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.

Irregular Frequency Removal and Convergence in Higher-Order BEM for Wave Diffraction/Radiation Analysis

2019 ◽  
Author(s):  
Tomoaki Utsunomiya
Keyword(s):  
Free Surface ◽  
Wave Diffraction ◽  
Higher Order ◽  
The Body ◽  
Diffraction Radiation ◽  
First Order ◽  
Irregular Frequency ◽  
Intersection Line ◽  
Order Quantities ◽  
Drift Forces

Abstract Higher-order boundary element method (HOBEM) for wave diffraction/radiation analysis is a powerful tool for its applicability to a general (curved) geometry. Inspired by the paper which examined the convergence of BIE code with constant panels (Martic, et al., 2018; OMAE2018-77999), the convergence characteristics of HOBEM with quadrilateral panels have been examined. Here, the effect of removal of irregular frequencies is particularly focused as discussed by Martic, et al. (2018). The irregular frequency removal has been made by the rigid-lid method which is applicable to HOBEM, where the intersection line between the body-surface and the free-surface should be carefully handled. The results show that for first order quantities the convergence is quite good for both cases with/without irregular frequency removal (except where the irregular frequencies affect for the case without irregular frequency removal). For mean drift forces, the convergence becomes poor particularly for the case without irregular frequency removal. The convergence characteristics are examined and some discussions are made.

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.

Approximation of Higher-Order Derivatives of the Frequency Domain Free Surface Green Function

2015 ◽  
Author(s):  
Yuyun Shi ◽  
Hui Li ◽  
Zhifu Li ◽  
Huilong Ren
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Higher Order ◽  
Boundary Element Methods ◽  
Source Distribution ◽  
Chebyshev Series ◽  
Surface Green Function ◽  
The Green Function ◽  
Derivatives Of

The higher-order derivatives of the free-surface Green Function are critically important in three-dimensional frequency-domain boundary element methods using mixed dipole-source distribution. To improve the accuracy and efficiency of numerical schemes, the computing domain is divided into five areas. Derivatives in four areas are calculated analytically since the Green function is defined analytically. The 5th area is divided into a number of sub-areas in which truncated Double Chebyshev series are used to approximate the Green function. Unlike the usual way in which the derivatives of Green function are obtained by differentiating the series, we re-approximate the derivatives by new Chebyshev series with new coefficients. Numerical results show that the new series are more accurate, in particular, second order derivatives.

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.

Influence of the Waterline Integral on the Solution of the Frequency-Domain Forward-Speed Radiation-Diffraction Problem of a Ship Advancing in Waves

2014 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
G. J. Lee ◽  
M. S. Shin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Surface Condition ◽  
Numerical Results ◽  
Forward Speed ◽  
Line Integral ◽  
Free Surface Condition ◽  
Surface Green Function

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.

scholarly journals Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory

2015 ◽  
Author(s):  
Godine Kok Yan Chan ◽  
Paul D. Sclavounos ◽  
Jason Jonkman ◽  
Gregory Hayman
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Wind Turbines ◽  
Time Domain ◽  
The Body ◽  
Nonlinear Loads ◽  
Frequency Wave ◽  
Linear And Nonlinear ◽  
The Time Domain ◽  
Nonlinear Free Surface

A hydrodynamics computer module was developed to evaluate the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The new formulation allows linear and nonlinear loads on floating bodies to be computed in the time domain. It also avoids the computationally intensive evaluation of temporal and spatial gradients of the velocity potential in the Bernoulli equation and the discretization of the nonlinear free surface. The new hydrodynamics module computes linear and nonlinear loads — including hydrostatic, Froude-Krylov, radiation and diffraction, as well as nonlinear effects known to cause ringing, springing, and slow-drift loads — directly in the time domain. The time-domain Green function is used to solve the linear and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.

