[American Institute of Aeronautics and Astronautics 37th AIAA Plasmadynamics and Lasers Conference -...

American Institute of Aeronautics and Astronautics

1

Spectral Optical Properties of Highly Ionized Plasma For Radiation Gas Dynamics

Sergey T. Surzhikov∗ Institute for Problems in Mechanics Russian Academy of Science, Moscow, Russia

Description of computing code ASTEROID_HT, which is intended for numerical prediction of spectral optical properties at simulation of radiation gas dynamic (RadGD) and plasmadynamic problems is submitted. The computing code is created for solving of the following problems that are linked with radiation heat transfer in heated gases and high-temperature plasmas at T = 300 ÷ 120 000 K: 1) Numerical simulation of elementary radiation process cross-sections; 2) Creation of spectral, multi-group, total and combined models of absorption and emission coefficients; 3) Creation of optimum radiative models for high-temperature plasmas of complex chemical composition; 4) Creation of electronic databases containing information about plasmas optical properties and intended for solving radiation gas dynamics problems. Examples of spectral optical properties of complex plasma compositions are presented.

Introduction Radiative gas and plasma dynamics is one of the most actively developing scientific directions of modern

physical gas- and plasma dynamics. Models of radiation gas dynamics (RadGD) are needed for solving numerous applied problems, such as: astrophysics, physics of stars and Sun, research of a structure of substance (atomic and molecular spectroscopy), interaction of laser radiation and high-energy beams with materials, generators of plasma used for scientific and technological applications, rocket engines (of chemical- plasma-, or laser types), spacecraft's thermal protection, heat exchange in steam boiler, in aircraft and rocket engines, in working volumes of various, power installations (including nuclear). Any model of RadGD includes at least the following two parts: the first one is the spectral model of absorption and emission (so-called the optical model), and the second one is the model of radiation transfer. For creation any RadGD model there is a necessity to determine (or to postulate) thermodynamic conditions in absorbing and emitting gas.

A spectral model of gas and plasma absorption coefficients compose a basis of any optical model. It is well known that the use of the “gray gas”-approximation results in large errors (in this case optical properties do not depend on radiation wavenumber). Researches of the last decades have shown, that even in elementary case, when to describe the process of radiation transfer the model of local thermodynamic equilibrium is applied, the adequate numerical solution of a problem is possible to obtain only at co-ordination of used models of optical properties and models of radiation transfer. If nonequilibrum physical-chemical processes are studied, the models of optical properties and of selective radiation transfer are necessary coordinate not only with thermodynamic models, but also with gas dynamical models of the phenomenon. In all these cases, the creation of absorption (or emission) spectral models adequate to the investigated phenomenon is the general problem.

The huge volumes of diverse information, which are necessary be kept and processed, make the problem of creation of such spectral models rather difficult even for modern computers. It is clear, that solution of self-consisting problems mentioned above is even more laborious. Therefore, at the solution of radiation gas dynamical problems, simplified radiative models are frequently used. So, the problem can be formulated as follows: there is a need to create simplified spectral optical model, which demonstrates extremely high processing speed for numerical simulation, and at the same time this model has to be adequate to studied physical phenomena of radiation transfer.

This work presents computing code ASTEROID_HT, which is intended for creation spectral optical models of gases and plasmas for temperatures T at the range 300...120 000 K, for pressures p up to 100 atm and for wave numbers at the range 1000 ÷ 500000 cm−1. At the present time the computing code has initial information and numerical simulation models for the following chemical elements: H, He, C, N, O, Ar, Fe, Ti, Al.

∗ Deputy Director, Professor. Associate Fellow AIAA.

37th AIAA Plasmadynamics and Lasers Conference5 - 8 June 2006, San Francisco, California

AIAA 2006-3767

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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Spectral optical properties of gases and plasmas of complex chemical composition can be created for the following three thermodynamic models: the first one is the model of Local Thermodynamic Equilibrium (LTE), the second one is the model of chemically non-equilibrium gases and plasmas, but equilibrium Boltzmann’s energy distributions for each particle, and the third one is the fully physically and chemically non-equilibrium gases and plasma. The paper presents the first kind of models.

