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Most of the floating wind turbine (FWT) sub-structure concepts are designed with long natural periods of the vertical motions to de-tune from the wave frequency range. The consequence is that the natural frequencies of heave, roll and pitch are excited by low frequency wave and wind loads. The paper focus is on the low frequency (LF) wave drift loads and the related heave and pitch responses of a semi-submersible type of FWT (12MW INO WINDMOOR). It presents several approaches to calculate the wave drift force coefficients and related forces in irregular waves, namely mean wave drift coefficients combined with Newman’s approximation, quadratic transfer functions (QTFs) neglecting the free surface integral from the 2nd order potential flow solution and QTFs based on the full 2nd order solution. The different approximations are used to perform nonlinear time domain simulations of the FWT motions and the results compared to the model test data (the model tests were performed in the ocean basin of SINTEF at a scale of 1:40). The LF damping of heave and pitch is represented by a linear and a quadratic damping coefficient identified from decay model tests. The coupled numerical solution requires a correct representation of the surge mode of motion. In this case, the wave drift forces are represented by empirical QTFs, while the LF damping includes a contribution from the calm water damping represented by a linear and a quadratic coefficient, together with a wave drift damping coefficient. The numerical results show a good agreement with the model test data in irregular waves when full QTFs are used to calculate the wave drift forces.

An accurate estimation of the low-frequency wave loads on floating wind turbines is important for design of mooring systems. In order to add wave drift viscous effects, to the potential flow loads from radiation/diffraction codes, one approach would be to use the drag term in Morison’s equation integrated to the instantaneous free surface. The aim of this study is to define the drag coefficients depending on distance to free surface and KC (Keulegan-Carpenter) number. A systematic series of CFD simulations of Stokes fifth order waves has been done for a fixed structure resembling the floating wind turbine structure studied in WINDMOOR project. Simulations are run with the CFD code STAR-CCM+. The structure is a tripod composed of three vertical columns joined at the bottom by pontoons and at the top by deck beams. As one of the steps towards the analysis of the whole structure, the sectional CFD forces on one of the columns is studied here. Morison mass and drag coefficients are determined for each cross section of the column from the CFD simulation. Obtained sectional coefficients and total forces are compared with the available experimental data in the literature for a circular cylinder. The possible interaction effects between the columns are investigated. Forces on the sections close to the free surface are addressed and the accuracy of the Morison formula for these sections is discussed.

Calculation of wave drift forces in the context of mooring analysis is usually performed by potential flow boundary element methods. For monohulls with large waterplane area, such as floating, production, storage and offloading vessels (FPSOs), the assumption is that heave and pitch damping is dominated by inviscid radiation of waves. The present study investigates the effects of heave and pitch wave frequency viscous damping on the horizontal wave drift forces of a FPSO. Experimental evidence indicates the presence of non-negligible viscous damping in case of moderate and severe seastates. Such observation is confirmed by computational fluid dynamic (CFD) simulations of forced harmonic motions with different periods and amplitudes. On a second step, a numerical analysis shows that the surge wave drift forces increase significantly at the low frequency range when realistic heave and pitch viscous damping is considered. The frequency range where standard potential flow calculations appear to underestimate wave drift forces coincides with the range where design seastates have most of the energy. Finally, the wave drift coefficients calculated with realistic additional viscous damping are compared with empirical coefficients identified from model test data. The identification procedure follows a second order signal analysis technique known as cross bi spectral analysis.

A number of incidents of wave-induced loss of position for dynamically positioned semi-submersible under normal operating conditions have occurred in the Norwegian offshore sector in recent years. A study has been carried out to seek their cause. One hypothesis for the cause has been slamming load from an extremely tall and steep wave that is not effectively counteracted by the DP system due to delays in signal filters and thruster response. Another cause could the loads from a train of tall and steep waves. A linear single-degree-of-freedom numerical model is made for a vessel with DP. The model is essential in that it represents the basic characteristics of the DP system: State observer/filter and feedback control. The model is used to calculate the frequency response and the impulse response of the dynamically positioned semi-submersible. By calculating extreme impulsive load based on published theory it is established that slamming will not cause great vessel excursion. Still, due to delays, the DP system gives more than twice as large excursion as a mass-spring-damper system with identical restoring stiffness and damping. Using an advanced model for vessel with DP, three-hour simulations of stochastic vessel response are carried out for five steep wave states of moderate significant height, The likely cause of large vessel excursion is found to be wave-drift. Due to additional viscous loads on the semi’s columns the wave-drift loads will be significantly larger than predicted with potential theory.

