Numerical rebuilding of two trajectory points ( ?s and ?s) of the Fire II mission has been carried out to predict the radiative heat flux for nonequilibrium and close-to-equilibrium conditions. The simulations have been performed with eilmer3 in an uncoupled way and using a tangent slab method for the radiation transport. Different population models (QSS and Boltzmann) have been compared, and the influence of catalytic wall condition was taken into account. An analysis on the spectral range and on the spectral resolution has also been carried out. 1. Introduction During atmospheric (re)entries, planetary probes encounter high heat fluxes due to their significant speed (up to 11?km/s for an Earth reentry). Such excessive thermal loads can damage the on-board equipment and compromise the safety of the passengers in case of a manned-flight mission. As a consequence, the sizing of the thermal protection system (TPS) is a crucial step in the preliminary design study of a probe. The Fire II mission took place in May 22nd, 1965 [1]. Its main goal was the assessment of the radiative heating environment during an Earth reentry. The vehicle geometry was an Apollo type with a reentry velocity of 11.4?km/s. The fore body consisted in a three layer configuration formed by phenolic-asbestos heat-shield sandwiched between beryllium calorimeters. The contribution from the radiation of the hot plasma to the total heat flux received by the probe was up to 40%. This paper concentrates on this radiative contribution. The reconstruction of radiation spectra for the Fire II experiment has been already discussed in numerous papers [2–4]. Two points of the trajectory of the Fire II mission have been numerically rebuilt. The first one at ?s corresponds to nonequilibrium conditions whereas the second one at ?s is close to equilibrium conditions, even if a small region behind the shock is nonequilibrium. Figure 1 gives the temperature profiles of the translational-rotational temperature and the vibrational-electronic temperature for the two simulations. Figure 1: Temperature profiles on the stagnation line for the two trajectory points. In this work, the code retained for the simulations is eilmer3, a multiblock compressible Navier-Stokes solver described in Section 2. Section 3 is dedicated to the results of the simulations. An analysis of the spectral range has been performed to assess the wavelength range of interest and the number of points needed for a good accuracy. Then two different population models (QSS and Boltzmann) have been compared and the influence of the
References
[1]
D. L. Cauchon, “Radiative heating results from the FIRE II flight experiment at a re-entry velocity of 11. km/s,” Tech. Rep. TM X-1402, NASA, 1967.
[2]
C. O. Johnston and B. R. Hollis, “Nonequilibrium stagnation-line radiative heating for Fire II,” Journal of Spacecraft and Rockets, vol. 45, no. 6, pp. 1185–1195, 2008.
[3]
D. R. Olynick, W. D. Henline, L. H. Chambers, and G. V. Candler, “Comparison of coupled radiative flow solutions with project fire II flight data,” Journal of Thermophysics and Heat Transfer, vol. 9, no. 4, pp. 586–594, 1995.
[4]
R. B. Greendyke and L. C. Hartung, “Convective and radiative heat transfer analysis for the fire II forebody,” Journal of Spacecraft and Rockets, vol. 31, no. 6, pp. 986–992, 1994.
[5]
P. A. Jacobs, “MB CNS: a computer program for the simulation of transient compressible flows; 1998 update,” Tech. Rep. 7/98, Department of Mechanical Engineering, The University of Queensland, Brisbane, Australia, 1998.
[6]
D. Potter, S. Karl, and P. Leyland, “TN032—EPFL Contribution to ESA-TRP AMOD,” Tech. Rep., ESA, 2009.
[7]
R. J. Gollan, Computational modelling of high-temperature gas effects with application to hyper-sonic flows, Ph.D. thesis, School of Engineering, The University of Queensland, June 2008.
[8]
M. N. Macrossan, “The equilibrium flux method for the calculation of flows with non-equilibrium chemical reactions,” Journal of Computational Physics, vol. 80, no. 1, pp. 204–231, 1989.
[9]
Y. Wada and M. S. Liou, “A flux splitting scheme with high-resolution and robustness for discontinuities,” Tech. Rep. 94-0083, AIAA, January 1994.
[10]
P. A. Gnoffo, R. N. Gupta, J. L. Shinn, and United States, “Conservation equations andphysical models for hypersonic air flows in thermal and chemical equilibrium,” Tech. Rep. TP-2867, NASA, 1989, Book, microform.
