Transient wave model testing for the evaluation of extreme motions and loads of ships and semisubmersibles

Abstract

This paper describes techniques to synthesize deterministic task-related ‘rogue’ waves or critical wave groups for engineering applications. These extreme events, represented by local characteristics like tailored design wave sequences, are integrated in a random or deterministic seaway with a defined energy density spectrum. If a strictly deterministic process is established, cause and effect are clearly related: at any position the non-linear surface elevation and the associated pressure field as well as the velocity and acceleration fields can be determined. Also the point of wave/structure interaction can be selected arbitrarily, and any test can be repeated deliberately. Wave-structure interaction is decomposable into subsequent steps: surface elevation — wave kinematics and dynamics — forces on structure components and the entire structure — structure motions. Firstly, the generation of linear wave groups is presented. The method is based on the wave focussing technique. For a target Fourier wave spectrum a tailored wave sequence can be assigned to a selected position. This wave train is linearly transformed back to the wave maker and — by introducing the electro-hydraulic and hydrodynamic transfer functions of the wave generator — the associated control signal is calculated. The generation of steeper and higher wave groups requires a more sophisticated approach as propagation velocity increases with wave height. With a semi-empirical procedure the control signal of extremely high wave groups is determined, and the propagation of the associated wave train is calculated by iterative integration of coupled equations of particle tracks. In general, extremely high ‘rogue’ waves or critical wave groups are rare events embedded in a random seaway. The most efficient and economical procedure to simulate and generate such a specified wave scenario for a given design variance spectrum is based on the appropriate superposition of component waves or wavelets. The desired characteristics like wave height and period as well as crest height and steepness are defined by an appropriate objective function. The subsequent optimization of the initially random phase spectrum is solved by a Sequential Quadratic Programming method (SQP). The linear synthetization of critical wave events is expanded to a fully nonlinear simulation by applying the subplex method. For investigating the consequences of specific extreme sea conditions this paper analyses the seakeeping behaviour of a semisubmersible and a FPSO in the Draupner New Year Wave, embedded in extreme irregular seas. In addition, extreme roll motions and the capsizing of a Ro-Ro vessel in a severe storm wave group are evaluated, and the procedures for safe ship design and operation are discussed.