This paper presents a comparison study on wave drift models as well as corresponding low frequency (LF) drift motions for mooring analysis of a spread moored FPSO in moderate seastates with and without current. There are four wave drift force models applied in this study, including two numerical models from potential theory with Newman’s approximation and full quadratic transfer functions (QTFs), two combined models determined from cross bi-spectral (CBS) analysis of model test data and merged with two numerical potential flow wave drift force models at low and high frequencies, respectively. The comparison is performed in terms of both diagonal and off diagonals with constant difference frequency. The equations of motion are solved in the time domain with a fully coupled method, accounting for different wave drift forces models. Both the LF motion response spectra and the time domain series are presented and discussed. The LF damping is adjusted by comparing simulations to the corresponding model test data and tuning the results. The results show the underestimates of wave drift forces as well as the corresponding LF motions by second order potential flow theory, especially in the cases with current. Application of full QTFs can improve the simulation results in terms of phasing of LF responses.

State of the art ULS/ALS mooring analysis is based on potential flow calculated wave drift forces. However, it is acknowledged that higher order effects in steep sea states increase the wave drift forces as compared to the potential flow 2nd order models. This is the background for the EXWAVE 2 JIP where semi-empirical methods to correct wave drift forces were implemented and checked, which shows the significance of this problem to the industry. This publication aims at applying CFD simulations to better understand the physics of wave drift loads in steep sea states and to identify higher than 2nd order effects. Calculations are performed with a RANSE-VOF based CFD code and with a linear potential flow code for a floating production storage and offloading (FPSO) unit in deep water regular waves with three periods and three wave steepnesses. The vessel is restrained from moving to make a simple and a consistent comparison between the results from the two approaches. Comparisons for small amplitude waves provide an assessment of the quality of the CFD simulations, while increasing wave steepness conditions are used to identify higher than second order effects on the wave drift forces. CFD simulation resulting force time series are decomposed into mean value and harmonics by means of a Fourier analysis and compared against potential theory estimated mean and first order forces. The comparisons for small wave amplitudes show a good agreement, which proofs the correctness of the applied CFD setup. Further, the CFD results show an increasing trend of the mean wave forces normalized by the wave amplitude squared with increasing wave steepness for the two shorter wave periods. The trend is unclear for the longer wave period.

Model tests were performed with a model of the INO WINDMOOR 12 MW floating wind turbine in the Ocean Basin at SINTEF Ocean. The tests were done at a scale of 1:40. RealTime Hybrid Model testing was used for the modelling of the wind turbine rotor and aerodynamic loads. A subset of the results is analysed to study the influence of the wind on the platform motions, the acceleration at tower top, the loads at base of tower and the relative wave elevation. The study is based on the comparison of the quantities of interest for different tests with the same moderate sea-state but with different wind modelling: no wind, constant thrust force, turbulent wind of 11.5 m/s and turbulent wind of 25 m/s. The wind modelling has a minimal influence on the platform surge and pitch response in the wave-frequency range. On the other hand, the aerodynamic loads, including wind turbine controller dynamics and turbulent wind, has an important impact on the low-frequency surge and pitch response. The aerodynamic loads are important for the loads at tower base due to the dominance of the tower-RNA induced gravitational loads at low-frequency. Maximum relative wave elevation was found to be mainly dependent on the thrust induced mean pitch angle.

