[American Institute of Aeronautics and Astronautics 10th AIAA/ASME Joint Thermophysics and Heat...

Contribution of Vacuum-Ultraviolet (VUV) Transitions

of Molecular Nitrogen During Atmospheric Reentry.

H. Liebhart∗, G. Herdrich†, H.–P. Roser‡

Institut fur Raumfahrtsysteme (IRS), Universitat Stuttgart, Stuttgart, Baden–Wurttemberg, 70596, Germany

M. Fertig§

Deutsches Zentrum fur Luft– und Raumfahrt e.V. (DLR), Braunschweig, Niedersachsen, 38108, Germany

Within this work we investigate the radiative properties of molecular nitrogen withrespect to the highly excited electronic states giving rise to radiative transitions occuring inthe spectral range of vacuum ultraviolet (VUV) radiation. This is done in order to shed lightthe role of VUV radiation of molecular nitrogen on the radiative heat load encountered bya vessel during highspeed atmospheric reentry. The considered transitions are the Lyman-Birge-Hopfield (a1Πg − X1Σ+

g ), Birge-Hopfield I (b1Πu − X1Σ+g ), Birge-Hopfield II (b′1Σ+

u −X1Σ+

g ), Caroll-Yoshino (c′41Σ+

u − X1Σ+g ), Worley-Jenkins (c3

1Πu − X1Σ+g ), Worley (o3

1Πu −X1Σ+

g ), and e′1Σ+u − X1Σ+

g bands. The approach to retrieve the relevant parameters forthe line by line radiation simulation follows common methods of calculation, which are thereconstruction of the potential energy function via the Rydberg-Klein-Rees (RKR) methodand subsequently solving the corresponding radial Schrodinger equation. Absorption andemission spectra are calculated for a known equilibrium test condition of air plasma toillustrate the contribution of the VUV transitions to the radiatation. The influence of theVUV radiation on the heat load experienced by a reentry vehicle is illustrated with a CFDcalculation.

I. Introduction

The knowledge of the radiative properties of hot gaseous media are of great interest for the atmosphericentry of space vehicles. As many celestial bodies have significantly dense atmospheres an in-depth inves-

tigation of these atmospheres or exploration of the surface requires a superorbital entry into the atmosphere.When the vehicle enters the atmosphere it encounters high heat loads from convective as well as radiativefluxes. The knowledge of the overall thermal load is crucial for sizing and designing of the thermal protectionsystem (TPS). Due to the high kinetic energy of the vehicle during superorbital reentry flight, excitationof high energy levels, giving rise to strong radiation becomes significantly probable. In case of superorbitalearth reentry flights certain electronic states of molecular nitrogen, giving rise to transition bands in theVacuum-Ultraviolett (VUV) (i.e. λ < 200 nm), gain in relevance. The design of a TPS is nowadays commlysupported by numerical predictions by means of computational fluid dynamic (CFD) simulations. In orderto simulate atmospheric entries numerically it is crucial for the modeling to take all relevant processes intoaccount. Radiative processes result in radiation cooling of the gas in the shock layer and influence the heatload encountered by the vessel. Around europe there are several codes available for radiation modelinglike SPARTAN1 and PARADE,2 and ongoing effort is spent to build an extensive online database GPRD3

containing the neccessary information. At the Institute of Space Systems of Universitat Stuttgart a set ofconstantly improving numericals tools has been developed to serve this need and has been successfully ap-plied to numerous reentry calculations.4 This set consists of the CFD code URANUS (Upwind Relaxation

∗Research Associate, Raumtransporttechnologie, Pfaffenwaldring 31, 70569 Stuttgart, D .†Head of Raumtransporttechnologie Department, Pfaffenwaldring 31, 70569 Stuttgart, D, AIAA Member.‡Managing Director IRS, Pfaffenwaldring 31, 70569 Stuttgart, D, AIAA Member.§Scientist, German Aerospace Center, Lilienthalplatz 7, 38108 Braunschweig, D, AIAA Senior Member.

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American Institute of Aeronautics and Astronautics

10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference28 June - 1 July 2010, Chicago, Illinois

AIAA 2010-4774

Copyright © 2010 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

Algorithm for Nonequilibrium Flows of the University of Stuttgart),5 the Plasma Radiation DatabasePARADE2,6 for radiation calculation and the High Enthalpy Radiation Transport Algorithm HERTA.7,8

The objective of this work is to provide a further step to completion of the picture of radiation ofnonequilibrium flows by means of expanding the description of the radiative band system of molecularnitrogen included in PARADE towards higher energies namely into the range of VUV transition bands.

