Abstract
On December 7th, 1995, the Galileo descent probe entered Jupiter’s atmosphere at a relative velocity of 47.4 km s−1. Flight data revealed an unforeseen recession profile: while the stagnation region had been significantly oversized, the shoulder almost completely ablated. In an attempt to understand why numerical predictions diverge from the flight data, several sensitivity studies were performed at the 180 km altitude point. The inaccuracy of the Wilke/Blottner/Eucken model at temperatures above 5000 K was confirmed. When applied to Galileo’s entry, it predicts a narrower shock with higher peak temperatures compared to the Gupta/Yos model. The effects of He and H2 line-by-line radiation were studied. Inclusion of these systems increased radiative heating by 9% at the stagnation point, even when precursor heating is unaccounted for. Otherwise, the internal excitation of H2 due to absorption of radiation originating from the highly emitting shock layer promotes H2 emission before dissociation occurs at the shock, yielding 196% higher radiative heat fluxes. This emphasizes the importance of H2 radiation not only on the recession experienced by Galileo but also for future entries in gas giants. Accordingly, thermal nonequilibrium resulted in 25% lower radiative heating when compared to an equilibrium solution, contrary to previous investigations that neglected H2. Ablation products absorption was shown to counteract the increased emission due to precursor heating of H2. However, the ablation layer temperature must be accurately predicted using a material-response code coupled to the flowfield since radiative heating has been shown to significantly depend on this energy-exchange interaction. Finally, the tangent-slab and ray-tracing models agreed to within 12%.
ACKNOWLEDGMENTS
M. Lino da Silva’s work has been funded by the Portuguese FCT–Fundação para a Ciência e Tecnologia through the Project No. UID/FIS/50010/2019. The authors would like to thank Markus Fertig for the thoughtful suggestions regarding the modeling of shoulder expansion and Domenico Bruno for general comments about this work, provided during the European Space Agency-sponsored 8th International Workshop on Radiation of High Temperature Gases.
REFERENCES
- 1. P. Reynier, G. D’Ammando, and D. Bruno, “Modelling chemical kinetics and convective heating in giant planet entries,” Prog. Aerosp. Sci. 96, 1–22 (2018). https://doi.org/10.1016/j.paerosci.2017.11.002, Google ScholarCrossref
- 2. F. S. Milos, Y.-K. Chen, T. Squire, and R. Brewer, “Analysis of Galileo probe heatshield ablation and temperature data,” J. Spacecr. Rockets 36, 298–306 (1999). https://doi.org/10.2514/2.3465, Google ScholarCrossref
- 3. J. O. Arnold, “Planetary entry probes 1953–2036: A technologist’s perspective,” in 10th International Planetary Probe Workshop, 2013. Google Scholar
- 4. B. Lopez and M. Lino Da Silva, “SPARK: A software package for aerodynamics, radiation and kinetics,” in 46th AIAA Thermophysics Conference (AIAA, 2016), p. 4025. Google ScholarCrossref
- 5. M. Lino da Silva, B. Lopez, and S. Espinho, SPARTAN 2.6 User’s Manual, 2016. Google Scholar
- 6. M. Lino da Silva, “An adaptive line-by-line—Statistical model for fast and accurate spectral simulations in low-pressure plasmas,” J. Quant. Spectrosc. Radiat. Transfer 108, 106–125 (2007). https://doi.org/10.1016/j.jqsrt.2007.03.005, Google ScholarCrossref
