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Water entry of a wedge with rolled-up vortex sheet

Published online by Cambridge University Press:  27 November 2017

Yuriy A. Semenov  and
G. X. Wu Open the ORCID record for G. X. Wu [Opens in a new window]
Yuriy A. Semenov
Affiliation:
Department of Mechanical Engineering, University College London, London WC1E 6BT, UK
G. X. Wu*
Affiliation:
Department of Mechanical Engineering, University College London, London WC1E 6BT, UK
*
†Email address for correspondence: g.wu@ucl.ac.uk
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Abstract

The problem of asymmetric water entry of a wedge with the vortex sheet shed from its apex is considered within the framework of the ideal and incompressible fluid. The effects due to gravity and surface tension are ignored and the flow therefore can be treated as self-similar, as there is no length scale. The solution for the problem is sought through two mutually dependent parts using two different analytic approaches. The first one is due to water entry, which is obtained through the integral hodograph method for the complex velocity potential, in which the streamline on the body surface remains on the body surface after passing the apex, leading to a non-physical local singularity. The second one is due to a vortex sheet shed from the apex, and the shape of the sheet and the strength distribution of the vortex are obtained through the solution of the Birkhoff–Rott equation. The total circulation of the vortex sheet is obtained by imposing the Kutta condition at the apex, which removes the local singularity. These two solutions are nonlinearly coupled on the unknown free surface and the unknown vortex sheet. This poses a major challenge, which distinguishes the present formulation of the problem from the previous ones on water entry without a vortex sheet and ones on vortex shedding from a wedge apex without a moving free surface. Detailed results in terms of pressure distribution, vortex sheet, velocity and force coefficients are presented for wedges of different inner angles and heel angles, as well as the water-entry direction. It is shown that the vortex shedding from the tip of the wedge has a profound local effect, but only weakly affects the free-surface shape, overall pressure distribution and force coefficients.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 512 - 539
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Copyright
© 2017 Cambridge University Press 

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