The general influence of the VUV radiation in plamsa wind tunnel experiments was shown before byRock9 for methane mixtures. The relevance of VUV radiation on the heat load of a reetry vehicle was shownin previous numerical simulation of FIRE II, carried out by Merrifield and Fertig.4 It was found that thecontribution of the VUV radiation in the wavelength intervall between 80 nm and 200 nm was up to 90% ofthe overall radiative surface heat flux.

Within the scope of the AURORA program and the Mars sample return program new high-speed Earthreturn flights are likely to be scheduled in the near-future. Experimental investigations are also likely to bescheduled in support to such missions. Relevance of this topic may also arise for the ORION crew vehicle.The structure of this article is as follows: In section II we describe the general method of line by line radiationmodeling and the methods used to retrieve the required parameters. In section III we discuss the varietyof the available datasets and introduce the chosen sources alongside with the results of our calculations interms of potential energy functions. In Section IV we display calcultated absorption and emission spectraof a known test condition in order to illustrate the influence of the investigated transitions. Finally, we givean example of their impact on the heat load of a vehicle with a flow field – radiation calculation.

II. Radiation modeling

The most fundamental information neccesary for a line by line radiation calculation is knowlegde aboutthe position and the intensity of the lines of the radiative transitions. As the behavior of quantum mechanicalsystems like atoms and molecules is described by the Schrodinger equation HΨ = EΨ, all necessary infor-mation is generally accessible via solving this equation. The solutions of this eigenvalue problem are a set ofwavefunctions Ψi with their corresponding energy eigenvalues Ei. Although the general formulation of thiseigenvalue problem with the appropriate Hamiltonian and a properly chosen set of basis functions is possiblefor a real system, the solution however, is generally a difficult mathematical task and analytically not alwayspossible. Such an ab initio approach, although the most appropriate way to deal with the complicated en-tanglements of a radiative system, is cumbersome and rather costly concerning computational efforts. Sincethe purpose of the radiation calculation in our case is not on the first hand the calculation of high precisionand high resolution spectra but rather an estimation of the overall spectral properties of hot gaseous mediain order to obtain the radiative heat load on a surface, several common approximation and simplificationsintroduced below have been made to serve our needs. The concepts of these simplifying assumptions areonly briefly explained and not described in detail. Extensive derivations can be found in virtually any decenttextbook on the topic like the ones of Demtroder10 or Bernath.11 Although the physical concepts apply tomolecules in general, the derived formulas will differ for polyatomics, so we will use the term molecule onlyin the context of diatomic molecule throughout this article. The basic principles of Radiation modeling areonly explained in due brevity below as they have been outlined in detail before e.g. by da Silva.12

II.A. Determination of the Position of Lines

The position of the line of a radiative transition is derived from the difference of the energy of the upper andlower corresponding levels by the basic relation

E′ − E′′ = ∆E = hν, (1)

where E is the energy of the states, and ′ and ′′ denotes upper and lower level respectively, h is the Planckconstant and ν is the frequency of the radiation.

Generally the term energy of a molecular state denotes the energy eigenvalue Ei of the wavefunction Ψi

of its full hamiltonian.Within the Born–Oppenheimer approximation, following the separation of the Schrodinger equation into

electronic and nuclear motion according to the adiabatic theorem, and neglecting all coupling terms, thecorresponding separation of the wavefunction into its electronic and nuclear part leads to the product functionΨ = ψel · χN , with the electronic and nuclear wavefunctions ψel and χN describing the electronic and the

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nuclear contribution independently. The energy of the molecule is then written as a sum of the electronicenergy and the kinetic energy of the nuclei

T = Te + TN , (2)

with T = Ehc in cm−1. The separation of the kinetic energy of the nuclei into its vibrational and rotational

parts is analoguous to the treatment of the hydrogen atom with respect to its rotational symmetry employingspherical harmonics and leads to

TN = G(v) + Fv(J), (3)

where G(v) and Fv(J) represent the vibrational and rotational energy contributions respectively. For anarbitrary potential energy function this energy terms are expressed in terms of power series expansions thatread

