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.

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.

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.

The Drift Force and Moment on Ships in Waves

1967 ◽  
Vol 11 (01) ◽  
pp. 51-60 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Velocity Potential ◽  
The Body ◽  
Horizontal Force ◽  
Regular Waves ◽  
Slender Body Theory ◽  
Kochin Function ◽  
Field Velocity ◽  
Drift Force ◽  
The Waves ◽  
Body Theory

The second-order steady horizontal force and vertical moment are derived for a freely floating ship in regular waves. The fluid is assumed to be ideal and the motion is linearized. Momentum relations are used to derive general results for an arbitrary ship or other body, in terms of the Kochin function or far-field velocity potential of the body. Explicit results are derived for slender ships, based upon the assumptions of slender body theory. Computations are made for a Series 60 hull and are compared with experiments. The analysis of the vertical moment permits the prediction of stable heading angles in oblique waves, and it is shown that unless the waves are very short, the ship will be stable only in beam waves.

Solution for Free-Surface Flow in Porous Media Using Rayleigh-Ritz Expansions

1978 ◽  
Vol 5 (1) ◽  
pp. 52-54
Author(s):  
Henning Rasmussen
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Free Surface ◽  
Potential Problem ◽  
Velocity Potential ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow In Porous Media ◽  
Order Partial Differential Equation ◽  
First Order

Free-surface flow can be modelled by the Laplace equation for the velocity potential and a nonlinear first-order partial differential equation for the free surface. The potential problem is reformulated as a variational problem and then solved approximately by a Rayleigh-Ritz expansion. The free-surface equation is solved using finite differences. The procedure is applied to a particular problem, and excellent results are obtained.

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.

Incompressible potential flow past ‘not-so-slender’ bodies of revolution at an angle of attack

1975 ◽  
Vol 70 (4) ◽  
pp. 651-661 ◽  
Author(s):  
P. Sivakrishna Prasad ◽  
N. R. Subramanian
Keyword(s):  
Velocity Potential ◽  
Angle Of Attack ◽  
The Body ◽  
Virtual Mass ◽  
Bodies Of Revolution ◽  
Exact Theory ◽  
Pressure Distributions ◽  
Ellipsoid Of Revolution ◽  
Slender Bodies ◽  
Good Agreement

Using the method of matched asymptotic expansions, an expansion of the velocity potential for steady incompressible flow has been obtained to order ε4for slender bodies of revolution at an angle of attack by representing the potential due to the body as a superposition of potentials of sources and doublets distributed along a segment of the axis inside the body excluding an interval near each end of the body. Also, expansions of the coefficients of longitudinal virtual mass and lateral virtual mass have been found. The pressure distributions over an ellipsoid of revolution of thickness ratio ε = 0·3 at zero angle of attack and at an angle of attack of 3° obtained by the present method are compared with results obtained from the exact theory and that of Van Dyke. The virtual-mass coefficients are also compared with those obtained from the exact theory and are found to be in good agreement up to ε = 0·3.

On the Theory of Potential Flow About a Ship Advancing in Waves

1992 ◽  
Vol 36 (01) ◽  
pp. 17-29
Author(s):  
Francis Noblesse ◽  
Dane Hendrix
Keyword(s):  
Differential Equation ◽  
Potential Flow ◽  
Theoretical Basis ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Regular Waves ◽  
Integro Differential Equation ◽  
The Mean ◽  
The Green Function ◽  
Subsequent Integration

This study considers the three-dimensional potential flow due to a ship advancing with constant average speed in a train of regular waves. A modified integro-differential equation for determining the velocity potential on the mean position of the hull surface is obtained, and a solid theoretical basis for obtaining a numerical solution of the equation via a panel method is developed following the approach used by Kochin more than 50 years ago. In short, the approach is essentially based on a Fourier representation of the solution of a modified integro-differential equation. This approach circumvents the fundamental difficulties associated with the numerical evaluation of the Green function and its gradient, and their subsequent integration over the panels used to approximate the hull surface of a ship.

A solution for hypersonic flow past slender bodies

1971 ◽  
Vol 48 (1) ◽  
pp. 23-31 ◽  
Author(s):  
W. H. Hui
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Shock Waves ◽  
Body Shape ◽  
The Body ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Specific Heats ◽  
Slender Bodies

A solution to the hypersonic small disturbance equations is obtained for a class of two-dimensional bodies supporting logarithmic shock waves by reducing the partial differential equation to an ordinary differential equation. The body shape is calculated and shown not to be logarithmic if γ ≠ 1, where γ is the ratio of the specific heats of the gas.

A Numerical Calculation of Hydrodynamic Forces on a Seagoing Ship by 3-D Source Technique With Forward Speed

2004 ◽  
Author(s):  
Yoshiyiki Inoue ◽  
Md. Kamruzzaman
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Hydrodynamic Forces ◽  
The Body ◽  
Source Distribution ◽  
Accurate Estimation ◽  
Forward Speed ◽  
Surface Ship ◽  
Wave Patterns ◽  
Wigley Hull

In this paper, the hydrodynamic forces of a surface ship advancing in waves at constant forward speed are numerically calculated by using the 3-D source distribution techniques. The paper also deals with the numerical calculations of free surface flow around an advancing ship in calm water as well as in waves. The body boundary condition is linearised about the undisturbed position of the body and the free surface condition is linearised about the mean water surface. The potential is represented by a distribution of sources over the surface of the ship and its waterline. The problem is solved by the method of singularities distributed over the hull surface. Hess & Smith method is used to obtain the density of these singularities. The numerical solution of the surface ship case is approximately obtained by considering the hull as a position of plane polygonal elements, bearing a constant singularity distribution. The velocity potential of any particular point in the free surface around the moving hull is determined by using the 3-D Green function with forward speed which satisfies the boundary conditions for a pulsating source in the fluid. Contours of wave patterns around moving surface ships are calculated from the velocity potential. The numerical accuracy of the computer code is firstly checked by calculating the velocity potential of a translating, pulsating unit source with arbitrary frequency and forward speed. Free surface wave patterns generated by a Wigley hull advancing with steady forward speed are calculated by using this code. Some corresponding hydrodynamic coefficients of heave and pitch modes for the Wigley hull has been calculated. Exciting forces and motion amplitudes are also investigated. The numerical result of this code is validated by comparing the calculated results with the experimental ones and those calculated by other methods. From the comparison, the results predicted by the present calculations are found in fairly good agreement with the experiment. Finally, the effects of motion amplitude on the free surface elevation are analyzed. These will be helpful for the accurate estimation of sea keeping problems for a ship advancing in waves.

The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

1950 ◽  
Vol 1 (4) ◽  
pp. 305-318
Author(s):  
G. N. Ward
Keyword(s):  
Supersonic Flow ◽  
Velocity Potential ◽  
Operational Calculus ◽  
The Body ◽  
Body Of Revolution ◽  
Internal Flows ◽  
Flow Past ◽  
External Forces ◽  
Internal Pressures ◽  
Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

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