scholarly journals Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack

2018 ◽  
Vol 845 ◽  
pp. 682-712 ◽  
Author(s):  
Zhi Fu Li ◽  
Guo Xiong Wu ◽  
Chun Yan Ji
Keyword(s):  
Green Function ◽  
Circular Cylinder ◽  
Body Surface ◽  
Ice Sheet ◽  
Integral Form ◽  
Multipole Expansion ◽  
The Body ◽  
Wave Radiation ◽  
Surface Boundary ◽  
The Green Function

Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack are considered based on the linearized velocity potential theory together with multipole expansion. The solution starts from the potential due to a single source, or the Green function satisfying both the ice sheet condition and the crack condition, as well as all other conditions apart from that on the body surface. This is obtained in an integral form through Fourier transform, in contrast to what has been obtained previously in which the Green function is in the series form based on the method of matched eigenfunction expansion in each domain on both sides of the crack. The multipole expansion is then constructed through direct differentiation of the Green function with respect to the source position, rather than treating each multipole as a separate problem. The use of the Green function enables the problem of wave diffraction by the crack in the absence of the body to be solved directly. For the circular cylinder, wave radiation and diffraction problems are solved by applying the body surface boundary condition to the multipole expansion, through which the unknown coefficients are obtained. Extensive results are provided for the added mass and damping coefficient as well as the exciting force. When the cylinder is away from the crack, a wide spacing approximation method is used, which is found to provide accurate results apart from when the cylinder is quite close to the crack.

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.

Discussions on the Convergence of the Seakeeping Simulations Based on the Panel Methods

2018 ◽  
Author(s):  
Ivana Martić ◽  
Nastia Degiuli ◽  
Šime Malenica ◽  
Andrea Farkas
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Surface Condition ◽  
Wave Length ◽  
Boundary Integral ◽  
The Body ◽  
Numerical Code ◽  
Physical Parameters ◽  
Diffraction Radiation ◽  
Panel Methods

Numerical problems related to the convergence of the classical panel methods which are employed for the diffraction-radiation simulations are discussed. It is well known that, for the panel methods, the convergence issues are not exclusively related to the physical parameters (wave length, body shape, draught ...) but also to the one purely numerical phenomenon which occurs when the Boundary Integral Equation Method (BIEM) based on the use of Kelvin (wave) type Green’s function is used. Indeed, due to the fact that the Green’s function satisfies the free surface condition in the whole fluid domain below z = 0, the numerical solution is polluted, at some particular frequencies, by the solution of the unphysical problem inside the body. This phenomenon which is purely numerical, is known as the problem of irregular frequencies. From practical point of view, it is not always easy to distinguish if the irregularities in the final solution are coming, from the body mesh which is not fine enough, from the physical resonance of the system, from the problem of irregular frequencies or from something else!? In this paper the authors discuss these issues in the context of the evaluation of the seakeeping behavior of one typical FPSO (Floating Production Storage and Offloading). Both the linear (first order) as well as the second order quantities are of concern and the different methods for the elimination of the irregular frequencies are discussed. Special attention is given to the calculations of the different physical quantities at very high frequencies. The numerical tool used within this research is the Bureau Veritas numerical code HYDROSTAR which is based on the panel method with singularities of constant strength.

On the Green-function theory of the spin- Heisenberg ferromagnet

1968 ◽  
Vol 46 (9) ◽  
pp. 1021-1028 ◽  
Author(s):  
S. T. Dembinski
Keyword(s):  
Green Function ◽  
Curie Temperature ◽  
Low Temperatures ◽  
Random Phase Approximation ◽  
Function Theory ◽  
Random Phase ◽  
Exact Result ◽  
Heisenberg Ferromagnet ◽  
First Order ◽  
The Green Function

A new first-order decoupling scheme for the Green function appearing in the theory of the spin-[Formula: see text] Heisenberg ferromagnet is introduced. At low temperatures the magnetization has no spurious term in T3 and the coefficient of the term in T4 is within a few percent of the Dyson exact result. The Curie temperature is equal to the random phase approximation Curie temperature.

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