Radiative heating predictions for Huygens entry

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005je002627, 2006 Radiative heating predictions for Huygens entry L. Caillault, 1 L. Walpot, 2 T. E. Magin, 1,3 A. Bourdon, 1 and C. O. Laux 1 Received 28 October 2005; revised 21 February 2006; accepted 10 May 2006; published 12 September [1] Radiative heat flux predictions for the Huygens probe entry into Titan s atmosphere are presented in this paper. Radiative heating was computed with the radiation code SPECAIR, assuming a Boltzmann distribution of the excited electronic levels at a characteristic temperature taken as the vibrational temperature of the gas. CN violet is found to be the most intense emitter, followed by CN red, C 2 Swan, and at early trajectory points by the first and second positive systems of N 2. Solutions of the 1-D radiative transport equation along stagnation streamlines show that self-absorption by the plasma layer reduces the total emission by up to about 20%. The fine structure of the CN violet spectra (spin-splitting) was taken into account to accurately determine self-absorption by CN violet. The potential importance of argon radiation was estimated and shown to be negligible. The resulting fluxes were found to be sustainable by the Huygens s Thermal Protection System. The feasibility of the mission was deemed possible under the updated entry parameters and atmospheric composition. Citation: Caillault, L., L. Walpot, T. E. Magin, A. Bourdon, and C. O. Laux (2006), Radiative heating predictions for Huygens entry, J. Geophys. Res., 111,, doi: /2005je Introduction [2] Prior to the successful entry of the Huygens Probe in the atmosphere of Saturn s moon Titan on 14 January 2005, a thorough analysis of its aerothermal environment was performed by Alcatel Space (Cannes, France), EADS-ST (Les Mureaux, France), ESA-ESTEC, NASA-Ames, and ECP (Paris, France). The specific composition of Titan s atmosphere, mainly nitrogen with a small amount of methane (up to 2.2%), leads to the formation of CN in the shock layer, the radiation of which is responsible for the major part of the total heat flux reaching the probe s surface. Therefore the radiative part of the heat flux had to be factored into the probe s overall aeroheating. [3] The work presented in this paper is devoted to the assessment of the radiative heat fluxes reaching the Huygens probe surface during its entry into Titan s atmosphere. In the shock layer around Huygens, the nonequilibrium internal level populations can only be calculated using a collisionalradiative model. However, no experimentally validated collisional radiative model was available for this mission to accurately assess these populations. Therefore the excited states of atoms and molecules were assumed to follow Boltzmann distributions which provide an upper limit of the internal level populations as verified for two types of conditions, those of a shock tube experiment [Bose et al., 2005] and those of Huygens s entry [Magin et al., 1 Laboratoire EM2C, Ecole Centrale Paris, CNRS-UPR 288, Châtenay- Malabry, France. 2 AOES B.V., Leiden, Netherlands. 3 von Karman Institute for Fluid Dynamics, Rhode-Saint-Genèse, Belgium. Copyright 2006 by the American Geophysical Union /06/2005JE ]. Bose et al. [2005] presented heat flux measurements obtained with NASA-Ames shock tube facility in a N 2 /CH 4 mixture representative of the peak heating conditions of a Titan aerocapture trajectory (freestream pressure of 13.3 Pa corresponding to postshock pressures of 3273 Pa). They found that the heat flux computations based on the assumption of a Boltzmann distribution tended to overestimate the measured heat flux. They developed an electronic collisionalradiative model for the excited state CN(B), which was found to be more adequate to predict the measured heat flux in shock tubes. Magin et al. [2006] obtained the same conclusion with their simplified electronic collisional-radiative model for the CN(A,B) and N 2 (A,B,C) applied to the same shock-tube experiment. Furthermore, Magin et al. [2006] carried out nonequilibrium modeling for two trajectory points of Huygens s entry at t = 165 s and t = 187 s. At 165 s where the maximum pressure behind the shock is 992 Pa, the computed heat fluxes based on their collisionalradiative model are found to be fifteen times lower than the values of Boltzmann distributions. At t = 187 s where the maximum pressure behind the shock is 5664 Pa, the collisional-radiative approach provided heat fluxes