I. Equilibrium composition of multi-species gases and plasmas An equilibrium chemical composition is calculated in the following two temperature regions:

1300 20000T≤ ≤ K and 220000 100000T≤ ≤ K. Molecules, molecular ions, atoms and atomic ions are taken into account in the first temperature region. Atoms and multi-charged ions (up to 5th degree) are taken into account in the second region.

I.1. Equilibrium chemical composition in the first temperature region Using a symbolic formulation of the nth chemical reaction

, ,1 1

, 1,2, ,s sN N

j n j j n j rj j

a X b X n N= =

⎡ ⎤ ⎡ ⎤= =⎣ ⎦ ⎣ ⎦∑ ∑ … , (1)

the mole rate of formation of species j can be written for n-th chemical reaction as follows:

( ) ( ) ( ) ( ), ,, , , , , , , , , , , ,

1 1

dd

c ci n i n

N Na bj

f n j n j n j r n j n j n i j n j n f j j n j n r ji in

Xk b a X k a b X b a S a b S

t = =

⎛ ⎞= − − − = − − −⎜ ⎟

⎝ ⎠∏ ∏ , (2)

where , ,j n jna b are the stochiometric coefficients of the n-th reaction; [ ]jX is the chemical symbol of reagents and

products of reactions; rN is the number of chemical reactions; ,f nk , ,r nk are the rate constants of the forward and

reverse reactions; ,f jS , ,r jS are the rates of the forward and reverse reactions. Then the formation rate for the

species j is written in the following form: , ,j f j r jW S S= − .

The formation rate jW has dimension mol/(cm3⋅s), therefore the mass formation rate of species j, is determined

by the following formula: j j jM Wϖ = . To calculate mass rate of formation of species j there is a necessity to calculate the forward and reverse reactions

constants:

( ), ( ),( ), ( ), expf r nn f r n

f r n f r nE

k A TkT

⎛ ⎞= −⎜ ⎟

⎝ ⎠, ,

,

f nn

r n

kK

k= (3)

where ( ), ( ), ( ),, ,f r n f r n f r nA n E are the approximation coefficients for the forward (f) and reverse (r) reaction rates.

The equilibrium constants nK and thermodynamic properties of individual chemical species (at assumption of the Boltzmann distributions) are calculated by the following formulas:

2 1 2 31, 2, 3, 4, 5, 6, 7,ln ,n n n n n n n nG x x x x x x− −= ϕ + ϕ +ϕ + ϕ + ϕ +ϕ + ϕ 3

8,0

ln 10n n npK TGp

⎛ ⎞ = − + ϕ ×⎜ ⎟⎝ ⎠

, (4)

1 3 2 22, 3, 4, 5, 6, 7,

d 2 2 3 ,d n n n n n n

n

G x x x x xx

− − −⎛ ⎞ = ϕ − ϕ −ϕ + ϕ +ϕ + ϕ⎜ ⎟⎝ ⎠

38,

d 10dn n

n

Gh xTx

⎛ ⎞= + ϕ ×⎜ ⎟⎝ ⎠

, J/mol, (5)

22 4 3

2, 3, 4, 6, 7,2d 6 2 2 6 ,d n n n n n

n

G x x x xx

− − −⎛ ⎞= −ϕ + ϕ + ϕ + ϕ + ϕ⎜ ⎟

⎝ ⎠

22

, 2d d2d dp n

n n

G Gc x xx x

⎛ ⎞⎛ ⎞= + ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

, J/mol⋅K, (6)

where 0 101325p = Pa. Approximation constants for temperature region 298-20000 K are presented in Ref.1.

I.2. Equilibrium chemical composition in the second temperature region The Saha equation is used for prediction equilibrium chemical composition in the second temperature region:

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( )

( )

( )

( )

( )1 1 13 2 exp

m m mi e i i

m mi i

n n Q IA T

kTn Q

+ + +⎛ ⎞= −⎜ ⎟⎜ ⎟

⎝ ⎠, 1, 2, , pi N= … , (7)

where ( ) 115 3 3 24.85 10 , cm KA−

= × ; ( )min is the concentration of ions of m-th degree of ionization of i-th particle