G(v) = ωe

(v + 1

2

)− ωexe

(v + 1

2

)2 + ωeye

(v + 1

2

)3 + ωeze

(v + 1

2

)4 + . . . , (4)

Fv(J) = BvJ(J + 1)−DvJ2(J + 1)2 + HvJ3(J + 1)3 + . . . , (5)

Bv = Be − αe(v + 12 ) + γe

(v + 1

2

)2 + . . . , (6)

andDv = De + βe

(v + 1

2

)+ δe

(v + 1

2

)2 + . . . . (7)

The values of G(v) and Fv(J) are commonly determined in a semi empirical way by employing fit procedureslike a “least squares fit” to experimental data according to these expansions and retrieving the values of thespectroscopic constants ωe, ωexe, Be, αe, De, βe, ....

By employing a potential energy function in the form of a power series expansion and making use of thefirst order semiclassical quantization condition Dunham13 found that the energy levels of a vibrating rotatorcan be expressed in a more compact form as

EvJ = hc∑

ik

Yik

(v + 1

2

)i [J (J + 1)]k , (8)

the so called Dunham expansion.This leads to a relationship between the spectroscopic constants from equations (4) to (7) and the so

called Dunham coefficients Yik,

Y10 ≈ ωe ; Y01 ≈ Be ; Y11 ≈ −αe

Y20 ≈ −ωexe ; Y02 ≈ De ; Y12 ≈ βe

Y30 ≈ ωeye ; Y03 ≈ He ; Y21 ≈ γe

Y40 ≈ ωeze

and

Y00 =Be − ωexe

4+

αeωe

12Be+

α2eω

2e

144B2e

. (9)

The term energies of a given molecule are then calculated, provided the knowledge of the Dunhamcoefficients Yik of a the molecule, by applying the Dunham expansion equation (8). As stated above,thismethod relies on fits to experimental data and is in priciple only valid within the range of the experimentaldata, in terms of rovibrational energy level it has been derived from. The prediction of term energiesbeyound the validity range of the spectroscopic constants becomes increasingly inaccurate due to the typicalinstability of polynomial extrapolations. Furthermore with approaching the dissociation limit the Born–Oppenheimer approximation becomes increasingly inaccurate. Therefore, the prediction of higher lyingenergy levels requires a appropriate reconstruction technique of the potential and a reasonable extrapolationto the dissociation energy.

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II.B. Reconstruction of the Potential Energy Function

The method used for the reconstruction of the potential energy function is the first order Rydberg–Klein–Rees(RKR) method, based on the works of Rydberg,14,15 Klein16 and Rees.17 This is a widely used semiclassicalinversion procedure for the reconstruction of the potential energy function of an electronic state of a di-atomic molecule in terms of classical turning points from its spectroscopic constants. Although its capabilityof yielding high precicion potential energy functions this method is still based on semi empirical derivedspectroscopic constants and meets its limitations in the validity of these constants. How this limitation istreated is explained below after describing the RKR method itself.

The RKR method starts from the first order quantization condition from WKB theory (Wentzel–Kramers–Brillouin18–20) (

v +12

)π =

(2µ

h2

) ∫ r2

r1

√E − V (r)dr, (10)

where E denotes the total energy and V (r) the effective potential energy function, µ is the reduced massand r1 and r2 are the inner and outer classical turning points of the nuclear movement respectively. Thetwo Klein integrals

r2(v)− r1(v) = 2

√h2

2µ

∫ v

vmin

dv′1√

G(v)−G(v′)= 2f, (11)

and1

r1(v)− 1

r2(v)= 2

√2µ

h2

∫ v

vmin

dv′B(v′)√

G(v)−G(v′)= 2g, (12)

are obtained for the case of the non rotating and the rotating molecule after applying the appropriatealgebraic rearrangement and are known as the “vibrational” and “rotational” RKR equations, respectively.Combining equations (11) and (12) then yields the final turning point expressions

r1(v) =

√f

g+ f2 − f (13)

and

r2(v) =

√f

g+ f2 + f, (14)

which accurately describe the dependence on vibrational quantum number v and inertial rotational constantBv and may be used to determine the potential energy function in a pointwise manner. Still it is neccesaryto extrapolate the obtained potential curve to the dissociation limit. There are several methods to do solike direct-potential-fit (DPF)21 analysis, or Near-Dissociation Expansion (NDE)22 described in literature.In this work we chose a rather straight forward approach as offered by the programm we used to solve theradial Schrodinger equation.The extrapolation of the inner potential wall of the RKR potential was doneby fitting an exponential function to the last three inner turning points. The outward extrapolation of thepotential was done by applying a fit function as a sum of inverse-power terms specified by input parametersIRL,NCN and C of the form