equal to about half the values of the ones based on Boltzmann distributions. Thus the Boltzmann assumption appears to be conservative for Huygens s entry conditions. [4] Thus, assuming Boltzmann distribution of the electronic excited levels, we have computed the radiative fluxes with SPECAIR [Laux, 1993; Laux et al., 2003], using as inputs the thermo-chemical profiles of the shock layer computed with LORE, a multiblock finite-volume Navier- Stokes solver that accounts for thermal nonequilibrium effects and finite-rate chemistry. More details are given by Walpot et al. [2005, 2006]. Note that contrary to the approach of Wright et al. [2004], radiation is not coupled to the flowfield here. 1of11

2 Table 1. Definition Matrix for Huygens Entry Conditions a Sensitivity to gravity wave perturbations Sensitivity to atmospheric CH4 Sensitivity to atmospheric argon Nominal entry Post-Ta entry with wind correction Trajectory Cases 1. Yelle min [95-5-0] 68 GW110 b 2. Yelle min [95-5-0] 68 NoGW b 3. Yelle max [ ] 62 GW240 b 4. Yelle max [ ] 62 NoGW b 5. Yelle min(a) [97-3-0] 68 NoGW b 6. Yelle min(b) [99-1-0] 68 NoGW b 7. Yelle max(a) [92-1-7] 62 NoGW b 8. Yelle max(b) [97-1-2] 62 NoGW b 9. Yelle nom [95-3-2] 65 NoGW b 10. Yelle nom(a) [96-2-2] 65 NoGW b 11. Post-Ta [ ] 65 NoGW c 12. Post-Ta(A) [ ] 65 NoGW c 13. Post-Ta(B) [ ] 65 NoGW c a The name given for each case refers to the atmospheric model used (Yelle or Post-Ta), followed in brackets by the atmosphere composition with mole fractions of N 2,CH 4, and Ar, respectively, then the entry angle and finally the inclusion (or not) of gravity waves in simulations (with their phase, when relevant). b CFD computations based on the Titan s atmosphere model by Yelle et al. [1997] according to Voyager and ground-based observations. c CFD computations based on the Titan s atmosphere model by Flasar et al. [2005] according to in situ measurements performed with Cassini s Composite Infrared Spectrometer (CIRS) on 26 October [5] This work was initiated at the request of the joint NASA/ESA Aeroheating Convergence Work Group who had observed in June 2004 differences by up to a factor of 2 between the Boltzmann predictions of radiation by ESA, NASA and EADS for a given test point representative of the Huygens s conditions using the same flowfield. To reconcile the discrepancies between the various computations, we performed a new set of computations of the same test case with the SPECAIR code, paying particular attention to the issues of spectral resolution, self-absorption, the important species to consider, and the influence of ionized species. We also carried out, for the dominant radiating systems, a thorough validation of the spectral computations, as presented in Appendix A. The conclusions of this study led us to choose a 1000-point-per-nm spectral resolution at least in the spectral range of the dominant system, to consider absorption, and to neglect the contribution of ionized species. Some of these conclusions are illustrated in this paper for the trajectory case termed Post-Ta(B) [ ] 65 NoGW. Especially relevant for the final validation of the Probe s thermal protection system (TPS) design, this trajectory case was defined with an updated Titan s atmosphere composition, obtained from in situ measurements during the closest flyby of Titan by Huygens s carrier vehicle, Cassini, on 26 October 2004 (see section 3). In the detailed analysis of this trajectory case, we examine the postshock conditions and the individual spectral contributions of the radiative systems for one particular point at 190 s corresponding to the peak heat flux. We then present for the whole trajectory the contribution of individual species to the total radiative heat flux and the effects of absorption and of spin-splitting on the radiative heat flux. [6] Finally, we give results corresponding to the complete set of trajectories defined by ESA, focusing on the radiative heating predictions sensitivity to the flowfield parameters: atmospheric composition, flight path angle at entry interface and gravity waves. [7] The paper is organized as follows: in section 2, we describe the trajectory cases selected by ESA. In section 3, we introduce the radiation code SPECAIR and give the methodology used for the assessment of the radiative heat fluxes on the Probe s surface. Then, in section 4, we present a detailed analysis of the radiative heat flux calculations obtained for the Post-Ta trajectory case. Section 5 summarizes our predictions of radiative heat flux for all trajectories. 2. Trajectory Cases Selected by ESA [8] The CFD computations of the trajectories termed Yelle are based on the Titan s atmosphere model of Yelle Figure 1. time. Trajectories Yelle min, Yelle max, Yelle nom, and Post-Ta: (a) altitude and (b) speed versus 2of11

