Effects of Second-Order Sum- and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

To better access the abundant offshore wind resource, efforts are being made across the world to develop and improve floating offshore wind turbine technologies. A critical aspect of creating reliable, mature floating wind turbine technology is the development, verification, and validation of efficient computer-aided-engineering (CAE) tools. The National Renewable Energy Laboratory (NREL) has created FAST, a comprehensive, coupled analysis CAE tool for floating wind turbines, which has been verified and utilized in numerous floating wind turbine studies. Several efforts are underway to validate the floating platform functionality of FAST to complement its already validated aerodynamic and structural simulation capabilities. The research employs the 1/50th-scale DeepCwind wind/wave basin model test dataset, which was obtained at the Maritime Research Institute Netherlands (MARIN) in 2011. This paper describes further work being undertaken to continue this validation. These efforts focus on FAST’s ability to replicate global response behaviors associated with dynamic wind forces and second-order difference-frequency wave-diffraction forces separately and simultaneously. The first step is the construction of a FAST numerical model of the DeepCwind semi-submersible floating wind turbine that includes alterations for the addition of second-order difference-frequency wave-diffraction forces. The implementation of these second-order wave forces, which are not currently standard in FAST, are outlined and discussed. After construction of the FAST model, the calibration of the FAST model’s wind turbine aerodynamics, tower-bending dynamics, and platform hydrodynamic damping using select test data is discussed. Subsequently, select cases with coupled dynamic wind and irregular wave loading are simulated in FAST, and these results are compared to test data. Particular attention is paid to global motion and load responses associated with the interaction of the wind and wave environmental loads. These loads are most prevalent in the vicinity of the rigid-body motion natural frequencies for the DeepCwind semi-submersible, with dynamic wind forces and the second-order difference-frequency wave-diffraction forces driving the global system response at these low frequencies. Studies are also performed to investigate the impact of neglecting the second-order wave forces on the predictive capabilities of the FAST model. The comparisons of the simulation and test results highlight the ability of FAST to accurately capture many of the important coupled global response behaviors of the DeepCwind semi-submersible floating wind turbine.

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A Numerical Simulation of Non-Linear Air-Gap for Deepwater Semi-Submersible Platform

10.1115/omae2021-62553 ◽

2021 ◽

Author(s):

Zhuang Kang ◽

Yansong Zhang ◽

Haibo Sui ◽

Rui Chang

Keyword(s):

Air Gap ◽

Second Order ◽

Difference Frequency ◽

Hydrodynamic Performance ◽

Wave Loads ◽

Order Difference ◽

Motion Response ◽

Nonlinear Motion ◽

Non Linear ◽

Simulation Results

Abstract Air gap is pivotal to the hydrodynamic performance for the semi-submersible platform as a key characteristic for the strength assessment and safety evaluation. Considering the metocean conditions of the Norse Sea, the hydrodynamic performance of a semi-submersible platform has been analyzed. Based on the three-dimensional potential flow theory, and combined with the full QTF matrix and the second-order difference frequency loads, the nonlinear motion characteristics and the prediction for air gap have been simulated. The wave frequency motion response, the second-order nonlinear air gap response and nonlinear motion response of the platform have been analyzed. By comparing the simulation results, the air gap response of the platform considering the nonlinear motion is more intense than the results simulated by the first-order motion without considering the second-order difference frequency loads. Under the heavy metocean conditions, for the heave and pitch motion of the platform, the non-linear simulation values for some air gap points and areas are negative which means the wave slam has been occurred, but the calculation results of linear motion response indicate that the air gap above has not appeared the wave slamming areas. The simulation results present that the influence of the second-order wave loads is a critical part in the air gap prediction for the semi-submersible platform.

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The complete second-order diffraction solution for an axisymmetric body Part 2. Bichromatic incident waves and body motions

Journal of Fluid Mechanics ◽

10.1017/s0022112090001690 ◽

1990 ◽

Vol 211 ◽

pp. 557-593 ◽

Cited By ~ 75

Author(s):

Moo-Hyun Kim ◽

Dick K. P. Yue

Keyword(s):

Transfer Functions ◽

Integral Equation Method ◽

Axisymmetric Body ◽

Second Order ◽

Difference Frequency ◽

Irregular Waves ◽

Total Load ◽

Frequency Wave ◽

Order Diffraction ◽

Incident Waves

In Part 1 (Kim & Yue 1989), we considered the second-order diffraction of a plane monochromatic incident wave by an axisymmetric body. A ring-source integral equation method in conjunction with a novel analytic free-surface integration in the entire local-wave-free domain was developed. To generalize the second-order theory to irregular waves, say described by a continuous spectrum, we consider in this paper the general second-order wave–body interactions in the presence of bichromatic incident waves and the resulting sum- and difference-frequency problems. For completeness, we also include the radiation problem and second-order motions of freely floating or elastically moored bodies. As in Part 1, the second-order sum- and difference-frequency potentials are obtained explicitly, revealing a number of interesting local behaviours of the second-order pressure. For illustration, the quadratic transfer functions (QTF's) for the sum- and difference-frequency wave excitation and body response obtained from the present complete theory are compared to those of existing approximation methods for a number of simple geometries. It is found that contributions from the second-order potentials, typically neglected, can dominate the total load in many cases.

