Relative Wave Elevation Research Articles

On the hydrodynamic response and slamming impact of a cylindrical FPSO in combined wave-current flows

Owing to the lower construction and transportation costs, cylindrical floating production storage offloading (CFPSO) has received extensive attention in the industry. Currently, attention has primarily been focused on the damping performance of heave plate while few studies have touched upon hydrodynamic characteristics under complex combined wave-current condition. In this paper, we numerically investigate the hydrodynamic response and slamming impact of a CFPSO under combined wave-current flows. The active wave generating-absorbing boundary condition (GABC) along with the buoyancy-modified k-omega SST turbulence model are utilized to generate high-precision waves and current based on the open source computational fluid dynamics (CFD) framework OpenFOAM. A self-developed six degree of freedom (6DOF) motion module is used for solving rigid body motion and updating mesh motion. The numerical results of motion response and impact pressure are compared with the experimental data to verify the accuracy of present simulations. The correlation between impact pressure and relative wave elevation and wave velocity is analyzed and three types of slamming events have been identified. The flow fields such as vorticity, pressure and streamlines in the vicinity of the CFPSO are also presented and discussed, which provides a reference for structural design for the CFPSO under complex sea conditions.

An experimental study on added resistance focused on the effects of bow wave breaking and relative wave measurements

The added resistance is a resistance component that is not yet satisfactorily predicted, although its accurate estimation is crucial – both from an environmental and economic point of view – from the design stage of a ship until its operation. One of the possible sources of overprediction is the occurrence of bow wave breaking. The first aim of this paper is to study the effect of bow wave breaking on added resistance by combining visual observations with resistance tests. On the other hand, as the bow region of a ship appears to be the most dominant contributor to added resistance, this paper introduces a dynamic waterline detection method involving stereo vision. This experimental method is applied to reach the second aim of this paper, which is to stress the importance of the relative wave elevation in the bow region of the ship. By placing stereo rigs inside the hull of a semi-transparent ship, the waterline at each momnent in time can be tracked using an edge detection algorithm. By performing resistance tests on the Delft Systematic Deadrise Series ship model no. 523, the added resistance is observed to be proportional to the relative wave height squared. The data of the experiment and the information necessary to reproduce the experiment are shared through https://doi.org/10.4121/19525852.

An experimental study on characteristics of relative wave elevations around a tension leg platform in irregular waves

In this study, a series of model tests were performed to study the relative wave elevation responses around a tension leg platform (TLP) in extreme waves. It is well known that a high relative wave elevation causes a horizontal wave impact or a wave-in-deck impact which can result in a serious damage on both fixed and floating offshore structures. In particular, tension leg platform can be exposed to severe wave-in-deck impact events due to nonlinear wave amplifications inside the multiple columns. Irregular wave tests including the waves of 100-year return periods were carried out at Ocean Engineering Basin of KRISO. Focus is on the nonlinear characteristics of the relative wave elevations. Probability of exceedance as well as time series for relative wave elevation are suggested and discussion is made on the effect of location, wave and current. Also, wave-in-deck events are described based on the model test observations.

Analysis of Relative Wave Elevation Around Semi-submersible Platform Through Model Test: Focusing on Comparison of Wave Probe Characteristics

Recently, as the offshore structures are operated in the deep-sea oil fields, interest in the analysis of relative wave elevation around platforms is increased. In this study, it is examined how the analysis results differ depending on the characteristics of the wave probe when interpreting the relative wave elevation in the model test. First, by conducting the wave probe comparison experiment in the two-dimensional wave tank, it is confirmed how the measured values differ according to the type of wave probe for the same physical phenomenon. Two types of wave probe are selected, the resistance type and the capacitance type, and the causes of the difference in measured values is studied. After that, the model test of the semi-submersible platform is conducted to investigate the relative wave elevation. Relative wave elevation is measured with the wave probes used in the wave probe comparison experiment and analyzed to estimate the asymmetric factor and the extreme upwell. The results between the two types of wave probes are compared, and qualitative study for the cause of the difference is conducted by photographing the physical phenomenon using a high-speed camera. Through the above study, it is confirmed that the capacitance type wave probe shows a larger measured value than the resistance type under the breaking-wave condition, and the same results are obtained for the asymmetric factor and the extreme upwell. These results is thought to be due to the difference in the measurement principle between wave probes, which is whether or not they measured water bubbles. This implies that the model test should be conducted using appropriate wave probes by considering the physical phenomenon to be analyzed.

