Chemical and Vibrational Non-Equilibrium Nozzle Flow Calculation by an Implicit Upwind Method

  • C. Flament
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


The equations governing chemical and vibrational non-equilibrium nozzle flows are first presented. The resulting differential system is then discretized using a fully implicit non centered finite volume approach. The method is finally applied to two different hypersonic nozzle geometries. Results are compared with equilibrium as well as with previous space marching calculations.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. Candler and R. MacCormack: “The computation of hypersonic ionized flows in chemical and thermal nonequilibrium”, AIAA-88-0511, 1988.Google Scholar
  2. [2]
    J. G. Hall and C. E. Treanor: “Nonequilibrium effects in supersonic-nozzle flows”, CAL RT No. CAL-163, 1968.Google Scholar
  3. [3]
    Ph. Sagnier and L. Marraffa: “Parametric Study of Thermal and Chemical Non Equilibrium Nozzle Flow”, AIAA-89-1856.Google Scholar
  4. [4]
    C. Flament, L. Le Toullec, L. Marraffa, Ph. Sagnier: “Inviscid Nonequilibrium Flow in ONERA F4 Wind Tunnel”, Int. Conf. on Hyp. Aerodynamics, Manchester, 4-6 Sept. 1989.Google Scholar
  5. [5]
    C. Flament: “Cinétique chimique et relaxation vibrationnelle dans une tuyère hypersonique”, ONERA Report No 10/3637 AN, 1989.Google Scholar
  6. [6]
    J-H. Lee: “Basic governing equations for the flight regimes of Aeroassisted Orbital Transfer Vehicles”, AIAA-84-1729.Google Scholar
  7. [7]
    W. C. Gardiner Jr.: “Combustion chemistry”, Springer Verlag, 1984.Google Scholar
  8. [8]
    J. L. Shinn, J. N. Moss and A. L. Simmonds: “Viscous shock layer heating analysis for the shuttle winward plane with surface finite recombination rates”, AIAA-82-0842.Google Scholar
  9. [9]
    R. C. Millikan and D. R. White: “Systematics of vibrational relaxation”, J.Chem.Phys., Vol.36, N.12, pp 3209–3213, 1963.ADSCrossRefGoogle Scholar
  10. [10]
    C. Park: “Assessment of two-temperature kinetic model for ionizing air”, AIAA-87-1574.Google Scholar
  11. [11]
    J. Hilsenrath, M. Klein: “Tables of Thermodynamic Properties of Air in Chemical Equilibrium including Second Virial Correction from 1500 to 15000K”, AEDC TR65-58, 1965.Google Scholar
  12. [12]
    H. Hollanders and C. Marmignon: “Navier-Stokes high speed flow calculations by an implicit non-centered method”, AIAA-89-0282.Google Scholar
  13. [13]
    H. C. Yee and A. Harten: “Implicit TVD Schemes for Hyperbolic Conservation Laws in Curvilinear Coordinates”, AIAA-85-1513.Google Scholar
  14. [14]
    H. C. Yee and J. L. Shinn: “Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms”, NASA-TM-89415, 1986.Google Scholar
  15. [15]
    CE. Treanor, J.W. Rich, R.G. Rehm: “Vibrational relaxation of anharmonic oscillators with exchange-dominated collisions”, J. of Ch. Phys., Vol.48, pp 1798–1807, 1967.ADSCrossRefGoogle Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • C. Flament
    • 1
  1. 1.ONERAChatillonFrance

Personalised recommendations