DRAFT-OMAE2009-80187 WAVE ELEVATION BETWEEN ELLIPTICAL STRUCTURES

ABSTRACT The hydrodynamic interaction of waves with arrays of vertical elliptical cylinders is considered. The present paper aims at developing of an efficient calculation method for predicting the extreme elevation of the free surface, in the fluid domain between ship-shaped structures in close proximity. Linear potential theory is employed and the solution method is based on the semi-analytical formulation of the various velocity potentials in elliptical coordinates, using series expansions of Mathieu functions and the so-called addition theorem for Mathieu functions. INTRODUCTION The present paper deals with an important subject which is of both practical and academic interest. Namely, the extreme surface elevation, that is often observed by operators, between ship shaped structures in offshore applications into the open sea, which is apparently caused due to the resonant motion of the fluid confined between the vessels. It has been reported that the concerned impact is more pronounced in specific areas, the location of which with regard to length of the vessel, depends on the wave frequency and evidently, on the angle of heading

OMAE2006-92349 MOORING SYSTEM AND MOTION RESPONSE ANALYSIS OF A GAS IMPORT FLOATING TERMINAL IN OPERATING AND SURVIVAL CONDITIONS

ABSTRACT The present work is dealing with the quasi-static motion response analysis of a Gas Import Floating Terminal that is moored through a turret mooring system. The results of the analysis presented here is part of the work undertaken by the Division of Marine Structures, School of Naval Architecture and Marine Engineering, National Technical University of Athens (NTUA-MS), within the GIFT project that is supported by the EU (GIFT, 2005). The results concern the response of the mooring system and the associated behavior of the floating terminal under specific operating and survival conditions. In addition to the quasi-static responses, the slowly varying motions of the vessel are calculated by applying appropriate frequency domain solution techniques. Finally, some first comparisons between the numerical predictions and pertinent experimental data of physical model tests are given and discussed. INTRODUCTION The analysis of the dynamic behavior of moored floating structures is of particular importance for their detailed design procedure, especially in cases when active control means, i.e. DP thruster systems, are used to control the orientation and the weathervane ability of multiple interacting floating structures. This is directly applied to cases of side-by-side loading / unloading operations of large scale LNG terminals moored through a turret system to the sea bed and LNG carriers berthed alongside them. Among the subjects that deserve special attention are the hydrodynamic analysis of the isolated and the interacting floating structures, the evaluation of mean and slowly-varying wind, current and wave loads, the mooring system design, the motion response analysis of the moored terminal with and without having berthed a LNG carrie

A note on mixed boundary value problems involving triple trigonometrical series

This study was motivated by the two-dimensional hydrodynamic slamming problem of a steep wave hitting a vertical wall. The fundamental problem considers dual impact on the wall at the lower and upper regions resembling the impact of a wave at the time of its breaking. The solution method results into a mixed-boundary value problem that involves a triplet of trigonometrical series which, to the author’s best knowledge, has not been investigated in the past. The formulation of the mixed-boundary value problem is generic and could be used in different fields as well

Three-dimensional steep wave impact on a vertical plate with an open rectangular section

The present study treats the three-dimensional hydrodynamic slamming problem on a vertical plate subjected to the impact of a steep wave moving towards the plate with a constant velocity. The problem is complicated significantly by assuming that there is a rectangular opening on the plate which allows a discharge of the liquid. The analysis is conducted analytically assuming linear potential theory. The examined configuration determines two boundary value problems with mixed conditions which fully are taken into account. The mathematical process assimilates the plate with a degenerate elliptical cylinder allowing the employment of elliptical harmonics that ensure the satisfaction of the free-surface boundary condition of the front face of the steep wave, away from the plate. This assumption leads to an additional boundary value problem with mixed conditions in the vertical direction. The associated problem involves triple trigonometrical series and it is solved through a transformation into integral equations. To tackle the boundary value problem in the vertical direction a perturbation technique is employed. Extensive numerical calculations are presented as regards the variation of the velocity potential on the plate at the instant of the impact which reveals the influence of the opening. The theory is extended to the computation of the total impulse exerted on the plate using pressure-impulse theory

Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity. The linear theory of the velocity potential is employed by assuming inviscid, incompressible fluid and irrotational flow. As the problem is set in 3-D space, the employment of the Wagner condition is essential. The set of equations we pose, is presented as a mixed boundary value problem for Laplace's equation in 3-D. Apart from the mixed-type of boundary conditions, the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface. We make some simple assumptions at the start but otherwise we proceed analytically. We find closed-form relations for the hydrodynamic variables, namely the time dependent potential, the pressure impulse, the shape of the wave front (from the contact point to beyond the cylinder) and the slamming force

OMAE2006-92390 SOLUTION OF THE BOUNDARY LAYER PROBLEMS FOR CALCULATING THE NATURAL MODES OF RISER-TYPE SLENDER STRUCTURES

ABSTRACT The present work treats the problem of the calculation of the natural frequencies and the corresponding bending vibration modes of vertical slender structures. The originality of the study lies on fact that for the derivation of natural frequencies and the corresponding mode shapes, all physical properties that influence the bending vibration of the structure were considered including the aspect of the variation of tension. The resulting mathematical formulation incorporates all principal contributions such as the bending stiffness, the weight and the tension variation. The governing equation is treated using a perturbation approach. The application of this method results to the development of two boundary layer problems at the ends of the structure. These problems are treated properly using a boundary layer problem solution methodology in order to obtain asymptotic approximations to the shape of the vibrating riser-type structure. It should be noted that in this work the term 'boundary layer' is not connected with fluid flows but it is used to indicate the narrow region across which the dependent variable undergoes very rapid changes. Frequently these narrow regions adjoin the boundaries of the domain of intersect, especially when the small parameter multiplies the highest derivative