(m=1 correspond to neutral atom), 1/cm3; en is the electron concentration, 1/cm3; ( )miQ is the internal partition

function; pN is the number of kinds of particles taken into account; T is the temperature, K; ( )1miI + is the

ionization potential of i-th particle with m-th degree of ionization, erg. Note that equation (7) must be satisfied for any species in gas and plasma mixture. Internal partition function can

be calculated as following:

( ) ( )( ),

,0

expm

i jm mi i j

j

EQ g

kT

∞

=

⎛ ⎞⎜ ⎟= −⎜ ⎟⎝ ⎠

∑ , (8)

where ( ),m

i jg , ( ),m

i jE are the statistical weight and energy of j-th energy level for i-th particle with mth degree of ionization. It is well known that at high temperatures the sum is divergent series. This problem is solved by limitation of j (see, for example, Ref.2). Data base [3] was used for calculation of the partition functions.

Let us consider system of equations of ionizing equilibrium of multi-species composition. Thermal ionization of any species can be presented in the following form:

( ) ( )1m mi iA M A e M++ + + , (9)

where the equilibrium constant of the reaction is determined by Eq.(7). For convenience of numerical solution of the system of equations, let us rewrite Eq.(7) relative to partial pressure

( ) ( )m mi ip n kT= , (10)

Then, instead of Eq.(7) one can receive

( )

( )

( )

( )

( )1 1 15 2 exp

m m mi e i i

m mi i

p p Q IAk T

kTp Q

+ + +⎛ ⎞⎜ ⎟= −⎜ ⎟⎝ ⎠

. (11)

The equilibrium constant of reaction (9) looks now as follows:

( )( )

( )

( )

( )

( )1 1 1

0exp

m m mm i e i i

i m mi i

p p Q IAkKp kTp Q

+ + +⎛ ⎞⎜ ⎟= = −⎜ ⎟⎝ ⎠

, (12)

where 0p is the pressure of normalization. For example,

60 3

erg1.013 10 ,cm

p = × . (13)

Sometime it is convenient to rewrite Eq.(13) in the following form:

( )( )

( )

( )

( )

( )( )

1 1 10

,0 1 15 2

2exp

mm i i

i m m jm mmi e i i

j

p Q pK

p p Q IBTkT

−

− −

=

= =⎛ ⎞⎜ ⎟−⎜ ⎟⎝ ⎠

∏, (14)

2,3, ; 1, 2, , pm i N= =… … ,

where 3 5 2erg0.669,

cm KB kA= = .

So, equilibrium composition of any high temperature mixture in the LTE approximation can be predicted by the following equations:

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( ) ( ) ( )1

,0

, 1, 2, , ; II, III, IV, V,VImm ii e pm

i

pp p i N m

K− = = =… , (15)

( )5

1 2

pNm

i ei m

p p p= =

= +∑∑ , (16)

where p is the total normalized pressure of the mixture. Note, that relation (16) is the Dalton low for the mixture. Also one has to take into account conditions of nuclear

balance in the mixture, and condition of quasineutrality: ( ) ( ), , 0 0, , const, 1, 2, ,el i el i elx T p x T p i N= = = … , (17)

,1

0spN

j e jj

Q x=

=∑ , (18)

where ,i jQ is the stochiometric coefficient; ,el ix is the relative molar concentration of elements at the initial

condition 0 0,T p (in the given case, by definition, an element designates an atom); elN is the number of elements;

spN is the number of species (here, by definition, species designates any individual chemical substance (atom, ion, electron), including elements.

II. Spectral absorption coefficient The spectral absorption (emission) coefficient is comprised of two factors. There are: the population of the

absorbing species and the cross-section per particle (the absorption coefficient per one particle). The first of these factors is obtainable from the statistical physics, and in the given case is assumed as the Boltzmann. The second of these factors requires a quantum mechanical description of atomic structure to determine radiative transition probabilities. But for some plasma conditions which are of practical interest for aerospace applications the radiative transition probabilities can be predicted by a quasiclassical theory. This theory is based on the Kramers4 and Unsold5 quasiclassical approaches. Developed theory is used here for prediction spectral optical properties in wide region of temperatures of heavy particles and electrons.

The initial data for the quasiclassical theory are the volumetric concentration of particles of species, and temperature of heavy particles T and electrons eT (in LTE conditions T = eT ).

