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A non-linear theory for symmetric, supercavitating flow in a gravity field

Published online by Cambridge University Press:  28 March 2006

Charles W. Lenau  and
Robert L. Street
Charles W. Lenau
Affiliation:
University of Missouri
Robert L. Street
Affiliation:
Stanford University
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Abstract

An analysis is made of the effect of a longitudinal gravity field on two-dimensional supercavitating flow past wedges. Under the assumption that the flow is both irrotational and incompressible, a non-linear theory is developed for steady flow. By utilizing conformal mapping in combination with the Schwarz reflexion principle, the mathematical problem is reduced to a three-parameter, non-linear integral equation with one constraint. The equation is derived by reflecting the flow about the rigid boundaries; the constraint is obtained by requiring the net singularity strength inside the cavity-wedge system to be zero. A successive-approximation procedure is used to obtain a numerical solution of the integral equation. Typical results are presented in graphs and tables, and the results of the present work are compared to those of Acosta's linear theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 21 , Issue 2 , February 1965 , pp. 257 - 280
Copyright
© 1965 Cambridge University Press

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References

Acosta, A. J. 1961 The effect of a longitudinal gravity field on the supercavitating flow over a wedge. J. Appl. Mech. 28; Trans. ASME, 83, Series E, pp. 188–92.Google Scholar
Birkhoff, G. & Carter, D. 1957 Rising plane bubbles. J. Rat. Mech. Anal. 6, 6.Google Scholar
Birkhoff, G. & Zarantonello, E. 1957 Jets, Wakes, and Cavities. New York: Academic Press.
de Boor, C. 1961 Flow under a sluice gate. Report under Nonr-1866(34), Harvard University, Cambridge, Mass.
Dwight, H. B. 1961 Tables of Integrals and Other Mathematical Data, 4th ed. New York: Macmillan.
Geurst, J. A. 1961 Linearized theory of two-dimensional cavity flows. Doc. diss., Technische Hogeschool Te Delft.
Gilbarg, D. 1960 Jets and cavities, vol. IX, Encyclopedia of Physics. Berlin: Springer-Verlag.
Lenau, C. W. 1963 A nonlinear theory for supercavitating flow past a wedge in a longitudinal gravity field. Dept. of C.E. Tech. Rep. no. 28, Stanford University, Stanford, Calif.
Milne-Thompson, L. M. 1961 Theoretical Hydrodynamics, 4th ed. New York: Macmillan.
Nehari, Z. 1952 Conformal Mapping. New York: McGraw-Hill.
Parkin, B. R. 1957 A note on the cavity flow past a hydrofoil in a liquid with gravity. Engr. Div. Tech. Rep. no. 47-9, CIT, Pasadena, Calif.
Parkin, B. R. 1959 Linearized theory of cavity flow in two dimensions. RAND Corp. Rep. no. P1745, Santa Monica, Calif.
Scarborough, J. B. 1955 Numerical Mathematical Analysis. Baltimore, Md.: The Johns Hopkins Press.
Street, R. L. 1963 Supercavitating flow about a slender wedge in a transverse gravity field. J. Ship. Res. 7, 1, 14–23.Google Scholar