Christian E. Schmittner

Bending Moments of an FPSO in Rogue Waves

The increasing numbers of reported rogue waves with extreme crest and wave heights and unusual group pattern with the consequence of severe damages raise the question if such exceptional events have to be considered routinely for the design of ships and offshore structures. For the investigation of the effects of rogue wave impacts time domain simulation methods are required in addition to traditional frequency domain methods which may not be sufficient to consider these extreme events. In this paper the vertical bending moments at the midship section of an FPSO are investigated using state of the art numerical simulation tools in combination with experiments. For the seakeeping tests the extremely high New Year Wave (registered in the North Sea) is generated in the wave tank, and motions and structural forces are analyzed at model scale. For validation the results are evaluated deterministically and compared to numerical simulations. The time domain calculation allows to artificially change local wave characteristics. The steepness of the selected rogue wave is varied and the influence on wave induced loads is studied. A comparison with standard procedures of seakeeping analysis and classification rules closes the paper.Copyright

Numerical Wave Tank: Simulation of Extreme Waves for the Investigation of Structural Responses

For the deterministic analysis of extreme structure behavior, the hydrodynamics of the exciting wave field, i. e. pressure and velocity fields, must be known. Whereas responses of structures, e. g. motions, can easily be obtained by model tests, the detailed characteristics of the exciting waves are often difficult to determine by measurements. Therefore, numerical wave tanks (NWT) promise to be a handy tool for providing detailed insight into wave hydrodynamics. In this paper different approaches for numerical wave tanks are introduced and used for the simulation of rogue wave sequences. The numerical wave tanks presented are characterized by the following key features: a) Potential theory with Finite Element discretization (Pot/FE); b) Reynolds-Averaged Navier-Stokes Equations (RANSE) using the Volume of Fluid (VOF) method for describing the free surface. For the NWT using the VOF method three different commercial RANSE codes (CFX, FLUENT, COMET) are applied to calculate wave propagation, whereas simulations based on potential theory are carried out with a wave simulation code developed at T echnical U niversity B erlin (WAVETUB). It is shown that the potential theory method allows a fast and accurate simulation of the propagation of nonbreaking waves. In contrast, the RANSE/VOF method allows the calculation of breaking waves but is much more time-consuming, and effects of numerical diffusion can not be neglected. To benefit from the advantages of both solvers, i. e. the calculation speed (Pot/FE-solver WAVETUB) and the capability of simulating breaking waves (RANSE/VOF-solver), the coupling of both simulation methods is introduced. Two different methods of coupling are presented: a) at a given position in the wave tank; b) at a given time step. WAVETUB is used to simulate the propagation of the wave train from the start towards the coupling position (case A) or until wave breaking is encountered (case B). Subsequently, the velocity field and the contour of the free surface is handed over as boundary (case A) or initial values (case B) to the RANSE/VOF-solver and the simulation process is continued. To validate these approaches, different types of model seas for investigating wave/structure interactions are generated in a physical wave tank and compared to the numerical simulations.Copyright

Analysis of Design Wave Loads on an FPSO Accounting for Abnormal Waves

The paper presents an analysis of structural design wave loads on an FPSO. The vertical bending moment at midship induced by rogue waves are compared with rule values. The loads induced by deterministic rogue waves were both measured in a seakeeping tank and calculated by an advanced time domain method. Two procedures are used to calculate the expected extreme vertical bending moment during the operational lifetime of the ship. The first one relies on a standard linear long term prediction method, which results from the summation of short term distribution of maxima weighted by their probability of occurrence. The short term stationary seastates are represented by energy spectra and the ship responses by linear transfer functions. The second one is a generalization of the former and it accounts for the nonlinearity of the vertical bending moment, by using nonlinear transfer functions of the bending moment sagging peaks which depend of the wave height.

Experimental Optimization of Extreme Wave Sequences for the Deterministic Analysis of Wave/Structure Interaction

For the deterministic analysis of wave/structure interaction in the sense of cause-reaction chains, and for analyzing structure responses due to special wave sequences (e.g., three sisters phenomenon or other rogue wave groups) methods for the precise generation of tailored wave sequences are required. Applying conventional wave generation methods, the creation of wave trains satisfying given local wave parameters, and the generation of wave groups with predefined characteristics is often difficult or impossible, if sufficient accuracy is required. In this paper we present an optimization approach for the experimental generation of wave sequences with defined characteristics. The method is applied to generate scenarios with a single high wave superimposed to irregular seas. The optimization process is carried out in a small wave tank. The resulting control signal is then transferred to a large wave tank considering the electrical, hydraulic and hydrodynamical response amplitude operators (RAOs) of the respective wave generator in order to investigate wave/structure interaction at a large scale.