3 Table 2. Freestream Conditions for the Yelle Min Trajectory Cases: 1, 2, 5, and 6 t, s P 1,Pa T 1, K Mach Number Table 4. Freestream Conditions for the Yelle Nom Trajectory Cases: 9 and 10 t, s P 1, Pa] T 1, K Mach Number et al. [1997], which was derived from Voyager and groundbased observations. The last updated trajectories termed Post-Ta were computed on the basis of the in situ measurements of Titan s atmospheric composition as performed with Cassini s Composite Infrared Spectrometer (CIRS) on 26 October 2004 during the Orbiter s closest flyby of Titan at orbital point Ta (at 1174-km altitude, 38.6 latitude, and hours Local Solar Time) [Flasar et al., 2005]. These measurements at high altitudes ( km) indicated that Titan s atmosphere consists of N 2 with 1.8% (±0.5%) CH 4. No argon was detected. It is worth noting that the data obtained later by Huygens s Gas Chromatograph Mass Spectrometer (GCMS) instrument during the probe descent into Titan s atmosphere indicate that the mole fraction of methane in the stratosphere was finally about 1.4% [see Niemann et al., 2005]. [9] In the Yelle model, the methane mole fraction is 3% (±2%) and the argon mole fraction is 2% (with an upper bound of 10% and a lower bound of 0%). [10] The trajectories Yelle min (case2), Yelle max (case 4), Yelle nom (case 9), and Post-Ta (case 13) given in Table 1 are characterized by a flight path angle at entry interface of 62, 65, 68 and again 68 degrees, corresponding to the shallow, nominal, and steep entry trajectories as illustrated in Figure 1. Figure 1 also shows the similarity of the Post-Ta and Yelle nom trajectory cases, although wind corrections are taken into account only for the Post-Ta trajectory. For the points of the trajectories Yelle min, Yelle max, Yelle nom, and Post-Ta, the freestream conditions are presented in Tables 2, 3, 4, and 5, respectively. [11] As listed in Table 1, variations of these four main trajectories were defined by ESA to examine the sensitivity of the heat flux computations to gravity wave perturbations (cases 1 and 3), to the methane mole fraction (cases 5, 6, 10, 11, and 12), and to the argon mole fraction (cases 7 and 8). 3. Overview of the Radiation Code SPECAIR [12] The analysis of the radiative aerothermal environment of the Huygens Probe was performed with the radiation code SPECAIR developed by Laux [1993, 2002] and by Laux et al. [2003], on the basis of the NEQAIR code of Park [1985]. All SPECAIR simulations presented here assume that the internal energy levels follow Boltzmann Table 3. Freestream Conditions for the Yelle Max Trajectory Cases: 3, 4, 7, and 8 t, s P 1,Pa T 1, K Mach Number distributions. The rotational, vibrational, and electronic excitation temperatures are considered to be the gas temperature (T rot =T gas ), the vibrational temperature, and again the vibrational temperature (T elec =T vib ), respectively. The first assumption T rot = T gas is reasonable owing to fast collisional coupling between rotation and translation. The second assumption T elec =T vib follows from the recommendations of Park [1985]. [13] For the computations presented in the following sections, all transitions listed in Table 6 are considered, unless explicitly specified otherwise. The radiative database used in SPECAIR for these species is described by Laux [1993, 2002] and Laux et al. [2003]. As will be seen in this paper, the dominant radiator is CN violet (B! X transition). We have therefore carefully validated the SPECAIR model for this transition, first in relative intensity by comparison with high resolution spectra computed with the LIFBASE code [Luque and Crosley, 1999], and second in absolute intensity by comparison with a well-characterized, mediumresolution emission spectrum calibrated in absolute intensity, measured at Stanford University [Laux, 1993; Laux et al., 2003]. More details are given in Appendix A. Ions were not considered in our final computations because their inclusion in CFD simulations as well as in the radiation code (N 2 + and N + ) had a negligible influence on the resulting heat fluxes [Takashima et al., 2003; Wright et al., 2004; Walpot et al., 2005, 2006]. Indeed, at the entry velocities considered, the amount of ionization