V (r) = VLim −IRL−1∑m=0

CNCN+m/rNCN+m, (15)

fittet to an number (IRL) of outer turning points up to the dissociation limit VLim where known. Inthe cases where the dissociation limit was not know it was estimated using the relation De = ω2

e/4ωexe.After generating the overall potential curves, the vibrational level energies are determined via solving theradial Schrodinger equation, determining the engergy eigenvalues for this potential. Besides reobtaining thesame energy levels, within numerical uncertainties, considered as input in terms of spectroscopic constants,one also obtains the energies of extrapolated higher lying levels, up to the dissociation limit. Since theseextrapolated energy values do not depend on an inherently unstable Dunham polynomial expansion theyare generally more credible than the ones determined by the extrapolation of the Dunham expansion. Thecalculations in this work were carried out using the freely available codes RKR23 and LEVEL24 of Le Royfrom the University Waterloo.

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II.C. Determination of the Intensity of Lines

The estimation of the intensity of a radiative transition, which requires knowledge of the overall potentialenergy function, is outlined below. The power of a radiative transiton follows the relation

Pul = AulhνulNu, (16)

where Aul is the Einstein A coefficient of spontaneous emission between upper and lower level, ν is thefrequency of the radiation in s−1, Nu is the population of the upper level in 1

m3 . The Einstein A coefficientfor a rovibrational transition can be derived from general quantum mechanics as stated in the textbooks11

and reads

Aul =16π3ν3

3ε0hc3

1(2J ′ + 1)

|〈ψel′v′J′ |µ(r)|ψel′′v′′J ′′〉|2 , (17)

where µ(r) is the dipole moment, ε0 is the permittivity of free space and 〈ψel′v′J′ |µ(r)|ψel′′v′′J ′′〉 is theoverall transition moment.

By assuming seperability of the wavefunctions, and the electronic transition dipole moment to be eitherindependent of the internuclear distance r or by applying a simplified description of the electronic transitionmoment within r-centroid approximation, the overall transition moment can be factorized into its electronic,vibrational and rotational parts. However the full r-dependent transition moment should be used whereavailable.

After applying these simplifications A can be written as

Aul =16π3ν3

3ε0hc3

qv′−v′′ |Re(r)|2 S∆JJ ′′

(2J ′ + 1), (18)

with the electronic transition moment function (ETMF)

Re(r) = 〈ψel′ |µ(r)|ψel′′〉 , (19)

the Franck–Condon–Factor (FCF)qv′−v′′ = |〈ψv′ |ψv′′〉|2 , (20)

and the Honl–London–Factor (HLF)S∆J

J′′ . (21)

The FCF and ETMF are then derived by solving the radial Schrodinger equation numerically

− h2

2µ

d2

dr2ψv,J (r) + VJ(r)ψv,J(r) = Ev,Jψv,J(r) (22)

for the relevant transitions with the corresponding potential energy functions of the upper and lower levelvibrational wavefunctinos and building the transition matrix elements.

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III. Transition bands

III.A. Considered data and transitions

The spectrum of molecular nitrogen is rich with various transition bands in the VUV investigated by severalgroups already, compiled as a historical overview by Lofthus.25 A detailed compilation of observed linescan be found in literature26–29 . A historical compilation of the radiative transitions occuring in the VUValongside their spectral range as listed by Lofthus25 is given below:

o13Πu −X1Σ+

g Worley λ = 88− 95 nmc′14 Σ+

u −X1Σ+g Carroll–Yoshino λ = 80, 5− 96 nm

cn − a′′ Ledbetter Rydberg series λ = 82− 86, 5 nmc13Πu −X1Σ+

g Worley–Jenkins λ = 78− 96 nmb′1Σ+

u −X1Σ+g Birge–Hopfield II λ = 82− 129 nm

b1Πu −X1Σ+g Birge–Hopfield I λ = 85− 111 nm

a′′ −X1Σ+g Dressler–Lutz λ = 101 nm

C3Πu −X1Σ+g Tanaka λ = 107− 113 nm

w1∆u −X1Σ+g Tanaka λ = 114− 140 nm

a1Πg −X1Σ+g Lyman–Birge–Hopfield λ = 110− 260 nm

a′1Σ−u −X1Σ+g Ogawa–Tanaka–Wilkinson–Mulliken λ = 108− 200 nm

B′3Σ−u −X1Σ+g Ogawa–Tanaka–Wilkinson λ = 112− 224 nm

B3Πg −X1Σ+g Wilkinson λ = 164− 168, 5 nm

A3Σ+u −X1Σ+

g Vegard–Kaplan λ = 125− 532, 5 nm

For the special scenario of highspeed reentry a number of supposedly most relevant transitions has beenidentified and investigated before by Chauveau30,31 and recommended by da Silva.32 In addition to these wechose to also include the Lyman–Birge–Hopfield band due to its wide spectral range and the transition fromthe third Rydberg state of Σ symmetry e′ 1Σ+

u . The transitions we chose to investigate within the frame ofthis work are listed below with the abbreviated notation given in parentheses, which is used from now on.

o13Πu −X1Σ+

g Worley (W) λ = 88− 95 nmc′14 Σ+

u −X1Σ+g Carroll–Yoshino (CY) λ = 80, 5− 96 nm

c13Πu −X1Σ+

g Worley–Jenkins (WJ) λ = 78− 96 nmb′1Σ+

u −X1Σ+g Birge–Hopfield II (BHII) λ = 82− 129 nm

b1Πu −X1Σ+g Birge–Hopfield I (BHI) λ = 85− 111 nm

a1Πg −X1Σ+g Lyman–Birge–Hopfield (LBH) λ = 110− 260 nm

e′ 1Σ+u −X 1Σ+

g unnamed Rydberg Transition (e’X) λ = 75− 100 nm

III.A.1. Groundstate of Molecular Nitrogen

All the considered transitions relax to the electronic groundstate of molecular Nitrogen X 1Σ+g . The dataset

of the electronic groundstate according to the findings of Edwards33 is widely used30,31 and rather solidup to vibrational levels of v = 28. A more accurate analytic potential energy function of the electronicgroundstate is available due to recent investigations of Le Roy34 whose findings have been consolidated by aRKR reconstruction from da Silva35 as well. For our investigation we chose to use the analytical potentialenergy function given by Le Roy34 spanning over 61 vibratinoal levels.

III.A.2. Lyman–Birge–Hopfield Band System

The upper electronic state of the Lyman–Birge–Hopfield (LBH) band system has also been subject to nu-merous investigations36–40 . The information on the upper electronic state of the LBH band system wasbased on the work by Laher and Gilmore36,37 . The potential energy function was constructed fully from thespectroscopic constants given in their article. The transition dipole moment was given as a constant value.

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III.A.3. Rydberg Valence transitions

The Transition investigated by Chauveau listed above ( namely W, WJ, CY, BHI, BHII) are rising fromthe valence and rydberg states of 1Πu and 1Σ+

g symmetry and have been subject to a number of investiga-tions.41–48 The information in terms of dunham coefficients, and transition dipole moments, we used for ourwork is based on the recent ab initio work of Spelsberg and Meyer.45 These states are known to experiencestrong perturbation from other states of same symmetry, and it was stated that a ab initio configuration in-teraction treatment is desireable for the calculation of these state. The various perturbative interactions andpredissociation mechanisms have been discussed by several authors49–52 but will not be taken into accountin our work.

III.B. Potential Energy Functions

The potential energy functions, obtained via the RKR method described in section II and II.B are displayedin figure 1 below.

Figure 1. Potential energy functions of the electronic states of molecular Nitrogen considered for VUV radiation.

The RKR reconstruction of the potential energy functions followed the method as outlined in section IIand II.B. The RKR method was applied up to the validity of the Dunham coefficients in terms of vibrationallevels as stated in the sources. Beyond that the potentials were extrapolated as stated in section II.B to theknown or determined dissociation energy. As the behavior of the Rydberg states close to dissociation is notcompletely clear, the potential energy function were cut off at their convergence energy, that is the groundstate X2Σ+

g and first electronically excited state A2Πu of the molecuar ion N+2 as stated in Lofthus,25 leaving

vibrational levels above that energy unconsidered. The energies of the ground state and first electronicallyexcited state of the molecular ion N+

2 are marked in the plot with horizontal lines.

