Published Online: 15 October 2019
Accepted: September 2019
Physics of Fluids 31, 106104 (2019); https://doi.org/10.1063/1.5115264
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%.
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.
  1. 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. 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. 3. J. O. Arnold, “Planetary entry probes 1953–2036: A technologist’s perspective,” in 10th International Planetary Probe Workshop, 2013. Google Scholar
  4. 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. 5. M. Lino da Silva, B. Lopez, and S. Espinho, SPARTAN 2.6 User’s Manual, 2016. Google Scholar
  6. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 28. H. Yee, “Upwind and symmetric shock-capturing schemes,” Technical Report NASA-TM-89464, NASA, 1987. Google Scholar
  29. 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. 30. J. D. Anderson, Hypersonic and High-Temperature Gas Dynamics, 2nd ed. (AIAA Education, AIAA, 2006). Google ScholarCrossref
  31. 31. W. G. Vincenti and C. H. Kruger, Introduction to Physical Gas Dynamics, 1st ed. (John Wiley and Sons, 1965). Google Scholar
  32. 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. 33. K.-P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979). Google ScholarCrossref
  34. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 49. L. Biolsi, Jr., “Transport properties in the atmosphere of Jupiter,” Technical Report NASA-CR-158094, NASA, 1978. Google Scholar
  50. 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. 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. 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. 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. 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. 55. C. O. Johnston, “Nonequilibrium shock-layer radiative heating for Earth and Titan entry,” Ph.D. thesis, Virginia Tech, 2006. Google Scholar
  56. 56. H. Griem, Spectral Line Broadening by Plasmas, 1st ed. (Elsevier, 2012). Google Scholar
  57. 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. 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. 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. 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. 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. 62. H. M. Crosswhite, The Hydrogen Molecule Wavelength Tables of Gerhard Heinrich Dieke (Wiley-Interscience, 1972). Google Scholar
  63. 63. D. Bailly, E. Salumbides, M. Vervloet, and W. Ubachs, “Accurate level energies in the EF1Σg+, GK1Σg+, H1Σg+, B1Σu+, C1Πu, B′  1Σu+, D1Πu, I1Πg, J1Δg states of H2,” Mol. Phys. 108, 827–846 (2010). https://doi.org/10.1080/00268970903413350, Google ScholarCrossref
  64. 64. TOPBase: Online Atomic Database (2019) http://cdsweb.u-strasbg.fr/topbase/topbase.html; accessed 10 March 2019. Google Scholar
  65. 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. 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. 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. 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. 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. 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. 71. W. F. Huebner and W. D. Barfield, Opacity, Astrophysics and Space Science Library (Springer, 2014). Google Scholar
  72. 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. 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. 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. 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. 76. T. John, “Neutral bremsstrahlung from molecular hydrogen and nitrogen,” Astron. Astrophys. 67, 395–398 (1978). Google Scholar
  77. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
  90. Published under license by AIP Publishing.