Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T14:35:52.587Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Calculations of the Hypersonic Viscid–Inviscid Flow Inside Simple Ducts of Circular Cross-Section

Published online by Cambridge University Press:  07 June 2016

B. H. K. Lee
B. H. K. Lee*
Affiliation:
National Aeronautical Establishment, Ottawa, Canada
Get access

Summary

The method of characteristics and an implicit finite-difference scheme are used to investigate the interaction between the internal flow field and laminar boundary layer in ducts of circular cross-section under the conditions of high Mach number and low Reynolds number. The displacement thickness is added on to the body to form a new “effective body shape” which is used to re-calculate the inviscid flow. Iterations are performed and a solution is obtained when the surface pressures in two consecutive iterations converge to within a specified tolerance. The calculated surface pressures on a 10 degree conical duct placed in a hypersonic stream at M∞=8·34, Re∞=7·5 × 106 and M∞=10·4, Re∞=4·625 × 106 with γ=1·4 show good agreement with experiments. The results are computed for constant wall temperature, using a value of Tw/Tstag=0·23, and the Prandtl number is assumed to be constant and equal to 0·7 throughout the calculations. The type of shock-wave interaction near the axis of symmetry is determined and the computation terminates after the fluid properties behind the reflected shock have been calculated.

Type
Research Article
Information
Aeronautical Quarterly , Volume 22 , Issue 3 , August 1971 , pp. 233 - 256
Copyright
Copyright © Royal Aeronautical Society. 1971

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

1. Moretti, G. and Bastianon, R. Three-dimensional effects in intakes and nozzles. AIAA Paper 67-224, 1967.CrossRefGoogle Scholar
2. Hayes, W. D. and Probstein, R. F. Hypersonic flow theory. Academic Press, New York, 1959.Google Scholar
3. Lee, B. H. K. The initial phases of collapse of an imploding shock wave and the application to hypersonic internal flows. Canadian Aeronautics and Space Institute, CASI Transactions, Vol. 1, No. 2, pp. 57-67, 1968.Google Scholar
4. Lee, B. H. K. A modified shock layer theory for hypersonic internal flows. Canadian Aeronautics and Space Institute, CASI Transactions, Vol. 2, No. 2, pp. 67-74, 1969.Google Scholar
5. Hartree, D. R. Some practical methods of using characteristics in the calculations of non-steady compressible flow. US Atomic Energy Commission Report AECU-2713, 1953.Google Scholar
6. Katskova, O. N. and Chushkin, P. I. Three-dimensional supersonic equilibrium flow of a gas around bodies at angle of attack. NASA TTF-9790, Dec. 1965. Translation of “Trekhmernoye sverkhzvukovoye ravnovesnoye techeniye gaza okalo til pod uglom ataki” Zhurnal Vychislitel’ noy Mathematiki i Mathematicheskoy Fiziki, Vol. 5, No. 3, pp. 503-518, May-June 1965.Google Scholar
7. Blottner, F. G. and Flugge-Lotz, I. Finite difference computation of the boundary layer with displacement thickness interaction. Journal de Mécanique, Vol. II, No. 4, pp. 397-423, Dec. 1963.Google Scholar
8. Sells, C. C. L. Two-dimensional laminar compressible boundary layer programme for a perfect gas. RAE Technical Report 66 243, Sept. 1966.Google Scholar
9. Smith, A. M. O. and Clutter, D. W. Machine calculation of compressible laminar boundary layers. AIAA Journal, Vol. 3, No. 4, pp. 639-647, 1965.Google Scholar
10. von Neumann, J. Oblique reflection of shocks, John von Neumann collected works, Vol. VI, pp. 238-299, Macmillan, New York, 1963.Google Scholar
11. AMES RESEARCH STAFF. Equations, tables, and charts for compressible flow. NACA Report 1135, 1953.Google Scholar
12. Yasuhara, M. Axisymmetric viscous flow past very slender bodies of revolution. Journal of the Aerospace Sciences, Vol. 29, No. 6, pp. 667-688, June 1962.Google Scholar
13. Ames, W. F. Non-linear partial differential equations in engineering. Mathematics in Science and Engineering, Vol. 18, Academic Press, New York, 1965.Google Scholar
14. Rainbird, W. J. Errors in measurement of mean static pressure of a moving fluid due to pressure holes. National Research Council of Canada, DME/NAE Quarterly Bulletin, No. 1967 (3), 1967.Google Scholar