Design optimization of mooring systems is an important step towards the reduction of costs for the floating wind turbine (FWT) industry. Accurate prediction of slowly-varying horizontal motions is needed, but there are still questions regarding the most adequate models for low-frequency wave excitation, and damping, for typical FWT concepts. To fill this gap, it is fundamental to compare existing load models against model tests results. This paper describes a calibration procedure for a three-columns semi-submersible FWT, based on adjustment of a time-domain numerical model to experimental results in decay tests, and tests in waves. First, the numerical model and underlying assumptions are introduced. The model is then validated against experimental data, such that the adequate load models are chosen and adjusted. In this step, Newman’s approximation is adopted for the second-order wave loads, using wave drift coefficients obtained from the experiments. Calm-water viscous damping is represented as a linear and quadratic model, and adjusted based on decay tests. Additional damping from waves is then adjusted for each sea state, consisting of a combination of a wave drift damping component, and one component with viscous nature. Finally, a parameterization procedure is proposed for generalizing the results to sea states not considered in the tests.

This paper presents parameter sensitivity analysis for a FPSO numerical model updating. Generally, model test data are considered a better presentation of physical phenomena than its numerical counterpart. To minimize the discrepancy, model updating is of pragmatically importance. Model updating of a certain FPSO can be achieved by specific steps. In each step, the required properties of numerical model and test results are matched by means of tuning of the related parameters. To avoid inefficiency and physical meaning loss resulting from large modification of parameters which are insensitive to objective properties, parameter sensitivity analyses using the direct method are conducted in this paper. The investigated parameters mainly are the FPSO’s mooring line length, mooring line mass per unit length, mooring line cross-sectional area, fairlead position, FPSO hydrostatic stiffness, FPSO mass properties, linear and quadratic damping coefficients. According to the different stages of FPSO model updating, the objective functions are set to be the FPSO’s mooring line pretension, mooring system horizontal restoring force, the natural periods of the FPSO’s 6 degree of freedom motions and the standard deviation of motion response spectra under irregular waves.

This paper investigates three different approximations of the full Quadratic Transfer Function (QTF) for calculating horizontal plane second-order difference-frequency loads on FPSOs, namely Newman’s approximation, full QTF without free surface integral and the white-noise approximation. Second-order excitation loads obtained from approximated QTFs are compared in frequency-domain with those obtained by the full QTFs computed from second-order diffraction/radiation analysis in WADAM. The comparison is performed for a new-build FPSO in a range of water depths and environmental combinations. The full QTFs from second-order diffraction/radiation analysis are further compared to empirical QTFs as identified from cross bi-spectral analysis of model test results in irregular waves. A mesh convergence study is presented for calculating full QTFs by the near-field approach in a second-order diffraction/radiation analysis. The importance of including viscous damping in heave, roll and pitch is illustrated for the mean wave-drift force in surge and sway. FPSO motions and mooring line tensions from fully-coupled time-domain analysis in OrcaFlex is compared when using approximated QTFs and full QTFs from second-order diffraction/radiation analysis.

Prediction of shallow water low frequency (LF) motions of vessels in the context of mooring analysis is challenging. Model tests are often performed to calibrate and validate numerical models and, in this way, reduce the uncertainty. Model tests are part of the positioning system qualifying process. However, model tests also present challenges and uncertainties related to parasitic low frequency wave systems which are unavoidable in shallow water ocean basin conditions. The paper presents model tests with a ship moored in shallow water (20 m), the analysis and discussion of the test data and comparisons with numerical predictions. The focus is on the low frequency motions and related wave drift forces. The tests have been performed in harmonic waves, bi-harmonic waves and irregular seastates, including conditions with and without current. The first part of the study consists of analysing the wave field measured by a long array of wave sensors distributed along the ocean basin. The analysis provides split wave systems, namely the low frequency components including the bound wave, the incoming free parasitic wave, the reflected component and additional very long waves. The second part proposes a method to calibrate and validate mooring analysis numerical models, based on comparisons with model test data which includes the unavoidable effects from parasitic waves. Simulations of LF motions with the calibrated model show a good agreement with the measurements.

