrared absorption

at

high densities [1?-20]. The

most

extensive

_ones

have been carried

out

by

Bouanich

_et

al. [17-19] but,

to our

knowledge,

no measurements

have yet ^{been made}

at

high temperatures.

Some spectra

were

recorded in Orsay with the help of

_a

Bruker IFS 66V FT spectrometer with

_a

re~olution of 0.5

_cm~ ^'

full width

_at

half ma~imum (FWHM). We u;ed

_an

optical filter

_to

work in the frequency _range from 2 000

_to

6 000 cm~' _The spectrometer

wa~

accurately

(~) The quantity plotted

_is

the absorption coefficient divided by the square of the total density. Note

that since the absorption in the far wings is jroportional

_to

_{the square of the total} density (eas>ly ~hown

from

E~. j~l

when _{~ (,} »

y,), this normalized quantity

is

density independent.

Table IIa. Band model parameter

«

(cm~

^'

Am~')

i>s.

tempeiatu>.e.

O

lla(Tl (cm~l Am~ll

cm~l

lS0 K 150 K 200 K 300 K K K K

I-O Band

1600 0.831D-77 0.247D-57 0.717D-38 0.705D-25 o.766D-17 0,171D-10 0,141D-06 0.383D-04

1625 0.682D-71 0,671D-53 0.643D-35 0.644D-23 0.170D-15 0.126D-09 0.533D-06 0.975D-04

1650 0.343D-65 0.126D-48 0.452D-32 0.500D-21 0.336D-14 0.835D-09 0,181D-05 0.219D-03

1675 0,105D-59 0,164D-44 0.248D-29 0.330D-19 0.596D-13 0.517D-08 0.580D-05 0.462D-03

1700 0.983D-56 0,156D-41 0.244D-27 0.733D-18 0.531D-12 0.221D-07 o.154D-04 0.900D-03

1725 0.215D-49 0.881D-37 o.351D-24 0.886D-16 0,137D-10 0,169D-06 0.560D-04 0.205D-02

1750 o.142D-44 0.362D-33 0.906D-22 o.368D-14 0.187D-09 0.957D-06 0.181D-03 0.459D-02

1775 0.553D-40 o.looD-29 0.177D-19 o,121D-12 o.203D-08 0.420D-05 0.448D-03 o.789D-02 0.362D-01

1800 0.126D-35 0,185D-26 0.265D-17 0.337D-11 0,197D-07 0.178D-04 0.l14D-02 0.146D-01 0.556D-01

1825 o.168D-31 0.229D-23 o.308D-15

0.823D-lo'o.188D-06

0.807D-04 0.322D-02 0.298D-ol 0.933D-ol

1850 o.l12D-26 o.944D-20 o.780D-13 o.318D-08 o.222D-05 o.370D-03 o.815D-02 o.519D-ol

1875 0.434D-23 0.462D-17 0.481D-11 0.488D-07 0.145D-04 0.122D-02 0,175D-01 0.842D-01

1900 0.606D-19 o.592D-14 o.567D-09 o.l16D-05 o.1250-03 o.467D-02 o.404D-01 0.142D+00

1925 o.666D-16 o,l12D-11 o.184D-07 o.l14D-04 o.588D-03 0.124D-ol o.760D-ol o.213D+oo

1950 o,190D-12 0.438D-09 o.988D-06 0,164D-03 0.375D-02 o.405D-01 0,160D+00 0.331D+oo

0.221D-09 0.868D-07 0.332D-04 o,167D-02 o,180D-01o,lo6D+oo o.289D+oo 0.473D+00

0.lo4D-06 o.874D-05 o.709D-03 0,125D-01 0.705D-01o.249D+00 0.480D+00 o.616D+oo

0.507D-04 0.905D-03 0.156D-01 0.980D-01 0.285D+00 0.578D+00 0.770D+00 0.777D+00

o.318D-02 o,196D-01 0,l14D+00 o.336D+00 0.605D+00 o.838D+00 0.885D+oo 0.766D+00

0,137D+00 0.326D+00 0.726D+00 0,l12D+01 0.134D+01 0,130D+01 0,107D+01 0.773D+00

0.145D+01 o,180D+ol o.202D+01 0,195D+01 o,171D+010.127D+ol o.871D+00 0.585D+00

0.306D+ol o.263D+ol 0.202D~ol o,148D+ol o,lloD+01o.731D+oo o.508D+oo o.425D+oo

o.272D+01o.214D+ol o,149D+ol 0,lo3D+ol o.761D+00 o.580D+00 o.535D+00 o.552D+oo

o.339D+01 o.345D+01 0.318D+ol o.267D+ol 0.217D+01 o.161D+01 0,125D+01 0,103D+ol

o.408D+oo 0.768D+00 o,136D+ol o,180D+ol o.195D+01 o.176D+01 o.148D+ol o.124D+01

o.756D-02 0.401D-ol o.209D+00 0.598D+00 0.107D+01 0.143D+01 0.146D+01 0.131D+01

o.315D-05 o.l180-03 o.438D-02 0.480D-01 0.202D+00 o.540D+00 o.833D+oo o.943D+oo

o,174D-lo 0.136D-07 o.lo5D-04 0.879D-03 o.132D-ol o.984D-01 o.286D+00 o.473D+00

o.455D-18 o.283D-13 o.174D-08 o.268D-05 o.245D-03 o.784D-02 0.577D-ol 0.169D+oo

o.215D-32 o.522D-24 o.124D-15 o.468D-lo o,126D-06 o.583D-04 o.229D-02 o.200D-ol

2-0 Band

o.516D-71 0.229D-53 0.lllD-35 o.783D-24 o.174D-16 o.l12D-lo 0.418D-07 o.667D-05 o

3625 o.231D-67 0.lo3D-50 o.585D-34 o,lloD-22 o.lloD-15 0.372D-10 0.940D-07 0.l18D-04 0

3650 0.296D-63 0,l13D-47 0.516D-32 o,179D-21 0.657D-15 o,106D-09 o,175D-06 o,171D-04 0

3675 0.227D-60 0.208D-45 o.211D-30 0.241D-20 o.415D-14 0.355D-09 0.394D-06 0.300D-04 o

o,152D-56 0,136D-42 o,131D-28 o.316D-19 o.217D-13 0.937D-09 o.697D-06 0.416D-04 o

3725 o.860D-53 0.829D-40 o.873D-27 0.479D-18 o.132D-12 o.282D-08 0.138D-05 o.641D-04 o

o.357D-49 0.369D-37 o.419D-25 o.571D-17 o.720D-12 o.852D-08 o.290D-05 o.107D-03 o.

