Effect of springing and whipping on exceedance probability of vertical bending moment of a ship

Abstract

An extreme value distribution method for the vertical bending moment (VBM) is developed using a reduced order model (ROM) based on CFD-FEM coupling. A post-Panamax containership is considered to be a subject model and for which experiment was performed in our previous study. In ROM, VBM for all the components, i.e., wave-induced, whipping, and springing components, are calculated separately and superimposed. The vessel motions and wave-induced components are estimated from transfer functions derived from nonlinear strip theory and later corrected using CFD-FEM coupling. The whipping component is evaluated using von Karman's momentum theory with proper adjustment to specific hull parameters and additionally corrected using CFD-FEM coupling. A new semi-empirical springing ROM is developed based on CFD-FEM coupled analysis and experimental results. A numerous number of irregular waves are generated for a severe short-term sea state using random numbers, for which VBM time series is compared between ROM and coupled CFD-FEM analysis. The effect of springing and whipping in calculating the extreme value distribution of VBM is described for different probability levels. The effect of consecutive bow-stern slamming is also discussed. The development of this method will aid to attain real-time shipload prediction without expensive computational costs due to coupled CFD-FEM.