The paper presents calibration of a time domain numerical model for the motions of the Exwave Semi in high seastates with current. The time domain equations of motion combine linear radiation, linear diffraction and second order wave drift forces, based on MULDIF diffraction code, with nonlinear forces from quadratic damping and from the mooring system. Calibration is performed by comparing simulations with model test data and adjusting hydrodynamic coefficients known to be affected by uncertainty. These include wave drift force coefficients, damping and added mass coefficients. Correction of the drift coefficients is based on empirical quadratic transfer functions (QTFs) identified from the test data by a nonlinear data analysis technique known as “cross-bi-spectral analysis”. Initial “uncalibrated” numerical models are based on input from the mooring, vessel mass, MULDIF hydrodynamic analysis, decay tests and current coefficients. They need adjustments for surge and sway. Empirical drift coefficients, natural periods and damping coefficients are then adjusted by matching low frequency surge and sway spectra. Wave-frequency coefficients need no adjustment. Low frequency wave drift forces, damping and added mass need increase in high sea states, in particular with current. Final motion simulations show 30%–40% underestimation in initial simulations, while final calibrated simulations are close to the measured records. Calibration of a Time-Domain Numerical Hydrodynamic Model for Mooring Analysis of a Semi-Submersible

Model tests have been performed with four mobile offshore drilling units (MODUs) with the aim of identifying wave drift forces and low frequency damping. The MODUs configuration is different, namely on the number and diameter of columns, therefore the sample is representative of many of the existing concepts. The model scale is the same as well as the wave and current conditions. The experimental program includes irregular waves with systematic variations of the significant wave height, wave peak period, current velocity and vessel heading. The test data is post-processed to identify the surge and sway quadratic transfer functions (QTFs) of the slowly varying excitation, together with the linearized low frequency damping. The post-processing applies a nonlinear data analysis technique known as “cross-bi-spectral analysis” to estimate characteristics of second-order (quadratic) responses from the measured motions and undisturbed incident wave elevation. The empirical QTFs are then compared with numerical predictions to conclude on the role of viscous drift and the applicability of Newman’s approximation for calculation of drift forces in irregular waves. Finally, the empirical drift forces, empirical low frequency damping coefficients and low frequency motions statistics are compared for the three MODUs to conclude on the relation between the Semi configuration and the low frequency responses. Low Frequency Excitation and Damping of Four MODUs in Severe Seastates With Current

Today’s industry practice assumes wave drift forces on floating structures can be computed from zero current wave drift force coefficients for the stationary floater, while simplified correction models introduce current effects and slow drift velocity effects. The paper presents an alternative approach which overcomes some of the limitations of today’s procedures. The method, to be applied together with a time domain solution of the low frequency motions, is based on pre-calculation of mean wave drift force coefficients for a range of current velocities. During the low frequency motions simulation, the wave drift forces induced by the irregular waves are computed from the mean drift coefficients corresponding to instantaneous relative velocity resulting from the current and the low frequency velocities. A simple interpolation model, based on a quasi-steady assumption, is applied to obtain the drift forces in time-domain. Since calculation of the wave drift forces on Semi-submersibles in severe sea states with fully consistent methods is out of reach, a semi-empirical model is applied to correct the potential flow wave drift force coefficients. This model takes into account viscous effects, that are important in high seastates, and wave-current interaction effects. The paper compares the wave drift forces and the related low frequency motions computed by the proposed method, with results applying “standard” methods and with model test data. The test data was obtained in the scope of the EXWAVE JIP, with model tests designed to investigate wave drift forces in severe seastates and assess the wave-current interaction effects.

The paper presents realistic horizontal wave drift force coefficients and low frequency damping coefficients for the Exwave semi-submersible under severe seastates. The analysis includes conditions with collinear waves and current. Model test data is used to identify the difference frequency wave exciting force coefficients based on a second order signal analysis technique. First, the slowly varying excitation is estimated from the relationship between the incoming wave and the low frequency motion using a linear oscillator. Then, the full quadratic transfer function (QTF) of the difference frequency wave exciting forces is defined from the relationship between the incoming waves and the second order force response. The process identifies also the linear low frequency damping. The paper presents results from cases selected from the EXWAVE JIP test matrix. The empirical wave drift coefficients are compared to potential flow predictions and to coefficients from a semi-empirical formula. The results show that the potential flow predictions largely underestimate the wave drift forces, especially at the low frequency range where severe seastates have most of the energy.

