Finite-difference simulation of nonlinear ship waves

1985 ◽  
Vol 157 ◽  
pp. 327-357 ◽  
Author(s):  
Hideaki Miyata ◽  
Shinichi Nishimura
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Surface Condition ◽  
Vertical Direction ◽  
Cell System ◽  
The Body ◽  
Rectangular Cell ◽  
Ship Waves ◽  
Body Boundary ◽  
Hull Forms

A finite-difference solution method for nonlinear wave generation in the near field of ships of arbitrary three-dimensional configuration is developed. Momentum equations of finite-difference form in a fixed rectangular cell system are solved by a time-marching scheme. The exact inviscid free-surface condition is approximately satisfied at the actual location of the free surface, and the free-slip body boundary condition is implemented by use of approximation of the body configuration and a special pressure computation in body boundary cells. The degree of accuracy is raised by employing a variable-mesh system in the vertical direction. Computed results are presented for three hull forms: a mathematical and two practical hull forms. Agreement with experiment seems to be fairly good. In particular, the computed wave profiles and contour maps of bow waves show excellent resemblance to the measured ones, having some typical characteristics of nonlinear ship waves.

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.

Convergence Properties of the Neumann-Kelvin Problem for a Submerged Body

1987 ◽  
Vol 31 (04) ◽  
pp. 227-234
Author(s):  
Lawrence J. Doctors ◽  
Robert F. Beck
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Body Condition ◽  
Numerical Experiments ◽  
Surface Condition ◽  
The Body ◽  
Convergence Properties ◽  
Submerged Body ◽  
Body Boundary ◽  
The Galerkin Method

The Neumann-Kelvin method for solving the flow past a body moving at a steady speed requires that the body boundary condition be satisfied exactly, while the free-surface condition is satisfied in a linearized sense. The solution is generally obtained by discretizing the body surface into panels, each of which has an unknown singularity strength. In the present work, two types of numerical experiments have been carried out. In the first approach, the body condition is satisfied at one point on each panel (the collocation method). In the second approach, the body condition is satisfied in an integrated sense on each panel (the Galerkin method). Improved convergence properties are demonstrated by the second approach.

Towards Fully Non-Linear Floating Body Simulations by a Potential Method

2012 ◽  
Author(s):  
Heinrich Söding
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Computing Time ◽  
Potential Method ◽  
The Body ◽  
Floating Body ◽  
Rankine Source ◽  
Exact Boundary ◽  
Approximate Wave ◽  
Steep Waves

A 3-dimensional Rankine source panel method for simulating a rigid floating body in steep waves is being developed. The aim is to obtain the same quality as free-surface RANSE methods, which are well suited for this application, but to require only a small fraction of the computing time needed by RANSE methods. The body may have forward speed or perform maneuvering motions. The exact boundary conditions are satisfied at the actual location of the fluid boundaries. The waves are generated not by a material wave maker, but by an approximate wave potential which needs not satisfy the exact free-surface condition. No wave damping regions are required. Whereas for steep waves without a body the method appears satisfactory, it needs further improvements if a body is present.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

A multimodal method for liquid sloshing in a two-dimensional circular tank

2010 ◽  
Vol 665 ◽  
pp. 457-479 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Analytical Form ◽  
The Body ◽  
Liquid Sloshing ◽  
Two Dimensional ◽  
Surface Conditions ◽  
Natural Modes ◽  
Body Boundary ◽  
Multimodal Method

Two-dimensional forced liquid sloshing in a circular tank is studied by the multimodal method which uses an expansion in terms of the natural modes of free oscillations in the unforced tank. Incompressible inviscid liquid, irrotational flow and linear free-surface conditions are assumed. Accurate natural sloshing modes are constructed in an analytical form. Based on these modes, the ‘multimodal’ velocity potential of both steady-state and transient forced liquid motions exactly satisfies the body-boundary condition, captures the corner-point behaviour between the mean free surface and the tank wall and accurately approximates the free-surface conditions. The constructed multimodal solution provides an accurate description of the linear forced liquid sloshing. Surface wave elevations and hydrodynamic loads are compared with known experimental and nonlinear computational fluid dynamics results. The linear multimodal sloshing solution demonstrates good agreement in transient conditions of small duration, but fails in steady-state nearly-resonant conditions. Importance of the free-surface nonlinearity with increasing tank filling is explained.