Screening wave conditions for the occurrence of green water events on sailing ships

Design loads for extreme wave events on ships, such as slamming and green water, are hard to define. These events depend on details in the incoming waves, ship motions and structure layout, which requires high-fidelity tools such as CFD or experiments to obtain the correct loads. These tools (presently) do not have the capability to fully resolve the long-term statistics of rare events in all metocean conditions over the ship’s lifetime. The idea of ‘screening’ is to use lower-fidelity numerical methods to identify the occurrence of extreme load events based on an indicator. A good indicator has a strong correlation to the design load, but is easier to calculate. A high-fidelity tool can then be used to find the loads in these events. The low-fidelity statistics and the high-fidelity loads can be combined to define a design load and its probability. The present study compares different numerical screening indicators for green water loads on a containership against experiments. The quality of the identification of the critical events and the required computational time served as comparison metrics. This showed that screening both with potential flow tools and with coarse mesh CFD tools is feasible, provided the indicator, grid, time step and wave input settings are well chosen. The results from coarse mesh CFD are slightly better than from potential flow, but the computational costs are much higher. The results also show that the peaks and steepness of the relative wave elevation around the bow are suitable green water load indicators, as well as the undisturbed wave crests at the bow. Fine mesh CFD calculations were done for the identified events based on an example indicator, which resulted in a green water load distribution very close to that of the experiments. This study shows that screening could potentially reduce the required high-fidelity modelling time with up to ∼90% compared to common practice.

Study on Nonlinear Stochastic Process of Deck Slamming on Floating Offshore Platform

In this paper, a semi-analytic method is introduced to predict the deck-slamming probability and corresponding loads. This method is based on a nonlinear statistical approach that takes into account the linear and second-order components of the relative wave elevation up to the second order. The linear and second-order wave elevation is assumed to be a two-term Volterra series. The joint probability density function of the relative wave elevation and velocity are formulated using the Hermite-moment method, and the probability distributions of the wave crest and relative wave velocity are calculated. These probability distributions are verified using the data sampled from the linear and second-order relative wave elevation. Based on this formulation, the probabilities of deck slamming and slamming-induced loads are estimated. This method is applied to a tension leg platform (TLP) model, and the effects of the second-order component of the relative wave elevation on the deck slamming are investigated.

Multi-objective parametric optimization of FPSO hull dimensions

In order to achieve a good and competitive FPSO design, the building cost and the motion performances are the two most critical and conflicting KPIs to be considered. In this study, the author's previous work (Lee, et al., 2021) on the optimization of an FPSO's hull dimensions with 1800 MBBLs storage capacity at Brazil field was extended using a multi-objective parametric optimization with the hull steel weight and the operability which are closely related to the building cost and the operational cost during the lifetime, respectively. For the purpose of more realistic and practical FPSO design, the constraints related to crew comfort and the safe helicopter take-off and landing operation were newly added. Also, the green water on deck was calculated accurately to check the suitability of the designed freeboard height using a newly developed real-time calculation module for the relative wave elevations. With aids of this updated optimization formulation, we presented multiple optimal FPSO dimensions expressed as a Pareto set which aids FPSO designers to conveniently select the practical and competitive dimensions. The excellence of the developed approach was verified by comparing the optimization results with those of FPSOs dimensioned for operation at West Africa and Brazil field.

Effects of the asymmetric riser and bilge keel arrangements on FPSO green water assessment

This article aims to report important findings on how the asymmetric riser and bilge keel arrangements affect the motion response and green water assessment by using a real FPSO conversion project. Recently, the authors have proposed a practical approach for short-term and long-term green water prediction. In this paper, the method has been further extended to include the effect of truncated bilge keel by using Morrison elements. Numerical studies are conducted focusing on the effect induced by asymmetric riser arrangement and truncated bilge keels. Comparisons of short-term and long-term results between different models indicate that the FPSO’s motion is significantly affected by asymmetrically arranged appendages and attachments in a complicated way. The relative wave elevation is also affected by appendages and attachments, but not the same trend as the motion response. The effect of the asymmetric arrangement of risers and bilge keel on long-term relative wave elevation response has been captured by both traditional contour line approach and response-based analysis, but some discrepancy identified between the results from the two methods indicates the limitation of the traditional contour line approach.