- 7. M. Lino da Silva, “The line-by-line radiative code spartan” (2016), http://esther.ist.utl.pt/spartan/; accessed 24 May 2019. Google Scholar
- 8. M. E. Tauber and R. M. Wakefield, “Heating environment and protection during Jupiter entry,” J. Spacecr. Rockets 8, 630–636 (1971). https://doi.org/10.2514/3.59703, Google ScholarCrossref
- 9. M. Perrin, G. Colonna, G. D’Ammando, L. Pietanza, P. Riviere, A. Soufani, and S. Surzhikov, “Radiation models and radiation transfer in hypersonics,” Open Plasma Phys. J. 7, 114–126 (2014). https://doi.org/10.2174/18765343014070101114, Google ScholarCrossref
- 10. L. P. Leibowitz, “Measurements of the structure of an ionizing shock wave in a hydrogen-helium mixture,” Phys. Fluids 16, 59–68 (1973). https://doi.org/10.1063/1.1694174, Google ScholarScitation, ISI
- 11. F. R. Livingston and P. Y. Poon, “Relaxation distance and equilibrium electron density measurements in hydrogen-helium plasmas,” AIAA J. 14, 1335–1337 (1976). https://doi.org/10.2514/3.61466, Google ScholarCrossref
- 12. L. P. Leibowitz and T.-J. Kuo, “Ionizational nonequilibrium heating during outer planetary entries,” AIAA J. 14, 1324–1329 (1976). https://doi.org/10.2514/3.61465, Google ScholarCrossref
- 13. J. N. Moss, “A study of the aerothermal entry environment for the Galileo probe,” in Entry Heating and Thermal Protection (AIAA, 1980), pp. 3–25. Google Scholar
- 14. J. N. Moss, J. J. Jones, and A. L. Simmonds, “Radiative flux penetration through a blown shock layer for Jupiter entry conditions,” in Outer Planet Entry Heating and Thermal Protection (AIAA, 1978), pp. 22–41. Google Scholar
- 15. J. N. Moss, A. L. Simmonds, and E. C. Anderson, “Turbulent radiating shock layers with coupled ablation injection,” J. Spacecr. Rockets 17, 177–183 (1980). https://doi.org/10.2514/3.57726, Google ScholarCrossref
- 16. J. Moss and A. Simmonds, “Galileo probe forebody flowfield predictions during Jupiter entry,” in 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference (AIAA, 1982), p. 874. Google ScholarCrossref
- 17. S. N. Tiwari and K. Y. Szema, “Effects of precursor heating on chemical and radiative nonequilibrium viscous flow around a Jovian entry body,” in (AIAA, 1978), Vol. 64. Google ScholarCrossref
- 18. S. Matsuyama, N. Ohnishi, A. Sasoh, and K. Sawada, “Numerical simulation of Galileo probe entry flowfield with radiation and ablation,” J. Thermophys. Heat Transfer 19, 28–35 (2005). https://doi.org/10.2514/1.10264, Google ScholarCrossref
- 19. S. Matsuyama, Y. Shimogonya, N. Ohnishi, K. Sawada, and A. Sasoh, “Numerical simulation of Galileo probe entry flowfield with radiation,” in 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference (AIAA, 2002). Google ScholarCrossref
- 20. C. Park, “Injection-induced turbulence in stagnation-point boundary layers,” AIAA J. 22, 219–225 (1984). https://doi.org/10.2514/3.8371, Google ScholarCrossref
- 21. M. Furudate, I.-S. Jeung, and S. Matsuyama, “Nonequilibrium calculation of flowfield over Galileo probe,” in 44th AIAA Aerospace Sciences Meeting and Exhibit (AIAA, 2006), Vol. 7. Google ScholarCrossref
- 22. C. Park, “Effect of Lymann radiation on nonequilibrium ionization of atomic hydrogen,” in 37th AIAA Thermophysics Conference (AIAA, 2004), Chap. 2277. Google ScholarCrossref
- 23. C. Park, “Stagnation-region heating environment of the Galileo probe,” J. Thermophys. Heat Transfer 23, 417–424 (2009). https://doi.org/10.2514/1.38712, Google ScholarCrossref