3775 0.899D-47 0.252D-35 0.809D-24 0.457D-16 0.308D-11 o.207D-07 o.488D-05 o,143D-03 o

3800 o.256D-43 o.944D-33 o.392D-22 o.573D-15 o.173D-lo o.636D-07 o.lo2D-04 o.233D-03 o.

3825 0.613D-40 0.353D-30 0.223D-20 0.842D-14 o.104D-09 0.183D-06 o.188D-04 0.324D-03

3850 o.922D-37 0.806D-28 0.780D-19 0.872D-13 o.517D-09 o.513D-06 0.365D-04 0.495D-03 o

3875 o.102D-32 0.791D-25 o.634D-17 o.132D-11 0.287D-08 0.136D-05 0.638D-04 0.682D-03

3900 0.807D-30 0.120D-22 0,187D-15 0,132D-10 0,145D-07 o.386D-05 o,123D-03 0,102D-02 o.

3925 0.463D-27 0,138D-20 o.424D-14 o.986D-lo o.545D-07 0.855D-05 0.198D-03 o,135D-02 0

3950 0,197D-24 o,131D-18 0.918D-13 0.791D-09 0.227D-06 0.202D-04 0.321D-03 o.172D-02 0.

3975 o.381D-21 0.373D-16 0.365D-11 0.812D-08 0,lolD-05 0.478D-04 o.527D-03 0.227D-02 o.

4000 0.769D-19 o,198D-14 o.507D-10 o.464D-07 0.342D-05 o,lo8D-03 o.909D-03 o.319D-02

4025 0.559D-16 0.278D-12 0.137D-08 0.408D-06 0,145D-04 0.247D-03 0.140D-02 0.398D-02 0.

4050 0.229D-13 0.252D-10 0.271D-07 0.283D-05 0.518D-04 0.525D-03 0.218D-02 0.497D-02 0.

4075 0.528D-11 0.149D-08 0.406D-06 0.169D-04 0,173D-03 0,l10D-02 0.333D-02 0.639D-02

4100 0.682D-09 0.567D-07 0.449D-05 0.790D-04 0.461D-03 0.180D-02 0.398D-02 0.617D-02 0.

4125 o.492D-07 o,139D-05 o.371D-04 o.312D-03 o.l14D-02 o.30%D-02 0.549D-02 o.788D-02 o.

o.460D-05 o.421D-04 o.365D-03 o.143D-02 o.322D-02 o.567D-02 0.753D-02 o.886D-02 o.

4175 0.16%D-03 0.614D-03 0.20%D-02 o.42%D-02 0.624D-02 o.75%D-02 o.%17D-02 o.916D-02

4200 o.23%D-02 o.431D-02 o.713D-02 o.%%9D-02 o.924D-02 0.%26D-02 o.751D-02 0.%55D-02

4225 o.163D-ol 0.173D-ol 0,166D-01 o,143D-ol o,120D-010.940D-02 o.%72D-02 o.lolD-ol

0.159D-01 o,129D-01 0.935D-02 0.666D-02 0.532D-02 0.543D-02 o.719D-02 0.lo7D-ol

o.293D-ol o.241D-ol o,177D-01 o.126D-01 o.950D-02 o.%12D-02 0.960D-02 0.109D-01

o,1%2D-01 0.220D-Dl 0.250D-ol 0.245D-01o.221D-010,174D-ol o.152D-ol o.170D-ol

4325 0.417D-03 o.137D-02 o.442D-02 0.934D-02 o,140D-01o,165D-ol o.149D-ol o,lloD-ol o.764D-02

o.660D-02

Table IIb. Band model parameter (cm~')

i>s.

temperature.

ba(Tl (Cm~~l

K 3000 K

~~O

_{~~~ ~ 300 K 450 65° K ~~~~}

l-o Band

0.170D+02 o,129D+02 o.754D+ol 0.399D+01 o.230D+010,138D+ol o.lo2D+ol o.%92D+oo 0

1625 o.167D+02 o,129D+02 0.767D+01 o.405D+01 o.228D+ol o.130D+ol o.893D+oo o.729D+oo o

1650 o,165D+02 o.128D+02 o.784D+01 o.428D+ol o.2430+ol o,136D+ol o.899D+oo o.702D+oo o

1675 0.161D+02 0,126D+02 0.795D+01 o.450D+01 0.262D+01o,147D+ol 0.959D+00 0.730D~00 o

1700 o.154D+02 0.l17D+02 0.720D+ol o.419D+01 o.255D+ol 0.149D+ol 0.978D+oo o.743D+00

1725 o,153D+02 o.l19D+02 0.763D+01 0.445D+01 o.266D+ol o,152D+ol 0.978D+00 o.732D+00

1750 o.146D+02 o,lllD+02 o.695D+ol 0.406D+01 o.248D~ol o,146D+01 o.958D+oo 0.714D+00

1775 o,142D+02 o.lloD+02 o.713D+ol 0.441D+ol o.283D+ol o,171D+01 o.lloD+ol o.798D+oo

1800 0.138D+02 o,lo8D+02 o.718D+ol o.453D+01 o.291D+010,174D+01 o,l12D+ol 0.806D+oo

1825 0,130D+02 o.989D+ol o.633D+ol o.392D+01 o.254D+01o.157D+ol 0.lo5D+ol o.771D+oo

1850 0.125D+02 o.972D+ol o.656D+01 0.423D+ol o.280D+010,175D+ol o,l16D+ol o.833D+oo

1875 0,120D+02 0.948D+01 o.657D+01 o.434D+01 o.293D+ol 0,185D+01 o,122D+01 o.870D+oo

1900 0.lllD+02 0.880D+01 o.631D+01 o.439D+ol 0.303D+01o.190D+ol 0.124D+01 o.886D+oo

1925 o.108D+02 0.883D+01 0.659D+ol 0.460D+01 0.311D+ol 0,192D+01 0.127D+01 0.921D+00 0.

