Rankine Source Method for Seakeeping Analysis in Shallow Water

2014 ◽  
Author(s):  
Alexander von Graefe
Keyword(s):  
Boundary Condition ◽  
Shallow Water ◽  
Reference Frame ◽  
The Body ◽  
Forward Speed ◽  
Flat Bottom ◽  
Source Method ◽  
Rankine Source ◽  
Perturbation Potential ◽  
Fixed Reference

Following Hachmann approach, Söding’s Rankine source method describes the steady perturbation potential in the body-fixed reference frame. This is beneficial for seakeeping predictions at forward speed, because error-prone m-terms do not occur in the boundary condition on the ship hull. Although similar terms arise in the boundary condition on the free surface, numerical inaccuracies in these terms have much less influence on the behaviour of the ship than in the traditional approach, where m-terms are evaluated on the hull. The periodic flow is linearised with respect to the amplitude of the incident wave, taking into account the steady ship wave. A problem arises for shallow water problems if the Hachmann approach is used. For the shallow water problem, the boundary condition ‘no flow through the bottom’ must be fulfilled. Usually, this is done using image sources. If the steady perturbation potential is described in the body-fixed reference frame, this is not possible directly. This paper extends the Hachmann approach to treat this issue. Following the usual procedure for steady flow calculation, the boundary condition at the flat bottom of the steady problem is realised using image sources. For seakeeping computations, the steady perturbation potential is split into two parts, modelled respectively by steady sources above and below the flat bottom. The first part is assumed to be constant in the body-fixed reference frame, whereas the second part is assumed to be constant in the reference frame of the mirror image of the ship. This extended Hachmann approach fulfils the boundary condition at the flat bottom analytically. Computed ship motions with and without forward speed in shallow water are validated by model test results from Flanders Hydraulics Research, Antwerp, and from TU Berlin.

Second-Order Diffraction and Radiation of a Floating Body With Small Forward Speed

2010 ◽  
Author(s):  
Yan-Lin Shao ◽  
Odd M. Faltinsen
Keyword(s):  
Boundary Condition ◽  
Coordinate System ◽  
Traditional Method ◽  
Higher Order ◽  
Second Order ◽  
The Body ◽  
New Method ◽  
Forward Speed ◽  
Inertial Coordinate System ◽  
Body Boundary

The formulation of the second-order wave-current-body problem in the inertial coordinate system involves higher-order derivatives in the body boundary condition. A new method taking advantage of the body-fixed coordinate system in the near field is presented to avoid the calculation of higher-order derivatives in the body boundary condition. The new method has advantage over the traditional method when the body surface is with sharp corner or high curvature. The nonlinear wave diffraction and forced oscillation of floating bodies are studied up to second order in wave slope. A small forward speed is taken into account. The results of the new method are compared with that of the traditional method based on a formulation in the inertial coordinate system. When the traditional method applies, good agreement has been obtained.

A Forward-Speed Body-Exact Strip Theory

2015 ◽  
Author(s):  
Piotr J. Bandyk ◽  
George S. Hazen
Keyword(s):  
High Frequency ◽  
Numerical Data ◽  
The Body ◽  
Surface Boundary ◽  
Forward Speed ◽  
Rankine Source ◽  
High Frequency Oscillations ◽  
Surface Boundary Conditions ◽  
Strip Theory ◽  
Acceleration Potential

This paper develops an extension to the body-exact strip theory of Bandyk, Beck, and Zhang [1–8], focused on improved prediction of forward-speed effects. One of the known limitations of standard strip theory is the treatment of forward speed terms. The free surface boundary conditions completely neglect the forward speed, which is usually justified by the argument of high-frequency oscillations. The pressure equation on the body includes a speed-dependent term that must computed, most commonly using the Ogilvie-Tuck theorem or numerical approximations. The strip theory variation described here circumvents these deficiencies by applying the 2D+T approach. The model assumes that each two-dimensional frame, in which a boundary value problem (BVP) is solved, remains fixed relative to an earth-fixed frame. The numerical model is based on a time-domain Rankine source method, using the same body-exact approximation as described in earlier work [1]. A suitable acceleration potential BVP is derived. Added mass and damping coefficients are calculated for two Wigley hulls, using the the standard body-exact approach and forward-speed 2D + T variant, and compared to existing model test and numerical data.

Rankine Source Method for Ship-Ship Interaction Problems

2013 ◽  
Author(s):  
Alexander von Graefe ◽  
Vladimir Shigunov ◽  
Ould el Moctar
Keyword(s):  
Free Surface ◽  
Steady Flow ◽  
Test Data ◽  
Model Test ◽  
The Body ◽  
Ship Motions ◽  
Source Method ◽  
Rankine Source ◽  
Rankine Source Method ◽  
New Formulation

A Rankine source method is extended and applied to ship-ship interaction problems. The method covers the nonlinear steady flow and linear seakeeping in the frequency domain. The nonlinear steady flow solution accounts for the nonlinear free-surface conditions, ship wave and dynamic trim and sinkage. Periodic flow due to waves is linearized with respect to the wave amplitude, taking into account interactions with the nonlinear steady flow following Hachmann approach, which considers the steady perturbation potential as constant in the body-fixed reference frame. This is advantageous for the prediction of ship motions at moderate to high Froude numbers. In this context, a new formulation of the boundary condition for the multi-body case is derived. Two examples are considered, overtaking in calm water and replenishment at sea. For a feeder vessel overtaken by a container ship, computed forces and yaw moment are compared with model test data. As an example of replenishment operation, interaction between a frigate and a supply vessel is studied. Ship motions are computed for two relative positions and three forward speeds and compared with model test data for the largest forward speed. The Rankine source method proves as more accurate compared with a zero-speed free-surface Green function method.