The ray theory of ship waves and the class of streamlined ships

1979 ◽  
Vol 91 (3) ◽  
pp. 465-488 ◽  
Author(s):  
Joseph B. Keller
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Wave Pattern ◽  
Ray Theory ◽  
Optical Length ◽  
Ship Waves ◽  
Water Line ◽  
Excitation Coefficient ◽  
Low Froude Number ◽  
The Waves

A new theory is given for calculating the wave pattern and wave resistance of a ship moving at low Froude number F. It applies to ships of any width, either full-bodied or slender. In this theory, the waves travel along rays which start at source points, such as the bow and stern, on the water-line. They propagate with the speed of waves in deep water, but are also advected by the double body flow. This is the flow about the ship and its image in the undisturbed free surface. The phase of a wave at any point on a ray is the optical length of the ray from the source to that point. The amplitude is determined by an excitation coefficient, which determines its initial value, and by an integral along the ray. The total wave height at any point is the sum of the heights on all the rays through the point. The theory is incomplete because the excitation coefficients are known only for thin ships. As an illustration, the theory is applied to the thin ship case, and the results then agree with Michell's thin ship solution evaluated for F small.A new class of ships, which we call streamlined ships, is introduced next. The usual linear free surface condition applies to the waves they produce. The ray theory is developed for these waves at low F, and it involves straight rays produced at all points on the rear half of the water-line. In addition, as an alternative to the ray theory, another method is presented for obtaining the waves at low F. It involves a Schrödinger-like equation in which distance along the ship's centre-line is the time-like co-ordinate.

A Generalized Wagner Method for Three-Dimensional Slamming

2005 ◽  
Vol 49 (04) ◽  
pp. 279-287
Author(s):  
O. M. Faltinsen ◽  
M. Chezhian
Keyword(s):  
Free Surface ◽  
Body Surface ◽  
Surface Condition ◽  
Three Dimensional ◽  
Water Entry ◽  
The Body ◽  
Experimental Results ◽  
Vertical Force ◽  
Free Surface Condition ◽  
Drop Tests

Impact between the water and ship, that is, slamming, can cause important global and local effects. A numerical method has been applied to predict water entry loads on three-dimensional bodies. The problem is solved as an initial value problem using the boundary element method. The Green second identity is used to represent the velocity potential as a distribution of Rankine sources and dipoles over the body surface and free surface. The problem is stepped up in time using the information from the boundary conditions. The kinematic free-surface condition is used to determine the intersection between the body surface and free surface at each time step. The exact body boundary condition is used, whereas the dynamic free-surface condition, φ = 0, is approximated on to a horizontal line and not on the exact free-surface profile. The approach presented by Zhao et al (1996) for two-dimensional water entry problems was extended to arbitrary three-dimensional bodies in this presented work. An idealized shape, which consists of cylindrical mid-body and hemispherical ends, was studied. The wetted body surface is calculated with great detail and is considered to be more important than the free-surface elevation away from the body. Drop tests have been carried out to verify and validate the numerical simulation. The effect of the angle between the free surface and the body surface has also been studied. The agreement between theory and experiments is good, and the effect of three-dimensionality is documented. The presented computational method is found to be robust for engineering use and computationally less demanding. The experimental results for vertical force have a strong oscillatory nature, and this has been analyzed using a simplified hydroelastic model. The hydroelastic model gives reasonable representation of the dynamic oscillations found in the vertical force. Reasons for the observed deviations between the numerical and the experimental results are documented. Recommendations for conducting drop tests with minimal dynamic effects are also presented.

Lifting Effects for Wave Resistance or Sea-Keeping Calculations

2002 ◽  
Author(s):  
Jean Philippe Boin ◽  
Michel Guilbaud ◽  
Malick Ba
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Surface Condition ◽  
The Body ◽  
Source Distribution ◽  
Diffraction Radiation ◽  
First Order ◽  
Wigley Hull ◽  
The Green Function ◽  
Sailing Boat

We present the introduction of lifting effects in a code of calculation [1–3] based on a first order panel method using the diffraction-radiation with forward speed Green function satisfying a linearised free-surface condition and the radiation one. A mixed formulation has been used with a source distribution on the hull and a doublet one on the plane of symmetry and the wake of lifting parts of the body, leading to an integral equation derived from the 3 rd Green identity. The Green function and its derivatives are not computed but are directly integrated on elementary panels, segments or semi-infinite strips. Results are presented for semi-submerged ellipsoid, rectangular surface-piercing bodies, Wigley hull, Series 60 ship, sailing boat and military 5415 hull. Global forces, moments but also free surface elevations are compared with the results of other methods and with measurements, either in steady or in unsteady flows in the frequency domain.

Short Term Distribution of Loads Acting on a Cruise Vessel in Extreme Seas Using a Body Nonlinear Time Domain With Second Order Froude-Krylov Pressure

2015 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Surface Condition ◽  
Bending Moment ◽  
The Body ◽  
Short Term ◽  
Weakly Nonlinear ◽  
Strip Theory ◽  
Vertical Bending Moment ◽  
Nonlinear Time Domain

Short term probability distribution of the vertical bending moment acting on a cruise vessel in extreme seas is calculated using a body nonlinear time domain method based on strip theory. The hydrodynamic forces are calculated for the exact wetted surface area under the incident wave profile. The incident potential satisfies the weakly nonlinear free surface condition based on the Stokes expansion. The disturbance potential satisfies the linear free surface and body boundary conditions. Certain practical engineering techniques are employed for the calculation of the body nonlinear forces. The statistics and the probability of distribution of the numerical vertical bending moment are compared with the experimental results measured in the wave tank.

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