Reduced Atomic Collisional-Radiative Model for VUV Radiation Prediction in Earth s Reentry

Transcription

1 50th AIAA Aerospace Sciences Meeting including the ew Horizons Forum and Aerospace Exposition January 2012, ashville, Tennessee AIAA Reduced Atomic Collisional-Radiative Model for VUV Radiation Prediction Earth s Reentry A. LEMAL 1, M.-Y. PERRI 2, A. BOURDO 3 and C.O. LAUX 4 Laboratoire d Energétique Moléculaire et Macroscopique, Combustion (EM 2 C)-CRS UPR288 Ecole Centrale Paris, Grande Voie des Vignes, Chatenay-Malabry, France and E. RAYAUD 5 and P. TRA 6 EADS Astrium Space Transportation, 66 Route de Verneuil, Les Mureaux, France During hypervelocity reentry into Earth s atmosphere, a significant part of the radiative heat flux experienced by the spacecraft is emitted in the Vacuum Ultraviolet (VUV), in the nonequilibrium part of the post-shock region. Using radiation measurements for typical Moon or Mars return conditions performed at ASA Ames in the Electric Arc Shock Tube (EAST) facility, the main atomic electronic states responsible for the intense radiation this wavelength range have beedentified as being the fourth and fifth electronic states of atomic nitrogen and the fifth electronic state of atomic oxygen. We have developed a collisional-radiative (CR) model to predict the population of these emitting states and compared the predictions given by other CR models used in the aerospace community. The most significant mechanisms driving the evolution of these electronic states have been identified, leading to a reduced CR model to a set of sevelectronic states and twenty-eight reactions. U I. Introduction PCOMIG exploration missions to the Moon and Mars continue to generate strong interest in understanding and predicting the nonequilibrium high temperature radiation that a spacecraft will encounter during its reentry into Earth s atmosphere. During hypervelocity (V>10km.s -1 ) reentry into Earth s atmosphere, the radiatios mostly emitted by nitrogen and oxygen atoms[1,2] since molecular nitrogen and oxygen quickly dissociate. The radiatiomitted in the Vacuum Ultraviolet region (VUV) (below 200 nm) accounts for more than 50% of the total radiative heating[3-10]. The prediction of atomic radiation relies on an accurate prediction of the populations of the emitting states, which are strongly influenced by nonequilibrium conditions, themselves governed by collisional- radiative (CR) processes. The paper is divided in two sections. Section II presents the CR model used in this work to predict nonequilibrium radiation. In Section III, we first discuss VUV radiation measurements obtained in the Electric Arc Shock Tube (EAST) facility of ASA Ames Research Center for conditions relevant to hypervelocity reentry into Earth s atmosphere. The predominant atomic lines and corresponding emitting electronic states are identified. The most significant population/depletion mechanisms are identified and compared with various sources from the literature. Based on this analysis, a reduction of the CR model is presented. 1 : Ph.D student at Ecole Centrale Paris, Adrien. Lemal@em2c.ecp.fr, AIAA Student Member 2 : Senior Researcher at CRS, Marie_Yvonne.Perrin@em2c.ecp.fr 3 : Senior Researcher at CRS, Anne.Bourdon@em2c.ecp.fr 4 : Professor at Ecole Centrale Paris, Christophe. Laux@ecp.fr, AIAA Associate Fellow 5 : Aerothermodynamics Engineer at EADS, Elisabeth.Raynaud@astrium.eads.net 6 : Aerothermodynamics Engineer at EADS, Philippe.Tran@astrium.eads.net 1 Copyright 2012 by the authors. Published by the, Inc., with permission.

