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The Wave Formation and Sonic Boom due to a Delta Wing

Published online by Cambridge University Press:  07 June 2016

K Oswatitsch
Affiliation:
DFVLR-Institut für Theoretische Gasdynamik, Aachen
Y C Sun
Affiliation:
DFVLR-Institut für Theoretische Gasdynamik, Aachen
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Summary

By employment of the analytical method of characteristics and of a limiting procedure suitable for dealing with the trailing edge expansion, the influence of near-field flow on the far-field wave formation has been investigated for an incident flat delta wing with supersonic leading edges. Though confined in its scope to the front shock in the vertical plane of symmetry of the wing and to a homogeneous atmosphere without density and temperature gradients, the present analysis reveals features of flow which are interesting from the standpoint of the general theory of three-dimensional supersonic flow. It is found that the front shock due to a delta wing will as a rule be cancelled at a finite distance from the wing by the plane-wave expansion emanating from the trailing edge. The over-expansion must then give rise to a rear shock separate from the front one. Thus, at least in the plane of symmetry, a sharp-front wave signature can not, in general, be expected from the wing at a distance beyond the terminating point of the front shock. The boom signature then will be qualitatively different from that of a body of revolution. The general non-equivalence of a wing to a body of revolution in this respect should evoke some rethinking about sonic boom prediction and alleviation.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1972

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References

1. Whitham, G B The flow pattern of a supersonic projectile. Communications in Pure and Applied Mathematics, Vol 5, pp 301-349, 1952.CrossRefGoogle Scholar
2. Whitham, G B On the propagation of weak shock waves. Journal of Fluid Mechanics, Vol 1, pp 290-318, 1956.CrossRefGoogle Scholar
3. Walkden, F The shock pattern of a wing-body combination, far from the flight path. Aeronautical Quarterly, Vol IX, pp 164-194, May 1958.CrossRefGoogle Scholar
4. Oswatitsch, K Sun, Y C The influence of near-field flow on the sonic boom. ICAS Preprint 70-20, 1970.Google Scholar
5. Oswatitsch, K Das Ausbreiten von Wellen endlicher Amplitude. Zeitschrift fúr Flugwissenschaften, pp 130-138, 1962.Google Scholar
6. Oswatitsch, K Die Wellenausbreitung in der Ebene bei kleinen Störungen. Archiwum Mechaniki Stosowanej (Warsaw), Vol 14, pp 621-637, 1962.Google Scholar
7. Oswatitsch, K Analytische Berechnung von Charakteristikenflächen bei Strömungsvorgängen. Deutsche Luft- und Raumfahrt Forschungsbericht DLR FB 65-62, 1965.Google Scholar
8. Lin, C C On a perturbation theory based on the method of characteristics. Journal of Mathematics and Physics, Vol 33, pp 117-134, 1954.CrossRefGoogle Scholar
9. Schneider, W Analytische Berechnung achsensymmetrischer Überschallströmungen mit Stössen. DVL-Bericht 275, 1963.Google Scholar
10. Rothmann, H Analytische Unterordnung der Ausbreitung von Kugel- und Zylinderwellen. DVL-Bericht 280, 1963.Google Scholar
11. Sun, E Y C Nichtangestellte Deltaflügel mit Unterschall• und Schallvorderkanten. Journal de Mécanique, Vol 3, 2, pp 141-163, 1964.Google Scholar
12. Leiter, E Ein Beitrag zur Charakteristiken-Theorie der instationären ebenen und achsen- symmetrischen Strömungen (Parts I & II). Zeitschrift für Angewandte Mathematik und Mechanik, Vol 47, 3-4, pp 175-190 and 229-237, 1967.CrossRefGoogle Scholar
13. Pokorny, W Analytische Berechnung von ebenen Überschallfreistrahlen. Deutsche Luft- und Raumfahrt Forschungsbericht DLR FB 68-63, 1968.Google Scholar
14. Stuff, R Die vertikale Ausbreitung von ebenen Stosswellen in einer schweregeschichteten Atmosphäre mit einem Temperaturgradienten. Zeitschrift für Flugwissenchaften, Vol 18, 2/3, pp 80-83, 1970.Google Scholar
15. Sun, Y C Die Kopfwelle an einem nichtangestellten Deltaflügel in stationärer Überschall- strömung beim Übergang von Unterschall- zu Überschallvorderkanten. Journal de Méchaniaue, Vol 7, 4, pp 521-573, 1968.Google Scholar
16. Leiter, E Stationäre Expansionsströmungen an räumlichen Überschallkanten. Acta Mechanica, Vol 8, 3-4, pp 235-254, 1969.CrossRefGoogle Scholar
17. George, A R Van Moorhem, W K The accuracy of Landau-Whitham shock strength rule in some near field situations. NASA SP-255: 3rd Conference on Sonic Boom Research, pp 373-384, 1971.Google Scholar