Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T16:01:56.677Z Has data issue: false hasContentIssue false
  • English
  • Français

Inviscid radiating flow over a blunt body

Published online by Cambridge University Press:  28 March 2006

Ping Cheng  and
Walter G. Vincenti
Ping Cheng
Affiliation:
Now at Department of Aeronautics and Astronautics, New York University, Bronx, New York. Department of Aeronautics and Astronautics, Stanford University, Stanford, California
Walter G. Vincenti
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, California
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of thermal radiation is investigated for the axisymmetric flow over the blunt body associated with a given paraboloidal shock wave. Radiative transfer is treated by means of the differential approximation, which applies to multidimensional flow and is valid throughout the entire range of temperature and optical thickness. The gas is assumed to be perfect and optically grey, and molecular-transport processes are neglected. A semi-analytical solution for the flow and radiation fields is obtained by the method of series truncation.

Results are presented, in the strong-shock approximation, for various values of the appropriate dimensionless variables. In general, radiation is found to have a significant influence on temperature and density, moderate effect on velocity, and little effect on pressure. The stand-off distance between the shock wave and the body is found to decrease significantly with increasing radiation; the body shape is less affected. The anomalous behaviour of the gas temperature on the body streamline as obtained by earlier investigators in the optically thin case does not appear in the present work. The results thus show correct physical behaviour throughout the flow field for all values of optical thickness. The detailed flow quantities exhibit a number of features of multidimensional radiating flow. They also provide a check on the special assumptions made in other, more approximate treatments. Similarities between radiating flow and non-equilibrium reactive flow over blunt bodies are apparent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 27 , Issue 4 , 20 March 1967 , pp. 625 - 646
Copyright
© 1967 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

Cheng, P. 1964 Two-dimensional radiating gas flow by a moment method AIAA J. 2, 1662.Google Scholar
Cheng, P. 1965 Study of the flow of a radiating gas by a differential approximation. Ph.D. Dissertation, Stanford University.
Cheng, P. 1966 Dynamics of a radiating gas with application to flow over a wavy wall AIAA J. 4, 238.Google Scholar
Chernyi, G. G. 1961 Introduction to Hypersonic Flow. Academic Press.
Conti, R. J. 1966 A theoretical study of non-equilibrium blunt-body flows J. Fluid Mech. 24, 65.Google Scholar
Freeman, N. C. 1956 On the theory of hypersonic flow past plane and axially symmetric bluff bodies J. Fluid Mech. 1, 366.Google Scholar
Goulard, R. 1964 Preliminary estimates of radiative transfer effects on detached shock layers AIAA J. 2, 494.Google Scholar
Howe, J. T. & Viegas, J. R. 1964 Solutions of the ionized radiating shock layer, including reabsorption and foreign species effects, and stagnation region heat transfer. NASA Tech. Rept. R-159.Google Scholar
Kao, H. C. 1964 Hypersonic viscous flow near the stagnation streamline of a blunt body: I. A test of local similarity. AIAA J. 2, 1892.CrossRefGoogle Scholar
Lick, W. 1960 Inviscid flow of a reacting mixture of gases around a blunt body J. Fluid Mech. 7, 128.Google Scholar
Maslen, S. H. & Moeckel, W. E. 1957 Inviscid hypersonic flow past blunt bodies J. Aero. Sci. 24, 683.Google Scholar
Olstad, W. B. 1965 Stagnation-point solutions for an inviscid radiating shock layer. 1965. Heat Tr. and Fl. Mech. Inst., p. 138. Stanford University Press.
Ostrowski, A. M. 1960 Solution of Equations and Systems of Equations. Academic Press.
Swigart, R. J. 1963 A theory of asymmetric hypersonic blunt-body flows AIAA J. 1, 1034.Google Scholar
Thomas, P. D. 1965 Transparency assumption in hypersonic radiative gasdynamics AIAA J. 3, 1401.Google Scholar
Traugott, S. C. 1963 A differential approximation for radiative transfer with application to normal shock structure. 1963 Heat Tr. and Fl. Mech. Inst., p. 1. Stanford University Press.
Van Dyke, M. D. 1958 The supersonic blunt-body problem—review and extension J. Aero. Sci. 25, 485.Google Scholar
Van Dyke, M. D. 1965 Hypersonic flow behind a paraboloidal shock wave J. de MÉcanique, 4, 477.Google Scholar
Vincenti, W. G. & Kruger, C. H. 1965 Introduction to Physical Gas Dynamics. John Wiley and Sons.
Wang, K. C. 1964 The ‘piston problem’ with thermal radiation. J. Fluid Mech. 20, 447.Google Scholar
Wang, K. C. 1965 Radiating shock layers. Martin Co. Rept. RR-67.Google Scholar
Wang, K. C. 1966 Radiating and absorbing steady flow over symmetric bodies. Symposium on the Interdisciplinary Aspects of Radiative Transfer, Philadelphia, 24 to 26 Feb. 1966, to be published. (Also Martin Co. Rept. RR-73.)
Wilson, K. H. & Hoshizaki, H. 1965 Inviscid, nonadiabatic flow about blunt bodies AIAA J. 3, 67.Google Scholar
Yoshikawa, K. K. & Chapman, D. R. 1962 Radiative heat transfer and absorption behind a hypersonic normal shock wave. NASA TN D-1424.Google Scholar