2 II. Modeling The prediction of post-shock radiation requires to determine: 1) the flowfield temperatures and species concentrations, 2) the populations of the excited states and 3) the intensity emitted from these states. The flowfield computatios determined with EADS s 1D Euler code[11]. The high temperature air mixture considered in this study is composed of 11 species: 2, O 2, O,, O, 2 +, O 2 +, O +, +, O + and free electrons e -. The flowfield model solves species, mass, momentum, electron-vibration and total energy conservatioquations along a streamline. Chemical nonequilibrium is takento account by computing the species production/destruction with Park[12] chemistry set. Thermal nonequilibrium is takento account by assuming a two temperature model: Translational-Rotational-Gas T TRg and Vibrational-Electron T Ve temperatures. The thermal relaxatios given by Millikan and White relaxation law[13] with Park high temperature correction[14]. The radiatiomitted by the flowfield considered in this work was determined with the radiation code SPECAIR[15,16]. Briefly, SPECAIR models 1484 lines of atomic nitrogen (from nm to µm), 856 lines of atomic oxygen O (from nm to µm), computes emission and absorption coefficient using a lineby-line approach, given temperature and species mole fractions and solves the Radiative Transport Equation using the tangent slab approximation. Under Local Thermodynamic Equilibrium (LTE) conditions, the distribution of the electronic states is given by a Boltzmann distribution. Under nonequilibrium conditions, CR processes between these electronic states govern their distribution. itrogen and oxygen atoms have 261 and 234 bound electronic states, respectively, according to the IST database[17]. So as to make the computation tractable, atomic electronic states are lumped into grouped levels. For instance, let us consider nergy levels with degeneracies g n and energies E n. A lumped level i with degeneracy g i and energy E i can be constructed by grouping some of the n levels following [18]: g n E n (1) g i = g n, E i = 1 g i n i In a similar fashion, bound-bound radiative transitions are determined by averaging IST[17] transition probabilities withiach grouped levels. During atmospheric entry into Earth s atmosphere, 2 and O 2 molecules quickly dissociate. Electrons are primary created through associative ionization between atoms. Because of their low mass, and thus collision frequency, they drive the excitation of atomic species. The elementary processes governing the excitation of the electronic states of atoms are described in the following: - electron-impact excitation The process of excitation of alectronic level i to a higher level j may be written as: EXC k ij The reverse process of electron-impact de-excitation may be written as: n i X(i) +e X(j) +e,j>i (1) EXC k ji X(j) +e X(i) +e,j>i (2) The de-excitation rate constant is related to the corresponding excitation rate constant through detailed balance: E i E j kt e (3) eq k EXC EXC n ji =k i ij n where eq j eq n = g i eq e j g j The volumetric net rate of excitation of level i by electrompact is obtained by summing over the populating and depopulating reactions from the levels of the atom: 2

3 t = k EXC ji n j k EXC ij j i j i (4) - electron-impact ionization Ionization of level i by electrompact may be written as: The reverse process, electron-impact recombination, may be written as: k ic IO X(i) +e X + +2e (5) k ci REC X + +2e X(i) +e (6) The recombination rate constant is related to the corresponding ionization rate constant through detailed balance: k REC IO q eq ci =k + ic eq where q eq + eq = 2πm k T e B e 2 h P 3 2 2Q + g i e ' E ion E i kt e (7) where h P is the Planck constant (h P = J.s), k B the Boltzmann constant (k B = 1.381x10-23 J.K -1 ), m e the electron mass (m e = 9.109x10-31 kg), Q + ' is the iolectronic partition function, E ion is the ionizationergy of atom E ion lowered by Debye shielding ΔE ion : where λ D is the Debye length, given by: ΔE ion = λ D = q e 2 4πε 0 λ D (8) ε 0k B T e q e 2 (9) where ε 0 is the vacuum permittivity (ε 0 = 8.854x10-12 F.m -1 ) and q e the electron charge (q e = 1.602x10-19 C). The volumetric net rate of excitation of level i by electrompact ionizatios given by: t IO =k REC ci n + n 2 e k IO ic (10) - bound-bound radiative transitions Spontaneous and stimulated emission correspond to a transition from a higher state j to a lower state i, while absorption corresponds to a transition from a lower state i to a higher state j. The de-excitation process by spontaneous emission may be written as: A ji X(j) X(i) +hν,j>i (11) The phenomenon of absorptios complicated because the absorption at a given point is a function of the radiative intensity at that point, which is a function of the radiatiomitted throughout the flowfield. As a result, this process is usually approximated using the escape factor concept, which assumes that the depletion of level i due to absorptios some fraction of the population of level i by emission. This fraction or escape factor, defined as Λ j,i, may be interpreted as the fraction of radiation that escapes from a point. For Λ j,i equal to unity, all of the radiation escapes. This means the gas is transparent and there is no re-population by absorption. Conversely, if Λ j,i is equal to zero, then the population and depletion of a level i due to absorption and emission cancel out, which may be interpreted as no net escaping radiation. The net rate of population of level i by bound-bound radiative transitions may be written as: t RAD = Λ ij A ij (13) 3