1950 0.963D~01 o.777D+ol 0.577D+01 0.415D+01 0.295D+01 0,194D+ol o.133D+ol 0.975D+00

1975 o.883D+01 o.726D+ol 0.563D+ol 0.420D+ol o.302D+ol o,196D+01 o,134D+ol 0.977D+00 o.

2000 o.803D+01 o.673D+ol o.535D+01 0.406D+ol 0.299D+ol o.205D+ol o.147D+ol o.lo8D+01o

2025 0.671D+01 o.566D+ol o.465D+ol o.379D+ol o.298D+ol o.212D+ol o.150D+ol o,lo7D+ol o

2050 o.645D+ol o.580D+ol o.511D+ol o.427D+01 o.333D+01o.235D+01 o.166D+ol 0,l13D+01D.

2075 o.511D+ol o.468D+ol o.426D+ol o.375D+ol 0.312D+01o.234D+ol o,166D+ol o,lo7D+01

2100 0.448D+01 o.432D+01 0.414D+01 0.385D+ol o.336D+01 0.255D+ol o,169D+ol 0.962D+oo

2125 o.418D+ol o.419D+ol o.416D+ol o.393D+ol o.337D+ol 0.230D+ol 0.128D+ol o.720D+oo 0

2150 o.439D+01 0.441D+01 o.434D+01 0.385D+01 0.290D+01 0,177D+ol o,109D+ol o.728D+00

2175 0.374D+ol 0.364D+ol 0.355D+ol o.331D+ol o.278D+ol o,192D+ol o.123D+01 o.812D+00

2200 o.445D+ol o.405D+ol 0.375D+01 o.347D+01 0.299D+01 o.214D+ol o.139D+01 o.895D+00

2225 o.516D+01 o.423D+ol o.345D+ol 0.301D+01 o.264D+ol 0.204D+ol 0.142D+ol o.949D+oo

2250 o.683D+01 o.535D+ol o.396D+ol o.316D+ol o.268D+ol o.210D+ol o,151D+ol o.lo4D+ol

2275 D.877D+ol o.679D+01 0.478D+01 0.354D+ol 0.285D+010.224D+01 o.165D+01 0,l15D+01

2300 0.lo8D+02 o.838D+ol 0.580D+ol o.401D+ol o.295D+ol o.217D+01 o,166D+01 0.123D+ol o.91

2325 0.134D+02 o,lo6D+02 0.736D+01 0.506D+01 0.359D+01 o.241D+01 0.167D+01 o.120D+Dl o.934D+oo

2-o Band

3600 o.671D+01 o.458D+ol o.269D+ol o.172D+ol o.129D+ol o,lo7D+ol 0.lolD+01 o.lo2D+ol

3625 o.739D+ol 0.437D+ol 0.242D+01 0,160D+ol 0.121D+01 0.992D+00 0.922D+00 0.915D+00

3650 0.947D+01 0.572D+01 o.300D+ol 0,182D+ol 0,131D+ol o.104D+ol o.955D+00 0.946D+oo

3675 o.613D+ol 0.435D+ol o.274D+ol 0,181D+ol o.130D+01o.988D+oo o.872D+oo o.843D+oo

3700 o.787D+ol o.554D+ol o.329D+ol o.203D+ol o,142D+ol o,lo7D+01 o.945D+00 o.913D+oo

3725 o.873D+01 o.607D+ol o.358D+ol 0.217D+01 o.147D+010.lo6D+01 0.905D+00 o.856D+00

3750 o,124D+02 o.793D+ol 0.392D+01 o.214D+01 o.142D+010.lo2D+ol 0.849D+00 o.790D+oo o.

3775 0.976D+01 o.631D+01 0.361D+01 0.231D+ol o.162D+ol 0.l16D+ol o.944D+00 o.859D+oo o.834D+oo

3800 0.lo3D+02 o.656D+01 o.348D+01 0.209D+01 o.146D+ol 0.lo6D+01 o.879D+00 o.797D+oo o.768D+oo

3825 o.823D+ol 0.576D+01 0.360D+01 0.232D+01 0,162D+01 0.l15D+01 0.927D+00 0.823D+00 0.782D+00

3850 o.904D+01 o.610D+ol 0.364D+ol o.231D+ol o.163D+ol o,l17D+ol o.938D+00 o.824D+oo o.775D+oo

3875 o.l19D+02 0.834D+01 0.471D+01 0.270D+01 o,177D+01 o,122D+01 0.947D+00 0.800D+00 0.727D+00

3900 o.lo9D+02 0.760D+ol 0.441D+ol 0.265D+ol o,179D+01 0.126D+ol o.959D+00 0.763D+00

3925 0.l13D+02 0.819D+ol o.488D+01 o.294D+ol o.197D+ol 0.136D+01 o.998D+oo o.703D+oo

3950 0.102D+02 0.725D+ol o.454D+ol 0.299D+ol o.212D+01 0,147D+01 0.l10D+01 0.848D+oo 0.

