R. Pascoal

Ocean Wave Spectral Estimation Using Vessel Wave Frequency Motions

Wave spectra are estimated from wave frequency motions of a vessel at zero or low advance speed. Minimization of a cost functional that indicates how well the estimated spectrum results in the measured motion spectra was based on sequential quadratic programming and a genetic algorithm. Two procedures have been developed and applied to numerically simulated motions of a 59 m length offshore supply vessel.

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

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 and Numerical Study of the Motions of a Turret Moored FPSO in Waves

This paper presents the results of an experimental program carried out with a model of a FPSO (Floating Production, Storage and Offloading) unit moored and subjected to incoming waves. In regular waves, a wide range of wavelengths were tested and the effect of the wave amplitude was also investigated. In irregular waves the model was subjected to different sea states, including very severe significant wave heights. The measured responses include the six degrees of freedom absolute motions, relative motions, and the mooring forces. The experimental data of surge, heave, and pitch is compared with calculated results from a Green’s function panel method and a strip theory program. In general, the agreement between experimental and numerical data is very good. DOI: 10.1115/1.1951774

Design of a Mooring System With Synthetic Ropes for the FLOW Wave Energy Converter

Martifer Energia is developing a concept of a wave energy converter (WEC) to be used at near shore locations with water depths starting at around 40m. It is a floating device composed of two bodies connected by a one degree of freedom articulation. The energy is extracted at the articulation by a power takeoff system actuated by the relative motion between the bodies. One of the important components of many WECs is the mooring system, since usually the cost is large compared global cost of the device. In this case the WEC will be moored by a spread mooring that allows the device to weathervane with the environmental loads. The paper presents one design solution for the mooring system investigated during the development stage of the concept. It is composed of four hybrid lines, each one with a segment of nylon rope connected to the floating device and a part of chain that contacts with the sea bottom and ends at the anchor. The wave frequency hydrodynamics are first calculated with a frequency domain boundary element method. The nonlinear cable dynamics problem, which is coupled to the slow drift motions of the floater, is solved in the time domain by a finite difference method. The design considers the climatology of the future area of operation of the prototype. Since the loads on the lines depend on the characteristics of the lines themselves, the design solution is obtained iteratively. Appropriate safety factors are considered. The result is the number of mooring lines, their angular separation, length and diameter of each line component.Copyright

Experimental Study of the Probability Distributions of Green Water on the Bow of Floating Production Platforms

Results of an experimental program with a model of a moored floating production storage and offloading vessel are used to study the probability distributions associated with various phenomena related with green water loading. Separate analysis of wave height and crests are performed in order to assess the presence and significance of nonlinearities. Time series of pitch motion and relative motion are analyzed to check for linearity of the response process. Probability distributions of the occurrence of water on deck and of the conditional distribution water height above deck are also studied.

An Approach to Calculate the Probability of Wave Impact on an FPSO Bow

This work aims at characterizing the probability of wave impact and expected impact load on the bow geometry of an FPSO. In order to determine the instants when impact occurs, an experimental program was performed on a specific bow shape. The bow was instrumented with pressure transducers and the test program, also making use of video recordings, was designed such that it was possible to determine the correlation between undisturbed wave shape and the impact pressure time traces. It has been found that wave impact at the bow is highly correlated with the local wave steepness, which for very high waves has at least second order effects. A comparison between the probability distributions of local wave steepness of the experimental undisturbed wave time trace and numerical simulations of second order wave theory is provided and it confirmed that the latter is very adequate for calculations. The experimental results were further used to determine how the probability of impact varies with free surface vertical velocity. It was found that the significant wave height of the sea state itself does not have significant influence on the result and a regression model is derived for that type of bow. The proposed model for determining the probability of impact load is based on combining both models. The analytical nature makes it fast and easy to expand to other cases of interest and some example calculations are shown to demonstrate the relative ease of the procedure proposed. The position of the impact is determined by the non-linear wave crests and the ship motions. The ship motions can be determined based on a linear response to the non-linear waves considered.Copyright

Global Loads on a FPSO Induced by a Set of Freak Waves

The definition of wave induced structural loads for the design of ship structures nowadays is in most cases still based on empirical formulas from classification societies. However, as computers become faster and cheaper, there is a tendency to apply procedures based on direct calculations to define the design wave loads. These procedures rely on models of the hydrodynamics, which are derived from physical and mathematical considerations, together with a proper characterization of the stochastic properties of waves and of ship responses. There are several advantages from using these more advanced methods: eventually the design wave loads will be more accurate and tailored for the specific ship characteristics, novel ship concepts can be assessed while empirical formulas are, in principle, valid for existing ships only, and, besides global structural loads determined by integration along the hull and applied on a resisting transverse section, it is possible to obtain consistent pressures along the hull for finite element calculations, thus including the effects of these pressures on local structural elements. Several procedures have been proposed to calculate the maximum expected wave loads during the ship lifetime, accounting for the stochastic nature of the waves. However, apparently, conditions associated with the encounter of the ship with abnormal waves are not taken into account as the probabilistic models describing the waves do not seem to consider the abnormal waves. An abnormal wave is defined when its height divided by the significant wave height of the sea state is larger than 2. There are some reports from accidents that stated that the accidents resulted from the encounter of the vessels with waves that were much larger than those expected from the existing sea state. It is also believed by some authors that such abnormal waves were responsible for the mysterious vanishing of some ships. For this reason Faulkner and Buckley 1 suggested that the methods to determine the design loads should be revised to account for the effects of the abnormal waves on the ship structure. Existing calculation procedures do not consider abnormal wave conditions.

Global Loads on an FPSO Induced by a Set of Freak Waves

The paper presents a systematic study of the structural loads induced by abnormal waves on a FPSO. This work is a follow-up of a previous investigation that explored the possibility of using freak, abnormal or episodic waves as additional wave load conditions to be considered in the design of ships and offshore platforms. In the previous work, a procedure was developed and implemented to adopt deterministic time series of wave elevation, which may include abnormal waves, as reference design conditions to calculate the wave induced structural loads on ships. An application example was presented for a FPSO subjected to the well known New Year Wave trace that was measured during a severe storm in Central North Sea. In the present paper, the same procedure is applied to obtain the wave induced structural loads on a FPSO, but a systematic investigation is carried out by using a large set of wave traces. These wave traces have been measured at different occasions in the North Sea, additionally at one location in the Central Gulf of Mexico, and they all include episodic freak waves. In this way it is possible to assess the influence of realistic rogue wave characteristics on the wave induced structural loads. Finally, and based on the platform responses to all wave traces, some statistics are produced, regarding the platform responses and structural loads induced by rogue waves.Copyright

Analysis of Wave Drift Forces on a Floating Wave Energy Converter

Wave drift forces acting on floating wave energy converters (WEC) are often the most important loading component for the design of the mooring system. On one hand these forces may be, at least, one order of magnitude larger than wind and current forces, and on the other hand the floating structure and mooring system may respond dynamically to the slowly varying wave drift forces. The paper presents an analysis of the wave drift forces on an articulated floating wave energy converter. Particular attention is given to the effects of the wave energy extraction on the time history of the horizontal drift forces. The hydrodynamic calculations are carried out by a frequency domain Green function panel method, resulting on the transfer function of the WEC motions as well as the transfer function of the mean drift forces. The power takeoff system is represented by a simple linear model where the extracted power is related to the relative velocity in the articulation and the damper of the PTO. With the transfer function of the mean drift forces, the variance spectrum of these same forces is calculated for stationary irregular seastates, and finally time histories of the drift forces are produced for typical operational conditions.Copyright