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Reverse flow and supersonic interference

Published online by Cambridge University Press:  28 March 2006

Joseph H. Clarke
Joseph H. Clarke
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island
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Abstract

First, from a volumetric formulation of the momentum theorem of linearized theory, a general analytic proof is presented of the invariance of the drag of an arbitrary spatial distribution of horseshoe vortices and sources under reversal of the undisturbed flow. By consideration of the interference drag of two such singularity distributions, a reverse-flow relation for steady subsonic or supersonic flow is then obtained. This relation, a generalization of the Ursell-Ward theorem, may be applied to configurations with bodies whose surfaces are not quasi-cylindrical and whose surface pressures are quadratically related to the perturbation velocity.

The relation is used to discuss several interfering two-body arrangements in supersonic flow. It is shown that, in certain cases, the drag and lift may be determined without knowledge of the interference flow field associated with the arbitrarily prescribed body geometry. The simplicity of the results permits the formulation of optimum problems. The invariance of the drag under flow reversal with unchanged geometry is also established.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 6 , Issue 2 , August 1959 , pp. 272 - 288
Copyright
© 1959 Cambridge University Press

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References

Friedman, M. D. & Cohen, D. 1954 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 3345.
Graham, M. E. 1955 Douglas Aircraft Company, Rep. no. SM-19258.
Graham, E. W., Lagerstrom, P. A., Licher, R. M. & Beane, B. J. 1957 Nat. Adv. Comm. Aero., Wash., Tech. Mem. no. 421.
Hayes, W. D. 1947 North American Aviation, Rep. no. AL-222.
Heaslet, M. A. & Lomax, H. 1954 High Speed Aerodynamics and Jet Propulsion. Vol. VI, Sec. D, p. 122. Princeton University Press.
Heaslet, M. A. & Spreiter, J. R. 1953 Nat. Adv. Comm. Aero., Wash., Rep. no. 1119.
Jones, R. T. 1951 J. Aero. Sci. 18, 75.
Jones, R. T. 1956 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 3530.
Kármán, T. Von 1947 J. Aero. Sci. 14, 373.
Kármán, T. Von & Moore, N. B. 1932 Trans. Amer. Soc. Mech. Engin. 54, 303.
Lawrence, H. R. & Flax, A. H. 1954 J. Aero. Sci. 21, 289.
Licher, R. M. 1955 Douglas Aircraft Company, Rep. no. SM-19257.
Lighthill, M. J. 1945 Rep. Mem. Aero. Res. Counc., Lond., no. 2003.
Lighthill, M. J. 1948 Quart. J. Mech. Appl. Math. 1, 90.
Lighthill, M. J. 1954 High Speed Aerodynamics and Jet Propulsion. Vol. VI, Sec. E, p. 345. Princeton University Press.
Lomax, H. 1955 Nat. Adv. Comm. Aero., Wash., Res. Mem. no. A 55 A 18.
Lomax, H. & Heaslet, M. A. 1956a Nat. Adv. Comm. Aero., Wash., Rep. no. 1282.
Lomax, H. & Heaslet, M. A. 1956b J. Aero. Sci. 23, 1061.
Lomax, H., Heaslet, M. A. & Fulier, F. B. 1951 Nat. Adv. Comm. Aero., Wash., Rep. no. 1054.
Ursell, F. & Ward, G. N. 1950 Quart. J. Mech. Appl. Math. 3, 326.
Ward, G. N. 1949 Quart. J. Mech. Appl. Math. 2, 75.
Ward, G. N. 1952a Quart. J. Mech. Appl. Math. 5, 432.
Ward, G. N. 1952b Quart. J. Mech. Appl. Math. 5, 441.
Ward, G. N. 1955a Linearized Theory of Steady High-Speed Flow. Cambridge University Press.
Ward, G. N. 1955b The College of Aeronautics, Cranfield. Report 88.