The following types of elementary radiating processes are taken into account: the brake radiation of electrons in the ion fields, the “brake” absorption process (continuous absorption at free-free quantum transitions) and free electrons capture by ion with an emissivity of light quantum and photo-ionization processes, bound-bound quantum transitions.

Total coefficient of the bound-free absorption of hydrogen-like particle together with the free-free transitions in the fields of residual ions can be written in the form6:

( )2

e

1 22 2 6i e

i e e e3 3 2 3 2 3e ee e

1 4 2 ,3 3

I n kT

n n

N Nm I m ea e g N Tm kTT n hcm∗

∞Σ ∗ν

=

⎛ ⎞πκ = ⋅ ⋅ + ⎜ ⎟

ν ν ⎝ ⎠∑ N N

or, taking into account the numerical meanings of the coefficients, one can write

( )2

e2 2

25 8i e i ee e3 3 2 3 3 1 2

e e

10.535 10 3.69 10 ,I n kT

n n

N Nm I me g N TT n T∗

∞Σν

=

κ = × + ×ν ν

∑ N N, 1/cm (19)

If instead of spectral dependence from frequency to use wave number cω = ν , where c is the speed of light, than we shall receive the final required formula

( )2

e2 2

6 22i e i e e e3 3 2 3 3 1 2

e e

10.197 10 0.137 10 ,I n kT

n n

m I mN N e N N g N TT n T∗

∞Σ − −ν

=

κ = × + ×ω ω

∑ , 1/cm, (20)

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where iN , eN are the ions and electrons concentration in 1cm3; n is the principal quantum number; ( )e e,g N T is

the Gaunt factor. Fig. 1 illustrates correlation between kinetic energy of electron (2

2e em v

), energy levels of atomic

particle and potential of ionization (I).

Fig.1 Schematic of energy levels

The following formula was suggested in Ref.[7] for prediction of continuous spectra of absorption of atomic particles:

2 1 113

d475.9 1.44 exp 1.44 exp 1.44d

Mbf ff ll m M

mm m

p z C TmT T T

∗∗

∗

−′+

ω=

⎡ ⎤ω −ω⎛ ⎞ω −ωω ⎛ ⎞⎢ ⎥κ = × − + −⎜ ⎟⎜ ⎟ ⎜ ⎟ω ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦∑ , cm−1 (21)

4 410 , 10 , ,m mT T I E= ω = ω ω = −

where T is the temperature in K; ω is the wavenumber in cm−1; I, mE are the potential of ionization and energy of

the m-th level, cm−1; llmC ′ is the angular coefficient, the value of which is determined by a configuration of the m-th

power level. The formula (21) is based on the Unsold − Kramers theory. Photoionization absorption from discrete levels of

energy , 1,m m m∗ ∗= + 1M ∗ − (first summand in the right part of (21)). Photoionization absorption from levels of energy, located above the level M ∗ and brake processes of electrons in fields of ions are taken into account in the second summand of the right part of (21).

The level m∗ , from which the summation begins, corresponds to the first excited level. And the level M ∗ , which finish summation, gets out rather close to ionization limit.

Derivative d dmω presented in (21), occurs as the consequence of the assumption about continuous dependence of value ω from number of energy level. The closer is the level to the ionization limit, the greater validity for using such model. For lowest levels this model has not any physical substantiation. However surprising is the fact, that formal its use for lowest levels, including for levels of the basic state (ground levels), allows to receive quite acceptable results, which are not concede in accuracy to results obtained with use of other approached models.

In the given work derivative d dmω calculated with use of the following approximation:

( )

( ) ( ) ( )* * **

d 2 1 ,d

m

m

In m n m n mm n m

ωω ⎡ ⎤≈ + − =⎣ ⎦ ω, (22)

where I is the ionization potential corresponding to the given energy level m, and the values of energy of separate levels are taken from experimental data [3].

The submitted methods of calculations of probabilities of free-free and bound-free quantum transitions are the half-empirical approximating methods. The advantage of such methods consists in their high profitability and just such methods expediently to apply in computational codes, directly used at the solution of problems of radiative gas dynamics. A lack of these methods is the fact, that they have not a generality and universality.