4 Table 1 presents the different CR models studied in this work. We also specify in this table the number of grouped levels and the references for the rate constants of electron-impact excitation and ionization and the radiative probabilities. The atomic CR model, labeled Present model is also described in this table. For electron-impact excitation of the first three atomic grouped electronic states of nitrogen and oxygen respectively, the collision strengths provided by Frost et al.[19] and Zatsarinny et al.[20] were fitted up to T e =20,000K with a dedicated MATLAB program and the corresponding rate coefficients were computed. For electron-impact ionization of the first three atomic grouped electronic states of nitrogen and oxygen respectively, the rate constants provided by Huo[21] were fitted and the Binary-Encounter-Dipole model[22] was used. For the remaining processes, Drawin s formula[23,28] is used. Table 1: CR models investigated Model label Grouped levels Exc. rate constant Ion. rate constant Rad. probabilities Park (22), Park[24,25] O(19), Park[24,25] Park[24,25] Drawin[23,28] Park[24,25] Drawin (46), Bourdot al.[26] Drawin.[23,28] Drawin[23,28] Panesi et al.[28] Johnston Our model O(40), Bourdot al.[27] (35), Johnston[29] O(32), Johnston[29] (46), Bourdot al.[26] O(40), Bourdot al.[27] Johnston s AACR model[29] Frost et al.[19] for metastable states, Drawin[23] for remaining states Zatsarinny et al.[20] for metastable states, Drawin[23] for remaining states Johnston s AACR model[29] Huo[21] for metastable states Drawin[23,28] for remaining states BEB model[22] for metastable states Drawin[23,28] for remaining states Johnston s AACR model[29] Panesi et al.[28] Panesi et al.[28] Heavy particle impact excitation mechanisms were neglected since they were shown to be influential only in a narrow region behind the shock wave (a few millimeters) where the electron density is low[28]. Bound-free radiative mechanisms were also neglected because they were found to have a negligible influence on the evolution of atomic electronic electronic states for hypervelocity Earth s reentry conditions [28,30]. The Master Equation governs the electronic state populations of atoms and molecules. This differential equation, which must be solved for every state of a species, equates the rate of change of a level s population with all of the populating and depleting mechanisms. Therefore, the volumetric time-rate-of-change of the population of level i may be written as: t = n i t EXC + n i t IO + n i t RAD (14) t = + k EXC ji n j k EXC ij j =1 +k REC 2 ci n + j =1 k ic IO Λ ij A ij (15) There are various ways to couple CR processes between the electronic states of the species and chemical reactions between species. The most widely used approach is the Quasi Steady State (QSS) approach which is based on the assumption that the characteristic time of the processes involving excited states is much shorter than the characteristic time of the change of the ground state of the species. In other words, species concentrations are assumed to adjust almost instantaneously to the flowfield variations: t << n i t EXC + n i t IO + n i t RAD 4 for i > 1 (16)

5 QSS CR models[24,25,29,31-34] can be loosely coupled to flow codes. In this case, the profiles of the thermodynamic variables (pressure and temperatures) and species mass fractions are derived based on a flow calculation, then the populations of electronic states are obtained at each desired location the flow using the CR model. The second approach is called the time-dependent CR model. In this case, conservatioquations for the electronic states of the species are solved simultaneously without any assumption on characteristic relaxation times. Time-dependent CR models can be either loosely or directly coupled to CFD solvers. In the directly coupled approach[28,30], state-to-state equations are solved simultaneously with mixture mass, momentum, energy equations. In the loosely coupled approach[35], called Lagrangian approach, the populations of the electronic states are obtained by following in time a cell of fluid. In this work, we adopted the QSS approach since it was shown to give results comparable with those of the timedependent approach for the most emitting atomic electronic states[28,30]. Under the QSS assumption, Equation 15 reads: j =1 k EXC ji n j k ij EXC j =1 +k REC ci n + n 2 e k IO ic Λ ij A ij = 0 (17) Equation 15 was solved for each electronic state i>1 thanks to a ewton algorithm[36]. The population of the ground state is retrieved by ensuring that the total number density computed during the flow calculatios conserved in the QSS calculation[24,25]. III. Results III.A. Analysis of radiation measurements The identification of the most prominent atomic lines and corresponding emitting states was carried out by analyzing radiation measurements in the VUV range. The radiation measurements selected for this purpose were performed in 2010 at ASA Ames Research Center, in the EAST facility. The EAST facility is a cm diameter shock tube with alectric arc-heated driver. The arc in the driver is supported by a capacitor bank which can store up to 1.24 MJ of energy heated at 40kV. For a comprehensive review of the optical set-up, the calibration procedure and test conditions, the reader is referred to [37-41]. In the present work, we consider lunar return peak heating conditions corresponding to EAST T run (V =10.54km.s -1, T =293K, p =13.3Pa). Figure 1 presents amission spectra obtained in such conditions, close to LTE. LTE species mole fractions and temperature were computed with the CEA code[42] and then passed on to SPECAIR[15-16]. The Radiation Transport Equation was solved along a slab of uniform properties and length of cm. The electronic temperature was adjusted until the experimental and numerical spectra agreed with each other. The simulated spectra was then convolved with the apparatus slit function assumed to be a normalized Gaussian with full width at half maximum (FWHM) measured to be 0.6 nm. Figure 1 presents a comparison of the EAST T experimental spectrum with computed spectra with electronic temperatures being ± 10% of the equilibrium temperature. The experimental spectrum lies between these two bounds, indicating that the measured spectrum is indeed close to LTE. Table 2 gives the equilibrium species mole fractions and temperature. The measured spectrum contains two carbon lines at 156 and 165 nm, the carbon being from impurities. Table 3 summarizes the positions of the atomic lines observed in the experimental spectrum, complemented with additional lines previously referred in the literature[44,45] as well as the degeneracies and energies of the corresponding emitting grouped states. The intense radiation observed in the VUV range is mainly due to bound-bound transitions from two nitrogelectronic states (4,5,6,13,20). 5

