This paper aims at comparing different implementations of the Morison equation for seakeeping analysis in frequency domain. For more consistency, different wave models are considered and the total wave field (incoming wave, the diffracted and the radiated wave field) is included in the Morison equation. A state-of-the-art of theMorison equation and the drag force linearized forms are presented. The implementation procedure, based on an iterative frequency domain scheme, is developed for the regular and the irregular wave cases. Seakeeping analysis of an offshore wind turbine is considered as an application case. A comparison between numerical simulations and measured responses is presented. For the floater’s numerical model, skirts damping effect and hydrodynamic loads applied on cylindrical bracings are modeled using the Morison equation. The drag and inertia coefficients are considered constant for all sea states and calibrated using the experimental results. Response amplitude operators (RAOs) and short-termstatistics of motions show a good agreement between experimental and numerical results. The influence of different calculation parameters including the wave model (regular/irregular) and the wave fields (incident/total) are investigated.
When the long term behaviour of a floating unit is assessed, the environmental contour concept is often applied together with IFORM (Inverse First Order Reliability Method). This approach avoids direct computation on all sea-states, which is computationally very demanding, and most often simply not feasible. Instead, only a few conditions (the contour) are assessed and results in an accurate estimate of the long term extreme. However, most of available methods to derive the contour require the knowledge of the joint distribution of the different random variables (waves, wind, current...), which is often difficult to derive accurately. In fact, some complex dependences exist and are attempted to be simplified in too few coefficients. Another limitation of current environmental contour is its difficulty to deal with the dependence issue. Indeed, extreme sea-states arise by groups (storms, hurricanes...) and are not independent. While de-clustering techniques exist and are quite straightforward in univariate problems, this becomes difficult when the number of dimension increases. In an attempt to tackle those challenges, this paper presents a novel approach to derive IFORM contours. The method does not require any joint distribution and makes use of much more degrees of freedom to capture the dependence between variables. It also allows for an easy de-clustering. The approach is illustrated on two locations, using actual hindcast data of significant wave height and period; the resulting contours are compared to the ones obtained with more traditional methods.
Diffraction/Radiation theory is used to calculate the wave kinematics and the motions of a floating body in area of varying bathymetry. The bathymetry is modeled as a second body, which, without special measures, leads to spurious reflection at the edge of the mesh. A modified formulation of the Boundary Element Method is introduced to model partially transparent panels. Those panels, when properly used to smoothly extend the actual (opaque) bathymetry, allow much more accurate computation. The efficiency of the method is tested with regards of several parameters concerning the bathymetry size and the way to smooth the truncation. Numerical results are satisfactorily compared with a 3D shallow water code based on Green-Naghdi theory. The sensitivity to the slope on the ship response is then investigated (motion, added mass, radiation damping and second order loads). The differences with the constant depth calculations are significant, due to the modified incident wave field, but also due to modified added mass and radiation damping terms. The method presented here could be useful in the context of LNG terminals where the depth is quite shallow and the bathymetric variations significant.
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