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Symmetrical flow past a double wedge at high subsonic Mach numbers

Published online by Cambridge University Press:  12 April 2006

Jean-Jacques Chattot
Jean-Jacques Chattot
Affiliation:
Office Nationale d'Etudes et de Recherches Aérospatiales, 92320 Chatillon, France
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Abstract

Symmetrical flow past a double wedge is studied for a high subsonic Mach number. The main features of the flow field are discussed in the physical and the hodograph plane. It is shown how a regular solution to the hodograph equation exhibits limit lines in the physical plane, which are eliminated through a ‘cut’ corresponding to the shock wave. In the case of the wedge it is assumed that the shock which is likely to be the most stable is the weakest possible.

The boundary-value problem is solved in the hodograph plane using Telenin's method, which has proved to be successful when dealing with equations of mixed type. The bounded analytic solution which is thus constructed is regular in the hodograph plane but presents three folds in the physical plane.

The computation is carried out for flow past a 4·5° half-angle wedge at a Mach number M∞ = 0·89. These figures are chosen so that the problem may be justifiably treated by potential theory, the entropy gradient behind the shock being negligible. In this case the mapping of the solution into the physical plane gives the pressure distribution along the double wedge, the sonic line and the shock wave. Of particular interest is the point where the sonic line meets the shock. This configuration is in agreement with the hypothesis of Nocilla, according to which the shock terminates in the supersonic domain. Experimental evidence cannot be obtained, however, because of the lack of resolution in this region.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 1 , 15 May 1978 , pp. 161 - 177
Copyright
© 1978 Cambridge University Press

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References

Bryson, A. E. 1952 An experimental investigation of transonic flow past two-dimensional wedge and circular-arc sections using a Mach–Zehnder interferometer. N.A.C.A. Rep. no. 1094.Google Scholar
Cole, D. 1951 Drag of a finite wedge at high subsonic speeds. J. Math. Phys. 30, 79–93.Google Scholar
Ferrari, C. & Tricomi, F. 1968 Transonic Aerodynamics. Academic Press.
Germain, P. 1962 Problèmes mathématiques posés par l'application de la méthode de l'hodographe à l’étude des écoulements transsoniques. Symp. Transsonicum, IUTAM Symp. Aachen, vol. 2. Sitzung, p. 24.
Gilinskii, S. M., Telenin, G. F. & Tinyakov, G. P. 1964 A method for computing supersonic flow around blunt bodies, accompanied by a detached shock wave. Izv. Akad. Nauk SSSR Mekh. i Math. 4, 9–28. (See also N.A.S.A. Trans. TT F-297.)Google Scholar
Holt, M. & Ndefo, D. E. 1970 A numerical method for calculating steady unsymmetrical supersonic flows past cones. J. Comp. Phys. 5.Google Scholar
Lighthill, M. J. 1953 The hodograph transformation. In Modern Developments in Fluid Dynamics – High Speed Flow (ed. Howarth L.), vol. 1, chap. 7, pp. 222–266. Oxford University Press.
Nocilla, S. 1957 Flussi transonici attorno a profili alari simmetrici con onda d'urto attaccata (M 1). Atti. Accad. Sci. Torino, Classe Sci. Fis. Mat. Nat. 92, 282–307.Google Scholar
Nocilla, S. 1958 Flussi transonici attorno a profili alari simmetrici con onda d'urto attaccata (M 1). II. Atti. Accad. Sci. Torino, Classe Sci. Fis. Mat. Nat. 93, 124–148.Google Scholar