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.

On the Interaction of Waves With Intake/Discharge Flows Originating From a Freely-Floating Body

2002 ◽  
Author(s):  
B. Padmanabhan ◽  
R. C. Ertekin
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Floating Body ◽  
Wave Forces ◽  
Linear Potential ◽  
Rankine Source ◽  
Total Potential ◽  
Low Froude Number ◽  
Linear Potential Theory ◽  
Steady Potential

This work is motivated by the many instances of intake/discharge flows from openings on floating or submerged ocean vessels and structures that may affect the wave field around them. Damaged vessels may release oil, or water may enter these vessels through openings. In oil skimming operations, for example, a very thin layer of oil must be skimmed off a large surface area, and therefore, oil skimming vessels require large intakes. Floating OTEC plants also require large intake and discharge volumes to sustain their operations. A linear theory is developed to obtain the motions of a 2-dimensional, freely floating body (from which steady intake/discharge flows originate) that encounters incoming waves. The boundary-value problem is formulated within the assumptions of linear potential theory by decomposing the total potential into its oscillatory and steady components. The steady potential is further decomposed into the double-model and perturbation potentials. The time-harmonic potential is coupled with the steady potential through the free-surface condition. The potentials are obtained by use of the quadratic boundary-element method based on the Rankine source. The effect of the steady intake/discharge flows on the diffraction loads, hydrodynamic force coefficients, as well as the motions of a 2-dimensional prismatic body floating on the free surface are presented. It is shown that the exciting wave forces and the hydrodynamic coefficients other than the damping coefficients are not appreciably affected by the intake/discharge flows of low Froude number for a 100MW floating OTEC plant.

On the Interaction of Waves With Intake/Discharge Flows Originating From a Freely-Floating Body

2003 ◽  
Vol 125 (1) ◽  
pp. 41-47 ◽  
Author(s):  
B. Padmanabhan ◽  
R. C. Ertekin
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Floating Body ◽  
Wave Forces ◽  
Linear Potential ◽  
Two Dimensional ◽  
Rankine Source ◽  
Total Potential ◽  
Linear Potential Theory ◽  
Steady Potential

A linear theory is developed to obtain the motions of a two-dimensional, freely floating body (from which steady intake/discharge flows originate) that encounters incoming waves. The boundary-value problem is formulated within the assumptions of linear potential theory by decomposing the total potential into its oscillatory and steady components. The steady potential is further decomposed into the double-model and perturbation potentials. The time-harmonic potential is coupled with the steady potential through the free-surface condition. The potentials are obtained by use of the quadratic boundary-element method based on the Rankine source. The effect of the steady intake/discharge flows on the diffraction loads, hydrodynamic force coefficients, as well as the motions of a two-dimensional prismatic body floating on the free surface are presented. It is shown that the exciting wave forces and the hydrodynamic coefficients other than the damping coefficients are not appreciably affected in the case of low intake/discharge Froude numbers that are estimated, for example, for a 100 MW floating OTEC plant.

Computation of Wave Added Resistance by Control Surface Integration

2016 ◽  
Author(s):  
Zhiyuan Pan ◽  
Torgeir Vada ◽  
Kaijia Han
Keyword(s):  
Free Surface ◽  
Near Field ◽  
Momentum Conservation ◽  
Ship Hull ◽  
Control Surface ◽  
Floating Body ◽  
Added Resistance ◽  
Time Step ◽  
Rankine Source ◽  
Linearization Methods

A time domain Rankine source solver is extended to compute the wave added resistance of ships. The proposed approach applies the momentum conservation principle on the near field fluid volume enclosed by the wet surface of a floating body, the free surface and a control surface. The wave added resistance is then calculated by the integration over the control surface of the fluid velocities and free surface elevations. To be able to incorporate the proposed method with the Rankine source code, an interpolation scheme has been developed to compute the kinematics for the off-body points close to (or on) the free surface. Two Wigley ship models, a containership model S175 and a tanker model KVLCC2 are used to validate the present method. In general good agreement is found comparing with the model test data. The convergence behavior is examined for the proposed method including the selection of the time step and location of the control surface. Both Neumann-Kelvin and double body linearization methods are evaluated with the proposed method. It is found that the Neumann-Kelvin linearization can only be applied for slender ship hull, whereas double body method fits also for blunt ships. It is suggested to apply the proposed method with double body linearization to evaluate the wave added resistance of ships with a control surface close to the ship hull.

