Accuracy Effects of Low Frequency Wave Loads on Ships Offshore to LNG Marine Terminal Design

2004 ◽  
Author(s):  
Monica J. Holboke ◽  
Robert G. Grant
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
Surface Boundary ◽  
Wave Loads ◽  
Wave Load ◽  
Frequency Wave ◽  
First Order ◽  
Terminal Design

This paper presents the results of a two-body analysis for a moored ship sheltered by a breakwater in shallow water with and without free surface forcing in the low frequency wave load calculation. The low frequency wave loads are determined by second order interactions from the first order. The free surface forcing term arises from the free surface boundary condition, which is trivial to first order but is not at second order. We demonstrate in the frequency domain the importance of this term in a two-body analysis. Additionally, we show how inaccurate calculations of the off-diagonal terms of the Quadratic Transfer Function can translate to over or under prediction of low frequency wave loads on moored ships sheltered by breakwaters in shallow water. Low frequency wave load accuracy has direct consequence for LNG marine terminal design. Generally, LNG marine terminals are sited in sheltered harbors, however increasingly they are being proposed in offshore locations where they will require protection from persistent waves and swells. Since breakwaters typically cost twice as much as the rest of the marine facilities, it is important to optimize their size, orientation and location. In a previous paper we described this optimization process [1], which identified a key step to be the transforming of waves just offshore the breakwater into wave loads on the moored ships. The ability to do this step accurately is of critical importance because if the loads are too large, the breakwater will be larger and more expensive than necessary and if the loads are too small, the terminal will experience excessive downtime and loss of revenue.

Review of Approximations to Evaluate Second-Order Low-Frequency Load

2012 ◽  
Author(s):  
Guillaume de Hauteclocque ◽  
Flávia Rezende ◽  
Olaf Waals ◽  
Xiao-Bo Chen
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
The Body ◽  
Difference Frequency ◽  
Surface Boundary ◽  
First Order ◽  
Potential Part ◽  
The Difference

The second order low-frequency loads are one of main sources of excitation for moored systems. These loads are usually decomposed into the quadratic part, contributed only by first order quantities and potential part contributed by the second order potentials. In shallow water the second order incoming and diffracted potentials give a significant contribution to the low frequency forces. Therefore, the accuracy on the determination of this parcel of the low-frequency loads is a key issue for the assessment of mooring lines and operability of systems moored in shallow water area, as for example LNG terminals. Due to the complexity in computing the second order diffraction potential, which would involve a non-homogeneous free surface boundary condition, the so-called Pinkster approximation has been proposed. This approximation is based on the assumption that the major contribution to the potential part of low-frequency loads is given by the second order potential of the undisturbed incoming waves. The methods to compute the wave forces related to the second order potentials are based on scaling of the first order wave induced forces. Another approximation recently formulated in Chen and Rezende consists of developing the second-order bi-frequency load into a series of different orders of the difference frequency. The potential contribution to the term proportional to the difference-frequency can be evaluated efficiently by involving an integral over a small zone on the free surface around the body. In the present paper, the existing approximations are revisited and compared to analytical solution of exact second-order load on a vertical cylinder and for the case of floating body (LNG) in shallow water. Some guidelines in the practical use of different approximations will be derived.

Efficient Computations of Second-Order Low-Frequency Wave Load

2009 ◽  
Author(s):  
Xiao-Bo Chen ◽  
Fla´via Rezende
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
Wave Loads ◽  
Wave Loading ◽  
Wave Load ◽  
Frequency Wave ◽  
New Developments ◽  
Novel Method ◽  
The Difference ◽  
New Formulation

As the main source of resonant excitations to most offshore moored systems like floating LNG terminals, the low-frequency wave loading is the critical input to motion simulations which are important for the design. Further to the analysis presented by Chen & Duan (2007) and Chen & Rezende (2008) on the quadratic transfer function (QTF) of low-frequency wave loading, the new formulation of QTF is developed by the series expansion of the second-order wave loading with respect to the difference-frequency upto the order-2. It provides a novel method to evaluate the low-frequency second-order wave loads in a more accurate than usual order-0 approximation (often called Newman approximation) and more efficient way comparing to the computation of complete QTF. New developments including numerical results of different components of QTF are presented here. Furthermore, the time-series reconstruction of excitation loads in the motion simulation of mooring systems is analyzed and a new efficient and accurate scheme is demonstrated.

A Practical O(Δω) Approximation of Low Frequency Wave Loads

2013 ◽  
Author(s):  
Charles Monroy ◽  
Guillaume de Hauteclocque ◽  
Xiao-Bo Chen
Keyword(s):  
Free Surface ◽  
Order Term ◽  
Low Frequency ◽  
Radial Distance ◽  
Second Order ◽  
Radial Coordinate ◽  
Wave Loads ◽  
Surface Integral ◽  
Frequency Wave ◽  
The Difference

