Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-29T12:51:26.538Z Has data issue: false hasContentIssue false

A numerical simulation of the rarefied hypersonic flat-plate problem

Published online by Cambridge University Press:  11 April 2006

D. I. Pullin
Affiliation:
Department of Aeronautics, Imperial College, London
J. K. Harvey
Affiliation:
Department of Aeronautics, Imperial College, London

Abstract

The direct-simulation Monte-Carlo method for the full Boltzmann equation is applied to the problem of rarefied hypersonic flow of rotationally excited N2 past the leading edge of a two-dimensional flat plate aligned with the free stream. An approximate collision model representing rotational–translational energy exchanges is developed for use in the calculations. The effects of this and other inelastic collision models and of the single-parameter Maxwell gas–surface interaction law on the flow in the kinetic/transition regime are discussed.

Type
Research Article
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bird, G. A. 1970a Numerical simulation of the Boltzmann equation. Preprint Dept. Aero. Engng, Univ. Sydney.
Bird, G. A. 1970b Direct simulation of the Boltzmann equation Phys. Fluids, 13, 2676.Google Scholar
Borgnakke, C. & Larsen, P. S. 1973 Statistical collision model for Monte-Carlo simulation of polyatomic gas. Dept. Fluid Mech., Tech. Univ. Denmark, Lyngby Rep. AFM 73–08 (June 1973).Google Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn.Cambridge University Press.
Hamel, B. B. & Cooper, A. L. 1969 A first collision theory of the hyperthermal leading edge problem. In Rarefied Gas Dynamics (ed. Trilling & Wachman), suppl. 5?, vol. 1, p. 443. Academic.
Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. 1954 Molecular Theory of Gases and Liquids. Wiley.
Huang, A. B., Hwang, P. F., Giddens, D. P. & Strinivanan, R. 1972 High speed leading edge problem. School Aerospace Engng, Georgia Inst. Tech., Atlanta Preprint, no. 30332.
Kuhlthau, A. R. & Bishara, M. N. 1965 On the nature of the surface interaction between inert gas molecules and engineering surfaces. In Rarefied Gas Dynamics (ed. E de Leeuw), suppl. 3, vol. 2, p. 518. Academic.
KušČEr, I. 1974 Phenomenology of gas—surface accommodation. In Rarefied Gas Dynamics 9th Symp., vol. 2 (ed. Becker & Fiebig), paper E 1. Potz-Wahn: DFVLR Press.
Larsen, P. S. & Borgnakke, C. 1974 Statistical collision model for simulating polyatomic gas with restricted energy exchange. In Rarefied Gas Dynamics, 9th Symp., vol. 1 (ed. Becker & Fiebig), paper A 7. Potz-Wahn: DFVLR Press.
Lewis, J. H. 1971 An experimentally determined model for the noncontinuum flow at the leading edge in a high speed ratio stream. Dept. Aerospace Mech. Sci., Princeton Univ., Rep. no. 954.Google Scholar
Lordi, J. A. & Mates, R. E. 1970 Rotational relaxation in nonpolar diatomic gases Phys. Fluids, 13, 291.Google Scholar
Macpherson, A. K. 1971 Rotational temperature profiles of shock waves in diatomic gases J. Fluid Mech. 49, 337.Google Scholar
Parker, J. G. 1959 Rotational and vibrational relaxation in diatomic gases Phys. Fluids, 2, 449.Google Scholar
Pullin, D. I., Harvey, J. K. & Bienkowski, G. K. 1974 Hypersonic leading edge flow of a diatomic gas by the direct simulation method. In Rarefied Gas Dynamics, 9th Symp., vol. 1 (ed. Becker & Fiebig), paper D 5. Potz-Wahn: DFVLR Press.
Tannehill, J. C., Mohling, R. A. & Rakich, J. V. 1973 Numerical computation of the hypersonic rarefied flow near the sharp leading edge of a flat plate. A.I.A.A. Paper, no. 73–200.
Vogenitz, F. W., Broadwell, J. E. & Bird, G. A. 1969 Leading edge flow by the Monte-Carlo direct simulation technique. A.I.A.A. Paper, no. 69–141.