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.

Transient Free-Surface Hydrodynamics Using Rational Approximation of the Green’s Function

1999 ◽  
Vol 43 (02) ◽  
pp. 95-106 ◽  
Author(s):  
Christopher J. Damaren
Keyword(s):  
Free Surface ◽  
Frequency Domain ◽  
Source Function ◽  
The Body ◽  
Floating Body ◽  
Order Ordinary Differential Equation ◽  
Radiation Impedance ◽  
Rational Dependence ◽  
The Time Domain ◽  
Domain Source

Rational approximations in the frequency domain are developed for the source function of linear free-surface hydrodynamics using the recently uncovered fourth-order ordinary differential equation (ODE) satisfied by the time-domain source function. The radiation problem for a floating body in deep water is formulated using a source plus wave-free potential expansion for the fluid. The inherent rational dependence on frequency of the wave-free potentials as well as the source approximation are used to develop a system of constant-coefficient ODE's for the radiation impedance which can be used to develop the motion of the body in a simple manner. The technique is applied to the heaving motion of a floating sphere with good results. The application to more general body geometries is explored by formulating the frequency-domain problem using the variational principle of Chen and Mei and exploiting its polynomial dependence on frequency.

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.

Numerical Solution of Wave Diffraction Problem in the Time Domain With the Panel-Free Method

2004 ◽  
Vol 126 (1) ◽  
pp. 1-8 ◽  
Author(s):  
W. Qiu ◽  
J. M. Chuang ◽  
C. C. Hsiung
Keyword(s):  
Body Surface ◽  
Time Domain ◽  
Diffraction Problem ◽  
The Body ◽  
Floating Body ◽  
B Splines ◽  
Rankine Source ◽  
Diffracted Waves ◽  
The Green Function ◽  
The Time Domain

A panel-free method (PFM) was developed earlier to solve the radiation problem of a floating body in the time domain. In the further development of this method, the diffraction problem has been solved. After removing the singularity in the Rankine source of the Green function and representing the body surface mathematically by Non-Uniform Rational B-Splines (NURBS) surfaces, integral equations were globally discretized over the body surface by Gaussian quadratures. Computed response functions and forces due to diffracted waves for a hemisphere at zero speed were compared with published results.

Drift Motion of Floating Bodies Under the Action of Green Water

2021 ◽  
Author(s):  
Sasan Tavakoli ◽  
Luofeng Huang ◽  
Alexander V. Babanin
Keyword(s):  
Numerical Simulations ◽  
Water Waves ◽  
The Body ◽  
Green Water ◽  
Floating Body ◽  
Floating Bodies ◽  
Drift Motion ◽  
Upper Deck ◽  
Steep Waves ◽  
The Impact

Abstract Numerical simulations are peformed to model the dynamic motions of a free floating body exposed to water waves. The solid body has low freeboard and draft, and its upper deck can be washed by the steep waves. Thus, the green water phenomenon occurs as large waves interact with the floating body. The aim of the research is to improve the understanding of the green water emerging above the upper deck of a floating plate. A thin floating body with barriers is also modeled. For the case of the body equipped with barriers, no green water occurs. Green water has been seen to affect the wave field and the dynamic motions of the plate. It is observed that when water can wash the upper surface of the floating object, drift speed is slightly decreased as a proportion of the energy of waves is dissipated above the body. Water waves are seen to impact the upper surface of the thin floating body as the green water flows over its upper deck. Furthermore, water is seen to impact the plate as its front edge re-enters the water. The first water impact only occurs when the floating body is not equipped with any barrier. By sampling the numerical simulations, it is observed that the non-dimensional value of the impact pressure, resulting from the green water, is larger for the case of smaller wavelength.

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.

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.

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