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Solution of the wedge entry problem by numerical conformal mapping

Published online by Cambridge University Press:  29 March 2006

O. F. Hughes
Affiliation:
School of Mechanical and Industrial Engineering, The University of New South Wales

Abstract

An accurate quasi-analytic method of solution is presented for the classical hydrodynamics problem of the constant-velocity entry of a prismatic wedge into a weightless incompressible inviscid fluid. The method uses the Wagner function W, which reduces the problem to the determination of a mapping function Λ = [Lscr ](W) for the hodograph. [Lscr ](W) is constructed by using the hodograph for an unsymmetric diamond together with a modifying or ‘preparatory’ trans-formation. A computer method of conformal mapping is developed and is used to obtain this latter transformation. Results are presented for the case of a 90° wedge and show that the solution is both more accurate than previous solutions, having an error of less than 1 %, and more complete, as it portrays the entire flow field and furnishes information about the functional dependence among the variables.

Type
Research Article
Copyright
© 1972 Cambridge University Press

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References

Bisplinghoff, R. L. & Doherty, C. S. 1952 Some studies of the impact of vee wedges on a water surface. J. Franklin Int. 253, 547.Google Scholar
Borg, S. F. 1957 Some contributions to the wedge-water entry problem. J. Eng. Mech. Div., A.S.C.E. 93, Paper no. 1214.Google Scholar
Dobrovolskaya, Z. N. 1963 Investigation of the motion of an incompressible fluid. Appl. Math. Mech. 27, 1377.Google Scholar
Dobrovolskaya, Z. N. 1964 Sow. Phys. Dokl. 8, 1179.
Dobrovolskaya, Z. N. 1969 J. Fluid Mech. 36, 805.
Fabula, A. G. 1957 Ellipse-fitting approximation of impact of rigid bodies on water. Proc. 5th Mid-western Conf. on Fluid Mech. p. 299.Google Scholar
Garabedian, P. R. 1953 Oblique water entry of a wedge. Comm. Pure Appl. Math. 6, 157Google Scholar
Garabedian, P. R. 1965 Proc. Symp. on Appl. Math. 17.
Gurevich, M. I. 1965 Theory of Jets in Ideal Fluids, p. 435. Academic.
Hughes, O. F. 1971 Wedge penetration of a free surface. School Mech. Indust. Eng., University of New South Wales Rep. 1971/NA/2.Google Scholar
Man, K. H. 1957 Studies of some problems about unsteady fluid motion. Ph.D. thesis, Moscow State University.
Milne-Thomson, L. M. 1938 Theoretical Hydrodynamics. Macmillan.
Pierson, J. P. 1950 Penetration of a fluid surface by a wedge. Stevens Inst. Tech. ETT Rep. no. 381.Google Scholar
Shiffman, M. & Spencer, D. C. 1951 The force of impact on a cone striking a water surface. Comm. Pure Appl. Math. 4, 379.Google Scholar
Wagner, H. 1932 Über Stoss Gleitvorgange an der Oberflache von Flussigkeiten. Z. angrew. Math. Mech. 12, 193.Google Scholar