Probabilistic analysis of air gap of tension-leg platforms by a nonlinear stochastic approach

In this study, the statistical behavior of the air gap of a tension-leg platform was investigated using an efficient analytic approach. The potential flow theory up to second order can be used to model the wave elevation around the platform as a two-term Volterra series, whose statistical moments are available from an eigenvalue problem formulated with the wave spectrum and the frequency-domain transfer functions. Then, the Hermite-moment method is applied to estimate the probability distribution and the upcrossing rate of the wave elevation, which can be used to estimate the extreme air gap. The following two topics are mainly discussed: the effect of the short-crestedness of the sea state, and the effect of the set-down of the platform caused by horizontal displacement. A rational formulation for the upcrossing rate of the relative wave elevation is suggested, taking into account the non-Gaussian nature of the nonlinear wave elevation and the platform set-down.

Green sea loads in irregular waves with Finite Volume method

Extreme green sea loads upon a vertical deck structure of an Ultra Large Container Ship are calculated in this paper using Finite Volume based CFD simulations in full scale, where two different approaches for the definition of the Equivalent Design Wave are used. Linear frequency–domain method is used to calculate the long–term response in terms of Relative Wave Elevation, which in turn is used to define a deterministic Equivalent Design Wave which is then used in the CFD simulation. The simulations are conducted using a newly developed flow model that takes into account air compression in violent free–surface phenomena. Regular Equivalent Design Wave and Response Conditioned Wave approaches are used and compared in terms of loads exerted on the deck structure and required computational resources. Some differences in loads are found between the methods, whilst similar computational resources are required. The Regular Equivalent Design Wave gives larger loads, making it a safer choice. However, the Response Conditioned Wave takes into account the relevant ocean wave conditions as well as the response of the ship, resulting in smaller loads which would enable smaller structural scantlings and cost savings.

Study on green water prediction for FPSOs by a practical numerical approach

The growing usage of permanently moored floating production storage and offloadings (FPSO) in harsh environment regions increases the frequency and severity of the green water problem. Many numerical researches on green water prediction for FPSOs have been carried out. Most of the past researches chose to neglect or consider only part of the effects by appendages and attachments, such as bilge keel, mooring lines, and risers. The influences of these appendages on green water prediction have not been thoroughly studied. This paper presents a practical numerical approach of green water prediction for FPSOs in irregular waves. The calculation of relative wave elevation is conducted in frequency domain, including linear and nonlinear effects of bilge keels, spread mooring system, and asymmetrically arranged risers. Numerical approach was applied to calculate the statistical distribution of relative wave elevation for an FPSO. Comparison with experimental results showed that the accuracy of relative wave motion prediction is significantly improved by incorporating the linear and nonlinear effects of bilge keels, mooring, and risers. Analysis of the results by different numerical models further indicated that the relative wave elevation at sides of the FPSO in oblique waves was strongly affected by bilge keel, mooring, and risers.

Offshore Operational Availability of Onboard Direct Injection of CO2 into Sub-seabed Geological Formations

Offshore operational availability was investigated for the proposed handling system consisting of the carrier vessel equipped with dynamic positioning capability, on-board manual operation of picking-up the sea-surface float connected to the upstream end of the flexible riser pipe laid-dawn on sea floor.An offshore site was selected to collect the oceanographic off the southern part of Japan facing to the Pacific Ocean. The response amplitude operator of the proposed CO2 carrier vessel was calculated based on 3-D Singularity Distribution Method. Based on the result of the interview survey with captains of research vessels which showed that for offshore operations a vessel's pitch motion and service deck wetness are dominant factors which define a vessel's operational availability, the RAO of the pitch and relative wave elevation was evaluated.The hull motions and the relative wave elevation in unidirectional irregular waves and in multidirectional irregular waves were calculated by a conventional method based on the seakeeping theory using the RAOs, the wave spectrum and the directional wave spectrum.Under the assumption that the operational availability of the proposed CO2 carrier vessel is constrained by the pitch motion and the service deck wetness, the allowable upper limit values of the significant wave height were calculated by a conventional method based on the sea keeping theorem using the 1/10 maximum expected response value of pitch motion and the relative wave elevation evaluated in the above-mentioned calculation. The threshold value of operation availability was set at the pitch of 3.0 degrees and the relative wave elevation at the freeboard to the service deck, based on the result of the interview survey with captains of research vessels.Finally, the overall operational availability was estimated, on the assumption that the threshold value of operation availability was set at the pitch of 3.0 degrees and the relative wave elevation at the freeboard to the service deck.We concluded that the operational availability of the proposed CO2 carrier vessel reaches a target value of nearly 90% for both full year and four seasons in the case that freeboard of service deck for offshore buoy picking-up operations set greater than 2.3 m as a service platform.