Time-Domain Investigation of a Semisubmersible in Rogue Waves

Heave, pitch and roll motions as well as airgap are key characteristics of semisubmersibles in extreme seas which are defined by Ultimate Limit State design conditions (ULS) with a specified 100-year design wave height Hs and peak period Tp . The increasing number of reported rogue waves with unexpected large wave heights (Hmax /Hs > 2), crest heights (ζmax/ /Hmax > 0.6), wave steepness and group patterns (e.g. Three Sisters) may suggest a reconsideration of design codes by implementing an Accidental Limit State (ALS) with a return period of 104 years. For investigating the consequences of specific extreme sea conditions this paper analyses the seakeeping behaviour of a semisubmersible in a reported rogue wave, the Draupner New Year Wave embedded in irregular sea states. The numerical time-domain invegstigation using a panel method and potential theory is compared to frequency-domain results. In particular, the characteristics of the embedded rogue wave is varied to analyse the dynamic response of the semisubmersible in extreme wave sequences For validation, the selected sea condition is generated in a physical wave tank, and the sea-keeping behaviour of the semisubmersible is evaluated at model scale. In conclusion, the results deomstrate the consequences of rogue wave impacts, with respect to the relevance of present design methods and safety standards.Copyright

Non-Linear Calculation of Tailored Wave Trains for Experimental Investigation of Extreme Structure Behaviour

The experimental investigation of extreme wave/structure interaction scenarios puts high demands on wave generation and calculation. This paper presents different approaches for modelling non-linear wave propagation. Results of numerical simulations from two different numerical wave tanks are compared to models tests. A further approach uses analytical wave models which are combined with empirical terms to allow a fast and precise prediction of non-linear wave propagation for day-to-day use. All approaches can be used either separately or in combination — depending on their particular purpose. As an application, different special wave scenarios — both academic and realistic — are generated and validated by measurements. The advantages and disadvantages of the presented methods are discussed in detail with regard to their appropriate use for investigations of extreme structure behaviour.Copyright

Generation of Rogue Waves With Predefined Steepness

For the deterministic investigation of cause-reaction relationships and for analyzing structure responses due to special wave scenarios methods for the precise generation of tailored wave sequences are required. In this paper we present an optimization approach for the experimental generation of wave sequences with defined characteristics, in particular with predefined wave steepness. Firstly, target parameters, such as wave crest front steepness, wave height and wave period at a particular time are defined for a wave group. Starting with a random phase distribution in frequency domain the phases are optimized in order to satisfy the target parameter in time domain. From this optimized target wave sequence a control signal based on linear wave theory for the wave generator is derived and the wave sequence is registered in a physical wave tank. As nonlinear effects like wave-wave interaction and wave breaking are insufficiently covered by the generation process the registered wave train may differ from the target parameters defined. To improve the accuracy of the measured wave sequence at target location the control signal is iteratively improved by a fully automated optimization process, controlling the wave generator, measuring and analyzing the created waves and modifying the control signal. As a result of the optimization process, a control signal for a wave train, satisfying all target parameters is obtained. The method is applied to generate a breaking rogue wave with defined wave crest front steepness superimposed to irregular seas.

Rogue wave impact on offshore structures

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Systematically Varied Rogue Wave Sequences for the Experimental Investigation of Extreme Structure Behavior

For an improved design of ships and offshore structures with regard to their behavior under severe weather conditions, wave height and steepness as well as the shape of the wave profile have to be considered. In this paper, the extreme new year wave as documented in numerous publications is varied with respect to wave height and period. These varied wave sequences are realized and measured in a model tank and applied to the investigation of motions and bending moments of a floating production storage and offloading ship. The results are compared to the responses in the original wave train. An investigation of the riskiness of extreme wave sequences in comparison with existing rules concludes this paper.

Computational and Experimental Simulation of Nonbreaking and Breaking Waves for the Investigation of Structural Loads and Motions

For the analysis of loads and motions of marine structures in harsh seaways precise information about the hydrodynamics of waves is required. While the surface motion of waves can easily be measured in physical wave tanks other critical characteristics such as the instantaneous particle velocity and acceleration as well as the pressure field, especially under the wave crest are difficult and time-consuming to obtain. Therefore a new method is presented to approximate the wave potential of a given instantaneous wave contour. Numerical methods — so called numerical wave tanks (NWTs) — are developed to provide the desired insight into wave hydrodynamics. A potential theory method based on the Finite Element method (Pot/FE), a RANSE (Reynolds-Averaged Navier-Stokes Equations) method applying VOF (Volume of Fluid) and a combination of both is utilized for the simulation of different model wave trains. The coupling of both CFD (computational fluid dynamics) solvers is a useful approach to benefit from the advantages of the two different methods: The Pot/FE solver WAVETUB (wave simulation code developed at T echnical U niversity B erlin) allows a very fast and accurate simulation of the propagation of nonbreaking waves while the RANSE/VOF solver has the capability of simulating breaking waves. Two different breaking criteria for the detection of wave breaking are implemented in WAVETUB for triggering the automated coupling process by data transfer at the interface. It is shown that an efficient method for the simulation of breaking wave trains including wave-structure interaction in 2D and 3D is established by the coupling of both CFD codes. All results are discussed in detail.Copyright