6 O C C Figure 1: Comparison of EAST T experimental VUV spectrum, in the equilibrium post-shock region with SPECAIR simulations Table 2: Equilibrium conditions given by the CEA code[37] for EAST T run T eq K p eq Pa x eq () 5.78x10-1 x eq (O) 2.46 x10-1 x eq ( + ) 6.92x10-2 x eq (O + ) 1.85x10-2 x eq (e-) 8.78x10-2 6

7 Table 3: Atomic lines of importance under Earth s hypervelocity reentry Species Wavelength (nm) Reference A IST[17] ul (s -1 E ) u (cm -1 ) g u Grouped IST[17] IST[17] level[26,27] [44] 1.51x [45] 1.49x [45] 1.03x EAST+[44,45] 4.03x EAST+[44,45] 4.00x EAST+[44,45] 3.22x EAST+[44,45] 3.10x EAST+[44,45] 7.68x EAST+[44,45] 6.05x EAST+[44,45] 5.76x EAST+[44,45] 1.01x EAST+[44,45] 3.11x EAST+[44,45] 3.46x EAST+[44,45] 1.05x O [44] 5.28x O EAST+[44,45] 3.41x O EAST+[44,45] 2.03x III.B. Population of emitting electronic states III.B.1. Identification of key mechanisms As shown subsection III.A, the radiatiomitted in the VUV range can be attributed to bound-bound transitions from the (4,5) electronic states. We have therefore sorted out the significant mechanisms for populating and depleting these electronic states. Considering a transition between two electronic states l and i and following[30], we define: Inflows as the terms responsible for the population of the electronic state i by electronimpact excitation of electronic state l and Outflows as the terms responsible for the depletion of the electronic state i by electron-impact excitation to electronic state l: - Population term by electron-impact excitation: P EXC (l) =k li EXC n l (18) - Population term by electron-impact recombination: P REC =k REC 2 ci n + (19) - Depletion term by electron-impact excitation: D EXC (l) =k il EXC (20) - Depletion term by electron-impact ionization: D IO =k IO ic (21) Also are defined et Inflows : - by electron-impact excitation: I EXC =P EXC D EXC (22) - by electron-impact ionization: I IO =P REC D IO (23) 7