Experimental investigation on wave run-up characteristics along columns and air gap response of semi-submersible platform

This article mainly concentrates on a large-volume drilling semi-submersible platform, aiming to reveal wave run-up characteristics along square columns and give the relationship between air gap distributions and wave parameters. The tests with fixed model were conducted firstly on its encountering a series of monochromatic waves. A wide range of wave slope ( H/ L) were selected to investigate the air gap response in detail. As can be seen, larger wave steepness will generally cause smaller air gap in the same wave period, which indicates nonlinear effects of incoming wave can amplify wave elevation. Model tests with mooring condition were also conducted in the same wave conditions. As was expected, the maximum relative wave elevation reduces obviously compared with the fixed one. However, wave shape close to columns show higher harmonic characteristics due to interaction between waves and the columns of semi-submersible platform. Meaningful conclusions from the model tests are drawn in this article, which is helpful in air gap design of floating offshore platform to a certain extent. In addition, the experimental results will provide an important reference for further research on validation and update of theoretical models of air gap.

Statistics of Extreme Events in Airgap Measurements

The paper presents a study of the extreme value statistics related to airgap measurements on a scale model of a semisubmersible platform subjected to random waves in a wave basin. Relative wave elevation records corresponding to totally 24 h storm duration are considered, made up by 8×3 h realizations. The focus is on a comparison of two alternative methods for the prediction of extreme values from finite recordings at two different locations at the platform. One is a standard method used in the wave basin, making use of a Weibull-tail fitting procedure. The other is a novel method based on the level upcrossing function combined with an optimization procedure that allows prediction at extreme response levels. Similar results are obtained in the mean values by the two methods, while the latter shows less variability in the predictions from single 3 h records.

Analysis of hydrodynamic characteristics for arbitrary multihull ships advancing in waves

Multihull vessels have emerged as popular alternatives to conventional monohull ships for high-speed crafts. However, the bridging structures connecting the hulls are vulnerable to various wave actions and the wave impact on the bottom of them is the most serious problems associated with multihulled vessels. In this study, prediction of relative wave elevations under the bridging structures is investigated for multihull ships traveling with forward speed in waves. A computer code YNU-SEA using the three-dimensional (3D) Green function method with forward speed has been developed and used to analyze the hydrodynamic radiation and diffraction forces and motion responses for high-speed catamarans in waves. The results of the present calculations are compared with those of previous calculations as well as with experimental results. The numerical results reveal that the present computer code can be used as a powerful tool for the accurate numerical computation of seakeeping problems for multihull ships advancing in waves. Numerical calculations of wave pattern are also carried out including wave interactions between the hulls to analyze the effects of hull form on the free surface flow around catamarans advancing in waves. The analysis of the wave pattern allows the determination of relative wave height including radiation and diffraction waves. Finally, some discussions are included based on these numerical results which may be helpful for the accurate prediction of relative wave height and wave breaking load on the deck associated with multihull ships.