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Influence of Second-Order Difference-Frequency Wave Loads on the Floating Wind-Wave Hybrid Platform

Volume 7B: Ocean Engineering ◽

10.1115/omae2017-61273 ◽

2017 ◽

Cited By ~ 1

Author(s):

Hyebin Lee ◽

Yoon Hyeok Bae ◽

Kyong-Hwan Kim ◽

Sewan Park ◽

Keyyong Hong

Keyword(s):

Wind Wave ◽

Computational Effort ◽

Second Order ◽

Difference Frequency ◽

Linear Wave ◽

Wave Loads ◽

Wave Load ◽

Frequency Wave ◽

Order Difference ◽

Hybrid Platform

A wind-wave hybrid power generation system is a floating offshore energy platform which is equipped with a number of wind turbines and wave energy converters (WECs) to harvest energy from various resources. This wind-wave hybrid platform is moored by eight catenary lines to keep its position against wind-wave-current environment. In most cases, the resonant frequency of horizontal motion of moored platform is very low, so a resonance is hardly seen by numerical simulation with linear wave assumptions. However, the incident waves with different frequency components are accompanied by sum and difference frequency loads due to the nonlinearity of the waves. Typically, the magnitude of the second-order wave loads are small and negligible, but once the second-order wave loads excite the platform at its natural frequency, the resonance can take place, which results in adverse effects on the platform. In this paper, the second-order difference frequency wave load on the wind-wave hybrid platform is numerically assessed and time domain simulation by coupled platform-mooring dynamic analysis is carried out. As a result, the horizontal motions of the platform was highly excited and the increased motions led higher top tension of the mooring lines compared with the case of linear wave environment. Especially, the combination of the wind and wave loads excited the horizontal motions more and made the mooring top tension far higher than wave load was only applied. With regards to the second-order difference frequency wave load, the result with the Quadratic Transfer Function (QTF) is compared to the one with Newman’s approximation. As the simulation results between them was insignificant, the Newman’s approximation can be used instead of the complete QTF to reduce the computational effort.

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Second Order Difference Frequency Wave-Current Loading Using Kelvin-Newman Approximation

Volume 6A: Ocean Engineering ◽

10.1115/omae2020-18901 ◽

2020 ◽

Author(s):

Farid P. Bakti ◽

Moo-Hyun Kim

Keyword(s):

Second Order ◽

The Body ◽

Difference Frequency ◽

Computational Time ◽

Forward Speed ◽

Frequency Wave ◽

Order Difference ◽

First Order ◽

Current Interaction ◽

Current Loading

Abstract Kelvin & Newman introduced a linearization method to include the current (or forward speed) effect into the diffraction & radiation wave field for large-slender floating bodies. The K-N method assumes a steady far-field current while disregarding the steady potential field due to the presence of the body. The method is proven to be reliable when the Froude number is relatively small, the body shape is relatively slender (∂∂x≪∂∂y,∂∂z), and the sea condition is mild. This requirement is fulfilled for typical FPSOs and ship-shaped vessels in a typical current (or forward speed) condition. Several studies suggested that the presence of the current might change the first order hydrodynamic coefficients such as the first order diffraction force, added mass, and radiation damping. Currents also contributed to a change in the second-order slowly-varying drift force. However, the effect of current in the second-order difference-frequency force is yet to be investigated. By expanding the Kelvin-Newman approximation up to the second order, and solving the problem in the frequency domain, we can save computational time while expanding the accuracy of the scheme. The second order quadratic force is the main focus of this study, since it is the main contributor to the total second order difference frequency forces especially near the diagonal. By implementing the Kelvin-Newman wave current interaction approach up to the wave’s second order, we can assess the performance of the Kelvin-Newman wave current interaction formulation in various sea conditions.

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Second Order Difference Frequency Wave-Current Loading Using Kelvin-Newman Approximation

10.1115/1.0001140v ◽

2021 ◽

Author(s):

FARID BAKTI ◽

Moo-Hyun Kim

Keyword(s):

Second Order ◽

Difference Frequency ◽

Frequency Wave ◽

Order Difference ◽

Current Loading

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Investigation of Nonlinear Difference-Frequency Wave Excitation on a Semisubmersible Offshore-Wind Platform With Bichromatic-Wave CFD Simulations

ASME 2021 3rd International Offshore Wind Technical Conference ◽

10.1115/iowtc2021-3537 ◽

2021 ◽

Author(s):

Lu Wang ◽

Amy Robertson ◽

Jason Jonkman ◽

Yi-Hsiang Yu ◽

Arjen Koop ◽

...

