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On the lengthscales of laminar shock/boundary-layer interaction

Published online by Cambridge University Press:  26 April 2006

Edgar Katzer
Affiliation:
Institute of Theoretical Fluid Mechanics, DLR-AVA, Bunsenstr. 10, D-3400 Göttingen, FRG Present address: Institute for Informatics and Applied Mathematics, Christian-Albrechts University, D-2300 Kiel, Fedral Republic of Germany.

Abstract

The interaction of an oblique shock with a laminar boundary layer on an adiabatic flat plate is analysed by solving the Navier-Stokes equations numerically. Mach numbers range from 1.4 to 3.4 and Reynolds numbers range from 105 to 6 × 105. The numerical results agree well with experiments. The pressure distribution at the edge of the boundary layer is proposed as a sensitive indicator of the numerical resolution. Local and global properties of the interaction region are discussed. In the vicinity of the separation point, local scaling laws of the free interaction are confirmed. For the length of the separation bubble a new similarity law reveals a linear influence of the shock strength. A comparison with the triple-deck theory shows that, for finite Reynolds numbers, the triple deck tends to overestimate the lengthscale substantially and that this discrepancy increases with increasing Mach number. The triple-deck model of displacing the main part of the boundary layer is substantiated by the numerical results. An asymmetrical structure within the separation bubble causes a characteristic distribution of the wall shear stress.