Calculation of Deep-Water Wash Waves Using a Combined Rankine/Kelvin Source Method

2003 ◽  
Vol 47 (04) ◽  
pp. 313-326
Author(s):  
Carl-Erik Janson ◽  
Michael Leer-Andersen ◽  
Lars Larsson
Keyword(s):  
Boundary Condition ◽  
Deep Water ◽  
Outer Edge ◽  
Source Distribution ◽  
Far Field ◽  
Source Method ◽  
Rankine Source ◽  
Rankine Source Method ◽  
Outer Domain ◽  
Wigley Hull

This paper presents a method for computation of far-field wash waves in deep water. The method combines a nonlinear Rankine source method in an inner domain with a Kelvin source method for the far-field waves in an outer domain. Kelvin sources are distributed on a vertical matching wall, positioned at the outer edge of the inner domain. These sources are used to specify a boundary condition for the disturbance velocity potential on the matching wall. The boundary condition is used in the Rankine source solution of the inner domain. The size of the inner domain can be reduced in the transverse direction compared to a method using Rankine sources only, as the wave reflections at the edge of the inner domain are eliminated. Further, the far-field waves can be computed using the solution on the matching wall together with the Kelvin source distribution. The verification of the present method includes a comparison for a single Kelvin point source and a comparison to a Rankine source method at intermediate distances for the Wigley hull and for a catamaran. A grid dependence study for the position, size, and panel density on the matching wall is included for the Wigley hull. Computed and measured longitudinal wave cuts are compared for a catamaran both in the inner and the outer domain. Good agreement is obtained.

Second-Order Diffraction and Radiation of a Floating Body With Small Forward Speed

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Yan-Lin Shao ◽  
Odd M. Faltinsen
Keyword(s):  
Boundary Condition ◽  
Coordinate System ◽  
Traditional Method ◽  
Higher Order ◽  
Second Order ◽  
The Body ◽  
New Method ◽  
Forward Speed ◽  
Inertial Coordinate System ◽  
Body Boundary

The formulation of the second-order wave-current-body problem in the inertial coordinate system involves higher-order derivatives in the body boundary condition. A new method taking advantage of the body-fixed coordinate system in the near field is presented to avoid the calculation of higher-order derivatives in the body boundary condition. The new method has an advantage over the traditional method when the body surface has a sharp corner or high curvature. The nonlinear wave diffraction and forced oscillation of floating bodies are studied up to second order in wave slope. A small forward speed is taken into account. The results of the new method are compared with that of the traditional method based on a formulation in the inertial coordinate system. When the traditional method applies, good agreement has been obtained.

scholarly journals A Well-Balanced SPH-ALE Scheme for Shallow Water Applications

2021 ◽  
Vol 88 (3) ◽  
Author(s):  
Alberto Prieto-Arranz ◽  
Luis Ramírez ◽  
Iván Couceiro ◽  
Ignasi Colominas ◽  
Xesús Nogueira
Keyword(s):  
Shallow Water ◽  
Source Term ◽  
Arbitrary Lagrangian Eulerian ◽  
Flat Bottom ◽  
Riemann Solvers ◽  
Eulerian Formulation ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Numerical Fluxes ◽  
And Behavior

AbstractIn this work, a new discretization of the source term of the shallow water equations with non-flat bottom geometry is proposed to obtain a well-balanced scheme. A Smoothed Particle Hydrodynamics Arbitrary Lagrangian-Eulerian formulation based on Riemann solvers is presented to solve the SWE. Moving-Least Squares approximations are used to compute high-order reconstructions of the numerical fluxes and, stability is achieved using the a posteriori MOOD paradigm. Several benchmark 1D and 2D numerical problems are considered to test and validate the properties and behavior of the presented schemes.

scholarly journals A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

2021 ◽  
Vol 11 (6) ◽  
pp. 2722
Author(s):  
Zhiwen Qian ◽  
Dejiang Shang ◽  
Yuan Hu ◽  
Xinyang Xu ◽  
Haihan Zhao ◽  
...  
Keyword(s):  
Green’S Function ◽  
Shallow Water ◽  
Green's Function ◽  
Plane Waves ◽  
Spherical Wave ◽  
Sound Field ◽  
Efficient Computation ◽  
Image Source ◽  
Source Method ◽  
Pekeris Waveguide

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

Sign in / Sign up

Export Citation Format

Share Document