is less than 0.1%. [14] SPECAIR solves the radiative transport equation along a line-of-sight using a 1-D tangent slab method. This approximation assumes that the properties of the shock layer vary in only one direction, normal to the probe s surface. Thus the shock layer is considered to be an infinite planeparallel medium, divided in sublayers small enough to have uniform properties in them. The 1-D tangent slab approximation is often used for radiation assessment in the stagnation region of the flowfield, where gradients are mainly in the direction normal to the probe s surface. A correction factor a = 0.75 is then applied to the 1-D radiative heat flux values, to account for 3-D effects due to the Probe s surface curvature [Wright et al., 2004]. All heat flux results presented in the following sections use the 3-D correction factor. Table 5. Freestream Conditions for the Post-Ta Trajectory Cases: 11, 12, and 13 t, s P 1,Pa T 1, K Mach Number of11

4 Table 6. Radiative Transitions Considered in SPECAIR for Titan s Atmosphere (CH 4 /N 2 ) Species CN N 2 NH C 2 N C Transitions violet (B-X), red (A-X) first positive (B-A), second positive (C-B) A-X Swan (d-a) [ ] nm [ ] nm [15] When absorption is important, the radiative transport equation must be solved carefully: accurate spectroscopic constants are required and, for CN violet, spin-splitting must be taken into account. The spectral resolution also plays an important role. Converged radiative heating results were obtained with a spectral resolution in excess of 350 points per nm. Hence for all computations, a spectral resolution of 400 points per nm was used, except in the spectral domain [ nm] of the main radiator (CN violet), wherein a resolution of 1000 points per nm was taken to get at least four points per spectral line (Dl Doppler = nm for lines of the CN violet (0,0) band at 7000 K). 4. Radiative Heat Flux Computations for the Post-Ta(B) Trajectory [16] We have performed a detailed analysis of the radiative heating at the stagnation point for several trajectories in order to estimate the contribution of each species, the effect of absorption, and the effect of spin-splitting. We present below the conclusions obtained for the trajectory case termed Post-Ta(B) [ ] 65 NoGW. This case corresponds to an entry angle of 65 at the atmospheric entry interface, and a Titan s atmosphere composition of 98.2% N 2, 1.8% CH 4, and 0% argon. The incidence of gravity waves is neglected. [17] Figure 2 shows the profiles of temperature, CN mole fraction and total particle number density obtained with LORE and the (optically thin) volumetric emission profile computed with SPECAIR along the stagnation streamline at 191 s. The nonequilibrium region immediately behind the shock (region I), where T vib lags behind T gas, produces approximately 7.6% of the total emission. The near-thermal equilibrium region (II) produces the bulk (89.7%) of the total emission, and the boundary layer (region III) near the probe s surface amounts to about 2.7%. [18] Figure 3 shows the radiative contributions of individual species to the spectral emission of the shock layer for the conditions of the Post-Ta (B) trajectory point at 191 s. The systems of CN violet, N 2 second positive, C 2 Swan, and NH (A-X) radiate mainly in the spectral domain [ nm]. The systems of CN red and N 2 first positive radiate in a broader spectral domain [ nm]. Note that these spectra are obtained under a Boltzmann assumption and that the effect of collision limiting, as in a collisional-radiative approach, would change the ratio of the relative band intensities presented. Figure 2. Temperatures, CN mole fraction, and spectral emission coefficient distribution along the stagnation line at 191 s (Post-Ta(B) trajectory case) and radiative contributions of the relaxation zone (I) immediately behind the shock front, the near-thermal equilibrium zone (II), and the boundary layer (III) near the probe s surface (located at x = 0). 4of11

5 Figure 3 5of11