- 24. P. Reynier, “Numerical reconstruction of Galileo entry,” in 5th International Workshop on Radiation and High Temperature Gases in Atmospheric Entry, 2012. Google Scholar
- 25. G. D’Ammando, M. Capitelli, F. Esposito, A. Laricchiuta, L. D. Pietanza, and G. Colonna, “The role of radiative reabsorption on the electron energy distribution functions in H2/He plasma expansion through a tapered nozzle,” Phys. Plasmas 21, 093508 (2014). https://doi.org/10.1063/1.4895481, Google ScholarScitation, ISI
- 26. G. Colonna, G. D’Ammando, L. Pietanza, and M. Capitelli, “Excited-state kinetics and radiation transport in low-temperature plasmas,” Plasma Phys. Controlled Fusion 57, 014009 (2015). https://doi.org/10.1088/0741-3335/57/1/014009, Google ScholarCrossref
- 27. H. Yee, R. Warming, and A. Harten, “Implicit total variation diminishing (TVD) schemes for steady-state calculations,” J. Comput. Phys. 57, 327–360 (1985). https://doi.org/10.1016/0021-9991(85)90183-4, Google ScholarCrossref
- 28. H. Yee, “Upwind and symmetric shock-capturing schemes,” Technical Report NASA-TM-89464, NASA, 1987. Google Scholar
- 29. M. Furudate, “Nonequilibrium calculation of high-temperature radiating H2-He flowfield,” J. Thermophys. Heat Transfer 23, 651–659 (2009). https://doi.org/10.2514/1.43961, Google ScholarCrossref
- 30. J. D. Anderson, Hypersonic and High-Temperature Gas Dynamics, 2nd ed. (AIAA Education, AIAA, 2006). Google ScholarCrossref
- 31. W. G. Vincenti and C. H. Kruger, Introduction to Physical Gas Dynamics, 1st ed. (John Wiley and Sons, 1965). Google Scholar
- 32. U. Fantz and D. Wünderlich, “Franck–Condon factors, transition probabilities and radiative lifetimes for hydrogen molecules and their isotopomeres,” Technical Report INDC(NDS)-457, IAEA, 2004. Google Scholar
- 33. K.-P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979). Google ScholarCrossref
- 34. A. Kramida, Y. Ralchenko, J. Reader, and N. A. Team, “NIST atomic spectra database (version 5.5.6)” (2018), https://physics.nist.gov/asd; accessed: 10 May 2018. Google Scholar
- 35. G. Palmer, D. Prabhu, and B. A. Cruden, “Aeroheating uncertainties in Uranus and Saturn entries by the Monte Carlo method,” J. Spacecr. Rockets 51, 801–814 (2014). https://doi.org/10.2514/1.a32768, Google ScholarCrossref
- 36. F. Thivet, M. Perrin, and S. Candel, “A unified nonequilibrium model for hypersonic flows,” Phys. Fluids A 3, 2799–2812 (1991). https://doi.org/10.1063/1.858168, Google ScholarScitation, ISI
- 37. J. E. Dove and H. Teitelbaum, “The vibrational relaxation of H2. I. Experimental measurements of the rate of relaxation by H2, He, Ne, Ar, and Kr,” Chem. Phys. 6, 431–444 (1974). https://doi.org/10.1016/0301-0104(74)85027-5, Google ScholarCrossref
- 38. J. G. Kim, O. J. Kwon, and C. Park, “Master equation study and nonequilibrium chemical reactions for H + H2 and He + H2,” J. Thermophys. Heat Transfer 23, 443–453 (2009). https://doi.org/10.2514/1.41741, Google ScholarCrossref
- 39. J. Kim, O. Kwon, and C. Park, “State-to-state rate coefficients and master equation study for H2 + H2,” in (AIAA, 2009), p. 1023. Google ScholarCrossref
- 40. D. Bruno, C. Catalfamo, M. Capitelli, G. Colonna, O. De Pascale, P. Diomede, C. Gorse, A. Laricchiuta, S. Longo, D. Giordano et al., “Transport properties of high-temperature Jupiter atmosphere components,” Phys. Plasmas 17, 112315 (2010). https://doi.org/10.1063/1.3495980, Google ScholarScitation, ISI