3975 0.lo8D+02 o.816D+ol o.525D+01 0.331D+01 0.224D+01 o,152D+01 0.109D+01 0.718D+00

4000 0,109D+02 o.837D+ol o.529D+ol 0.321D+01 o.215D+01o.150D+ol 0.l14D+ol 0.900D+00 0.74

4025 o.994D+ol o.769D+ol 0.511D+01o.332D+01 0.232D+01 o.161D+ol o,lllD+ol o.684D+oo 0.446D+00

4050 o.958D+ol o.771D+ol 0.541D+01 o.356D+ol o.243D+01 0.166D+01 o,122D+ol 0.934D+oo

4075 o.904D+ol 0.738D+01 o.526D+01 o.352D+ol o.246D+01o.169D+ol 0.l14D+ol o.692D+00

4100 o.861D+ol o.734D+ol 0.570D+ol 0.413D+ol o.301D+ol 0.211D+01 o.149D+ol o,104D+ol

4125 o.812D+ol o.708D+ol 0.563D+ol o.410D+ol o.294D+ol o.195D+ol 0.123D+ol 0.749D+00

4150 0.670D+01 o.586D+ol 0.481D+ol o.370D+ol 0.282D+01 0.199D+ol o.130D+01 o.797D+00 o.562D+00

4175 0.609D+01 0.556D+01 0.490D+01 0.404D+ol 0.312D+ol o.207D+01 0.125D+01 o.814D+00

4200 o.557D+01 o.529D+ol 0.500D+01 o.457D+ol o.383D+01 o.250D+ol 0.133D+ol o.711D+00

4225 0.433D+ol o.423D+01 0.408D+ol o.368D+01 o.296D+ol o,185D+01 0.l12D+01 0.877D+00

4250 o.513D+ol o.516D+ol 0.501D+01 0.409D+01 o.271D+01 o.162D+01 o.996D+00 0.644D+00

4275 o.367D+ol o.370D+ol 0.371D+01 o.343D+01 o.259D+ol o.161D+ol o.133D+ol o.127D+ol

4300 0.327D+ol o.3030+01 0.286D+ol o.277D+01 o.255D+ol 0.178D+01 o.974D+oo o.625D+oo

4325 o.446D+ol 0.362D+ol 0.290D+01 o.254D+01 o.238D+ol o.230D+ol 0.224D+ol 0.207D+ol 0,180D+ol

4350 0.658D+ol o.508D+01

Table IIC. Band model parameter ^r for CO-N~ (cm~ Am~ )

_vs.

temperature.

O

rn(N~,Tl (cm~l Am~ll

650 K K K

I-O Band

0.624D-02 0.794D-02 0,l12D-ol o,158D-ol 0.217D-01o.321D-01 o.468D-01 o.664D-ol 0

o.679D-02 o.861D-02 o,120D-01o,169D-ol o.232D-ol o.341D-ol o.494D-ol o.702D-ol 0

0.739D-02 o.934D-02 o.130D-ol o,181D-ol 0.247D-ol o.361D-ol 0.521D-ol 0.738D-ol o

0.805D-02 o,lolD-01O,140D-01 0,195D-ol o.264D-ol 0.381D-ol 0.546D-ol 0.770D-01o

O.858D-02 O.l08D-Ol O.149D-ol O.207D-ol o.281D-01 0.406D-ol o.579D-ol o.811D-01o

0.955D-02 O,l19D-01 O,164D-Ol O.224D-Ol O.300D-01 0.426D-Ol O.601D-01 0.836D-010

o,lo4D-ol o,130D-ol o.177D-01 o.242D-Ol O.323D-Ol o.457D-ol 0.639D-Ol o.877D-Ol

o,l14D-01 0.141D-ol o,191D-ol 0.259D-01o.344D-010.483D-ol o.670D-01 o.915D-ol

o,124D-01 o,153D-ol o.206D-ol 0.277D-01 0.365D-010.510D-ol o.702D-01 o.952D-01 o.

o,136D-ol o,167D-ol o.222D-ol o.299D-ol o.392D-ol o.543D-01 o.740D-01 o.990D-ol o.

o,152D-ol 0,185D-ol o.244D-ol 0.323D-ol o.418D-01o.571D-01 o.771D-01 o,lo2D+oo 0.

o,166D-ol o.201D-01 o.264D-ol 0.347D-ol 0.447D-ol 0.606D-01 o.809D-01o,106D+00 0

1900 o,186D-ol o.224D-ol o.290D-01 0.375D-ol o.477D-ol o.638D-ol 0.842D-ol o,lo9D+oo 0.

1925 0.204D-01o.244D-ol 0.313D-ol o.403D-ol 0,509D-01o.675D-01 o.882D-ol o,l13D+00 o.

1950 o.229D-01 o.271D-01 0.343D-ol o.436D-01 0.544D-ol o.710D-ol o.914D-ol o,l15D+oo o.

1975 O.258D-ol O.302D-01 O.377D-ol O.472D-ol 0.582D-ol 0.749D-ol 0.950D-01 0,l18D+00 o.

2000 O.290D-01 O.336D-01 0.414D-Ol O.512D-Ol O.623D-Ol 0.789D-Ol O.984D-Ol 0.120D+00 O.

2025 O.335D-Ol O.383D-Ol O.462D-Ol O.560D-Ol O.669D-Ol 0.828D-Ol 0,lOlD+OO O.122D+00 O.

2050 O.379D-Ol O.427D-Ol O.5080-ol o.607D-ol o.715D-ol o.869D-ol o,lo4D+00 o,123D~00 O.

2075 o.438D-Ol O.486D-Ol O.565D-01 O.660D-Ol O.762D-01 O.906D-ol O,l06D+00 O,123D~00 O.

2100 0.505D-Ol 0.552D-Ol o.629D-01 o.719D-01 o.813D-01o.942D-01 o,108D+oo O,123D+OO o.

2125 O.578D-Ol 0.624D-Ol 0.696D-01 O.778D-Ol O.862D-Ol O.972D-01 O.109D+oo O,122D+OO O.

2150 o.615D-01 0.660D-ol 0.729D-01 o.806D-01 O.881D-ol O.976D-ol O,108D+00 O,122D+Oo O.

