Summary
Entropy-layer instabilities in the supersonic flow over a blunt flat plate are investigated. Two types of entropy-layer instabilities are identified with the linear, local, parallel stability theory. The most amplified mode is a two-dimensional one. In order to validate the numerical findings experiments were carried out: The computed steady, laminar mean-flow data agree with experimentally obtained mass-flow and Pitot-pressure distributions. The wall-normal distribution of the mass-flow eigenfunction of the most amplified entropy-layer instability is found in hot-wire data. The streamwise wave number and the wall-normal phase distribution of the numerically obtained density eigenfunctions agree with a Schlieren picture.
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References
K. F. Stetson, J. C. Donaldson, L. G. Siler: Laminar boundary layer stability experiments on a cone at Mach 8, Part 2: Blunt cone. AIAA Pap. 84-0006, 1984.
P. F. Brinich: Effects of leading-edge geometry on boundary layer transition at Mach 3.1. NACA TN 3659,1956.
P. F. Brinich, N. Sands: Effects of bluntness on transition for a cone and a hollow cylinder at Mach 3.1. NACA TN 3679, 1957.
D. W. Jillie, E. J. Hopkins: Effects of Mach-number, leading-edge bluntness, and sweep on boundary-layer transition on a flat plate. NASA TN D-1071, 1961.
V. I. Lysenko: Influence of the entropy layer on the stability of a supersonic shock layer and transition of the laminar boundary layer to turbulence. J. Appl. Mech. Tech. Phys., 31(6):868–873, 1990.
W. E. Moeckel: Some effects of bluntness on boundary-layer transition and heat transfer at supersonic speeds. NACA Rep. 1312, 1957.
A. V. Fedorov: Instability of the entropy layer on a blunt plate in supersonic gas flow. J. Appl. Mech. Tech. Phys., 31(5):722–728, 1990.
E. Reshotko, M. M. S. Khan: Stability of the laminar boundary layer on a blunted plate in supersonic flow. In Laminar-Turbulent Transition, Symposium Stuttgart, Germany 1979, Proc. IUTAM, p. 186-200, 1980.
M. M. S. Khan, E. Reshotko: Stability of the laminar boundary layer on a blunted plate in supersonic flow. CWRUFTAS/TR 79-142, 1980.
E. Kufher: Entropy and boundary layer instability of hypersonic cone flows — effects of mean flow variations. In Laminar-Turbulent Transition, Symposium Sendai, Japan, Proc. IUTAM, 1994.
G. Dietz, S. Hein: Entropy-layer instabilities over a blunted flat plate in supersonic flow. Phys. of Fluids, accepted, publication scheduled in January 1999.
Y. Wada, M.-S. Liou: A flux splitting scheme with high-resolution and robustness for discontinuities. NASA TM 106452 (also AIAA 94-0083), 1994.
B. Van Leer: Towards the ultimate conservative difference scheme v. A second-order sequel to Godunov’s method. J. Comp. Phys., 32:101–136, 1979.
A. Meijering, G. Dietz, S. Hein, U. Dallmann: Numerical investigation of the boundary layer instabilities over a blunt flat plate at angle of attack in supersonic flow. DLR IB 223-96 A44, 1996.
G. Dietz, A. Meijering: Numerical investigation of boundary-layer instabilities over a blunt flat plate at angle of attack in supersonic flow. In Notes on Numerical Fluid Mechanics 60, p. 103–110, 1996.
S. Hein, F.P. Bertolotti, M. Simen, A. Hanifi, D. Henningson: Linear nonlocal instability analysis-the linear NOLOT code-. DLR IB 223-94 A56, 1994.
M. Jacobs: Wärmeübergangsmessungen am Modell eines Deltaflügels in supersonischer Strömung. Diss. Aerodyn. Inst. RWTH-Aachen (DLR FB 97-44), 1997.
P. G. Drazin, W. H. Reid: Hydrodynamic Stability. Cambridge University Press, 1997.
D. C. Hill: Adjoint systems and their role in the receptivity problem for boundary layers. J. Fluid Mech., 292:183–204, 1995.
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© 1999 Springer Fachmedien Wiesbaden
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Dietz, G., Mählmann, S., Hein, S. (1999). Entropy-Layer Instabilities in Plane Supersonic Flow. In: Nitsche, W., Heinemann, HJ., Hilbig, R. (eds) New Results in Numerical and Experimental Fluid Mechanics II. Notes on Numerical Fluid Mechanics (NNFM), vol 72. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-10901-3_15
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DOI: https://doi.org/10.1007/978-3-663-10901-3_15
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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