Masashi Kashiwagi

A B-spline Galerkin scheme for calculating the hydroelastic response of a very large floating structure in waves

This paper presents an effective scheme for computing the wave-induced hydroelastic response of a very large floating structure, and a validation of its usefulness. The calculation scheme developed is based on the pressure-distribution method of expressing the disturbance caused by a structure, and on the mode-expansion method for hydroelastic deflection with the superposition of orthogonal mode functions. The scheme uses bi-cubic B-spline functions to represent unknown pressures, and the Galerkin method to satisfy the body boundary conditions. Various numerical checks confirm that the computed results are extremely accurate, require relatively little computational time, and contain few unknowns, even in the region of very short wavelengths. Measurements of the vertical deflections in both head and oblique waves of relatively long wavelength are in good agreement with the computed results. Numerical examples using shorter wavelengths reveal that the hydroelastic deflection does not necessarily become negligible as the wavelength of incident waves decreases. The effects of finite water depth and incident wave angle are also discussed.

A time-domain mode-expansion method for calculating transient elastic responses of a pontoon-type VLFS

Abstract A time-domain calculation method is described for elastic responses to arbitrary time-dependent external loads, on the basis of a general differential equation of second order including the convolution integral related to memory effects in the hydrodynamic forces. The time-dependent elastic deflection of a structure is represented by a superposition of mathematical modal functions, and a Galerkin scheme is employed to obtain a linear system of simultaneous differential equations for the amplitude of modal functions assumed. Special care is paid to numerical accuracy in computing the memory-effect function and the added mass at infinite frequency. The validity of the numerical results was confirmed through a comparison with time histories of the vertical deflection measured in an impulsive weight-drop test conducted at the Ship Research Institute and a comparison with existing numerical results for the same problem. To check the necessity of memory-effect terms, computations using a constant value for the hydrodynamic damping coefficient were also performed, and practical measures for reducing the computation time are discussed.

Application of CIP Method for Strongly Nonlinear Marine Hydrodynamics

Abstract A CFD approach based on the CIP (Constrained Interpolation Profile) method has been developed for predicting strongly nonlinear marine hydrodynamics. The numerical model uses a Cartesian grid for numerical solution and applies the CIP method for the flow solver and the free-surface interface capturing. An efficient interface capturing method by using a conservative CIP scheme is applied to two-dimensional sloshing. For strongly nonlinear wave-body interactions, a Cartesian grid method, in which the body surface is approximated by distributing virtual particles on it, treats the boundary condition at the body surface. A three-dimensional numerical simulation on a ship moving in large waves is presented.

Hydrodynamic Study on Added Resistance Using Unsteady Wave Analysis

It is known that the added resistance in waves can be computed from ship-generated unsteady waves through the unsteady wave analysis method. To investigate the effects of nonlinear ship-generated unsteady waves and bluntness of the ship geometry on the added resistance, measurements of unsteady waves, wave-induced ship motions, and added resistance were carried out using two different (blunt and slender) modified Wigley models. The ship-generated unsteady waves are also produced by the linear superposition using the waves measured for the diffraction and radiation problems and the complex amplitudes of ship motions measured for the motion-free problem in waves. Then a comparison is made among the values of the added resistance by the direct measurement using a dynamometer and by the wave analysis method using the Fourier transform of measured and superposed waves. It is found that near the peak of the added resistance where ship motions become large, the degree of nonlinearity in the unsteady wave becomes prominent, especially at the forefront part of the wave. Thus, the added resistance evaluated with measured waves at larger amplitudes of incident wave becomes much smaller than the values by the direct measurement and by the wave analysis with superposed waves or measured waves at smaller amplitude of incident wave. Discussion is also made on the characteristics of the added resistance in the range of short incident waves.

Pressure distribution computed by wave-interaction theory for adjacent multiple bodies

In spite of a mathematical limitation that each interacting body must be far enough apart from the other bodies, the wave interaction theory has been used successfully even for a case where the separation distance between the bodies is virtually zero. Numerical investigation is made in this paper on the practical applicability of the wave interaction theory by considering four identical box-shaped bodies as a simplified example and comparing computed results with correct ones obtained by the higher-order boundary element method. It is shown that the wave force in the horizontal direction can be obtained favorably by the interaction theory even if the separation distance between the bodies is very small. To make reasons of this somewhat peculiar phenomenon clear, not only the integrated hydrodynamic force but also the pressure distribution on the body surface is calculated and compared with the results by the higher-order boundary element method. Discussion is made on whether the pressure is correctly obtained on the regions very close to adjacent bodies and fortuitous cancellation in the integration of the pressure occurs between the two vertical planes in close proximity.