2175 0.539D-ol o.584D-01 0.658D-Ol 0.744D-ol O.833D-Ol O.949D-Ol O.lo8D+00 o,122D+oo 0.

2200 0.458D-01 0.505D-01 o.583D-01 0.676D-ol 0.774D-ol o.908D-ol 0,lo5D+00 o.122D+oo

2225 0.387D-Ol O.435D-01 O.512D-Ol O.606D-Ol o.710D-ol o.856D-01O,102D+00 0,121D+OO 0.

2250 o.312D-ol 0.358D-ol o.436D-01o.530D-01 0.635D-01 0.788D-ol o.967D-ol o,l17D+00 o.

2275 O.246D-Ol O.289D-Ol O.362D-01 O.454D-01 O.557D-01 0.710D-01 0.895D-01 0,lllD+00 0.

2300 O,190D-01 O.228D-Ol O.295D-01 O.380D-01 0.477D-01 0.623D-01 0.803D-Ol 0.l02D+00 O.

2325 0,133D-01 O,163D-Ol 0.218D-01 O.290D-01 O.376D-01 O.507D-Ol 0.672D-01 O.873D-01 0.

2-0 Band

3600 0.771D-02 0.983D-02 0.141D-01 O.206D-01 O.293D-01O.445D-01 0.645D-01 0.890D-01

3625 o.753D-02 0.982D-02 O,146D-01 O.216D-010.308D-01O.463D-Ol o.666D-Ol o.914D-Ol O.

3650 O.794D-02 o.lo2D-Ol o,147D-01 o.216D-ol o.308D-ol O.468D-ol o.679D-01 O.935D-Ol O.

3675 o.873D-02 o.l13D-ol 0,161D-01 o.233D-ol 0.326D-ol o.486D-ol o.699D-ol o.958D-ol o.

3700 O.905D-02 0,l15D-01 0.163D-01 0.235D-01 0.331D-010.498D-Ol 0.716D-01 0.978D-Ol O.

3725 o.953D-02 o.121D-ol o.170D-01 o.242D-ol o.338D-ol o.505D-ol o.726D-ol O.994D-Ol

3750 0.999D-02 o.125D-01 o.176D-ol 0.253D-Ol 0.356D-Ol O.528D-01 o.751D-ol o,102D+oo

3775 0,lo5D-ol o,133D-01 o.189D-01 o.270D-ol 0.373D-ol 0.545D-01 o.770D-ol o,lo4D+oo

3800 0,l12D-ol 0.140D-ol o,196D-01 0.279D-ol 0.386D-ol 0.563D-ol o.787D-01 0,lo5D+00

3825 0,121D-01 0,152D-ol o.210D-01 0.292D-ol 0.396D-ol o.570D-01 0.795D-01 0,106D+00

3850 0,128D-ol o,160D-ol o.221D-01 o.308D-ol 0.417D-ol 0.595D-01 o.818D-ol 0,lo8D+00

3875 0,139D-01 0,170D-ol o.229D-01 o.313D-ol 0.422D-01 0.605D-ol o.834D-01 0,lloD+00 0,134D+00

3900 0,149D-01 o,182D-01 0.245D-01 o.335D-ol 0.448D-01 o.628D-01 0.852D-01 0,lllD+00 o,135D+00

3925 0,159D-01 o,194D-ol o.258D-01 o.351D-01 0.467D-01 o.653D-01 o.879D-01 o,l13D~00

3950 O,170D-01 O.207D-Ol O.276D-01 O.371D-Ol O.487D-01 O.669D-01 0.893D-01 O.l14D~OO

3975 0.186D-01 O.224D-Ol O.292D-Ol O.384D-01 O.SOOD-01O.684D-01 O.907D-01 O,l15D+00

4000 O.200D-01 O.239D-Ol 0.311D-Ol O.410D-01 O.532D-Ol O.719D-01 O.936D-01O,l17D+OO

4025 O.219D-01 0.260D-Ol 0.333D-Ol O.431D-Ol O.550D-Ol O.733D-Ol o.948D-Ol o,l18D+OO

4050 o.240D-ol 0.283D-ol 0.358D-ol o.457D-ol o.577D-ol o.760D-ol 0.971D-01 o,120D+oo

4075 o.264D-ol o.309D-ol 0.386D-ol 0.488D-ol o.608D-ol o.788D-01 0.991D-ol 0.120D+oo

4100 o.291D-ol 0.337D-ol o.416D-ol 0.517D-ol 0.635D-01 0.810D-ol 0.lolD+00 o.121D+oo

0.320D-01 o.368D-01 o.448D-ol o.550D-ol 0.668D-ol o.840D-01 o.lo3D+00 o.122D+00

4150 0.361D-ol o.409D-01 o.490D-ol o.591D-ol 0.704D-01 0.866D-ol o,lo4D+00 o.122D+00

4175 0.408D-ol 0.457D-ol o.537D-ol o.636D-01o.744D-ol 0.896D-ol o,106D+00 o,122D+00

4200 o.461D-ol o.510D-01 o.589D-01 o.683D-ol o.784D-01o.921D-01 o,lo7D+00 0.121D+00

4225 0.530D-01 0.576D-ol o.652D-01 0.739D-01 0.831D-01o.952D-01 o,lo7D+00 o,122D~00

4250 O.597D-ol O.643D-Ol O.714D-Ol O.793D-01 0.866D-01 0.956D-01 0,106D~o0 O,ll9D~oo

O.596D-Ol 0.640D-Ol 0.711D-Ol O.790D-ol O.866D-ol O.946D-Ol O,105D+00 O,122D+OO

O.512D-Ol 0.556D-Ol 0.629D-Ol O.716D-Ol O.808D-Ol O.930D-Ol O,104D+00 O,l18D+00

0.416D-01 O.463D-01 0.538D-01 0.629D-Ol 0.730D-Ol O.874D-Ol 0,104D+00 O,123D+00

0.536D-Ol 0.637D-Ol

calibrated with lines of CO in the fundamental band. Thirty-two

_{scans were}

superimposed

_to

yield each interferogram and

_we

used

_a

four-term Blackmann-Harris apodization function.