Broaching prediction in the light of an enhanced mathematical model, with higher-order terms taken into account

We have attempted to develop a more consistent mathematical model for capsizing associated with surf-riding in following and quartering waves by taking most of the second-order terms of the waves into account. The wave effects on the hull maneuvring coefficients were estimated, together with the hydrodynamic lift due to wave fluid velocity, and the change in added mass due to relative wave elevations. The wave effects on the hydrodynamic derivatives with respect to rudder angles were estimated by using the Mathematical Modelling Group (MMG) model. Then captive ship model experiments were conducted, and these showed reasonably good agreements between the experiments and the calculations for the wave effects on the hull and the rudder maneuvring forces. It was also found that the wave effects on restoring moments are much smaller than the Froude–Krylov prediction, and the minimum restoring arm appears on a wave downslope but not on a wave crest amidship. Thus, an experimental formula of the lift force due to the heel angle of the ship is provided for numerical modelling. Numerical simulations were then carried out with these second-order terms of waves, and the results were compared with the results of free-running model experiments. An improved prediction accuracy for ship motions in following and quartering seas was demonstrated. Although the boundaries of the ship motion modes were also obtained with both the original model and the present one, the second-order terms for waves are not so crucial for predicting the capsizing boundaries themselves.

Air Gap Response of Floating Structures: Statistical Predictions Versus Observed Behavior

The air gap response of a specific semi-submersible platform subjected to irregular waves is considered. Detailed model tests for this structure are studied in depth. Using time-histories of both motions and air gap, statistical analyses both for the absolute near-structure wave elevation (with respect to a fixed observer), and the relative wave elevation (with respect to the moving structure) are performed. Statistics of wave crest amplification, due to diffraction, are established. Corresponding amplification factors are derived from linear diffraction theory, and the results of theory and observations are critically compared.

Wave Loads Acting on a Blunt Ship in Regular and Irregular Extreme Waves with Green Sea Loading on Decks (1st Report : Model Tests)

Wave basin experiments of a blunt ship model were conducted comprehensively in regular and irregular extreme waves. Six degrees of motions, vertical as well as horizontal bending moments at the midship section, hydrodynamic pressures on the hull at 20 locations, relative wave elevations at 5 locations and green sea loads on fore deck and two hatch covers were measured in a quite systemic manner. The selected regular wave conditions were 5 different wave encountering angles, 6 different wave frequencies and 4 different incident-wave heights, while the selected irregular ones were only the head and beam seas with the significant wave height of 10.6 meters and the mean wave period of 14 seconds. The main purpose of the experiments is to investigate and understand the characteristics on the wave-induced motions, hydrodynamic pressures and loads in extreme waves especially as the green sea loading on the decks. And the final objective of this study is to establish practical approaches of evaluating wave loads in extreme waves qualitatively and quantitatively. As the first report of this study, this paper mainly introduces the results obtained by the experiments. The nonlinear characteristics with respect to wave height of wave-induced ship motions and loads in extreme waves are also discussed with the phenomenon of the green sea loading on the decks.

On the Stability and Wave Profile of a Ship in Oblique Waves

In the paper, the analyses of the stability and resultant wave profile for a ship advancing in oblique waves are made. A time simulation technique based on the previously well developed strip theory is used to calculate the ship motion and the relative wave elevation along the ship. An Instant Grid-Generation (IGG) technique is also applied to reduce the laborious work for the input preparation. The resultant wave elevation includes not only the incident wave but also the diffraction and radiation waves. To analyze the ship stability in waves, the instantaneous wave profile along the ship is derived. The wave profile prediction is also improved by using a more accurate estimation between the incident wave and hull side. The related hydrodynamic coefficients are treated in the manner of large ship motion, hence it is a nonlinear problem. From the present analysis, it is found that the ship stability in waves indeed differs from that in calm water. The authors regard that the present technique can offer more general ship stability analysis and will be helpful to understand the ship capsizing behavior in waves.

An Analysis of Water Shipping Between Two Floating Platforms in the Beam Waves

This paper presents a frequency domain method for predicting the relative wave elevation due to the hydrodynamic interaction between two floating structures in the beam waves. The strip method has been found to be a practically useful technique to analyze the hydrodynamically coupled motions of two parallel structures in waves. The two-dimensional procedure which is an integral equation method is therefore used in this paper. The present study uses the linearized resultant pressure including the interaction effect to calculate the wave elevation. Both diffraction and radiation cases are considered. The relative wave elevations at each hull are investigated and the wave elevation amplitudes along the sea surface between two structures are also analyzed. It was found that some significant waves occur at the coupled resonance of the body motion. Therefore, the water shipping must be considered as an important factor for the safety of cargo transfer problem. The results shown in the paper may be regarded as analytically reasonable from the viewpoint of energy conservation.