Physico-chemical State of the Air at the Stagnation Point during the Atmospheric Reentry of a Spacecraft
Hypersonic flows around spatial vehicles during their
reentry phase in planetary atmospheres are characterized by intense
aerothermal phenomena. The aim of this work is to analyze high
temperature flows around an axisymmetric blunt body taking into
account chemical and vibrational non-equilibrium for air mixture
species. For this purpose, a finite volume methodology is employed
to determine the supersonic flow parameters around the axisymmetric
blunt body, especially at the stagnation point and along the wall of
spacecraft for several altitudes. This allows the capture shock wave
before a blunt body placed in supersonic free stream. The numerical
technique uses the Flux Vector Splitting method of Van Leer. Here,
adequate time stepping parameter, along with CFL coefficient and
mesh size level are selected to ensure numerical convergence, sought
with an order of 10-8
[1] B. Van Leer, "Flux Vector Splitting for the Euler Equations," Lecture
Notes in Physics. 170, (1982), 507-512.
[2] R. Haoui, A. Gahmousse, D. Zeitoun, " Condition of convergence
applied to an axisymmetric reactive flow (Condition de convergence
appliquée ├á un écoulement réactif axisymétrique)," 16th CFM, n┬░738,
Nice, France, 2003.
[3] R. Haoui, A. Gahmousse, D. Zeitoun, " Chemical and vibrational
nonequilibrium flow in a hypersonic axisymmetric nozzle(Ecoulement
hors d-équilibre chimique et vibrationnel dans une tuyère hypersonique
axisymétrique), " International Journal of Thermal Sciences, article n┬░ 8
, volume 40, (2001), pp787-795.
[4] Goudjo, J.A. Désidéri, " a finite volume scheme to resolution an
axisymmetric Euler equations (Un schéma de volumes finis décentré
pour la résolution des équations d-Euler en axisymétrique), " Research
report INRIA 1005, 1989.
[5] L. Landau, E. Teller, "Theory of sound dispersion," Physikalische
Zeitschrift der Sowjetunion. 10, (1936), 34-43.
[6] Blackman, "Vibrational relaxation in Oxygen and Nitrogen,"
Technical Report, Palmer phys. Laboratory, Princeton University, 1955.
[7] K.L.Wray, "Shock tube study of the vibrational relaxation of Nitric
Oxide," Journal of Chemical Physics. 36 (10) (1962) 2597-2603.
[8] W.C. Gardiner, "Combustion chemistry," Springer Verlag, New-
York, 1984.
[9] S.H. Lee, "Electron impact vibrational excitation in the flow field of
aero assisted orbital transfer vehicles," Progress in Astronautics and
Aeronautics, Thermophysical aspects of re-entry flows. 103 (1986) 197-
224.
[10] J.H. Kiefer, R.W. Lutz, "The effect of Oxygen atoms on the vibrational
relaxation of Oxygen," 11th Symposium on combustion. Pittsburg, 1967,
pp 67-74.
[11] W.D. Breshears, P.F. Bird, "Effects of Oxygen atoms on the vibrational
relaxation of Nitrogen," The journal of chemical physics, 48 (10) (1968).
[12] F. Thivet, " Modeling of nonequilibrium of vibration in reactive flow
(Modélisation du déséquilibre vibrationnel dans un écoulement réactif),"
Management report, laboratory of molecular and macroscopic
10nergetic, combustion, CNRS/ECP, September-December 1989.
[13] Y. Burtschell, " Performances, dimensioning and numerical simulation
of a hypersonic shock tunnel with reflected shock of free piston
(Performances, dimensionnement et simulation numérique d-une
soufflerie hypersonique ├á choc réfléchi ├á piston libre)," thesis of
Doctorate, university of Aix-Marseilles I, France, 1990.
[14] M-C. Druguet, "Contribution to the study of nonequilibrium reactive
hypersonic Euler-s flows (Contribution ├á l-étude des écoulements
eulériens hypersoniques en déséquilibre thermochimique)," Thesis of
Doctorate. University of Provence, France, 1992.
[15] R. Haoui, "Finite volumes analysis of a supersonic non-equilibrium flow
around the axisymmetric blunt body," International Journal of
Aeronautical and space Sciences, 11(2), (2010), pp59-68.
[1] B. Van Leer, "Flux Vector Splitting for the Euler Equations," Lecture
Notes in Physics. 170, (1982), 507-512.