Type
Research Article
Copyright
© 1989 Cambridge University Press

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References

Ackeret, J., Feldmann, F. & Rott, N. 1946 Untersuchungen an Verdichtungsstöβen und Grenzschichten in schnell bewegten Gasen. Mitt. Inst. f. Aerodynamik, ETH Zürich, Nr. 10. (English transl.: NACA TM 1113, 1947.)Google Scholar
Adamson, T. C. & Messiter, A. F. 1980 Analysis of two-dimensional interactions between shock waves and boundary layers. Ann. Rev. Fluid Mech. 12, 103138.Google Scholar
Beam, R. M. & Warming, R. F. 1978 An implicit factored scheme for the compressible Navier-Stokes equations. AIAA J. 16, 393402.Google Scholar
Bodonyi, R. J. & Smith, F. T. 1986 Shock-wave laminar boundary layer interaction in supercritical transonic flow. Computers & Fluids 14, 97108.Google Scholar
Brown, S. N. & Williams, P. G. 1975 Self-induced separation, III. J. Inst. Maths. Applics. 16, 175191.Google Scholar
Burggraf, O. R. 1975 Asymptotic theory of separation and reattachment of a laminar boundary layer on a compression ramp. AGARD-CP 168.Google Scholar
Burrggraf, O. R., Rizzetta, D. Ph., Werle, M. J. & Vatsa, V. N. 1979 Effect of Reynolds number on laminar separation of a supersonic stream. AIAA J. 17, 336343.Google Scholar
Carter, J. E. 1972 Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner. NASA TR R-385.Google Scholar
Cebeci, T., Keller, H. B. & Williams, P. G. 1979 Separating boundary-layer flow calculations. J. Comput. Phys. 31, 363378.Google Scholar
Chapman, D. R., Kuehn, D. M. & Larson, H. K. 1958 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. NACA Rep. 1356.Google Scholar
Degrez, G., Boccadoro, C. H. & Wendt, J. F. 1987 The interaction of an oblique shock wave with a laminar boundary layer revisited. An experimental and numerical study. J. Fluid Mech. 177, 247263.Google Scholar
Deiwert, G. S. 1975 Numerical simulation of high Reynolds number transonic flows. AIAA J. 13, 13541359.Google Scholar
Delery, J. & Marvin, J. G. 1986 Shock-wave boundary layer interactions. AGARDograph AG-280.Google Scholar
Greber, I., Hakkinen, R. J. & Trilling, L. 1958 Laminar boundary layer oblique shock wave interaction on flat and curved plates. Z. Angew. Math. Phys. 9b, 312331.Google Scholar
Haase, W., Wagner, B. & Jameson, A. 1984 Development of a Navier-Stokes method based on a finite volume technique for the unsteady Euler equations. Fifth GAMM-Conf. on Numerical Methods in Fluid Dynamics, Rome 1983, Proceedings: Notes on Numerical Fluid Mechanics 7, pp. 99107. Vieweg.
Hakkinen, R. J., Greber, I., Trilling, L. & Abarbanel, S. S. 1959 The interaction of an oblique shock wave with a laminar boundary layer. NASA Memo 2-18-59W.Google Scholar
Hankey, W. L. & Holden, M. S. 1975 Two-dimensional shock wave boundary layer interactions in high speed flows. AGARDograph AG-203.Google Scholar
Katzer, E. 1985 Numerische Untersuchung der laminaren Stoβ-Grenzschicht-Wechselwirkung. DFVLR-FB 85-34. (English transl: ESA-TT-958, 1986.)Google Scholar
Kluwick, A. 1979 Stationäre, laminare wechselwirkende Reibungsschichten. Z. Flugwiss. Weltraumforschung 3, 157174.Google Scholar
Le Balleur, J. C., Peyret, R. & Viviand, H. 1980 Numerical studies in high Reynolds number aerodynamics. Computers Fluids 8, 130.Google Scholar
Li, C. P. 1976 A mixed explicit-implicit splitting method for the compressible Navier-Stokes Equations. Proc. Fifth Intl Conf. on Numerical Methods in Fluid Dynamics, Enschede 1976, Lecture Notes in Physics, vol. 59, pp. 285292. Springer.
Liepmann, H. W. 1946 The interaction between boundary layer and shock waves in transonic flow. J. Aeronaut. Sci. 13, 623637.Google Scholar
Liepmann, H. W., Roshko, A. & Dhawan, S. 1952 On reflection of shock waves from boundary layers. NACA Rep. 1100.Google Scholar
MacCormack, R. W. 1969 The effect of viscosity in hypervelocity impact cratering. AIAA Paper 69-354.Google Scholar
MacCormack, R. W. 1971 Numerical solution of the interaction of a shock wave with a laminar boundary layer. Proc. Second Intl. Conf. on Numerical Methods in Fluid Dynamics, Berkely 1970, Lecture Notes in Physics, vol. 8, pp. 151163. Springer.
MacCormack, R. W. 1982 A numerical method for solving the equations of compressible viscous flow. AIAA J. 20, 12751281.Google Scholar
MacCormack, R. W. & Baldwin, B. S. 1975 A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions. AIAA Paper 75-1.Google Scholar
Messina, N. A. 1977 A computational investigation of shock waves, laminar boundary layers and their mutual interaction. Ph.D. thesis Department of Aerospace and Mechanical Science, School of Engineering and Applied Science, Princeton University.
Neiland, V. Ya. 1971 Flow behind the boundary layer separation point in a supersonic stream. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 3, 1921. (English transl.)Google Scholar
Oswatitsch, K. & Wieghardt, K. 1942 Theoretische Untersuchungen über stationäre Potentialströmungen und Grenzchichten bei hohen Geschwindigkeiten. Lilienthal-Bericht S13/1, pp. 724. (English transl.: NACA TM 1189, 1948.)Google Scholar
Reyhner, T. A. & Flügge-Lotz, I. 1968 The interaction of a shock wave with a laminar boundary layer. Intl. J. Non-Linear Mech. 3, 173199.Google Scholar
Rizzetta, P. D. Burggraf, O. R. & Jenson, R. 1978 Triple-deck solutions for viscous supersonic and hypersonic flow past corners. J. Fluid Mech. 89, 535552.Google Scholar
Skoglund, V. J. & Gay, B. D. 1969 Improved numerical techniques and solution of a separated interaction of an oblique shock wave and a laminar boundary layer. University of New Mexico, Bueau of Engineering Research, Rep. ME-41 (69) S-068.Google Scholar
Stanewsky, E. 1973 Shock-boundary layer interaction in transonic and supersonic flow. Von Kármán Inst. for Fluid Dynamics, Lecture Series 59.Google Scholar
Stewartson, K. 1974 Multistructured boundary layers on flat plates and related bodies. Adv. Appl. Mech. 14, 145239.Google Scholar
Stewartson, K. 1981 D'Alembert's Paradox. SIAM Rev. 23, 308343.Google Scholar
Stewartson, K. & Williams, P. G. 1969 Self-induced separation.. Proc. R. Soc. Lond. A 312, 181206.Google Scholar
Stewartson, K. & Williams, P. G. 1973 On self-induced separation II. Mathematika 20, 98108.Google Scholar
Wagner, B. & Schmidt, W. 1978 Theoretische Untersuchungen zur Stoβ-Grenzschicht-Wechselwirkung in kryogenem Stickstoff. Z. Flugwiss. Weltraum. 2, 8188.Google Scholar
Williams, P. G. 1974 A reverse flow computation in the theory of self-induced separation. Proc. Fourth Intl Conf. on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics, vol. 35, pp. 445451. Springer.