At simultaneous Doppler and Stark broadening the structure of a line is described by the Voigt function:

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( )( )

( )( )

2

1 2 22

expd

ln 2D

yx y

x y

∞

−∞

−ακ = π

γ π α + −∫ , (23)

( ) ( )( )1 220 ln 2ln 2

,L

D Dx

ω−ωγα = =

γ γ,

where 0ω is the wavenumber of center of the line. Instead of integral (21) it appears convenient to use rather simple approximation of the Voigt function. If to enter designations ( )0 ,v L vη = ω−ω γ ξ = γ γ ( vγ is the half-width of a line with the Voigt contour), then [8]:

( )( ) ( ) ( ) ( )

( )1 2 2 2

1,

ln 2 1 exp ln 2 1v vz

αξ − ξα αξκ η ξ = + −

⎡ ⎤γ π − ξ −η πγ + η⎣ ⎦

, (24)

( )1 22 24

2D L D

v

γ + γ + γγ = , ( )( ) ( ) ( ) 12 2 41.5 ln 2 1 0.66exp 0.4 40 5.5vz

−⎡ ⎤= πγ + + ξ − η − − η +η⎢ ⎥⎣ ⎦.

The use of Eqs.(22) allows to calculate the profile of the Voigt line with accuracy 3%, that quite enough for practical purposes.

The total absorption coefficient in a spectral range ∆ω with atomic lines is determined by the formula:

( ),N

ci

iω ∆ωκ = κ + κ ω ω∑ , (25)

where c∆ωκ is the background absorption coefficient in a quasicontinuous spectrum; ( )0 ,i iκ ω ω is the spectral

absorption coefficient, caused by the i-th line located at 0iω ; N is the number of lines, getting in ∆ω .

III. Numerical simulation results Figures 2−17 illustrate typical numerical simulation results obtained by code ASTEROID-HT. Figures 2, 3 show

equilibrium chemical composition of mixture C(34%) + N(33%) + O(33%) at pressure 1p = and 100 atm, and figs. 4, 5 show equilibrium composition of mixture N(78.68%) + O(21.09%) + Ar(0.23%) at 1p = atm and 100p = atm.

Spectral optical properties were calculated with using these chemical compositions. Figures 6 and 7 show spectral optical model of mixture N(78.68%) + O(21.09%) + Ar(0.23%) at pressure 1p = atm. Spectral calculations were performed here and further in 300 000 points (number of spectral groups equal to 31, and spectral points inside each spectral group equal to 10000).

Figures 8−11 present spectral optical model of mixture C(34%) + N(33%) + O(33%) at pressure 1p = atm, and figs. 12−15 – at pressure 100p = atm.

Last two figures show comparison of spectral (line-by-line) and group optical models of mixture C(34%) + N(33%) + O(33%) at pressure 100p = atm. It is obviously from this comparison that the group optical model is sufficiently rough then corresponding spectral model. But, at the same time, calculations of radiation heat transfer in different radiation gas dynamics applications show that such group models allow predict energy transfer with good enough accuracy.

Acknowlegments This work has been supported by ISTC (contract #3358p) and Russian Foundation of Basic Research (project

No. 04-01-00237). The author thanks Dr. I. Wysong and Dr. J.-L. Cambier for many useful discussions.

References 1Gurvich, L., Veyts, I., and Alcock, C., eds., Thermodynamic Properties of Individual Substances, 4th Edition, Hemisphere

Publishing Corporation, New York, 1991. 2Capitelli, M., Colonna, G., Giordano, D., et al. , “Tables of Internal Partition Functions and Thermodynamic Properties of

High-Temperature Mars-Atmosphere Species from 50 K to 50000 K,” EAS STR-246, October 2005, 267 P.

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3http://physics.nist.gov/PhysRefData. 4Kramers, H.A., Quantum Mechanics, North-Holland Publishing Co., Amsterdam. Translated by D. ter Haar, 1958. 5Unsold, A., Ann. Phys., 1938, Vol.33, P. 607. 6Surzhikov, S.T., Capitelli, M., Colonna, G. “Spectral optical properties of nonequilibrium hydrogen plasma for radiation

heat transfer,” AIAA02-3222, 2002, 11 P. 7Surzhikov, S.T., ”Computing System for Mathematical Simulation of Selective Radiation Transfer,” AIAA 2000-2369, 34th

Thermophysics Conference, June 19-22, 2000, Denver, CO. 8Matveev, V.S., Approximation Formulas for Profiles of Absorption Coefficients and Equivalent Widths of Voigt’s Lines,

Journal of Applied Spectroscopy, 1972, Vol.16, No.2, P.228 (in Russian).

