scholarly journals Splash formation at the nose of a smoothly curved body in a stream

1999 ◽  
Vol 40 (4) ◽  
pp. 421-436 ◽  
Author(s):  
E. O. Tuck ◽  
S. T. Simakov
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Velocity Potential ◽  
Integral Form ◽  
The Body ◽  
Front Face ◽  
Separation Condition ◽  
Polygonal Approximation ◽  
Side Condition ◽  
Two Dimensional Flow

AbstractIn two-dimensional flow past a body close to a free surface, the upwardly diverted portion may separate to form a splash. We model the nose of such a body by a semi-infinite obstacle of finite draft with a smoothly curved front face. This problem leads to a nonlinear integral equation with a side condition, a separation condition and an integral constraint requiring the far-upstream free surface to be asymptotically plane. The integral equation, called Villat's equation, connects a natural parametrisation of the curved front face with the parametrisation by the velocity potential near the body. The side condition fixes the position of the separation point, whereas the separation condition, known as the Brillouin-Villat condition, imposes a continuity relation to be satisfied at separation. For the described flow we derive the Brillouin-Villat condition in integral form and give a numerical solution to the problem using a polygonal approximation to the front face.

On the harmonic oscillations of a rigid body on a free surface

1965 ◽  
Vol 21 (3) ◽  
pp. 427-451 ◽  
Author(s):  
W. D. Kim
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Rigid Body ◽  
Potential Problem ◽  
Harmonic Oscillation ◽  
Added Mass ◽  
The Body ◽  
Rigorous Solution ◽  
Damping Coefficients

The present paper deals with the practical and rigorous solution of the potential problem associated with the harmonic oscillation of a rigid body on a free surface. The body is assumed to have the form of either an elliptical cylinder or an ellipsoid. The use of Green's function reduces the determination of the potential to the solution of an integral equation. The integral equation is solved numerically and the dependency of the hydrodynamic quantities such as added mass, added moment of inertia and damping coefficients of the rigid body on the frequency of the oscillation is established.

A Second-Order Theory for the Potential Flow About Thin Hydrofoils

1984 ◽  
Vol 28 (01) ◽  
pp. 55-64
Author(s):  
Colen Kennell ◽  
Allen Plotkin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Potential Flow ◽  
Order Theory ◽  
Wave Drag ◽  
Second Order ◽  
The Body ◽  
Surface Shape ◽  
Surface Boundary ◽  
Free Surface Boundary Condition

This research addresses the potential flow about a thin two-dimensional hydrofoil moving with constant velocity at a fixed depth beneath a free surface. The thickness-to-chord ratio of the hydrofoil and disturbances to the free stream are assumed to be small. These small perturbation assumptions are used to produce first-and second-order subproblems structured to provide consistent approximations to boundary conditions on the body and the free surface. Nonlinear corrections to the free-surface boundary condition are included at second order. Each subproblem is solved by a distribution of sources and vortices on the chord line and doublets on the free surface. After analytic determination of source and doublet strengths, a singular integral equation for the vortex strength is derived. This integral equation is reduced to a Fredholm integral equation which is solved numerically. Lift, wave drag, and free-surface shape are calculated for a flat plate and a Joukowski hydrofoil. The importance of free-surface effects relative to body effects is examined by a parametric variation of Froude number and depth of submergence.

Numerical Study of Forward-Speed Ship Motion and Added Resistance

2017 ◽  
Author(s):  
D. C. Hong ◽  
T. B. Ha ◽  
K. H. Song
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
The Body ◽  
Experimental Results ◽  
Surface Boundary ◽  
Forward Speed ◽  
Added Resistance ◽  
Following Seas