8 (a): (4) (b): (5) Figure 2: et Inflows obtained with the present model Figures 2.a,b present the main contributors to the (4) and (5) electronic state population and depletion respectively. It is shown that the collisional processes among these particular states and first three lowest metastable states are of critical importance in the nonequilibrium part of the post shock region. For instance, the (4) and (5) electronic states are populated by electrompact collisional processes from the metastable states and depleted by electrompact collisional processes to higher states up to x=0.3cm. For distances greater than 0.3cm from the shock, the flow reaches equilibrium and this trend reverses. A literature review of some of these rate constants was therefore conducted. Figure 3 presents some of the rate constants found in the literature. Significant differences exist between the various rate constants. Therefore, we investigate the influence of these rate constants on the populations of the (4) and (5) electronic states. (a): k14 (b): k25 (c): k35 Figure 3: Electrompact excitation rate constants from the literature Park[23,24], Panesi et al.[28], Frost et al.[19] III.B.2. Prediction of electronic states populations by various CR models The various CR models listed in Table 1 were then applied to the analysis of the EAST T spectrum. Figures 4.a,b present the evolution of the (4) and (5) population the post shock region predicted by the CR models. The populations were computed under the thick approximation (Λ=0), which was shown to be a very good approximation under similar conditions to those conditions studied in this work[43]. 8

9 (a): (4) (b): (5) Figure 4: Post shock evolution of (4) and (5) electronic states predicted by various CR models (a):, x = 0.3 cm (b):, x = 3.0 cm (c): O, x = 0.3 cm (d): O, x = 3.0 cm Figure 5: Boltzmann diagrams (thick approximation, Λ=0) 9

10 Figures 5.a,b,c,d present the distribution of the electronic states of nitrogen and oxygen at two locations in the post-shock zone assuming the medium optically thick. Close to the shock front (x=0.3cm), two behaviours are observed: the low-lying metastable states closely follow the Boltzmann distribution at electron temperature, whereas the high lying levels follow the Saha-Boltzmann distribution. The three resonant states, responsible for the intense radiation the VUV lie between the Boltzmann and Saha-Boltzmann distributions. Discrepancies of about a factor of 5 are noted in the population predicted by the various CR models. Further in the post-shock region (at x=3.0cm), all distributions predicted by the CR models collapse, as expected, to the Boltzmann distribution at the LTE temperature. Figure 6 presents present the distributions of the electronic states of nitrogen and oxygen at two locations in the post-shock zone assuming the medium optically thin. In the nonequilibrium portion of the post-shock region, the electronic states are depleted by bound-bound transitions. In the equilibrium region, the electronic levels follow a Boltzmann distribution at the electron temperature, showing that electron-induced collisional processes dominate over radiative processes. (a):, x = 0.3 cm (b):, x = 3.0 cm Figure 6: Boltzmann diagrams (thin approximation, Λ=1) of III.C. Reduction of the CR model III.C.1. Principle of the method As shown subsection III.B.1, the populations of the (4) and (5) electronic states are respectively governed by a few electronduced collisional processes from the metastable states and some higher states. The analysis of the results presented in paragraph III.B for the atomic electronic states suggests that the possibility exists to reduce the number of levels considered in the CR models. Many electronic states, owing to reduced energy spacing, are likely to be iquilibrium with each other due to afficient collisional coupling. The various behaviours of the low lying (states 1 to 6) and high lying electronic states require a separate grouping. Firstly, the high lying levels, which are located close to the ionization limit and do not radiate significantly, were shown to be in chemical ionizatioquilibrium with the free electrons. Therefore, the calculation of the detailed physico-chemical processes for these electronic states result in ancrease of the computational effort without improving the accuracy of the model. Secondly, the low lying states, which are less efficiently coupled by collisions owing to larger energy spacing and which radiate strongly in the VUV, were kept ungrouped. Subsequently, the initial grouping of Bourdot al.[26] was further subdivided as detailed in Table 6 by further lumping the levels close to the ionization limit. Table 6: Reduction of the CR models umber of Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 levels Initial grouped levels from Bourdot al.[26]

11 III.C.2. Elementary processes for lumped levels To model the flow with the reduced model, it is necessary to determine the rates of the CR processes of the grouped states based on the rates of the elementary processes between ungrouped states. Following [36], it is proposed to average the rates of the elementary processes between ungrouped states, assuming that these states follow a Boltzmann distribution at the electron temperature. For instance, let us consider i ungrouped electronic states belonging to a lumped state I and j ungrouped electronic states belonging to a lumped state J. The forward electron-impact excitation and ionization rates are given by Equations 24, 25 respectively : K IJ ( T e ) = i I j J E i ( ) g i e k B T e k ij T e i I g i e E i k B T e (24) K Ic ( T e ) = i I E i ( ) g i e k B T e k ic T e i I g i e E i k B T e (25) The backward rates are computed using the detailed balance principle, based on lumped levels I and J. Figures 7.a,b present the post-shock evolution of the (4) and (5) electronic state populations predicted by both the initial model (46 levels) and the reduced model (7 levels). The two models agree to within 15%. (a): (4) (b): (5) Figure 7: Predictions of nitrogelectronic states population with the initial and the reduced present CR models Finally, Figure 8 presents the computer time cost reduction due to the lumping of the high lying levels. A factor five decrease is noted. 11