- 41. D. Bruno, M. Capitelli, C. Catalfamo, R. Celiberto, G. Colonna, P. Diomede, D. Giordano, C. Gorse, A. Laricchiuta, S. Longo, D. Pagano, and F. Pirani, “Transport properties of high-temperature Mars-atmosphere components,” Technical Report STR-256, European Space Agency, 2008. Google Scholar
- 42. G. E. Palmer and M. J. Wright, “Comparison of methods to compute high-temperature gas viscosity,” J. Thermophys. Heat Transfer 17, 232–239 (2003). https://doi.org/10.2514/2.6756, Google ScholarCrossref
- 43. G. Palmer and M. Wright, “A comparison of methods to compute high-temperature gas thermal conductivity,” in 36th AIAA Thermophysics Conference (AIAA, 2003), p. 3913. Google ScholarCrossref
- 44. C. Wilke, “A viscosity equation for gas mixtures,” J. Chem. Phys. 18, 517–519 (1950). https://doi.org/10.1063/1.1747673, Google ScholarScitation, ISI
- 45. F. G. Blottner, M. Johnson, and M. Ellis, “Chemically reacting viscous flow program for multi-component gas mixtures,” Technical Report SC-RR-70-754, Sandia Labs., Albuquerque, New Mexico, 1971. Google ScholarCrossref
- 46. R. N. Gupta, J. M. Yos, R. A. Thompson, and K.-P. Lee, “A review of reaction rates and thermodynamic and transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations to 30000 K,” Technical Report NASA-RP-1232, NASA, 1990. Google Scholar
- 47. J. M. Yos, “Approximate equations for the viscosity and translational thermal conductivity of gas mixtures,” Technical Report AVSSD-0112-67-RM, AVCO Corporation, Wilmington, Massachusetts, 1967. Google Scholar
- 48. I. A. Sokolova, “Collision integrals for components of high-temperature hydrogen-helium mixture,” Teplofiz. Vys. Temp. 15, 734–743 (1977), original document in Russian. Google Scholar
- 49. L. Biolsi, Jr., “Transport properties in the atmosphere of Jupiter,” Technical Report NASA-CR-158094, NASA, 1978. Google Scholar
- 50. D. Bruno, C. Catalfamo, M. Capitelli, G. Colonna, P. Diomede, C. Gorse, A. Laricchiuta, S. Longo, F. Pirani et al., “Transport properties of high-temperature Jupiter-atmosphere components,” Technical Report STR-256, European Space Agency, 2008. Google Scholar
- 51. M. Capitelli, D. Cappelletti, G. Colonna, C. Gorse, A. Laricchiuta, G. Liuti, S. Longo, and F. Pirani, Chem. Phys. 338(1), 62–68 (2007). https://doi.org/10.1016/j.chemphys.2007.07.036, Google ScholarCrossref
- 52. M. J. Wright, D. Bose, G. E. Palmer, and E. Levin, “Recommended collision integrals for transport property computations. Part 1: Air species,” AIAA J. 43, 2558–2564 (2005). https://doi.org/10.2514/1.16713, Google ScholarCrossref
- 53. L. Biolsi, “Transport properties in the Jovian atmosphere,” J. Geophys. Res.: Space Phys. 83, 1125–1131, https://doi.org/10.1029/ja083ia03p01125 (1978). https://doi.org/10.1029/ja083ia03p01125, Google ScholarCrossref
- 54. B. McBride and S. Gordon, “Computer program for calculation of complex chemical equilibrium compositions and applications II. Users manual and program description,” Technical Report NASA-RP-1311, NASA, 1996. Google Scholar
- 55. C. O. Johnston, “Nonequilibrium shock-layer radiative heating for Earth and Titan entry,” Ph.D. thesis, Virginia Tech, 2006. Google Scholar
- 56. H. Griem, Spectral Line Broadening by Plasmas, 1st ed. (Elsevier, 2012). Google Scholar
- 57. A. Döhrn, P. Nowack, A. Könies, S. Günter, and V. Helbig, “Stark broadening and shift of the first two Paschen lines of hydrogen,” Phys. Rev. E 53, 6389 (1996). https://doi.org/10.1103/physreve.53.6389, Google ScholarCrossref