[11]
B. J. McBride and S. Gordon, “Computer program for calculation of complex chemical equilibrium compositions and applications, part 2: users manual and program description,” Tech. Rep. 1311, NASA, 1996.
[12]
R. N. Gupta, J. M. Yos, R. A. Thompson, and K. Lee, “A review of reaction rates and thermodynamicand transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations to 30000?K,” Tech. Rep., NASA STI/Recon, August 1990.
[13]
M. J. Wright and E. Levin, “Collision integrals for ion-neutral interactions of air and argon,” Journal of Thermophysics and Heat Transfer, vol. 19, no. 1, pp. 127–128, 2005.
[14]
M. J. Wright, D. Bose, G. E. Palmer, and E. Levin, “Recommended collision integrals for transport property computations, part 1: air species,” AIAA Journal, vol. 43, no. 12, pp. 2558–2564, 2005.
[15]
M. J. Wright, H. H. Hwang, and D. W. Schwenke, “Recommended collision integrals for transport property computations part 2: mars and venus entries,” AIAA Journal, vol. 45, no. 1, pp. 281–288, 2007.
[16]
NIST Chemical Kinetics Database, Ver. 7.0, 2003.
[17]
S. Chauveau, M. Y. Perrin, P. Rivière, and A. Soufiani, “Contributions of diatomic molecular electronic systems to heated air radiation,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 72, no. 4, pp. 503–530, 2002.
[18]
Y. Babou, P. Riviere, M. Y. Perrin, and A. Soufiani, “High-temperature and non equilibrium partition function and thermodynamic data of diatomic molecules,” International Journal of Thermophysics, vol. 30, pp. 416–438, 2009.
[19]
C. Johnston, Nonequilibrium shock-layer radiative heating for Earth and Titan entry, Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, Va, USA, 2006.
[20]
S.-Y. Hyun, Radiation code SPRADIAN07 and its applications, Ph.D. thesis, School of Mechanical, Aerospace and Systems Engineering, Division of Aerospace Engineering, KAIST, Daejeon, Korea, 2009.
[21]
R. M. Frost, P. Awakowicz, H. P. Summers, and N. R. Badnell, “Calculated cross sections and measured rate coefficients for electron-impact excitation of neutral and singly ionized nitrogen,” Journal of Applied Physics, vol. 84, no. 6, pp. 2989–3003, 1998.
[22]
M. Gryziński, “Classical theory of electronic and ionic inelastic collisions,” Physical Review, vol. 115, no. 2, pp. 374–383, 1959.
[23]
W. H. Soon and J. A. Kunc, “Thermal nonequilibrium in partially ionized atomic oxygen,” Physical Review A, vol. 41, no. 2, pp. 825–843, 1990.
[24]
M. Panesi, Physical models for nonequilibrium plasma flow simulations at high speed re-entry conditions, Ph.D. thesis, von Karman Institute for Fluid Dynamics, Rhode-Saint-Genèse, Belgium, 2009.
[25]
O. Zatsarinny and S. S. Tayal, “Electron collisional excitation rates for O I using the B-spline R-matrix approach,” Astrophysical Journal, Supplement Series, vol. 148, no. 2, pp. 575–582, 2003.
[26]
M. Lino da Silva, V. Guerra, and J. Loureiro, “Two-temperature models for nitrogen dissociation,” Chemical Physics, vol. 342, no. 1–3, pp. 275–287, 2007.
[27]
C. Park, “Review of chemical-kinetic problems of future NASA missions, I: earth entries,” Journal of Thermophysics and Heat Transfer, vol. 7, no. 3, pp. 385–398, 1993.
[28]
R. C. Millikan and D. R. White, “Systematics of vibrational relaxation,” The Journal of Chemical Physics, vol. 39, no. 12, pp. 3209–3213, 1963.
[29]
J. P. Appleton and K. N. C. Bray, “The conservation equations for a nonequilibrium plasma,” Journal of Fluid Mechanics, vol. 20, no. 4, pp. 659–672, 1964.
[30]
M. F. Modest, Radiative Heat Transfer, Academic Press, London, UK, 2nd edition, 2003.
[31]
G. E. Palmer, T. White, and A. Pace, “Direct coupling of the NEQAIR radiation and DPLR computational fluid dynamic codes,” Journal of Spacecraft and Rockets, vol. 48, pp. 836–845, 2011.