The EXWAVE Joint Industry Project (JIP) was initiated with the aim of improving methods and standard industry practice in design prediction of nonlinear wave loadings on Mobile Offshore Drilling Units (MODUs) induced by severe and steep seastates. The focus is on slowly varying wave excitation, including wave-current interaction effects. The present paper describes the technical background which led to the EXWAVE JIP, the project objectives, the planned work program and initial results. An important part of the work program consists on performing model tests with representative floating structures. Two floating structures have been selected for investigation, namely a semi-submersible drilling rig and a floating production storage and offloading vessel (FPSO). Comparisons between experimental results and standard numerical calculations are presented for the semi-submersible. Computational fluid dynamics (CFD) is applied for detailed analysis and interpretation of complex physical phenomena.

The time domain method is further extended here in order to calculate the hydroelastic response of an ultra large containership in regular waves. Based on strip theory, the hydrodynamic and the hydrostatic forces are calculated for the instantaneous wetted surface area. Slamming forces are calculated using a Von Karman approach in which the water pile up during slamming is neglected. Timoshenko beam which takes into account the shear deformation and rotary inertia is used to model the structural dynamic characteristics of the hull. The beam is discretized using the finite element method and the ship vibration is solved using the modal analysis. The method is used to calculate the vertical bending moment acting on an ultra large containership in large amplitude regular waves. The results are compared with the experimental results measured in wave tank.Copyright © 2015 by ASME

Short term probability distribution of the vertical bending moment acting on a cruise vessel in extreme seas is calculated using a body nonlinear time domain method based on strip theory. The hydrodynamic forces are calculated for the exact wetted surface area under the incident wave profile. The incident potential satisfies the weakly nonlinear free surface condition based on the Stokes expansion. The disturbance potential satisfies the linear free surface and body boundary conditions. Certain practical engineering techniques are employed for the calculation of the body nonlinear forces. The statistics and the probability of distribution of the numerical vertical bending moment are compared with the experimental results measured in the wave tank.

The paper analyzes the effect of 2nd order waves on the vertical ship responses in extreme seas. The numerical simulations are carried out using a body nonlinear time domain code based on strip theory. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship for each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. First order Froude Krylov pressures are replaced with a second order model for the present study. The 2nd order Froude-Krylov pressures are integrated upto the exact wetted surface area for each time instant. The ship responses in regular waves with varying steepness are analyzed. Finally, the vertical ship responses are compared with the responses in design waves measured in the wave tank.

This paper discusses the numerical analysis of an ultra large containership model in severe head seas. A body nonlinear time domain code based on the strip theory is used for the calculation of the rigid body response of the vessel. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship at each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. The numerical vertical bending moment is compared with the experimental results. The experiment was conducted on a flexible model in both regular and irregular waves. The model comprised six segments that were joined with an aluminum backbone of variable stiffness characteristics in order to replicate the hydroelastic behavior of the real ship. The model was tested for two ship speeds, 15 and 22 knots. For the first three harmonic values of the vertical bending moment, a good agreement between the numerical and the experimental results are found. However, higher harmonics significantly contributed to the total experimental vertical bending moment, in regular waves with 8m wave height and a ship speed of 15 knots. Similarly, the value of the fourth harmonic was 32% of the first harmonic values when the ship encountered a 5m regular wave with 22 knots speed. On comparison of the rigid body response in irregular seas, the hydroelastic loads resulted in 49% increase in the maximum value of the vertical bending moment.