- 58. T. Wujec, A. Jazgara, J. Halenka, and J. Musielok, “Stark broadening of the hydrogen Paschen γ transition at electron densities of the order of cm,” Eur. Phys. J. D 23, 405–408 (2003). https://doi.org/10.1140/epjd/e2003-00084-x, Google ScholarCrossref
- 59. C. Stehlé and S. Fouquet, “Hydrogen Stark broadened Brackett lines,” Int. J. Spectrosc. 2010, 1. https://doi.org/10.1155/2010/506346, Google ScholarCrossref
- 60. K. Pachucki and J. Komasa, “Nonadiabatic corrections to rovibrational levels of H2,” J. Chem. Phys. 130, 164113 (2009). https://doi.org/10.1063/1.3114680, Google ScholarScitation, ISI
- 61. H. Abgrall, E. Roueff, F. Launay, J.-Y. Roncin, and J.-L. Subtil, “The Lyman and Werner band systems of molecular hydrogen,” J. Mol. Spectrosc. 157, 512–523 (1993). https://doi.org/10.1006/jmsp.1993.1040, Google ScholarCrossref
- 62. H. M. Crosswhite, The Hydrogen Molecule Wavelength Tables of Gerhard Heinrich Dieke (Wiley-Interscience, 1972). Google Scholar
- 63. D. Bailly, E. Salumbides, M. Vervloet, and W. Ubachs, “Accurate level energies in the , , , , C1Πu, B′, D1Πu, I1Πg, J1Δg states of H2,” Mol. Phys. 108, 827–846 (2010). https://doi.org/10.1080/00268970903413350, Google ScholarCrossref
- 64. TOPBase: Online Atomic Database (2019) http://cdsweb.u-strasbg.fr/topbase/topbase.html; accessed 10 March 2019. Google Scholar
- 65. T. Ohmura and H. Ohmura, “Electron-hydrogen scattering at low energies,” Phys. Rev. 118, 154–157 (1960). https://doi.org/10.1103/physrev.118.154, Google ScholarCrossref
- 66. A. M. Frolov, “On the absorption of radiation by the negatively charged hydrogen ion. I. General theory and construction of the wave functions,” preprint arXiv:1110.3432 (2011). Google Scholar
- 67. C. Ramsbottom and K. Bell, “Photodetachment cross sections for the 1s2s2p metastable state of the negative helium ion,” J. Phys. B: At., Mol. Opt. Phys. 32, 1315–1333 (1999). https://doi.org/10.1088/0953-4075/32/5/021, Google ScholarCrossref
- 68. J. A. R. Samson and G. N. Haddad, “Total photoabsorption cross sections of H2 from 18 to 113 eV,” J. Opt. Soc. Am. B 11, 277–279 (1994). https://doi.org/10.1364/josab.11.000277, Google ScholarCrossref
- 69. M. Yan, H. Sadeghpour, and A. Dalgarno, “Photoionization cross sections of He and H2,” Astrophys. J. 496, 1044–1050 (1998). https://doi.org/10.1086/305420, Google ScholarCrossref
- 70. M. Yan, H. Sadeghpour, and A. Dalgarno, “Erratum: Photoionization cross sections of He and H2,” Astrophys. J. 559, 1194 (2001). https://doi.org/10.1086/322775, Google ScholarCrossref
- 71. W. F. Huebner and W. D. Barfield, Opacity, Astrophysics and Space Science Library (Springer, 2014). Google Scholar
- 72. A. Heays, A. Bosman, and E. van Dishoeck, “Photodissociation and photoionisation of atoms and molecules of astrophysical interest,” Astron. Astrophys. 602, A105 (2017). https://doi.org/10.1051/0004-6361/201628742, Google ScholarCrossref
- 73. H. Abgrall, E. Roueff, and I. Drira, “Total transition probability and spontaneous radiative dissociation of B, C, B′ and D states of molecular hydrogen,” Astron. Astrophys., Suppl. Ser. 141, 297–300 (2000). https://doi.org/10.1051/aas:2000121, Google ScholarCrossref
- 74. S. Geltman, “Free-free radiation in electron-neutral atom collisions,” J. Quant. Spectrosc. Radiat. Transfer 13, 601–613 (1973). https://doi.org/10.1016/0022-4073(73)90019-8, Google ScholarCrossref
