Summary
The hypersonic flow condition is defined as the flow condition towards which the flow pattern tends as the free stream Mach number tends to infinity. Similarity laws for this region were first derived by Tsien. In the present report a different approach involving the shock wave equations is used. It is found that the pressure coefficients and lift forces are obtained, for hypersonic speeds, independent of the free stream Mach number and in the case of slender bodies, proportional to the square of the thickness ratio, in both plane and three dimensional flow. The lift of lifting surfaces is in the main proportional to the square of the angle of attack. A discussion of the importance of the Tsien similarity parameter is given.
A paper on the same subject will be published in ZAMP (see also [7])
Reprinted from KTH-AERO TN 16 (1950) with permission.
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References
H. Tsien, Similarity laws of hypersonic flows. Journal of Mathematics and Physics. Vol. XXV (1946) pp. 247–251.
S. V. Falkowich, Two-dimensional motions of a gas at large supersonic velocities. NACA TM 1239.
W. D. Hayes, On hypersonic similitude. Quarterly of Applied Mathematics. Vol. V (1947) pp. 105–106.
S. F. Shen, Hypersonic flow over a slender cone. Journal of Mathematics and Physics. Vol. XXVII (1948) pp. 56–66.
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W. Hantzsche and H. Wendt, Mit Überschallgeschwindigkeit angeblasene Kegelspitzen. Jahrbuch 1942 der deutschen Luftfahrtforschung. S. I. 80–90.
K. Oswatitsch, Ähnlichkeitsgesetze für Hyperschallströmung. (To be published in ZAMP).
R. D. Linnell, Two-dimensional airfoils in hypersonic flow. Journal of Aeronautical Science. January 1949, pp. 22–30.
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© 1980 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH Braunschweig
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Oswatitsch, K. (1980). Similarity Laws for Hypersonic Flow. In: Schneider, W., Platzer, M. (eds) Contributions to the Development of Gasdynamics. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-91082-0_8
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DOI: https://doi.org/10.1007/978-3-322-91082-0_8
Publisher Name: Vieweg+Teubner Verlag
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