Similarity solution for oblique water entry of an expanding paraboloid

Wu, G.X.; Sun, Shuzheng

doi:10.1017/jfm.2014.111

Cited by 46 publications

(16 citation statements)

References 23 publications

(23 reference statements)

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“…When the new shape of the interface, together with the new normal velocity, is found, the solution procedure is repeated for the upper liquid wedge. This is virtually an impact problem similar to an expanding solid surface with prescribed normal velocity (Wu & Sun 2014). Its solution provides the pressure distribution on the upper side of the interface, which is used again in (2.35) and (2.36).…”

mentioning

confidence: 99%

Impact of liquids with different densities

Semënov

Korobkin

2015

J. Fluid Mech.

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The collision of liquids of different densities is studied theoretically for the case of liquids having wedge-shaped configuration before the impact. Both liquids are assumed to be ideal and incompressible, and the velocity potential theory is used for the flow of each liquid. Surface tension and gravity effects are neglected. The problem is decomposed into two self-similar problems, one for each liquid. Across the interface between the liquids, continuity of the pressure and the normal component of the velocity is enforced through iteration. This determines the shape of the interface and other flow parameters. The integral hodograph method is employed to derive the solution consisting of analytical expressions for the complex-velocity potential, the complex-conjugate velocity, and the mapping function. They are all defined in the first quadrant of a parameter plane, in which the original boundary-value problem is reduced to a system of integro-differential equations in terms of the velocity magnitude and the velocity angle relative to the flow boundary. They are solved numerically using the method of successive approximations. The results are presented through streamlines, interface and free-surface shapes, the pressure and velocity distributions. Special attention is given to the structure of the splash jet rising as a result of the impact

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confidence: 99%

Impact of liquids with different densities

Semënov

Korobkin

2015

J. Fluid Mech.

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“…The problem at each time step will be solved by the 3D boundary element method. This is similar to the mathematical model and solution procedure in Wu and Sun (2014) and Sun and Wu (2014). It allows us to capture some local results with high resolution.…”

Section: Introductionmentioning

confidence: 85%

A three dimensional infinite wedge shaped solid block sliding into water along an inclined beach

Sun

2016

Journal of Fluids and Structures

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The three dimensional (3D) problem of a solid block sliding into water along an inclined beach is investigated. The main part of the block is an infinite wedge cylinder and the front of the body is part of an elliptical cone. Incompressible velocity potential theory is used together with fully nonlinear boundary conditions. When gravity is ignored, it is found that self-similar solution is possible. The boundary element method is used to solve the problem. The free surface shape is updated together with the potential on the free surface until the flow has become self-similar. Convergence studies are taken with respect to marching step and element size. Simulations are made for different bodies and different beach angles. Extensive results are provided for the pressure as well as the free surface shape, and their implications in physics are discussed.

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“…In fact, in Wagners theory, the width of the equivalent plate is continuously stretching. Wu & Sun (2014) investigated attached flow for an expanding three dimensional paraboloid. Semenov & Wu (2016) considered a stretching finite wedge.…”

Section: Introductionmentioning

confidence: 99%

Water entry of an expanding body with and without splash

Semënov

2019

J. Fluid Mech.

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A self-similar flow generated by water entry of an expanding two-dimensional smooth and curved body is studied based on the incompressible velocity potential theory, with gravity and surface tension effects being ignored. At each expansion speed, mathematical solutions for detached flow with a splash jet and attached flow with jet leaning on the body surface are obtained, both of which have been found possible in experiment, corresponding to hydrophobic and hydrophilic bodies, respectively. The problem is solved using the integral hodograph method, which converts the governing Laplace equations into two integral equations along the half real and imaginary axes of a parameter plane. For the detached flow, the conditions for continuity and finite spatial derivative of the velocity at the point of flow departing form the body surface are imposed. It is found that the Brillouin–Villat criterion for flow detachment of steady flow is also met in this self-similar flow, which requires the curvatures of the free surface and the body surface to be the same at the detachment point. Solutions for the detached flow have been obtained in the whole range of the expansion speeds, from zero to infinity, relative to the water entry speed. For the attached flow there is a minimal expansion speed below which no solution cannot be obtained. Detailed results in terms of pressure distribution, free surface shape and streamlines and tip angle of the jet are presented. It is revealed that when solutions for both detached and attached flows exist, the pressure distributions on the cylinder surface are almost the same up to the point near the jet root. Beyond that point, the pressure relative to the ambient one drops to zero at the detachment point in the former, while it drops below zero in the jet attached on the body and then returns to zero at the contact point in the latter.

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Similarity solution for oblique water entry of an expanding paraboloid

Cited by 46 publications

References 23 publications

Impact of liquids with different densities

Impact of liquids with different densities

A three dimensional infinite wedge shaped solid block sliding into water along an inclined beach

Water entry of an expanding body with and without splash

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