×

Nonlinear problem of flat-plate entry into an incompressible liquid. (English) Zbl 1151.76382

Summary: The self-similar flow and free-surface shape induced by a flat plate entering an inviscid and incompressible liquid are investigated for arbitrary initial conditions. An analytical solution, which is based on two governing expressions, namely the complex velocity and the derivative of the complex potential, is obtained. These expressions are derived in an auxiliary parameter plane using integral formulae proposed for the determination of an analytical function from its modulus and argument given on the boundary of the parameter region. We derive a system of an integral and an integro-differential equation in terms of the velocity modulus and the velocity angle at the free surface, which are determined by the dynamic and kinematic boundary conditions. A numerical procedure for solving these equations is carefully validated by comparisons with results available in the literature. The results are presented in terms of the free surface shape, the angles at the tip of the splash jet, the contact angles at the intersection with the plate surface, pressure distribution and force coefficients. New features caused by the flow unsteadiness are found and discussed.

MSC:

76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1017/S0022112005007329 · Zbl 1082.76013
[2] DOI: 10.1002/zamm.19320120402 · Zbl 0005.12601
[3] DOI: 10.1017/S002211200600276X · Zbl 1111.76008
[4] DOI: 10.1017/S0022112007004983 · Zbl 1116.76013
[5] Gurevich, Theory of Jets in Ideal Fluids (1965)
[6] DOI: 10.1016/S0141-1187(98)00034-0
[7] Green, Proc. Camb. Phil. Soc. 31 pp 589– (1935)
[8] DOI: 10.1063/1.1714667 · Zbl 1186.76242
[9] DOI: 10.1023/B:engi.0000018157.35269.a2 · Zbl 1041.76503
[10] DOI: 10.1023/B:engi.0000018156.40420.50 · Zbl 1041.76504
[11] DOI: 10.1023/B:engi.0000018188.68304.ae · Zbl 1041.76502
[12] DOI: 10.1017/S0022112091001076 · Zbl 0717.76021
[13] Faltinsen, Hydrodynamics of High-speed Marine Vehicles pp 454– (2005)
[14] DOI: 10.1017/S0022112069001996 · Zbl 0175.51402
[15] Cointe, ASME J. Offshore Mech. Arc. Engng 109 pp 237– (1987)
[16] Chekin, Prikl. Mat. Mekh. 53 pp 300– (1989)
[17] Chaplygin, About Pressure of a Flat Flow on Obstacles. On the Airplane Theory pp 49– (1910)
[18] Zhukovskii, Math. Coll. 15 pp 121– (1890)
[19] DOI: 10.1017/S002211209300028X · Zbl 0766.76008
[20] Wang, J. Ship Res. 23 pp 43– (1979)
[21] Wang, J. Ship Res. 21 pp 44– (1977)
[22] DOI: 10.1017/S0956792506006759 · Zbl 1120.76015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.