A time domain code based on strip theory is applied to calculate the probability distributions of relative motions and bending moments of a cruise ship in a set of extreme seas. The code includes two levels of complexity. The simpler one combines linear radiation and diffraction forces with nonlinear Froude-Krylov forces, hydrostatic forces and shipping of green water on the bow. Cummins formulation is used to represent the radiation forces. The second approach is a generalization of the first one and, although the formulation is based on the linear assumption (of the radiation forces), the effects of body nonlinearity are considered by a simplified method: the memory functions, infinite frequency added masses and the radiation restoring coefficients are assessed at each time instant as function of the instantaneous wetted surface. A similar procedure is used to calculate the diffraction forces. The code is used to analyze the responses of a cruise ship in a set of extreme sea conditions. The nonlinear radiation and diffraction effects on the responses are analyzed by comparing the “fully nonlinear” results with the numerical predictions assuming linear radiation and diffraction forces. The short term nonlinear responses are represented by empirical probability distributions, obtained from time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data.

The present investigation focuses on the motions and global structural loads induced by abnormal waves on a bulk carrier. A nonlinear time domain method based on strip theory is used to predict the ship responses. The results are compared with experimental data obtained at the model scale. The time domain hydrodynamic forces are calculated by convolution of linear memory functions, while nonlinear contributions arise from Froude-Krylov forces, hydrostatic forces and shipping of green water. The time domain simulations are compared directly with experimental records from bulk carrier model tests with in head waves for two Froude numbers. Extreme wave conditions (such as the New Year Wave) previously measured at sea during real storms were replicated both at the seakeeping tank and by the numerical code. The comparison analyses show a good agreement between numerical and experimental with good accuracy.Copyright © 2013 by ASME

In the last years the identification and investigation of critical wave sequences regarding offshore structure responses became one of the main topics in the ocean engineering community. Thereby the area of interest covers the entire field of application spectra at sea — from efficient and economic offshore operations in moderate sea states to reliability as well as survival in extreme wave conditions. For most cases, the focus lies on limiting criteria for the design, such as maximum global loads, maximum relative motions between two or more vessels or maximum accelerations, at which the floating structure has to operate or to survive. These criteria are typically combined with a limiting characteristic sea state (Hs, Tp) or a rogue wave. For the investigation of offshore structures as well as the identification of critical wave sequences, different approaches are available — most of them are based on linear transfer functions as it is an efficient procedure for the fast holistic evaluation. But, for some cases the linear method approach implies uncertainties due to nonlinear response behavior, in particular in extreme wave conditions. This paper presents an approach to these challenges, a response based optimization tool for critical wave sequence detection. This tool, which has been successfully introduced for the evaluation of the applicability of a multi-body system based on the linear method approach, is adjusted to a nonlinear task — the vertical bending moment of a chemical tanker in extreme wave conditions. Therefore a nonlinear strip theory solver is introduced into the optimization routine to capture the nonlinear effects on the vertical bending moment due to steep waves acting on large bow flares. The goal of the procedure is to find a worst case wave sequence for a certain critical sea state. This includes intensive numerical investigation as well as model test validation.

Efficient operation of mooring systems is of paramount importance to reduce floating offshore wind (FOW) energy costs. MooringSense is an R&D project which explores digitization to enable the implementation of more efficient integrity management strategies (IMS) for FOW mooring systems. In this work, the MooringSense concept is presented. It includes the development of several enablers such as a mooring system digital twin, a smart motion sensor, a structural health monitoring (SHM) system and control strategies at the individual turbine and farm levels. The core of the digital twin (DT) is a high-fidelity fully coupled numerical model which integrates simulation tools to allow predictive operation and maintenance (O&M). Relevant parameters of the coupled model are updated as physical properties evolve due to damages or degradation. The DT assimilates information coming from the physical asset and environmental sensors. Besides, a smart motion sensor provides feedback of the attitude, position, and velocity of the floater to allow the computation of virtual loads in the mooring lines, the detection of damages by the SHM system and the implementation of closed-loop control strategies. Finally, the IMS takes advantage of the mooring system updated condition information to optimize O&M, reduce costs and increase energy production.