A New Slender-Ship Theory Valid for all Oscillatory Frequencies and Forward Speeds

A new theory is presented for the radiation problem of heave and pitch of a slender ship advancing at arbitrary forward speed. The theory has no restriction on the order of forward speed and oscillation frequency. The general inner solution is constructed by the source distribution with Green function over the ship’s hull surface plus a line distribution along the ship’s centerline on the free surface with the radiation-wave related residue part of the Green function. By matching the inner solution with the outer solution, the source strengths on both hull surface and line distribution can be obtained. Numerical results of the added-mass and damping coefficients based on the present theory are shown for two modified Wigley models and compared with the unified theory and experiment results.Copyright

Nonlinear analysis on wave-plate interaction due to disturbed vertical elastic plate

Hydroelastic behavior of wave-plate interaction due to an initial deflection of a vertical elastic plate is simulated by using a Mixed Eulerian Lagrangian method for the fluid and a Finite Element Method for the plate. An implicit boundary-condition method is developed to solve the coupled motions of fluid and plate. A hybrid wave absorbing beach is installed to prevent the wave reflection from a vertical wall at the end of the wave tank. The 4th order Runge-Kutta scheme with uniform time step is used for time marching. First, numerical results of the elastic vibration of a vertical plate induced by deformation of itself at initial time are validated by comparing with corresponding analytical solution. Then, further comparison between the results from mode-expansion method and FEM is made. Finally, the influences of the edge condition at the top of plate and the plate stiffness on the wave-plate interaction are investigated systematically.

Ship Motion Predictions: A Comparison Between a CFD Based Method, a Panel Method and Measurements

In the past 50 years the research into the behavior of ships in seaway has shown a great deal of progress. From analytical solutions of 2-d hydrodynamics as derived by Ursell in 1949 to complex 3-d CFD numerical solutions that can be used nowadays. The first consistent approach for ship motions in time domain was derived by prof. T.F.Ogilvie [] as presented in his seminal paper in Bergen in 1964. Throughout the years however ship hull forms developed and the need for validation of computational procedures for the calculation of the ship motions has never gone away. In this paper we present a selection of results of a benchmark study performed by some 12 companies and universities using their state of the art computational tools. In this benchmark study the results of model tests of a modern container vessel are used. The results presented in this paper show that the panel method as described in this paper, based on the disturbed steady flow, leads to acceptable transfer functions for ship motions. The CFD approach used in this paper also produces acceptable motion transfer functions. However the results from the CFD computation for the internal load transfer functions do show a larger scatter when comparing with the results from model test.Copyright

Improvement of Rankine Panel Method for Seakeeping Prediction of a Ship in Low Frequency Region

Rankine panel methods have been studied for solving 3D seakeeping problems of a ship with forward speed and oscillatory motions. Nevertheless, there is a drawback in the numerical method for satisfying the radiation condition of outgoing waves at low frequencies, because the waves generated ahead of a ship reflect from the outward computational boundary and smear the flow around the ship. The so-called panel shift technique has been adopted in the frequency-domain Rankine panel method, which is effective when the generated waves propagate downstream of a ship. In this paper, in addition to this conventional panel shift method, Rayleigh’s artificial friction is introduced in the free-surface boundary condition to suppress longer wave components in a computational region apart from the ship. With this practical new method, it is shown that there is no prominent wave reflection from the side and/or upstream computational boundaries even in the range of low frequencies. As a consequence, the unsteady pressure, hydrodynamic forces, wave-induced ship motions, added resistance are computed with reasonable accuracy even in following waves and in good agreement with measured results in the experiment using a bulk carrier model which is also conducted for the present study.Copyright

Wave drift forces on two ships in close proximity

Numerical calculation methods are studied for evaluating the wave drift forces and moments on two ships located in close proximity. Hydrodynamic interactions are taken into account by solving the integral equation for the first-order velocity potentials on the whole wetted surface of both ships with a higher-order boundary-element method. The second-order steady forces on each ship are computed by the near-field method and a new far-field method applying the momentum-conservation principle in a fluid region encompassing only either ship. Good numerical accuracy is confirmed by computations for two identical ellipsoids. Computed results are also compared with measured ones for the side-by-side arrangement of a modified Wigley model and a rectangular barge model, and good agreement is found