Keyword(s):

Potential Flow ◽

Low Frequency ◽

Flow Theory ◽

Second Order ◽

Difference Frequency ◽

Offshore Wind ◽

Viscous Drag ◽

Cfd Simulations ◽

Frequency Wave ◽

Potential Flow Theory

Abstract The natural surge and pitch frequencies of semisubmersible offshore wind platforms are typically designed to be below the wave frequencies to avoid direct excitation. However, surge or pitch resonance can be excited by the nonlinear low-frequency loads generated by irregular incident waves. Second-order potential-flow models with added Morison drag have been found to underpredict this low-frequency excitation and response. As part of the OC6 project1, the authors performed computational fluid dynamics (CFD) simulations to enable a better understanding of the low-frequency loads and the limitations of lower-fidelity models. The focus of this paper is to set up a computationally cost-effective CFD simulation of a fixed semisubmersible platform to investigate nonlinear difference-frequency loads and establish the corresponding uncertainty in the results. Because of the high computing cost, CFD simulations of irregular waves can be challenging. Instead, simulations were performed with bichromatic waves having a shorter repeat period. A preliminary comparison with quadratic transfer functions from second-order potential-flow theory shows that CFD models consistently predict higher nonlinear wave loads at the difference frequency, likely because of flow separation and viscous drag not accounted for in potential-flow theory.

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Mean- and Low-Frequency Wave Forces on Semisubmersibles

Society of Petroleum Engineers Journal ◽

10.2118/10941-pa ◽

1982 ◽

Vol 22 (04) ◽

pp. 563-572

Author(s):

J.A. Pinkster

Keyword(s):

Low Frequency ◽

Second Order ◽

Irregular Waves ◽

Wave Forces ◽

Frequency Wave ◽

First Order ◽

Wave Drift ◽

Frequency Components ◽

Wave Drift Forces ◽

Drift Forces

Abstract Mean- and low-frequency wave drift forces on moored structures are important with respect to low-frequency motions and peak mooring loads. This paper addresses prediction of these forces on semisubmersible-type structures by use of computations based on three-dimensional (3D) potential theory. The discussion includes a computational method based on direct integration of pressure on the wetted part of the hull of arbitrarily shaped structures. Results of computations of horizontal drift forces on a six-column semisubmersible are compared with model tests in regular and irregular waves. The mean vertical drift forces on a submerged horizontal cylinder obtained from model tests also are compared with results of computations. On the basis of these comparisons, we conclude that wave drift forces on semisubmersible-type structures in conditions of waves without current can be predicted with reasonable accuracy by means of computations based on potential theory. Introduction Stationary vessels floating or submerged in irregular waves are subjected to large first-order wave forces and moments that are linearly proportional to the wave height and that contain the same frequencies as the waves. They also are subjected to small second-order mean- and low- frequency wave forces and moments that are proportional to the square of the wave height. Frequencies of second-order low-frequency components are associated with the frequencies of wave groups occurring in irregular waves.First-order wave forces and moments cause the well-known first-order motions with wave frequencies. First-order wave forces and motions have been investigated for several decades. As a result of these investigations, methods have been developed to predict these forces and moments with reasonable accuracy for many different vessel shapes.For semisubmersibles, which consist of a number of relatively slender elements such as columns, floaters, and bracings, computation methods have been developed to determine the hydrodynamic loads on those elements without accounting for interaction effects between the elements. For the first-order wave loads and motion problem, these computations give accurate results.This paper deals with the mean- and low-frequency second-order wave forces acting on stationary vessels in regular and irregular waves in general and presents a method to predict these forces on the basis of computations.The importance of mean- and low-frequency wave drift forces, from the point of view of motion behavior and mooring loads on vessels moored at point of view of motion behavior and mooring loads on vessels moored at sea, has been recognized only within the last few years. Verhagen and Van Sluijs, Hsu and Blenkarn, and Remery and Hermans showed that the low-frequency components of wave drift forces in irregular waves-even though relatively small in magnitude-can excite large-amplitude low- frequency horizontal motions in moored structures. It was shown for irregular waves that the drift forces contain components with frequencies coinciding with the natural frequencies of the horizontal motions of moored vessels. Combined with minimal damping of low-frequency horizontal motions of moored structures, this leads to large-amplitude resonant behavior of the motions (Fig. 1). Remery and Hermans established that low-frequency components in drift forces are associated with the frequencies of wave groups present in an irregular wave train.The vertical components of the second-order forces sometimes are called suction forces. SPEJ p. 563

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