CO-N~ high-temperature spectra

were

recorded in Rennes by using

_a

Bruker IFS 120 HR FT spectrometer ^with

a

resolution of 0.2

cm~

full width

at

half maximum (FWHM). A liquid nitrogen ^cooled Insb detector

_was

used and the spectral _range

was

limited by

an

optical filter from 800

to

2 600 cm~'. Spectra

were

obtained by addition of 40 interferograms.

The pressures

were

measured with

_a

0-160 bar strain-gage _{type pressure} transducer

(accuracy ^{0. §b full} scale)

as

previously described [2 ii. For given _pressure P and temperature T the densities of CO and N~ ⁱⁿ Amagats units (4) have been computed by using the data of

references [22] and [23], respectively. In the present work, three absorption cells have been used. These

_{are a}

300.8

_cm

long, high _pressure (up

to

500 bar) room-temperature ^{cell and}

two

(7. and 19.9

_cm

long) high _pressure (up

to

100 bar) high temperature (up

to

800 K) cells.

The transmission coefficient (or transmittance) _r,,

at

wavenumber

«

is obtained from the ratio of

_two

measurements, I-e-

r~

=

I,,(D)/I~(0), (8)

where I~(0) and I~(D)

are

transmitted intensities obtained with

_an

empty ^and

a

pressurized

cell, respectively. In order

_to

eliminate data affected by any slow drift of the

source

intensity,

we

accepted only ^such measurements for which the empty-cell spectra ^{recorded before and} after the sample spectrum

were

the

_same.

Let

_us note

that when _r,, takes significant values in the spectral _range studied

(r,,

not too

small),

one

may deduce the absorption coefficient (or absorbance) _cr~ and its normalized value cr~°~~ from knowledge of the cell length L and

_:

cr~

=

In [r~]/L and

_cr

)°'~~

=

cr~/ Abs cr~ da. (9)

region

When

measurements are

made under strong absorption conditions (large Ii DL), absorption by

the very intense v~ band of CO~

traces

in the gas mixture is significant in the 2 300-2 400

_cm ^'

range. This penurbation is larger

at

high temperatures, ^{since iron} and/or nickel carbonyls, present

as

traces in the steel cylinder containing CO, _may catalyse carbon monoxide

recombination leading

to

carbon dioxide. In order

_{to correct}

for this absorption, C02

contribution

_was

computed and subtracted from measured spectra by using equations (2), (4) and the data for CO~-N~ given ^{in reference [24].}

4. Results.

The band-center and band-wing regions

_are

the

_most

interesting for the _test of high density

models. Then the central part ^{of the P and R branches show}

a

greater absorption than predicted by Lorentzian line-shapes

_on

the other hand, the latter strongly overestimate absorption in the

wings.

4,I BAND-CENTER

_REGIONS.

Room temperature results in the 2-0

overtone

band for pure

CO and CO-N~,

are

given in figures ^{2 and 3.} They show that the LBLL and LDNBSM

_are

very inaccurate in the central part ^{of the band whereas the LBLC and GNBSM} give satisfactory

results.

(4) Since the ideal gas law may

^not

be valid

_at

elevated densities the usual

atm _or

bar units

cannot

be used. The density D(P, T) in Amagat (Am) units is defined by DIP, T)

= v

(I atm, 273.15 K)/

v(P, T) where v(P, T) is the molar volume

at

P and T. For

_an

ideal gas D(P, T)

=

P(atm)

_x

[273.15/T(K)].

0.014

aNorm (cmi

0.012 it

ii

0.01

0.008

0.006

0.004

0.002

'

a<cm.ii

0

4150 4200 4250 4300 4350

Fig. 2. Normalized absorption coefficients for pure CO

_at

94.5 Am (105 bar) and 297 K. (.)

_;

experimental results from reference [17] calculated by using ^the models

_:

(... GNBSM,

LBLC, (- -) LDNBSM, (- -) LBLL.

0.012

«Norm (cmj

0.01 jl

~

j1

.

0.008

0.006

-,-j-'1"' ^"',

~

0.004

0.002 "~

i 0

4130 4190 4250 4310 a(cm.ll 4370

Fig. 3. Normalized absorption coefficients for CO-N~

_at

453 Am (970 bar) and 297 K. (.);

experimental results from reference [18] calculated by using the models

_:

(... GNBSM,

LBLC, (- -) LDNBSM, (- -) LBLL.

The inaccuracy of the Lorentzian approach results from the neglecting of line-mixing effects which redistribute the intensity within the band, moving absorption from the less absorbing

to

the

_more

absorbing regions. These effects

_are

significant under the conditions of figures 2 and 3 since the line half-widths

_are

of the order of,

_or

greater than, the separation between adjacent

lines (the values of _y

_are

about 7.5 and 36

_cm~ ^'

in Figs. 2 and 3, respectively, whereas the line

separation is 4

cni~

').

The inaccuracy of the LDNBSM results from

two

approximations [3, 4]. The first is the

_use

of the Lorentzian model and the second is that computations

_are

made in the

[« ha,

_« +

ha interval by assuming ^that lines outside this interval

_are

similar

_to

those

inside. Let

_{us note}

that the second approximation tends

_to

compensate ^the underestimation of

absorption resulting from the

_use

of the Lorentzian shape

near

the maxima of the R and P branches.

Discrepancies between predictions of the LBLC and GNBSM models and

measurements are

partly due to the neglect of pressure induced line-shifts nevertheless,

_most

of the inaccuracy

results from the very rough modelling of line-mixing effects through the introduction of the ( correction function. Note that the

_use

of energy corrected sudden scaling laws which

correctly account for these effects enables

_a

satisfactory agreement ^with experiments [25].