6 Figure 4. Contribution of individual species to the total radiative flux for the Post-Ta (B) trajectory. Figure 5. Effect of absorption on the radiative heat flux predictions of the Post-Ta (B) trajectory. Figure 4 shows the contributions of the main radiators to the total radiative heat flux for the trajectory Post-Ta(B). CN violet has by far the largest contribution to the heat flux. As time increases, the relative contribution of CN violet radiation decreases and the contribution of CN red increases. The first and second positive systems of N 2 produce about a third of the total radiative heat flux at the early times, and then become negligible. C 2 Swan radiation rises with time but its contribution remains always negligible. The radiation of N, C and NH is also negligible. [19] Although N 2 produces significant radiation at the early times of the trajectories, our assumption of a Boltzmann distribution for the emitting states of N 2 is probably overly conservative because these states may be deexcited by collisions with other molecules present in Titan s atmosphere (e.g., N 2 *+M! M+N 2,M=N 2,C,N...). However, we have chosen a conservative approach and have kept the assumption of a Boltzmann distribution of the excited states of N 2 in the calculations presented here. The resulting heat fluxes are therefore conservative. It should be noted that when the coupling between the radiation and the flowfield is taken into account, the postshock T vib decreases to a level where N 2 radiation becomes negligible [Wright et al., 2004]. [20] Figure 5 presents the radiative heating predictions obtained with and without absorption. The solid curves include the radiation of all systems, whereas the dotted curves exclude N 2 radiation. For this trajectory case at 191 s, up to 17% of the radiation is absorbed. Since absorption cannot be neglected for Huygens s entry, all computations presented in the next section include absorption. [21] The upper and lower states of the CN violet system are spin doublets. Calculations with SPECAIR include the effect of spin-splitting, and we find as shown in Figure 6 that the level of absorption is about 5% lower when spinsplitting is taken into account versus the case where spinsplitting is neglected. 5. Sensitivity of the Radiative Heat Fluxes to the Flowfield Parameters [22] We examine in this section the sensitivity of radiative heat flux predictions to the atmospheric composition and to the flight path angle at entry interface. The sensitivity analysis presented below was performed on the basis of the Yelle atmosphere model and was then checked for the Post-Ta model when it became available at the later stages of the present work. The thirteen cases selected by ESA were examined using the flowfield conditions determined with the CFD code LORE [Walpot et al., 2005, 2006]. [23] Figure 7 shows a comparison of the three baseline cases of entry angle and atmosphere composition. Yelle nom [95-3-2] 65 NoGW is the nominal atmosphere/ trajectory case. It corresponds to a composition of 95% N 2,3%CH 4, 2% Ar, an entry angle of 65 degrees, and the effect of gravity waves is neglected. Yelle max [ ] 62 NoGW corresponds to the shallowest entry trajectory, the lower limit of methane mole fraction (1%) and the upper limit of argon mole fraction (10%) according to the Yelle model, and no gravity waves. This case is found to produce a peak radiative heat flux equal to about half the peak radiative heat flux of the nominal trajectory. The heat load, which corresponds to the integral of the heat flux over the entire trajectory, is slightly higher than for the nominal trajectory (35 MJ/m 2 as compared with 36.5 MJ/m 2 for the nominal trajectory [Walpot et al., 2005, 2006]). Yelle min [95-5-0] 68 NoGW corresponds to the steepest entry trajectory, the upper limit of methane mole fraction (5%) and the lower limit of argon mole fraction (0%) of the Yelle model, and no gravity waves. As can be seen from Figure 7, Figure 3. Spectra of individual species for the Post-Ta (B) trajectory point at 191 s. The systems considered are (a) CN violet (B-X), (b) CN red (A-X), (c) first positive of N 2 (B-A), (d) second positive of N 2 (C-B), (e) NH (A-X), (f) C 2 Swan (d-a), and atomic lines (g) of N and (h) of C. 6of11

7 Figure 6. Effect of spin-splitting on the radiative heat fluxes of the Post-Ta (B) trajectory. the peak heat flux is about 25% higher than for the nominal trajectory. However, the heat load is again comparable to that of the nominal trajectory (33 MJ/m 2 versus 36.5 MJ/m 2 [Walpot et al., 2005, 2006]). The negligible influence of the entry flight path angle on heat loads led ESA to select the nominal trajectory for the probe s descent. Therefore the Post-Ta trajectory cases correspond to nominal trajectories with an entry angle of 65 and wind corrections (see Figure 1). [24] Yelle min 68 and Yelle max 62 have been selected as the limiting cases for the estimation of gravity wave impact on the stagnation point peak heating. Figure 8 presents the predicted