[2] R. Haoui, A. Gahmousse, D. Zeitoun, " Condition of convergence
applied to an axisymmetric reactive flow (Condition de convergence
appliquée ├á un écoulement réactif axisymétrique)," 16th CFM, n┬░738,
Nice, France, 2003.
[3] R. Haoui, A. Gahmousse, D. Zeitoun, " Chemical and vibrational
nonequilibrium flow in a hypersonic axisymmetric nozzle(Ecoulement
hors d-équilibre chimique et vibrationnel dans une tuyère hypersonique
axisymétrique), " International Journal of Thermal Sciences, article n┬░ 8
, volume 40, (2001), pp787-795.
[4] Goudjo, J.A. Désidéri, " a finite volume scheme to resolution an
axisymmetric Euler equations (Un schéma de volumes finis décentré
pour la résolution des équations d-Euler en axisymétrique), " Research
report INRIA 1005, 1989.
[5] L. Landau, E. Teller, "Theory of sound dispersion," Physikalische
Zeitschrift der Sowjetunion. 10, (1936), 34-43.
[6] Blackman, "Vibrational relaxation in Oxygen and Nitrogen,"
Technical Report, Palmer phys. Laboratory, Princeton University, 1955.
[7] K.L.Wray, "Shock tube study of the vibrational relaxation of Nitric
Oxide," Journal of Chemical Physics. 36 (10) (1962) 2597-2603.
[8] W.C. Gardiner, "Combustion chemistry," Springer Verlag, New-
York, 1984.
[9] S.H. Lee, "Electron impact vibrational excitation in the flow field of
aero assisted orbital transfer vehicles," Progress in Astronautics and
Aeronautics, Thermophysical aspects of re-entry flows. 103 (1986) 197-
224.
[10] J.H. Kiefer, R.W. Lutz, "The effect of Oxygen atoms on the vibrational
relaxation of Oxygen," 11th Symposium on combustion. Pittsburg, 1967,
pp 67-74.
[11] W.D. Breshears, P.F. Bird, "Effects of Oxygen atoms on the vibrational
relaxation of Nitrogen," The journal of chemical physics, 48 (10) (1968).
[12] F. Thivet, " Modeling of nonequilibrium of vibration in reactive flow
(Modélisation du déséquilibre vibrationnel dans un écoulement réactif),"
Management report, laboratory of molecular and macroscopic
10nergetic, combustion, CNRS/ECP, September-December 1989.
[13] Y. Burtschell, " Performances, dimensioning and numerical simulation
of a hypersonic shock tunnel with reflected shock of free piston
(Performances, dimensionnement et simulation numérique d-une
soufflerie hypersonique ├á choc réfléchi ├á piston libre)," thesis of
Doctorate, university of Aix-Marseilles I, France, 1990.
[14] M-C. Druguet, "Contribution to the study of nonequilibrium reactive
hypersonic Euler-s flows (Contribution ├á l-étude des écoulements
eulériens hypersoniques en déséquilibre thermochimique)," Thesis of
Doctorate. University of Provence, France, 1992.
[15] R. Haoui, "Finite volumes analysis of a supersonic non-equilibrium flow
around the axisymmetric blunt body," International Journal of
Aeronautical and space Sciences, 11(2), (2010), pp59-68.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59065", author = "Rabah Haoui", title = "Physico-chemical State of the Air at the Stagnation Point during the Atmospheric Reentry of a Spacecraft", abstract = "Hypersonic flows around spatial vehicles during their
reentry phase in planetary atmospheres are characterized by intense
aerothermal phenomena. The aim of this work is to analyze high
temperature flows around an axisymmetric blunt body taking into
account chemical and vibrational non-equilibrium for air mixture
species. For this purpose, a finite volume methodology is employed
to determine the supersonic flow parameters around the axisymmetric
blunt body, especially at the stagnation point and along the wall of
spacecraft for several altitudes. This allows the capture shock wave
before a blunt body placed in supersonic free stream. The numerical
technique uses the Flux Vector Splitting method of Van Leer. Here,
adequate time stepping parameter, along with CFL coefficient and
mesh size level are selected to ensure numerical convergence, sought
with an order of 10-8", keywords = "Chemical kinetic, dissociation, finite volumes,frozen, hypersonic flow, non-equilibrium, Reactive flow, supersonicflow , vibration.", volume = "4", number = "9", pages = "1278-10", }