12 Figure 8: CPU time reduction IV. Conclusions In this work, radiation measurements in the VUV range carried out at ASA Ames EAST facility for lunar peak heating conditions were analyzed. We identified the nitrogen (4,5,6,13,20) electronic states as being responsible for the intense radiatiomitted in the VUV. Predictions of these electronic state populations with various CR models used in the aerospace community were obtained and showed that the key mechanisms responsible for their population and depletion were the collisional processes between these states and the metastable states. The initially developed CR model was reduced to a set of 7 electronic states and 28 collisional processes. This reduced model provides results that are within 15% of the initial model results and reduced the CPU time by a factor 5. Future work will consist of validating the rate constants of the key mechanisms using available experimental data. Further work will be undertaken to analyze the remaining radiation measurements for higher speed and lower pressure, inferring the electronic states and temperature distributions of the shocked air mixture. Acknowledgments The authors thank Dr. Brett Cruden (ASA Ames Research Center) and Dr. Aaron Brandis (The University of California Santa Cruz) for having provided the radiation measurement data. Thanks are due to Dr. Alexis Bourgoing and Dr. Jacques Soler (EADS Astrium Space Transportation) for having provided the flowfield. Financial support from EADS Astrium is gratefully acknowledged. References [1] J. M. Lamet. Transferts radiatifs dans les écoulements hypersoniques de rentrée atmosphérique terrestre. Ph.D thesis (in French), Ecole Centrale Paris, France, [2] T. Soubrié. Prise en compte de l ionisatiot du rayonnement dans les rentrées terrestres et martiennes. Ph.D thesis (in French), ISAE-ESAE, France, [3] C. O. Johnston. onequilibrium shock-layer radiative heating for Earth and Titantry. Ph.D thesis, Virginia Polytechnic Institute and State University, USA, [4] D. Bose, E. Mac Corkle, C. Thompson, D. W. Bogdanoff, D. Prabhu, G. A. Allen, and J. H. Grinstead. Analysis and model validation of shock layer radiation air. AIAA paper , [5] C. O. Johnston. A comparaison of EAST shock-tube radiation measurements with a new air radiation model. AIAA paper , [6] C. O. Johnston, A. Mazaheri, P. Gnoffo, B. Kled, K. Sutton, D. Prabhu, A. M. Brandis, and D. Bose. Assessment of radiative heating uncertainty for hyperbolic Earth entry. AIAA paper , [7] G. Yamada, H. Takayanagi, T. Suzuki, and K. Fujita. Vacuum ultraviolet spectroscopy for shock layer radiation measurement. AIAA paper ,