radiative heat fluxes for an entry angle of 68 degrees, 95% N 2 and 5% CH 4 mole fractions without and with 110 -phase gravity wave perturbations. In Figure 9, the predicted radiative heat fluxes are plotted for an entry angle of 62 degrees, 89% N 2,1%CH 4, and 10% Ar mole fractions without and with 240 -phase gravity Figure 8. Stagnation heat flux sensitivity to gravity waves for the Yelle min 68 trajectory. wave perturbations. As shown in both figures, the impact of gravity wave perturbations on the peak heat flux is negligible. [25] To determine the influence of methane on the radiative heat fluxes, we examine in Figure 10 the predicted radiative heat fluxes for a fixed entry angle of 68 degrees, no gravity waves, zero argon mole fraction, and for methane mole fractions of 1, 3, and 5%. As can be seen from Figure 10, the peak heat flux increases by about 70% when the methane mole fraction increases from 1 to 3%, and then stays about constant when the methane mole fraction is further increased to 5%. It should be noted that changing the mole fraction of methane changes the flowfield conditions, in particular the mole fraction of CN and the shock stand-off distance. CN radiation follows mainly the evolution of the CN mole fraction (see Figure 2). Raising the mole fraction Figure 7. models. Radiative heat flux for the three basic Yelle Figure 9. Stagnation heat flux sensitivity to gravity waves for the Yelle max 62 trajectory. 7of11

8 Table 7. Argon Radiation at Early Times of the Yelle Max 62 NoGW Trajectory 155 s 165 s 1-D radiative heat flux of f Ar = 9.5 kw/m 2 f Ar = 7.5 kw/m 2 Ar assuming: T ex =T elec 1-D radiative heat flux of f Ar = 18.5 kw/m 2 f Ar = 27.5 kw/m 2 Ar assuming: T ex =T gas 1-D total radiative heat flux f tot = 345 kw/m 2 f tot = 547 kw/m 2 Figure 10. Stagnation heat flux sensitivity to CH 4 mole fractions of 1%, 3%, and 5% for the Yelle min 68 NoGW trajectory. of methane leads to a nonlinear increase of the mole fraction of CN (e.g., maximum CN mole fractions of 0.84%, 1.9%, and 2.2% at 1%, 3%, and 5% methane mole fractions, respectively) and also to a shortened stand-off distance (e.g., stand-off distance of 10.4 cm, 10.4 cm, and 9.9 cm at 1%, 3%, and 5% methane mole fractions, respectively). Therefore the radiative heat flux value (i.e., the integrated emission over the stand-off distance) changes little when the methane mole fraction increases from 3 to 5%. [26] Figure 11 shows the influence of methane on the radiative heat fluxes for the Yelle nominal trajectory (3% methane, 2% argon) and for the same trajectory with a lower methane mole fraction (2%). The peak heat flux increases by about 21% when methane increases from 2 to 3%. It is clear that the radiative heat flux is very sensitive to the methane mole fraction which must therefore be determined as accurately as possible. [27] Finally, we examine the influence of argon on the radiative heat fluxes. For this, we consider the Yelle Max trajectory ( 62 degree entry angle) with a methane mole fraction of 1% and an argon mole fraction of 10%. Argon radiation is expected to be most intense for this trajectory because it has both the highest argon mole fraction (argon 10%) and the highest temperatures (especially at the early times of the trajectory where T max gas K, T max elec K). In addition, we consider variants of this case with lower argon mole fractions of 2 and 7%. [28] Because argon radiation is not computed by SPE- CAIR at present, we calculated its value on the basis of the experimentally determined total emission coefficient S eq of pure argon in LTE at 1 atm given by Owano [1991] as h i S eq W=m 3 ¼ 1: exp T LTE On the basis of equation (1), we can express the optically thin radiative heat flux produced by argon along the stagnation streamline as h i F W=m 2 ¼ 1 2 Z L 0 ð1þ 1: exp P T ex 10 5 c Ardx ð2þ Figure 11. Stagnation heat flux sensitivity to CH 4 mole fractions of 2% and 3% for the Yelle nom 65 NoGW trajectory. Figure 12. Stagnation heat flux sensitivity to argon mole fractions of 2%, 7%, and 10% for the Yelle max NoGW trajectory. 8of11