The influence of temperature ^is illustrated by the results in figures 4 and 5. Those

_at

low temperatures ^confirm the conclusions of figures 2, 3. Furthermore, all models lead

to

similar and satisfactory results in figure 5 since the density is quite low and line-mixing effects

_are

small.

o.ois

«Norm jcm) .

o.oi

O

0

4150

190

4,2 BAND-wiNG

REGIONS,

Pure CO transmissivitie~ in the 1-0 band

at two

temperatures

are

plotted in figures 6a and 6b. They confirm the well-known inaccuracy of the Lorentzian shape

when far line-wings

_are

considered. The LDNBSM underestimates absorption, due

_to

the fact that lines outside the considered [« ha,

_{« +}

ha interval

_are

assumed

_to

be similar

_to

those inside [3, 4] indeed when this interval contains

_no

significant lines, absorption predicted by

the LDNBSM is then

_zero

whereas wings of outside lines may be significant. The LBLC and GNBSM approaches lead

_to

practically identical results in

_a

good agreement with

_measure-

ments

; this is expected since absorption is then governed by the

_X

factor which has been fitted

to

measurements.

Note that discrepancies in the high frequency wing

_are

due

to

the uncertainty

of the correction for CO~ absorption.

Results for CO-N~ mixtures, which

_are

plotted in figures 7a and 7b, lead to similar

conclusions. The importance of CO~ absorption is illustrated in figure 7b, where uncorrected

experimental results have been plotted.

~

0.8

0.6

0.4

0.2

a<cm-11

0

1900 2000 2100 2200 2300 2400

a)

~

0.8

0.6

0.4

~~

~,,'

0.2

,~ _,~"

,,~'~

jam.ij

0

^'

1900 2000 2100 2200 2300 2400

b)

Fig. 6. Transmissivities (L 7.[

_cm

for pure CO. (...)

_;

experimental results from thi~ work

calculated by using the models GNBSM and LBLC (similar), (- -) LDNBSM,

(---) LBLL. a) 63.7 Am (70 bar) and 297 K b) 26.4 Am (70 bar) and 691 K.

1 '

/

08 '

0.6

0.4 ,,~_ _~,,"

0.2 ~',,~ ,,"~'

"~, "~

a<cm.ii

~

l 900 2000 2100 2200 2300 2400

a)

0.8

_~,

, ,

, ,'

, ,

0.6

', ,'

, ,

, ,

, ,

, j

0.4

,

, ,

0.2

~

jam.ij 0

1900 2000 2100 2200 2300 2400

b)

Fig. 7. Transmissivities for CO-N~. (...); experimental results from this work;

calculated by using the models ( )GNBSM and LBLC (similar), (-.-.-)LDNBSM,

(---) LBLL. a) 46 Am (51 bar), 1.05 % CO, 7. I

_cm

and 297 K b) 23 Am (53 bar). 8 % CO, 19.9

_cm

and 601K.

4.3 EQUIVALENT

_wiDTHs.

The equivalent width of

_a

band W(«~,~, «~~,), ^defined by

"M,,

W("M<n. "Max)

_~

II T<,> d"

,

M<,> ('0)

enables interesting

tests

of models when heat transfer applications

are

involved indeed, the intensity emitted by the gas ^column in the [«~,~, «~~~> ^{interval is} given by equation (10) in which the blackbody intensity is inserted in the integrand.

Comparisons between measured and computed equivalent widths in the 2-0 band of pure CO

at room

temperature

are

plotted in figure 8. They confirm the accuracy of the LBLC model,

whereas the GNBSM, which gives satisfactory results

at

low and high densities, understimates

absorption

at

intermediate _pressures. This discrepancy is illustrated

_on

the spectrum in figure 9

240

W<cm.'1

,,

200 ^"'

160 j

120

~

~ ^~

~

/

~

80 1'

4o

P <aim)

0

0 20 40 60 80 100 120

Fig. 8. Equivalent ^widths for pure CO

_{at room}

temperature ^{in the 2-0 band} («~,~

₌

3 500 cm~'

«Max 5 000

_cm ^~'

for

L

5.02

_cm.

Experimental values from

_:

(.) Reference [20]. (o) reference [17]

_;

calculated by using the models

_:

(... ) GNBSM, ) LBLC, (- -) LDNBSM, (- -)

LBLL.

0.8

0.6

~~

0.4 ~-"~

"

a<cm-11

0.2

4150 4200 4250 4300 ₄₃₅₀

Fig. 9. Transmissivities of pure CO

_{at room}

temperature ^{and 9.I Am} (10 bars). (.) Experimental

values from reference [20], calculated with the model ( LBLC, (... ) GNBSM. (- )

LBLL in the weak absorption regime (X

I

in Eq. (7)).

and results from the

_use

of the exponential inverse intensity distribution function [1, 3, 4] _; indeed, the latter has the

_correct

linear and square-root ^{behaviour in} the weak and strong absorption limits, but underestimates the equivalent width in the intermediate regime (see Refs. [1, 4]

_or

Fig. of Ref. [27>).

The results in figure 10 confirm those of figure 8. Note that underestimation by the LBLC model is due

_to

the CO~ contribution,

_{as can}

be

_seen

in figures 6 and 7

_near

2 300 cm~' _Note

that

_errors

in the modelling of the far wing contributions lead,

at

high densities,

to

overestimation (resp. underestimation) of equivalent widths by the Lorentzian model (resp.

low density

_narrow

band statistical model).

400

W<cm-')

,,,'

350

₁

>""

/.I _-'~

~'~

/~ ~.~

^~

300

/

I

/

~

.

~.

,>.l'

250

^,"

/

/ ^' P<&<mi

200

0 10 20 30 40 50 60 70 80

Fig. 10. Equivalent width~ for pure CO in the 1-0 band («~,~ 000

cm~ ^' «~~~

3 200

cm~ ^'

for

L

7.10

_cm.

Experimental values from thi; work for (.) T 297 K, (o) T 690 K

_;

calculated by

using the models (... ) GNBSM, ( LBLC, (- -) LDNBSM, (- -) LBLL.