The added resistance of a ship was calculated using Maruo’s formula [1] involving the three-dimensional Kochin function obtained using the source and normal doublet distribution over the wetted surface of the ship. The density of the doublet distribution was obtained as the solution of the three-dimensional frequency-domain forward-speed Green integral equation containing the exact line integral along the waterline. Numerical results of the Wigley ship models II and III in head seas, obtained by making use of the inner-collocation 9-node second-order boundary element method have been compared with the experimental results reported by Journée [2]. The forward-speed hydrodynamic coefficients of the Wigley models have shown no irregular-frequencylike behavior. The steady disturbance potential due to the constant forward speed of the ship has also been calculated using the Green integral equation associated with the steady forward-speed free-surface Green function since the so-called mj-terms [3] appearing in the body boundary conditions contain the first and second derivatives of the steady potential over the wetted surface of the ship. However, the free-surface boundary condition was kept linear in the present study. The added resistances of the Wigley II and III models in head seas obtained using Maruo’s formula showing acceptable comparison with experimental results, have been presented. The added resistances in following seas obtained using Maruo’s formula have also been presented.

Radiation and diffraction of second-order surface waves by floating bodies

1988 ◽  
Vol 196 ◽  
pp. 65-91 ◽  
Author(s):  
P. D. Sclavounos
Keyword(s):  
Free Surface ◽  
Linear Problem ◽  
Velocity Potential ◽  
Surface Condition ◽  
Second Order ◽  
The Body ◽  
Green Functions ◽  
Floating Bodies ◽  
Free Surface Condition ◽  
Body Boundary

The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of initial-value problems that ensure they satisfy the proper radiation condition at infinity. The second-order velocity potential is expressed as the sum of a particular and a homogeneous component. The former satisfies the non-homogeneous free-surface condition and is expressed explicitly in terms of the second-order Green functions. The latter is subject to the homogeneous free-surface condition and enforces the body boundary condition by the solution of a linear problem. An analysis is carried out of the singular behaviour of the second-order potential near the intersection of the body boundary with the free surface.

Lateral Force and Moment on Ships in Oblique Waves

1962 ◽  
Vol 6 (02) ◽  
pp. 40-50
Author(s):  
Pung Nien Hu
Keyword(s):  
Differential Equation ◽  
Free Surface ◽  
Velocity Potential ◽  
Lateral Force ◽  
Exciting Force ◽  
The Body ◽  
Regular Waves ◽  
Oblique Waves ◽  
Added Masses ◽  
Slender Bodies

A method for evaluating the exciting force and moment on surface ships as well as on fully submerged bodies in oblique waves is developed, based on the assumptions of long regular waves and slender bodies. The differential equation, together with the boundary conditions, for each component of the velocity potential is studied. Momentum theorems for slender-body sections are derived and applied to the evaluation of stripwise force and moment on bodies in the presence of a free surface. The result is found to be directly related to the added masses of the body sections. Lateral added masses of body sections in the presence of a free surface are investigated in detail and numerical values are presented for Lewis sections.

Blockage with a Free Surface

1976 ◽  
Vol 20 (04) ◽  
pp. 199-203
Author(s):  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Finite Depth ◽  
Wave Resistance ◽  
Steady Flows ◽  
Two Dimensional ◽  
Present Context ◽  
Two Dimensional Flow ◽  
Field Radiation ◽  
Radiation Conditions

The occurrence of blockage, or a jump in the velocity potential between the upstream and downstream infinities, is well known for steady two-dimensional flow past a body in a rigid channel. This paper considers the analogous situation where there is a free surface, as in the wave resistance problem for submerged two-dimensional bodies in a fluid of finite depth. It is shown that blockage occurs in spite of the free surface, taking values which depend not only on the dipole moment but also upon the Froude number based on depth. The occurrence of blockage, in the present context, has a bearing primarily upon the correct formulation of far-field radiation conditions for steady flows with finite depth.

scholarly journals Asymmetric impact between liquid and solid wedges

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120203 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Mapping Function ◽  
Solution Procedure ◽  
Contact Angles ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Complex Velocity Potential ◽  
The Impact

The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complex-velocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.

scholarly journals Smoothly attaching bow flows with constant vorticity

2001 ◽  
Vol 42 (3) ◽  
pp. 354-371
Author(s):  
S. W. McCue ◽  
L. K. Forbes
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Surface Flow ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Front Face ◽  
Infinite Body ◽  
Constant Vorticity

AbstractThe free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a comer is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.

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