9 Figure 13. Stagnation heat flux sensitivity to CH 4 mole fractions of 1.8, 2.3, and 3.3% for the Post-Ta trajectory. where T ex characterizes the excitation temperature of the excited electronic states of argon, c Ar the argon mole fraction, and P (in Pa) the pressure at position x along the stagnation streamline. Since T ex is unknown, we consider the two limiting values T ex =T elec and T ex =T gas. [29] Using equation (2), we calculated the radiative heat flux produced by argon along the stagnation streamline (assumed to be optically thin) for two points at the early times of this trajectory, 155 and 165 s. [30] The results presented in Table 7 show that argon radiation represents at most 6% of the total radiative heating flux. The present calculations were made under the optically thin layer assumption and should be even lower when absorption is considered. In addition, argon radiation is in general further decreased owing to quenching by N 2 [Gordon and Kruger, 1993]. Thus argon radiation can be neglected for all Huygens trajectories even if argon mole fraction were to be as high as 10%, which is anyway a gross overestimation according to Post-Ta measurements (foreboding low argon mole fraction, certainly less than at high altitudes). [31] Nevertheless, the amount of argon present in Titan s atmosphere changes the thermo-chemical profiles of the shock layer, which could affect the overall radiative heat fluxes. However, reducing the argon content from 10% to 2% (while keeping the methane mole fraction constant) only reduces the radiative heat flux (of species other than argon) by less than 12% (see Figure 12). Thus the argon mole fraction has little influence on the radiative heat fluxes. In any case, the Post-Ta measurements suggested that the argon mole fraction is close to zero in Titan s atmosphere. [32] Measurements of the Post-Ta CIRS data provided a more accurate assessment of the methane mole fraction in Titan s atmosphere: 1.8 ± 0.5%. Figure 13 shows the influence of methane on the radiative heat fluxes for the Post-Ta trajectory. In this case, the entry angle is 65 degrees, and the methane mole fraction is 1.8, 2.3 or 3.2%. The peak heat flux increases approximately linearly with the methane mole fraction from 751 to 903 kw/m 2. Thus the uncertainty on the methane mole fraction allows the determination of the radiative heat flux to within ±10%. 6. Conclusions [33] We have detailed a method to compute the radiative heat fluxes along the stagnation streamline of the Huygens probe for the nominal entry trajectory into Titan s atmosphere and examined the influence of various flowfield parameters. For these computations, a spectral resolution of at least 400 points per nanometer must be considered, except in the spectral domain of CN violet where a 1000-points-per-nm spectral resolution is recommended. Spin-splitting is shown to have an influence of at most 5% on the self-absorption computations. The main radiators are the CN violet and red systems, as well as the first and second positive systems of N 2 for the early trajectory times. Figure A1. SPECAIR/LIFBASE spectra for a 1-cm plasma layer of pure CN at equilibrium T LTE = 7000 K. 9of11

10 Figure A2. SPECAIR/LIFBASE spectra for a 1-cm plasma layer of pure CN under nonequilibrium conditions (T gas =T rot = 7000 K and T elec =T vib = 4000 K). The concentration of methane has a determining influence on the radiative heat fluxes. Argon is found to have a negligible influence on the radiation. [34] The results from this work were used as a reference for the analysis of the previous predictions (June 2004) of NASA, ESA-ESTEC, and EADS-ST and convergence was achieved between the four codes. [35] In this work, the radiative heat fluxes were determined assuming Boltzmann distributions for the populations of excited states of all species. Separate results obtained with a simplified electronic collisional-radiative model [Magin et al., 2006] have confirmed that the Boltzmann approach should provide a reasonable upper bound for the radiative heat fluxes. Unfortunately, no measurements of the heat flux were performed in situ during the Huygens s entry to better assess the degree of conservatism of the Boltzmann approach. Nevertheless, even the conservative Boltzmann heat fluxes were found to be sustainable by the Huygens s Thermal Protection System. On the basis of these results, survivability of the probe from an aerothermal standpoint was thus established. This favored the decision to launch Huygens from the Cassini orbiter on 25 December Appendix A [36] We have validated the SPECAIR predictions in relative intensities under equilibrium (T LTE = 7000 K) and nonequilibrium conditions (T vib =T elec = 4000 K and T rot = T gas = 7000 K) by comparison with the spectroscopic code LIFBASE developed by Luque and Crosley [1999], and which provides spectra in relative intensities. A 1-cm wide plasma layer of pure CN was considered. As