Spyros A. Mavrakos

Comparison of methods for computing hydrodynamic characteristics of arrays of wave power devices

A comparison of methods for the calculation of the hydrodynamic characteristics of arrays of wave power devices is presented. In particular, the plane-wave approximation and an exact multiple scattering formulation have been used to compute exciting wave forces, hydrodynamic coefficients and q factors for arrays of interacting wave power devices. The results obtained are compared with each other, and accuracy aspects of the computations are stressed and critically assessed.

Non-linear cable response and model testing in water

Abstract It is shown that the dynamics of an elastic cable submerged in a heavy fluid, such as water, are dominated by its elastic stiffness; hence dynamic similitude is ensured only if the elasticity of the line is properly modelled. The dynamic tension may reach large values, possibly exceeding the static tension, and then the free falling velocity of the cable becomes a critical parameter.

Comparative study on mooring line dynamic loading

This paper presents a comparative study on the dynamic analysis of suspended wire and chain mooring lines. This study was initiated by the International Ship and Offshore Structures Congress (ISSC), Committee I2 (Loads) and is briefly described in the 1997 report presented at Trondheim, Norway. The paper provides more complete documentation of the study. A total of 15 contributions were provided giving analytical results based on time or frequency domain methods for a chain mooring line suspended in shallow water and a wire line in somewhat deeper water. Bi-harmonic top end oscillations representing combined wave and drift induced excitation were specified. The mooring line damping results calculated for chain are compared with limited available experimental data, results provided by the participants showing fair agreement despite the complexity of the numerical methods. Predictions of dynamic tension based on time-domain methods are in broad agreement with each other, the estimates of damping showing more scatter. There are wider discrepancies between results based on frequency-domain methods.

Hydrodynamic interaction among vertical axisymmetric bodies restrained in waves

This paper deals with the linearised hydrodynamic interaction problem of regular, small amplitude, surface gravity waves and a stationary group of large, vertical axisymmetric bodies. The developed numerical procedure is based on the physical idea of multiple scattering in conjunction with appropriate eigenfunction expansions for the velocity potential in the fluid domain around each body of the configuration. By superposing the incident harmonic wave and various orders of scattering, due to the remaining bodies, the velocity potential in the vicinity of each particular body is obtained. The method presented is applicable to an arbitrary number of vertical bodies of revolution having any geometrical arrangement and individual body geometries. Numerical results concerning the exciting wave forces and moments for configurations, commonly used in offshore applications, are presented and compared with those of other authors and pertinent experimental data.

DEEP WATER MOORING DYNAMICS

The dynamics of mooring lines for deep water applications with submerged buoys attached to them are studied both experimentally and numerically. First, the theoretical background is outlined. The experimental set-up, as well as the data acquisition procedures, are then detailed. This is followed by a presentation of the obtained results and their comparison with numerical predictions using both time and frequency domain computer codes. Very good correlation is obtained. Finally, the beneficial effects of buoys in reducing the mooring line dynamic tension is shown, provided that proper selection of their size, number and location is performed.

Hydrodynamic coefficients for groups of interacting vertical axisymmetric bodies

Abstract The paper deals with the linearized hydrodynamic forces acting on multiple vertical axisymmetric bodies forced to oscillate either independently or as a unit in water of finite depth. For the solution of the radiation problem an exact semi-analytical method is developed which combines the single body hydrodynamic characteristics with the physical idea of the multiple scattering approach in order to account for interaction phenomena. By superimposing various orders of radiated/scattered waves emanating from one body oscillating in the vicinity of the others, the velocity potential around each body of the multi-component system is obtained. The present method is applicable to arrays consisting of an arbitrary number of vertical axisymmetric bodies having any geometrical arrangement and individual geometry, provided that their vertical projections do not intersect. Extensive numerical results are presented concerning both the hydrodynamic coefficients of various multi-component structures and the corresponding interaction coefficients among their individual members for configurations commonly used in offshore applications.

Bounded and unbounded coupled transverse response of parametrically excited vertical marine risers and tensioned cable legs for marine applications

The paper deals with the non-linear dynamic response in the transverse direction of vertical marine risers or a tensioned cable legs subjected to parametric excitation at the top of the structure. The dynamic model contains both elastic and bending effects. The analytical approach reveals that the dynamic lateral response is governed by effects originated from the coupling of modes in transverse direction. The mathematical model is being treated numerically by retaining a sufficient number of transverse modes. Numerical results are given for specific case studies and refer both to the time histories of the lateral response for all modes of motion, and to the corresponding power spectral densities obtained through FFT. The numerical predictions are suitably plotted and discussed. The calculations concern both the undamped and the damped dynamic system. The damping in the system is a non-linear Morison type term, which describes the effect of the hydrodynamic drag. Both coupled and uncoupled equations are treated and points as well as regions of coupled and uncoupled stability and instability are defined. It is shown that the impacts originated from the coupling, evaluate new instabilities for the respective undamped system. The numerical results obtained through FFT of the time histories, provide qualitative conclusions for the features of the dynamic response for the modes of motions considered. Special attention has been paid to the effect of the hydrodynamic drag for the parametric excitation frequencies that guide the dynamic system to lie within a region of coupled instability.

Wave loads on a stationary floating bottomless cylindrical body with finite wall thickness

Abstract This paper aims at presenting a method for solving the linearised diffraction problem of the interaction between regular sinusoidal, small amplitude incident waves and a bottomless cylindrical floating body with a vertical symmetry axis and finite wall thickness, through the idealisation of the flow field around the structure using ring elements. The horizontal and vertical excitation forces, the rolling moment, the resulting wave motion inside the cylinder, as well as the pressure distribution on the wetted surface of the structure are obtained by solving the diffraction boundary-value problem through the implementation of the Galerkin method. The analytical predictions are compared with other analytical results and pertinent experimental data. Finally, the influence of the wall thickness on the wave loads and the fluid motion inside the pond is examined.

Hydrodynamic coefficients for a thick-walled bottomless cylindrical body floating in water of finite depth

Abstract The paper deals with the linearized hydrodynamic forces acting on a thick-walled, bottomless cylindrical body having vertical symmetry axis and oscillating in water of finite depth. For the solution of the radiation problem, the flow field around the structure is subdivided into ring-shaped fluid regions, in each of which an axisymmetric eigenfunction expansion for the velocity potential is made. By implementing Galerkins method the various potential solutions are then matched and numerical results concerning the hydrodynamic coefficients for heave, surge and pitch motions, as well as the coupling terms between the last two modes are obtained.

Power Absorption by Arrays of Interacting Vertical Axisymmetric Wave-Energy Devices

The paper deals with the evaluation of the optimum wave-power absorption characteristics of arrays of interacting wave-energy devices. The hydrodynamic interference effects among the devices are exactly accounted for using a method that can solve the problem to any desired accuracy. The method is based on single body hydrodynamic characteristics that are properly combined through the physical idea of multiple scattering to account for interaction effects. Extensive numerical results for a variety of different array arrangements and individual device geometries are presented and comparisons are made to predictions based on approximate theories, the accuracy of which is critically assessed.