5. Conclusion.

The

_tests

presented ^{in this work} confirm the interest of the corrected models proposed in

paper1 [3] when high densities

_or

thick optical paths

_are

considered. Contrary

to

previous models, they enable _easy and quick computations and satisfactory accounting for line-mixing

and far wing non-Lorentzian absorption effect~. A good _agreement with

measurements

is

obtained in the

_case

of CO infrared spectra ⁱⁿ

a

wide den;ity and temperature range. Note that the Generalized Narrow Band Statistical Model give; _very satisfactory results, although CO

at room

temperature I;

not a

good candidate for ;uch model;

_:

indeed, there

_are

few line, of

significant absorption (one _every 4cm~')

so

that the

_use

of statistical representations is

approximate. One _may predict that such

_an

approach would give better results for molecules, such

_as

CO~

_or

H,O, whose spectra ^contain many

more

significant absorption lines

at

low

temperatures.

Acknowledgements.

The authors

_are

grateful

to

Pr. C. Boulet for helpful discussions.

Appendix.

Procedure for computations with the G- and LD- NBSM.

.

The first computational _step consists in interpolations within the values of tables IIa-IIC in order

to

determine the parameters «j"(T). &j"(T) and rj"(N~, T) for each of the

Table III. Ai>era,qe iatifis [y~/y~~]~~ of hioadenin,q _parameters of CO lines by peiturber _g

w.ith >.espec.t

to

bioadenin,q b_i'N~.

iw2nN2iAv iycotm2iAv iyco2/yN21Av iyR2~vw2iAv iyo2/w2iAv iyA~r/w2iAv

1.00 1.05 1.30 1.90 0.82 0.96

wavenumbers

_«

of interest

_at

the considered temperature. ^Since rj~'corresponds

_to

CO-N~ collisions, the value in the mixture is given by the following approximate (5)

expression

r?[,,

A<,

Vi,

,

f,,~, ^T)

=

rl[,,A<,(N~, T) z fg1)((~

^~~ _,

^{(A. i)}

«

I,,g

,

where the average ratios of broadening by _gas g and by N~

are

given in table III

([... ]~~ ^denotes

an

average

over

all lines).

.

The parameter

_X

^{for the mixture is} computed in

_a

similar way, I-e-

x (« _«,, /,,

,

/,,~, ^T)

⁼

z ~lj~~j~~ ~~x

(« _«,, o.

,

/~,

,

o, T), (A.2)

g

=,.,,

^N~

where X(« _«,, 0,

,

f~,

,

0, T) corresponds

to

the correction function for CO-g colli- sions.

.

The parameter ^{A involved in the} ( correction

_can

then be calculated, for each absorption

band (1-0

or

2-0), from the following approximation of equation (3)

:

A ~fl, /2, /n~, ^{D, T)}

=

j~

^{°~ U}

^{Sinh (hCU/2 bT)}

^~~

^{Y~~~fl' In}

^,

^{D, T)}

~

°'

"~~ ~i"h(h~"~12 _bT)

^{~ ~ ~}

^~~~

^~

^{~~~~ ~~} _{(" "~~)~}

+

~~~fl,~.--,

fn~, ^D, T)~

~~

l~

^{w ~}

^{~j~~ ~~~~/~ ~~j}

^~

lY ^{~~~fl, In}

'

D' T)

x (U

_U

[ fj,

,

f~, T)

^~

~

da

~

U~~ Sinh(hCU~~ IT

~

(" "~~)~

₊

Y~~~fl'

,

fn~'D, ^T)

(A.3) where «~~ _and y~~

_are

the band-average wavenumber and half-width

~~~ '

b,~

bJnd

~~~~~~ '~~

~

~~~j ~~)(T)j

'~~~ ~'~~~~ ' ~ <Pi<on hJnd

~ ~~

Y~~~/1, /2,

,

/,>~, ~)

"

=

~ ^«j"(T) Drj"~fj, f~,

,

f,,, T)j/ ~ «j"(T)j

g

<,~^e Jh,orp><on bJnd «, ^e Jb,o,pi<an bJnd

.

The average transmissivity is then computed by using equation (7).

Computer time and programming

_can

be saved by using ^{the far} wing properties of the GNBSM. Let

_us note

Ap the integer such that 6 (Ap 1/2 )

»

1(o ^is defined in Eq. (7)) for all

wavenumbers

_«

and considered column conditions. A possible choice for Ap ^is

~~ ~ ~~~j~~~ l~

^~

^{~~~~ ~~~~~~~ ~~~~}

_'

^lA.5)

(~) ^This procedure is only approximate but is quite

accurate

since the ratio of broadening parameters

by

two

different collision partners ^{is almost} independent

on

the considered line.

where the upperscript

_max

refers

_to

the maximum value

_over

all temperatures that the

_user

may encounter. Equation (7)

_can

then be written under the simplified form

~j<,GNBSM

=

~<i<,iAp)GNBSM-L°Cd'

x

exp i- L/i D~ C«i

,

~A.6~

where r(Ap)~~~~'~~~°~"' is given by equation (7), restricting the summation

_over

p

^to

the [- Ap,

+

Ap] interval. C,, is

_a

«

continuum

_»,

which depends

_on

temperature and mole

fractions only

C~,(f,, f,,~, ^T)

=

jj fi C~(g, T), (A.7)

Y"

""t with

C«~~ T)

=

~,~

,,~ "~~»~~~~~

li>li~~°ii.1/8~

^...~

^{°~ ~~}

^x

x

~'

Sinh [«hc/2 bT]

~'~

~ ^~" ~~~'~ l(~'+ _P ha ) hc/2 bT] ^~ ~~'~"' °,

,

fg,

,

0, T)j

C~,(g, T) is

_{a «}

continuum

_»

which depends

_on

temperature and

_on

the perturbing molecule g only. It

_can

be tabulated by using the preceding equations

_once

Ap is chosen.

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