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Depression of an infinite liquid surface by an incompressible gas jet

Published online by Cambridge University Press:  28 March 2006

W. E. Olmstead  and
S. Raynor
W. E. Olmstead
Affiliation:
Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Illinois
S. Raynor
Affiliation:
Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Illinois
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Abstract

The problem of small angle depressions in a liquid surface due to an impinging two-dimensional potential jet is considered. Using conformal mapping methods and finite Hilbert transforms, the problem is formulated as a non-linear singular integral equation. The integral equation is approximated by a set of non-linear algebraic equations which are solved numerically by a method of repeated linear corrections. In addition, an asymptotic solution (for low jet velocity) is derived.

From the numerical solutions of the integral equation, the liquid-surface profiles and the free streamlines of the jet are calculated for four cases. These results verify the appearance of lips on the liquid surface which have been observed experimentally by others.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 4 , August 1964 , pp. 561 - 576
Copyright
© 1964 Cambridge University Press

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References

Banks, R. B. & Chandrasekhara, D. V. 1963 J. Fluid Mech. 10, 13.
Birkhoff, G. 1956 Los Alamos Sci. Lab. Report LA-1927.
Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes and Cavities, p. 130. New York: Academic Press.
Milne-Thomson, L. M. 1960 Theoretical Hydrodynamics, p. 291. London: Macmillan.
Muskhelishvilli, N. I. 1953 Singular Integral Equations, p. 376. Gronigen: P. Noordhoff N. V.
Tricomi, F. G. 1957 Integral Equations, p. 173. New York: Interscience.