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After reconstructing the potential curves the calculation of the transition matrix elements in terms ofFranck–Condon–Factors and Transition moment function were carried out by solving the radial Schrodingerequation employing the code LEVEL from Le Roy.24

The transition dipole moment functions for some transition were available from the ab initio calculationsof Spelsberg and Meyer45 and were simply extrapolated beyond their given range to a asymptotic value. Forillustration the diabatic potential curves and dipole transition moments are displayed in figure 2.

(a) Potential energy functions of Πu states. (b) Potential energy functions of Σ+u states.

(c) Dipole transition moments of Πu states. (d) Dipole transition moments of Σ+u states.

Figure 2. Diabatic RKR Potential energy functions of the rydberg and valence states of 1Πu and 1Σ+u symmetry,

reconstructed with the coefficients given by Spelsberg and Meyer.45 Dipole transition moments between these statesand the electronic groundstate as given by Spelsberg and Meyer45 (symbols), extrapolated to smaller and largerinternuclear distances (lines).

As can be seen from the plots the expansion of the validity range of the dipole transition moments wasrather open-hearted and is not based on physical evidence. Still the effect of this expansion is supposedlysmall for the transition, due to the narrow potential curves of the rydberg states c, o, c′ and e′, but ofsignificance for the transitions from b and b’. Further improvement like extension of the validity range ofthe dipole transition moment from ab initio calculations or further information from experimental data isdesirable.

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IV. Results

IV.A. Absorption Spectra

With the obtained transition matrixelements (FCF and ETMF) from the solution of the Schrodinger equationa spectrum of one position of the equilibrium condition testcase investigated by Laux53 at 7000K wascalculated using PARADE. The principles of radiation calculation follow the determination of line positionand line strength as stated in section II, they are discussed in detail by Smith et al.2

The contribution of the single transition to the overall radiation in terms of its absorption coefficient isshown below in figure 3. As can be seen the most prominent bands in the range from 100 nm < λ < 160 nmare BHI and BHII while the LBH band is rather weak compared to the others. The Rydberg transitions W,WJ, CY, e’X gain relevance in the region between 70 nm < λ < 100 nm.

800 1000 1200 1400 1600 1800 2000Wavelength λ in [Å]

0,0001

0,001

0,01

0,1

1

10

100

1000

10000

Abs

orpt

ion

coef

ficie

nt α in

[m-1

]

Lyman - Birge - Hopfield bandVUV bands of NOBirge - Hopfield II bandBirge - Hopfield bandWorley bandCarroll - Yoshino bande - X bandWorley - Jenkins bandVUV bands omittedtotal absorption

Absorption of hot gasT = 7000 K, equilibrium composition of LAUX testcase

Figure 3. Contribution of the electronic states to the VUV radiatiton of molecular Nitrogen. Overall absorption isdisplayed in grey.

The comparison of the absorption coefficient calculated with the previous available data in PARADEand the recently extended radiative systems is shown in figure 4 on the next page. There is a rather goodaggreement over the range of 100 nmλ < 160 nm. The shape of the spectrum is very similar but the overallmagnitude is about one order of magnitude smaller. The most obvious difference appears in the structure ofthe peaks at around λ = 95 nm originating from a superposition of the CY and WJ band system, not includedin the previous dataset. Furthermore the spectral range of the radiative systems is obviously extended upto λ = 70 nm, far beyond the range of the previous dataset ceasing steeply at λ = 87nm.

As already stated, some of the discussed transitions have been investigated before in similar terms byother groups. A comparison of the calculated spectra in terms of absorption coefficient is illustrated belowin figure 5 on page 11. The parameters obtained by Chauveau31 were based on the works of Stahel andLeoni.42 The comparison of the spectra shows good agreement nont only in the overall structure but alsoin magnitude of the absorption coefficient. The structure of the peaks at λ = 95nm is not in very goodagreement but shifted by some nm against each other. This is most likely due to the different sources of theDunham coefficients. The most obvious difference in this case is the spectral range of the radiative transitions.