can be seen in Figures A1 and A2, excellent agreement is obtained in the range nm between the two spectral models, which both account for spin-splitting. In particular, note that the positions of the spectral features are nearly identical, and that the relative intensities of the rotational lines and of the (1,1) and (0,0) vibrational bands are very close. The same test case was run by J. Hornkohl (University of Figure A3. SPECAIR/Hornkohl spectra for a 1-cm plasma layer of pure CN under nonequilibrium conditions (T gas =T rot = 7000 K and T elec =T vib = 4000 K). Figure A4. Measured radial temperature profiles at 1 cm downstream of the nozzle exit in the Stanford 50 kw RF plasma torch. 10 of 11

11 Figure A5. Comparison of SPECAIR computations with a reference experimental spectrum measured with the Stanford 50 kw plasma torch. Tennessee Space Center, private communication, 2004) under equilibrium conditions (T LTE = 7000 K) and excellent agreement was also obtained with his relative-intensity spectrum (see Figure A3). [37] Because LIFBASE only provides spectra in relative intensity, we have tested the absolute intensity CN spectra computed with SPECAIR with experimental spectra calibrated in absolute intensities and obtained in a 50 kw RF inductively coupled plasma torch facility by Laux [2002] and by Laux et al. [2003]. The very stable plasma torch operates at atmospheric pressure, with air containing approximately 330 ppm of CO 2. At the high temperatures of that experiment (about 7500 K), N 2 and CO 2 molecules dissociate to form CN. Measurements of the electronic, vibrational and rotational profiles in Figure A4 show that the plasma is close to thermal equilibrium. [38] Moreover, because the residence time of the plasma (10 ms) is much longer than the characteristic time for chemical relaxation (1 ms), the plasma is also close to chemical equilibrium. [39] Therefore the populations of all species and all internally excited levels can be calculated assuming a unique LTE temperature. More details are given by Laux [2002] and Laux et al. [2003]. In Figure A5, the reference experimental spectrum is compared with SPECAIR predictions in the range nm. The spectrum contains spectral features of the first negative system of N 2 + and of the violet system of CN. [40] As shown in Figure A5, the absolute-intensity SPE- CAIR predictions agree with the reference experimental spectrum within better than 20%, which is also the quoted uncertainty on the measured spectrum. Note that the intensity of CN violet spectrum is very sensitive to the temperature. The SPECAIR predictions would be in excellent agreement with the measurements if one were to base the simulation on a slightly modified temperature profile, higher by about 2%, which is also the quoted uncertainty on the measured temperature profile. [41] Acknowledgments. The authors gratefully acknowledge Jean- Pierre Lebreton from the European Space Agency (ESTEC) for initiating and supporting this work. We are also deeply grateful to Thierry Blancquaert and Rafael Molina (ESA-ESTEC) for their technical guidance. We thank Lionel Marraffa (ESA-ESTEC), Philippe Tran (EADS-ST), and Michael Wright (NASA-Ames) for helpful discussions. References Bose, D., M. Wright, D. Bogdanoff, G. Raiche, and J. G. A. Allen (2005), Modeling and experimental validation of CN radiation behind a strong shock wave, paper presented at 43rd AIAA Aerospace Meeting and Exhibit, Am. Inst. of Aeronaut. and Astronaut., Reno, Nev., Jan. Flasar, F. M., et al. 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Caillault, R. Molina, C. O. Laux, and T. Blancquaert (2006), Convective and radiative heat flux prediction of Huygens entry on Titan, J. Thermophys. Heat Transfer, in press. Wright, M., D. Bose, and J. Olejniczak (2004), The impact of flowfieldradiation coupling on aeroheating for Titan aerocapture, paper presented at 42nd Aerospace Sciences Meeting and Exhibit, AIAA Pap , Am. Inst. of Aeronaut. and Astronaut., Reno, Nev. Yelle, R. V., D. F. Strobell, E. Lellouch, and D. Gautier (1997), Engineering models for Titan s atmosphere, Eur. Space Agency Spec. Publ., ESA SP-1177, A. Bourdon, L. Caillault, C. O. Laux, and T. E. Magin, Laboratoire EM2C, Ecole Centrale Paris, CNRS-UPR 288, Grande Voie des Vignes, F Châtenay-Malabry, France. (anne.bourdon@em2c.ecp.fr; lise.caillault@ em2c.ecp.fr; christophe.laux@em2c.ecp.fr; thierry.magin@em2c.ecp.fr) L. Walpot, AOES B.V., Haagse Schouweg 6G, 2332 Leiden, Netherlands. (louis.walpot@aoes.com) 11 of 11