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Inviscid–viscous interaction on triple-deck scales in a hypersonic flow with strong wall cooling

Published online by Cambridge University Press:  26 April 2006

S. N. Brown ,
H. K. Cheng  and
C. J. Lee
S. N. Brown
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
H. K. Cheng
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089–1191, USA
C. J. Lee
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089–1191, USA
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Abstract

Inviscid–viscous interaction in a high supersonic flow is studied on the triple-deck scales to delineate the wall-temperature influence on the flow structure in a region near a laminar separation. A critical wall-temperature range O(Tw*) is identified, in which the pressure–displacement relation governing the lower deck departs from that of the classical (Stewartson, Messiter, Neiland) formulation, and below which the pressure–displacement relation undergoes still greater changes along with drastic scale changes in the triple deck. The reduced lower-deck problem falls into three domains: (i) supercritical (Tw* [Lt ] Tw), (ii) transcritical (Tw = O(Tw*)) and (iii) subcritical (Tw [Lt ] Tw*). Readily identified is a parameter domain overlapping with the Newtonian triple-deck theory of Brown, Stewartson & Williams (1975), even though the assumption of a specific-heat ratio approaching unity is not required here. Computational study of the compressive free-interaction solutions and solutions for a sharp-corner ramp are made for the three wall-temperature ranges. Finite-difference equations for primitive variables are solved by iterations, employing Newton linearization and a large-band matrix solver. Also treated in the program is the sharp-corner effect through the introduction of proper jump conditions. Comparison with existing numerical results in the supercritical Tw range reveals a smaller separation bubble and a more pronounced corner behaviour in the present numerical solution. Unlike an earlier comparison with solutions by interactive-boundary-layer methods for ramp-induced pressure with separation, the IBL results do approach closely the triple-deck solution at Re = 108 in a Mach-three flow, and the differences at Re = 106 may be attributed in part to the transcritical temperature effect. Examination of the numerical solutions indicates that separation and reattachment on a compressive ramp cannot be effectively eliminated/delayed by lowering the wall temperature, but lowering Tw drastically reduces the triple-deck dimension, and hence the degree of upstream influence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 220 , November 1990 , pp. 309 - 337
Copyright
© 1990 Cambridge University Press

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References

Bogdonoff, S. M. & Hammitt, A. G., 1956 J. Aero Sci. 23, 108.
Brown, S. N., Cheng, H. K. & Lee, C. J., 1989 University of Southern California Dept. Aerospace Eng. Rep. USCAE 148. (Superceeding a paper of the same title in the Proc. Conf. Prediction and Exploitation of Separated Flows, Roy. Aero. Soc. London, April 18–20, 1989.)
Brown, S. N. & Stewartson, K., 1975 Q. J. Mech. Appl. Maths 28, 75.
Brown, S. N., Stewartson, K. & Williams, P. G., 1975 Phys. Fluids 18, 633.
Cheng, H. K., Hall, G. J., Golian, T. & Hertzberg, A., 1961 J. Aero. Sci. 28, 353.
Gajjar, J. & Smith, F. T., 1983 Mathematika 30, 77.
Hayes, W. D. & Probstein, R. F., 1959 Hypersonic Flow Theory. Academic.
Jenson, R.: 1977 Ph.D. dissertation, the Ohio State University.
Kluwick, A.: 1987 Z. Angew. Math. Mech. 67, 4.
Lighthill, M. J.: 1953 Proc. R. Soc. Lond. A 217, 478.
Messiter, A.: 1979 Proc. 8th US Natl Appl. Mech. Congr., Los Angeles, Ca, USA.
Moore, F. K.: 1964 The Theory of Laminar Flow (ed. F. K. Moore), p. 439. Princeton University Press.
Neiland, V. Ya., 1969 Izv. Mekh Zhid Gaza 4, 40.
Neiland, V. Ya., 1970 Akad. Nauk. SSSR 3, 19.
Rizzetta, D. P., Burggraf, O. R. & Jenson, R., 1978 J. Fluid Mech. 89, 535.
Smith, F. T.: 1982 IMA J. Appl. Maths 82, 207.
Smith, F. T.: 1986 Ann. Rev. Fluid Mech. 18, 197.
Smith, F. T. & Stewartson, K., 1973 J. Fluid Mech. 58, 143.
Stewartson, K.: 1955 J. Aero Sci. 22, 303; also see Theory of Laminar Boundary Layer in Compressible Fluids. Oxford University Press (1964).
Stewartson, K.: 1974 Adv. Appl. Mech. 14, 146.
Stewartson, K.: 1981 SIAM Rev. 23, 308.
Stewartson, K. & Williams, P. G., 1969 Proc. R. Soc. Lond. A 312, 181.
Stewartson, K. & Williams, P. G., 1973 Mathematica 20, 98.
Sychev, V. V.: 1974 Izv. Akad. Nauk. SSSR, Mekh. Zhid. Gaza 3, 47; translated in Fluid Mechanics. Plenum Press (1974).
Sychev, V. V.: 1987 Asymptotic Theory of Separated Flow (in Russian), Moscow Science Pub. Physico-Math. Literature. (Distributed by USSR Nat. Comm. Theor. Appl. Mech.)
Werle, M. J., Dwoyer, D. L. & Hankey, W. L., 1973 AIAA J. 11, 525.
Werle, M. J. & Vatsa, V. N., 1974 AIAA J. 12, 1491.
Williams, P. G.: 1965 Proc. 4th Intl Conf. Num. Methods in Fluid Dyn. Lecture Notes in Physics, vol. 35, p. 445. Springer.