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80 90 100 110 120 130 140 150 160 170 180 190 20010-1

100

101

102

103

104

Old N2 VUV-Band Systems (black)

i.e. only BHII from NEQUAIR

New VUV-Band Systems (red)i.e. BHI, BHII, LBH, CY, W, WJ, e'X

VUV-Radiation of molecular Nitrogen in hot AirT=7000 K, equilibrium condition, gas composition of Laux Testcase

Abs

orpt

ion

coef

ficie

nt

in m

-1

Wavelength in nm

Figure 4. Absorption spectra of molecular Nitrogen VUV radiation. Comparison of the previous and the extendedradiation band systems

While the spectra calculated with the parameters from Chauveau31 drops steeply at around λ = 85nm thespectrum calculated from the parameters of this works goes on until λ = 70nm before it drops significantly.The major reasons for this is firstly the inclusion of the transitions originating from the e′ 1Σ+

u state that hasnot been considered by Chauveau and secondly difference in the treatment of the dissociation behavior of theRydberg states. While Chauveau took into account assumptions on predissiociative behavior our potentialcurves were simply cut off at their corresponding convergence energy neglecting predissociative effects leadingto a further spectral range. It is also noteworhty that the radiation at wavelengths below λ ≈ 74 nm is ratherquestionable, since the energies of the convergence states of the rydbergstates X2Σ+

g ≈ 125667 cm−1 andA2Πu ≈ 135683 cm−1 relative to the groundstate of molecular Nitrogen are associated with radiation ofλ ≈ 76 nm and λ ≈ 74 nm respectively. Again experimental data is desireable here for validation .

Finally, to evaluate the influence of the extended band system in the VUV on the heat load experiencedby a reentry vehicle, flow field radiation simulations were carried out by Fertig. The results are shown in thefigures 6 on page 12 below. The comparison of the calculation of the radiative heat flux with and withoutthe extended VUV band system shows a decrease of about 30 % on the vehicle. This is due to the fact thatthe boundary layer is optically thick in the VUV region and, therefore, absorbs more radiation due to thehigher absoption in this spectral range.

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600 800 1000 1200 1400 1600 1800 2000Wavelength λ in [Å]

0,001

0,01

0,1

1

10

100

1000

10000

Abs

orpt

ion

coef

ficie

nt α in

[m-1

]

Chauveau data derived from Stahel and Leonithis work derived from Spelsberg and Meyer

Absorption of hot gasT = 7000 K, equilibrium composition of LAUX testcase

Figure 5. Absorption spectra molecular Nitrogen VUV radiation. Comparison of the spectra calculated with coefficientsof Chauveau and of this work.

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r (m)

q rad

(W/m

2 )

0.1 0.2 0.3 0.4

5.0x10+05

1.0x10+06

1.5x10+06

(a)

r (m)

q rad

(W/m

2 )

0.1 0.2 0.3 0.4

5.0x10+05

1.0x10+06

1.5x10+06

(b)

r (m)

Rad

iativ

eH

eatF

lux

(W/m

2 )

0.1 0.2 0.3 0.40

500000

1E+06

80 - 200 nm200 - 320 nm320 - 440 nm440 - 560 nm560 - 680 nm680 - 800 nm800 - 920 nm920 - 1040 nm1040 - 1160 nm1160 - 1280 nm1280 - 1400 nm

(c)

r (m)

Rad

iativ

eH

eatF

lux

(W/m

2 )

0.1 0.2 0.3 0.40

500000

1E+06


(d)

r (m)

Rad

iativ

eH

eatF

lux

(W/m

2 )

0.1 0.2 0.3 0.4102

103

104

105

106


(e)

r (m)

Rad

iativ

eH

eatF

lux

(W/m

2 )

0.1 0.2 0.3 0.4102

103

104

105

106


(f)

Figure 6. Calculated radiative heat flux to the surfaxe of the high speed reentry vehicle Radflight with the previousVUV band systems (left) and the extended band systems (right).

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V. conclusion

In this work the influence of radiation in the spectral region of Vacuum–Ultraviolett was investigated.Comparisons with the existing database on VUV transition in PARADE show a significant effect of the ex-tension of the radiative systems. Comparison with similar calculations of other groups show good agreementfor the calculation of equilibrium plasma flow at 7000 K investigated by Laux in terms of absorption. It wasfound that the numerically detemined radiative heat flux to a high speed reentry vehicle is reduced by 30 %due to the higher absorption in the optically thick boundary layer.

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