Temperature, K

N,1

/cm

**3

20000 40000 60000 80000 100000105

107

109

1011

1013

1015

1017

1019

1021

CNOE-C+C++C+++C++++C+++++N+N++N+++N++++N+++++O+O++O+++O++++O+++++

Fig. 2. Equilibrium composition of mixture C (34%) + N(33%) + O(33%), p = 1 atm

Temperature, K

N,1

/cm

**3

20000 40000 60000 80000 100000105

107

109

1011

1013

1015

1017

1019

1021

CNOE-C+C++C+++C++++C+++++N+N++N+++N++++N+++++O+O++O+++O++++O+++++

Fig. 3. Equilibrium composition of mixture C(34%) + N(33%) + O(33%), p = 100 atm

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Temperature, K

N,1

/cm

**3

20000 40000 60000 80000 100000105

107

109

1011

1013

1015

1017

1019

1021

NOArE-N+1N+2N+3N+4N+5O+1O+2O+3O+4O+5Ar+1Ar+2Ar+3Ar+4Ar+5

Fig. 4. Equilibrium composition of mixture N(78.68%) + O(21.09%) + Ar(0.23%), p = 1 atm

Temperature, K

N,1

/cm

**3

20000 40000 60000 80000 100000105

107

109

1011

1013

1015

1017

1019

1021

NOArE-N+1N+2N+3N+4N+5O+1O+2O+3O+4O+5Ar+1Ar+2Ar+3Ar+4Ar+5

Fig. 5. Equilibrium composition of mixture N(78.68%) + O(21.09%) + Ar(0.23%), p = 100 atm

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Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 500000

10-3

10-2

10-1

100

101

102

103

T=20 000 K

Fig. 6. Spectral absorption coefficient of mixture N(78.68%) + O(21.09%) + Ar(0.23%), p = 1 atm

Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 500000

10-3

10-2

10-1

100

101

102

103

T=36 000 K

Fig. 7. Spectral absorption coefficient of mixture N(78.68%) + O(21.09%) + Ar(0.23%), p = 1 atm

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Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 50000010-3

10-2

10-1

100

101

102

103

T=20 000 K

Fig. 8. Spectral absorption coefficient of mixture C(34%) + N(33%) + O(33%), p = 1 atm

Wavenumber, 1/cm

Spec

trala

bsor

ptio

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ient

,1/c

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100000 200000 300000 400000 500000

10-3

10-2

10-1

100

101

102

103

T=36 000 K


Dow

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Lib

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11

Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 500000

10-4

10-3

10-2

10-1

100

101

102 T=52 000 K


Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 500000

10-4

10-3

10-2

10-1

100

101

102T=68 000 K


Dow

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rary

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26, 2

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.200

6-37

67


12

Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 500000

101

102

103

104

T=20 000 K


Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 500000100

101

102

103

104

T=36 000 K


Dow

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ded

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Lib

rary

at I

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Sep

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26, 2

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6-37

67


13

Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 500000

100

101

102

103

104T=52 000 K


Wavenumber, 1/cm

Spec

trala

bsor

ptio

nco

effic

ient

,1/c

m

100000 200000 300000 400000 500000

100

101

102

103

104 T=68 000 K


Dow

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ded

by U

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rsity

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rary

at I

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14

Wavenumber, 1/cm

Spec

trala

bsoe

rptio

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effic

ient

,1/c

m

100000 200000 300000 400000 500000

101

102

103

104

T=20 000 KT=20 000 K

Fig. 16. Spectral and group absorption coefficient of mixture C(34%) + N(33%) + O(33%), p = 100 atm

Wavenumber, 1/cm

Spec

trala

bsor

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effic

ient

,1/c

m

100000 200000 300000 400000 500000

100

101

102

103

104 T=68 000 KT=68 000 K

Fig. 17. Spectral and group absorption coefficient of mixture C(34%) + N(33%) + O(33%), p = 100 atm

Dow

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6-37

67

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