- 75. S. Chauveau, “Constitution de bases de données spectroscopiques relatives à un plasma d’air: Application au calcul de transferts radiatifs,” Ph.D. thesis, Châtenay-Malabry, Ecole centrale de Paris, 2001. Google Scholar
- 76. T. John, “Neutral bremsstrahlung from molecular hydrogen and nitrogen,” Astron. Astrophys. 67, 395–398 (1978). Google Scholar
- 77. A. M. Brandis, B. A. Cruden, T. R. White, D. A. Saunders, and C. O. Johnston, “Radiative heating on the after-body of Martian entry vehicles,” in 45th AIAA Thermophysics Conference (AIAA, 2015), p. 3111. Google ScholarCrossref
- 78. C. O. Johnston and A. M. Brandis, “Features of afterbody radiative heating for Earth entry,” in 11th AIAA/ASME Joint Thermophysics and Heat Transfer Conference (AIAA, 2014), p. 2675. Google ScholarCrossref
- 79. C. O. Johnston, “Influence of radiative absorption on non-Boltzmann modeling for Mars entry,” J. Thermophys. Heat Transfer 28, 795–799 (2014). https://doi.org/10.2514/1.t4044, Google ScholarCrossref
- 80. C. O. Johnston and A. Mazaheri, “Impact of non-tangent-slab radiative transport on flowfield-radiation coupling,” J. Spacecr. Rockets 55, 899–913 (2018). https://doi.org/10.2514/1.a34072, Google ScholarCrossref
- 81. Á. González, “Measurement of areas on a sphere using Fibonacci and latitude–longitude lattices,” Math. Geosci. 42, 49 (2010). https://doi.org/10.1007/s11004-009-9257-x, Google ScholarCrossref
- 82. G. J. Elbert and P. Cinnella, “Truly two-dimensional algorithms for radiative heat transfer calculations in reactive flows,” Comput. Fluids 24, 523–552 (1995). https://doi.org/10.1016/0045-7930(95)00008-z, Google ScholarCrossref
- 83. M. Lino Da Silva and J. Beck, “Contribution of CO2 IR radiation to Martian entries radiative wall fluxes,” in 49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (AIAA, 2011), p. 135. Google ScholarCrossref
- 84. J. Beck, P. Omaly, M. Lino da Silva, and S. Surzhikov, “Radiative heating of the exomars entry demonstrator module,” in 7th European Symposium on Aerothermodynamics, 2011. Google Scholar
- 85. C. O. Johnston, P. A. Gnoffo, and A. Mazaheri, “Influence of coupled radiation and ablation on the aerothermodynamic environment of planetary entry vehicles,” in Radiation and Gas-Surface Interaction Phenomena in High Speed Re-entry (2013); available at https://www.vki.ac.be/index.php/component/jevents/eventdetail/312/-/sto-avt-218-radiation-and-gas-surface-interaction-phenomena-in-high-speed-re-entry?Itemid=816. Google Scholar
- 86. M. Lino da Silva, “Simulation des propriétés radiatives du plasma entourant un véhicule traversant une atmosphère planétaire à vitesse hypersonique—Application à la planète Mars,” Ph.D. thesis, Université d’Orléans, 2004. Google Scholar
- 87. M. Lino da Silva, “Arrays of radiative transition probabilities for CO2–N2 plasmas,” J. Quant. Spectrosc. Radiat. Transfer 102, 348–386 (2006). https://doi.org/10.1016/j.jqsrt.2006.02.018, Google ScholarCrossref
- 88. T. Furtenbacher, I. Szabó, A. G. Császár, P. F. Bernath, S. N. Yurchenko, and J. Tennyson, “Experimental energy levels and partition function of the 12C2 molecule,” Astrophys. J., Suppl. Ser. 224, 44 (2016). https://doi.org/10.3847/0067-0049/224/2/44, Google ScholarCrossref
- 89. P. J. Bruna and F. Grein, “Spectroscopy of the C2 molecule: Valence and Rydberg states in the 7-10 eV region. An ab initio study,” Can. J. Phys. 79, 653–671 (2001). https://doi.org/10.1139/cjp-79-2-3-653, Google ScholarCrossref
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