13 [8] G. Yamada, H. Takayanagi, T. Suzuki, and K. Fujita. Analysis of the shock layer radiation vacuum ultraviolet region for Hayabusa return conditions. AIAA paper , [9] C. O. Laux, R. J. Gessman, and C. H. Kruger. Modelling the UV and VUV radiative emission of high temperature air. AIAA paper , [10] C. O. Laux, M. Winter, J. Merrifield, A. Smith, and P. Tran. Influence of ablation products on the radiation at the surface of a blunt hypersonic vehicle at 10 km/s. AIAA paper , [11] A. Bourgoing and J. Soler, Internal note, May [12] C. Park. Stagnation point radiation for ApolloIV: a review and current status. AIAA paper , [13] R. C. Millikan and D. R. White, Systematics of vibrational relaxation. The journal of Chemical Physics, 39(12), [14] C. Park. Review of chemical kinetic problems for future ASA missions. I. Earth entries. Journal of Thermophysics and Heat Transfer, 7(3), [15] C. O. Laux. Optical diagnostics and radiative emission of air plasmas. Ph.D thesis, The University of Stanford, USA, [16] C. O. Laux. Radiation and nonequilibrium collisional radiative models. VKI Special course on: Physicochemical models for high enthalpy and plasma flow modelling, June [17] Available at : [18] J.-L. Cambier and S. Moreau. Simulations of a molecular plasma in collisional radiative nonequilibrium. AIAA paper , [19] R. M. Frost, P. Awakowicz, H. P. Summers, and. R. Badnell. Calculated cross sections and measured rate coefficients for electrompact excitation of neutral and singly ionized nitrogen. Journal of Applied Physics, 84(6), [20] O. Zatsarinny and S. Tayal. Electron collisional excitation rates for O using the BSRM approach. The Astrophysical Journal, 148(2), [21] W. Huo. Electrompact excitation and ionisation of air. Technical Report RTO-E-AVT-162, ATO, [22] Available at : [23] H. W. Drawin. Collision and transport cross sections. Technical Report EUR-CEA-FC-383, [24] C. Park. onequilibrium hypersonic Aerothermodynamics. John Wiley and Sons, Inc, [25] C. Park. onequilibrium Air Radiation (EQAIR) program: user s manual, [26] A. Bourdon and P. Vervisch. Three-body recombination rate of atomic nitrogen low-pressure plasma flows. Physical Review E, 54(2), [27] A. Bourdon, Y. Térésiak and P. Vervisch. Ionization and recombination rates of atomic oxygen hightemperature air plasma flows, 57(4), [28] M. Panesi, T. E. Magin, A. Bourdon, A. Bultel, and O. Chazot. FireII flight experiment analysis by means of a collisional-radiative model. Journal of Thermophysics and Heat Transfer, 23(2), [29] C. O. Johnston, B. Hollis, and K. Sutton. on-boltzmann modeling for air shock-layer radiation at lunarreturn conditions. Journal of Spacecrafts and Rockets, 45(5), [30] C. O. Johnston. onequilibrium shock-layer radiative heating for Earth and Titantry. PhD thesis, Virginia Polytechnic Institute and State University, USA, [31] E. Raynaud, P. Tran, J. Soler, and M. Baillon. Huygens aerothermal environment: radiative heating. In the proceedings of the Third International Planetary Probe Workshop, Anavyssos, Greece, [32] S. Y. Hyun. Radiation code SPRADIA07 and its applications. Ph.D thesis, KAIST, South Corea, [33] D. Bose, E. Mac Corkle, D. W. Bogdanoff, and G. A. Allen. Comparaisons of air radiation model with shock tube measurements. AIAA paper , [34] D. Potter. Modelling of radiating shock layers for atmospheric entry in Mars and Earth. Ph.D thesis, The University of Queensland, Australia, [35] T. E. Magin, L. Caillaut, A. Bourdon, and C. Laux. onequilibrium radiative heat flux modelling for the Huygens entry probe. Journal of Geophysical Research, 111(8), [36] L. Pierrot, L. Yu, R. J. Gessman, C. Laux, and C. H. Kruger. Collisional-radiative modelling of nonequilibrium effects in nitrogen plasmas. AIAA paper , [37] B. A. Cruden, R. Martinez, J. H. Grinstead, and J. Olejnniczak. Simultaneous vacuum ultraviolet through near infrared absolute radiation measurements with spatio-temporal resolution alectric arc shock tube. AIAA paper , [38] D. W. Bogdanoff. Shock tube experiments for Earth and Mars entry conditions. Technical Report RTO-E- AVT-162, ATO,

14 [39] J. H. Grinstead, M. C. Wilder, J. Olejnniczak, D. Bogdanoff, G. A. Allen, K. Dang, and M. J. Forrest. Shock heated air radiation measurements at lunar return conditions. AIAA paper , [40] J. H. Grinstead, M. C. Wilder, D. C. Reda, C. J. Cornelison, B. A. Cruden, and D. W. Bogdanoff. Shock tube and ballistic range facilities at ASA Ames research center. Technical Report RTO-E-AVT-186, ATO, [41] J. H. Grinstead, M. C. Wilder, D. C. Reda, B. A. Cruden, and D. W. Bogdanoff. Advanced spectroscopic and thermal imaging instrumentation for shock tube and ballistic range facilities. Technical Report RTO-E-AVT- 186, ATO, [42] Available at : [43] I. Sohn, Z. Li, and D. A. Levin. Effect of excape factor to a hypersonic nonequilibrium flow implemented in DSMC photon Monte Carlo radiation. AIAA paper , [44] D. A. Levin. Modeling of the VUV radiation at high altitudes. AIAA paper , [45] C. O. Johnston, B. Hollis, and K. Sutton. Spectrum modelling for air shock-layer radiation at lunar return conditions. Journal of Spacecrafts and Rockets, 45(5),