Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-07-04T19:35:44.501Z Has data issue: false hasContentIssue false

The hypersonic laminar boundary layer near sharp compression and expansion corners

Published online by Cambridge University Press:  29 March 2006

A. W. Bloy
Affiliation:
von Kármán Institute for Fluid Dynamics, Rhode-Saint-Genese, Belgium
M. P. Georgeff
Affiliation:
Education Department, La Troba University, Bundoora, Victoria, Australia

Abstract

The momentum integral method of Klineberg is shown to provide a good description of the major characteristics of two-dimensional laminar viscous-inviscid interactions a t hypersonic speeds. Surface pressure and heat-transfer-rate measurements were made for sharp compression and expansion corners at Mach 12.2 and are compared with the theoretical predictions. The agreement is found to be good for attached, incipient and fully separated flows.

Some theoretical comparisons between methods based on the Klineberg formulation are made which suggest that the full boundary-layer equations are well described using integral methods that incorporate the energy equation. It is further shown that the properties associated with the stability of the governing differential equations are mathematical properties of the analytical model and should not be associated with any physical characteristics of the boundary layer.

A correlation of hypersonic, cold-wall, incipient separation data is also presented.

Type
Research Article
Copyright
© 1974 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

Ball, K. O. W. & Korkegi, R. H. 1968 An investigation of the effect of suction on hypersonic laminar boundary-layer separation, A.I.A.A. J. 6, 239243.Google Scholar
Baum, E. & Denison, M. R. 1967 Interacting supersonic laminar wake calculations by a finite difference method. A.I.A.A. J. 5, 12241230Google Scholar
Bloy, A. W. 1973 Hypersonic laminar boundary layer flow over sharp compression and expansion corners. Ph.D. thesis, University of London.
Bray, K. N. C., Gadd, G. E. & Woodger, M. 1960 Some calculations by the Crocco-Lees and other methods of interactions between shock waves and laminar boundary layers, including effects of heat transfer and suction. Aero. Res. Counc. 21, 834Google Scholar
Brown, S. N. & Stewartson, K. 1969 Laminar separation. Ann. Rev. Fluid Mech. 1, 45Google Scholar
Cofien, C. B. & Reshotko, E. 1956a Similar solutions for the compressible laminar boundary layer with heat transfer and pressure gradient. N.A.C.A. Rep. no. 1293.Google Scholar
Cohen, C. B. & Roshotko, E. 1956b The compressible laminar boundary layer with heat transfer and arbitrary pressure gradient. N.A.C.A. Rep. no. 1294.Google Scholar
Crocco, L. 1955 Considerations on the shock-boundary layer interaction. Proc. Conf. on High-speed, Aeron. Polytech. Inst. Brooklyn, pp. 75112.Google Scholar
Crocco, L. & Lees, L. 1952 A mixing theory for the interaction between dissipative flows and nearly isentropic streams. J. Aero. Sci. 19, 649676.Google Scholar
Curle, N. 1961 The effects of heat transfer on laminar boundary-layer separation in supersonic flow. Aero. Quart. 12, 309330Google Scholar
van Driest, E. R. 1952 Investigation of laminar boundary layer in compressible fluids using the Crocco method. N.A.C.A. Tech. Note, no. 2597.Google Scholar
Garvine, R. W. 1968 Upstream influence in viscous interaction problems. Phys. Fluids, 11, 14131423.Google Scholar
Georgeff, M. P. 1971 On the behaviour of viscous layers in viscous interaction problems. Imperial College Aero. Rep. no. 71–17.Google Scholar
Georgeff, M. P. 1972 Hypersonic boundary layer theory. Ph.D. thesis, University of London.
Harvey, W. D. 1968 Experimental investigation of laminar flow separation on a flat plate induced by deflected trailing-edge flap at Mach 19. N.A.S.A. Tech. Note, D-4671.Google Scholar
Holden, M. S. 1965 An analytical study of separated flows induced by shock wave-boundary layer interaction. Cornell Aero. Lab. Rep. AI-1972-A-3.Google Scholar
Holden, M. S. 1967 Theoretical and experimental studies of laminar flow separation on flat plate-wedge compression surfaces in the hypersonic strong interaction regime. Cornell Aero. Lab. Rep. AF-1894-A-2.Google Scholar
Holden, M. S. 1971 Boundary layer displacement and leading edge bluntness effects on attached and separated boundary layers in a compression corner. Part 2. Experimental study. A.I.A.A. J. 9, 8493Google Scholar
Hunter, J. A. 1969 Theory and operation of the equipment used a t Imperial College to measure heat transfer rate in hypersonic flow. Imperial College, Dept. Aeron. Intern. Memo. no. 69–001.
Klineberg, J. M. 1968 Theory of laminar viscous-inviscid interactions in supersonic flow. Ph.D. thesis, California Institute of Technology. (See also A.I.A.A. J. 7 (1969), 22112221.
Lees, L. S: Reeves, B. L. 1964 Supersonic separated and re-attaching laminar flows: 1. General theory and application to adiabatic boundary-layer/shock-wave interactions. A.I.A.A. J. 2, 1907-1920.Google Scholar
Miller, D. S., Hyman, R. & Childs, M. E. 1964 Mach 8 to 22 studies of separation due to deflected control surfaces. A.I.A.A. J. 2, 312321Google Scholar
Murphy, J. D. 1969 A critical evaluation of analytic methods for predicting laminar boundary layer, shock wave interaction. N.A.S.A. Special Paper, no. 228, pp. 515539. (See also N.A.S.A. Tech. Note, D-7044 (1971).)Google Scholar
Needham, D. A. 1965 Laminar separation in hypersonic flow. Ph.D. thesis, University of London.
Reyhner, T. A. & Flugge-Lotz, I. 1966 The interaction of a shock wave with a laminar boundary layer. Intern. Tech. Rep. Div. Engng Mech., Stanford University, no. 163. (See also Int. J. Non-Linear Mech. 3 (1968), 173199.)
Richards, B. E. & Enkenhus, K. R. 1970 Hypersonic testing in the VKI Longshot free-piston tunnel. A.I.A.A. J. 8, 10201025Google Scholar
Shamroth, S. I. 1969 On integral methods for predicting shear layer behaviour. J. Appl. Mech., Trans. A.S.M.E. E36, 673681.Google Scholar
Stewartson, K. 1949 Correlated incompressible and compressible boundary layers. Proc. Roy. Soc. A 200, 84108.Google Scholar
Stewartson, K. & Williams, P. G. 1969 Self-induced separation Proc. Roy. Soc. A 312, 181206.Google Scholar
Stollery, J. L. & Hankey, W. L. 1970 Subcritical and supercritical boundary layers. A.I.A.A. J. 8, 13491351Google Scholar
Stollery, J. L., Maull, D. J. & Belcher, B. J. 1960 The Imperial College Hypersonic Gun Tunnel. J. Roy. Aero. Soc. 64, 2432Google Scholar
van Dyke, M. D. 1964 Perturbation. Methods in Fluid Mechanics. Academic.
Weinbaum, S. & Garvine, R. W. 1969 On the two-dimensional viscous counterpart of the one.dimensional sonic throat. J. Fluid Mech. 39, 5785Google Scholar