Background. New challenges in LNG shipping, such as ship size growth, trading routes with more severe weather conditions, need for operating with unrestricted filling level and new propulsion systems attract very much attention in marine and offshore oriented community. One of the main concerns is the prediction of loads caused by violent fluid motion in cargo tanks. In the paper we address the problem of determining characteristic extreme values of sloshing pressures for structural design. This involves estimating ship motion in a long-term period, fluid motion in the tank, excited pressures, and relevant structural responses. Method of Approach. Ship motion analysis is based on linear strip theory. In order to investigate the dependence of the sloshing response on sea conditions, an approach based on statistical characteristics of the tank motion is utilized as well as a multimodal approach for fluid motion in a tank. However, an appropriate theoretical/numerical approach, which can be used for a realistic prediction of the most extreme pressure has not yet been developed. Thus, experiments are utilized for the most severe sea states for a chosen tank filling level. Results. Our main contribution in the paper includes the statistical analysis of experimental short term pressure distribution. The choice and fit of probability distribution models is addressed, with due account of different physical mechanisms causing impacts. The models are evaluated. The most critical tank areas for sloshing loads are briefly discussed. Appropriate dynamic response of the tank structure needs to be investigated by accounting for temporal and spatial distribution of sloshing loads. These two factors are also addressed in the paper. The variability of results obtained by processing data from multiple test runs is discussed. Conclusions. The three-parameter Weibull and generalized Pareto statistical models are fitted to the data and evaluated. They prove to accurately describe sloshing excited pressures. However, the highest data points are underestimated by the both distributions. Generalized Pareto model results in more conservative estimates. The threshold level of peaks used in a fit of generalized Pareto distribution was investigated. Based on this, it is set to a level of a 0.85–0.87 quantile of peak values. The big influence of spatial and temporal distribution on the estimates is reported. Uncertainty in measured pressures originating from inherent fluid motion variability exceeds the uncertainty resulting form ship motions' variability. Moreover, generalized Pareto model results in higher variability.
A need has been identified to improve the knowledge about extreme slamming loads from breaking waves on vertical columns, such as offshore platforms and wind turbine foundations. Due to strongly nonlinear physical mechanisms and large statistical variability, more and improved experimental data are needed, as well as better qualified design procedures. In this paper, model test data and CFD simulations from a recent study with a fixed vertical column are compared and investigated in more detail. Selected individual extreme slamming events due to energetic breaking waves in 1:40 and 1:125 scaled model tests are presented and considered. Waves correspond approximately to extreme breaking wave occurrences in steep energetic sea states with 10-4 annual probability in the Norwegian sector. Slamming pressures on the column wall are measured in time and space by means of a 7 × 7 pressure sensor array covering 19m2 (full scale). Significant spatial variations are observed. When spatially averaged over the array, the observed highest pressures are typically in the range 1MPa–3MPa (full scale), while smaller measuring areas give higher values. This compares roughly to levels found from recent results in the literature; although exact comparison is difficult due to statistical uncertainty issues. Experiences obtained from parallel CFD and PIV activities are also compared to the experiments, from which free-surface particle velocities up to 25m/s (full scale) are estimated in the worst cases. Finally, a simple empirical formula for a slamming coefficient depending on the actual pressure integration area is suggested based on the results.
The long-term extreme pressure in the membrane LNG tank and structural response of the Mark III containment system are addressed. The effect of hull slamming-induced vibrations on the vertical acceleration is investigated and found to be important in certain situations. Determining structural response due to sloshing requires a stepwise approach considering long-term variation of the sea state, ship motion in a stochastic seaway, fluid motion in the tanks, pressures acting on the tank structure, structural load effects, and their comparison with the appropriate resistance. This paper is focused on the determination of the critical conditions to limit the number of combinations of sea states, vessel heading, and speed that need to be considered in estimating extreme sloshing pressures. In this context, an approximate method is introduced and validated. These sea states are determined by a full linear long-term analysis. The response quantiles suitable for the contour line approach are also found using simplified criteria. The effect of avoiding heavy weather in vessel operation on sloshing and whipping-induced pressures is investigated. Sloshing experiments and various scaling approaches are described. Application of the generalized Pareto distribution and correctly determining its shape parameter is discussed. Structural response of the LNG membrane tank wall is investigated. The importance of accounting for the steel flexibility in calculating sloshing response is shown. A new method for approximating the time history of sloshing impact pressure is suggested.
The paper addresses the problem of determining characteristic extreme values of sloshing pressures for structural design. This involves estimating ship motion in a long-term period, fluid motion in the tank, excited pressures and relevant structural responses. Ship motion analysis is based on linear strip theory. In order to investigate the dependence of the sloshing response on sea conditions, a multimodal approach for an initial prediction of pressures in the tank is utilized. However, an appropriate theoretical / numerical approach which can be used for realistic prediction of the most extreme pressure has not yet been developed. Thus, experiments are utilized for the most severe sea states for a chosen tank filling level. In the analysis of experimental short term pressure distribution the choice and fit of probability distribution models is addressed, with due account of different physical mechanisms causing impacts. The most critical tank areas for sloshing loads are briefly discussed. Appropriate dynamic response of the tank structure needs to be investigated by accounting for temporal and spatial distribution of sloshing loads. These two factors are also addressed in the paper.
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