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Two-dimensional subsonic and sonic flow past thin bodies

Published online by Cambridge University Press:  28 March 2006

J. B. Helliwell  and
A. G. Mackie
J. B. Helliwell
Affiliation:
The Royal College of Science and Technology, Glasgow
A. G. Mackie
Affiliation:
St. Salvator's College, University of St. Andrews
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Abstract

Hodograph methods are applied to determine the flow at high subsonic and sonic velocities past two-dimensional, thin, symmetrical bodies. The boundary value problem for the determination of the stream function Ψ, which in the present theory is a solution of Tricomi's equation, is simplified by the assumption of a free stream breakaway at sonic velocity from the shoulder of the body. A solution is obtained in terms of Bessel functions.

In § 2 and 3 the flow past a wedge of small angle is discussed and expressions are obtained for the pressure on the nose, the drag coefficient and the width of the wake. A comparison with the corresponding results in the case of sonic velocity derived by the more complex analysis of Guderley & Yoshihara (1950) shows that the present simpler theory yields very similar values for the pressure over the nose.

In § 4 the flow at sonic velocity past a profile which is a first-order perturbation upon a wedge profile is analysed on the basis of the same free streamline theory. The flow pattern is obtained past an arbitrarily specified body by an application of the Hankel inversion theorem and an expression is deduced for the drag.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 1 , October 1957 , pp. 93 - 109
Copyright
© 1957 Cambridge University Press

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References

Cole, J. D. 1951 J. Math. Phys. 30, 79.
Guderley, G. & Yoshihara, H. 1950 J. Aero. Sci. 17, 723.
Imai, I. 1952 J. Aero. Sci. 19, 496.
Lighthill, M. J. 1947 Proc. Roy. Soc. A, 191, 352.
Mackie, A. G. & Pack, D. C. 1955 J. Rat. Mech. Anal. 4, 177.
Roshko, A. 1954 Nat. Adv. Comm. Aero., Wash., Tech. Note no. 3168.