The low-frequency quadratic transfer function (QTF) is defined as the second-order wave loads occurring at the frequency equal to the difference frequency (ω1 − ω2) of two wave frequencies (ω1, ω2) in bi-chromatic waves of unit amplitude. The exact formulation of the QTF which is recalled here is difficult to implement due to numerical convergence problems mainly related to the evaluation of an arduous free surface integral. This is why several approximations have been used for practical engineering studies. They have been the subject of a detailed review in [5]. Following this work, two closely-related formulations are investigated in this paper. In [2], the classical formulations of QTF are examined by an analysis based on the Taylor development with respect to Δω for Δω ≪ 1 and an expansion of QTF in power of Δω is then obtained. It is shown that the zeroth-order term is a pure real function equal to the drift loads and that the term of order O(Δω) is a pure imaginary function. The second-order low-frequency wave loading of order O(Δω) contains a free-surface integral representing the second-order corrective forcing on the free surface. Since the integrand is of order O(1/R4) with R as the radial coordinate, the free-surface integral converges rapidly with the radial distance. Unlike what has been assumed in previous studies of particular cases, this free-surface contribution is, in general, not negligible for high Δω compared to other components and the complete QTF. Depending whether we use the O(Δω) approximation for the whole QTF or only for this free surface integral, it leads to two different approximations. The first one is called original O(Δω) approximation, because it is on this form that the O(Δω) approximation was first described in [2]. If we use the O(Δω) approximation only for the free surface integral, we call this approximation the practical O(Δω) approximation. It is shown in this paper that the original formulation fails to predict the behaviour of the QTF even for small O(Δω). Comparison for the O(Δω) approximation of the free surface integral is performed against the analytical solution and the exact numerical formulation. The results are improved compared to when we neglect this free surface integral for the range of Δω of interest, but still the agreement with the exact solution is not ideal. A path for further improvement is finally proposed.

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

2017 ◽  
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.

Laboratory Wave Modelling for Floating Structures in Shallow Water

2006 ◽  
Author(s):  
Carl Trygve Stansberg
Keyword(s):  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
Wave Groups ◽  
Large Wave ◽  
Frequency Wave ◽  
Wave Modelling ◽  
Floating Structures ◽  
Wave Basin ◽  
Wave Drift Forces

The analysis of moored floating vessels in shallow water requires special attention, when compared to similar problems in deep water. In particular, low-frequency wave drift forces need to be studied. Model testing is essential in validation of numerical prediction tools for these problems. Wave-group induced low-frequency wave components is an important part of the problem. Their reproduction in laboratories needs special attention. In general, two types of low-frequency waves are present: “bound” waves following the wave groups, and “free” waves propagating with their own speed. The former is included in second-order numerical codes for floater is included in second-order numerical codes for floaters, while the latter is normally not. Therefore, identification and possible reduction of the free components is of interest. A practical way to do this in a large wave basin is described in this paper. Results from generation of bi-chromatic waves without and with correction are presented. Corrected results show a clear reduction of the free wave component.

Approximation of Second-Order Low-Frequency Wave Loading in Multi-Directional Waves

2010 ◽  
Author(s):  
Flavia C. Rezende ◽  
Xiao-bo Chen
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
Wave Loads ◽  
Wave Loading ◽  
Frequency Wave ◽  
New Developments ◽  
Directional Waves ◽  
Novel Method ◽  
The Difference ◽  
Accurate Scheme

Further to the studies by Chen & Rezende (OMAE2009) on the quadratic transfer function (QTF) of low-frequency wave loading in which the QTF is developed by the series expansion associated with the difference-frequency up to the order-Δω2, new formulations have been developed in order to take into account the effect of interactions between waves of different headings. It provides a novel method to evaluate the low-frequency second-order wave loads in a more accurate than usual order-Δω approximation (often called Newman approximation) and more efficient way comparing to the computation of complete QTF in multi-directional waves. New developments including numerical results of different components of QTF are presented here. Furthermore, the time-series reconstruction of excitation loads by quadruple sums in the motion simulation of mooring systems is analyzed and a new efficient and accurate scheme using only a triple sum is demonstrated.

scholarly journals Uncertainty Assessment of CFD Investigation of the Nonlinear Difference-Frequency Wave Loads on a Semisubmersible FOWT Platform

2020 ◽  
Vol 13 (1) ◽  
pp. 64
Author(s):  
Lu Wang ◽  
Amy Robertson ◽  
Jason Jonkman ◽  
Yi-Hsiang Yu
Keyword(s):  
Low Frequency ◽  
Uncertainty Assessment ◽  
Difference Frequency ◽  
Offshore Wind ◽  
Wave Loads ◽  
Wave Excitation ◽  
Wave Load ◽  
Frequency Wave ◽  
Floating Offshore Wind Turbines ◽  
Frequency Excitation

Current mid-fidelity modeling approaches for floating offshore wind turbines (FOWTs) have been found to underpredict the nonlinear, low-frequency wave excitation and the response of semisubmersible FOWTs. To examine the cause of this underprediction, the OC6 project is using computational fluid dynamics (CFD) tools to investigate the wave loads on the OC5-DeepCwind semisubmersible, with a focus on the nonlinear difference-frequency excitation. This paper focuses on assessing the uncertainty of the CFD predictions from simulations of the semisubmersible in a fixed condition under bichromatic wave loading and on establishing confidence in the results for use in improving mid-fidelity models. The uncertainty for the nonlinear wave excitation is found to be acceptable but larger than that for the wave-frequency excitation, with the spatial discretization error being the dominant contributor. Further, unwanted free waves at the difference frequency have been identified in the CFD solution. A wave-splitting and wave load-correction procedure are presented to remove the contamination from the free waves in the results. A preliminary comparison to second-order potential-flow theory shows that the CFD model predicted significantly higher difference-frequency wave excitations, especially in surge, suggesting that the CFD results can be used to better calibrate the mid-fidelity tools.

Mean- and Low-Frequency Wave Forces on Semisubmersibles

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

Low-Frequency Phenomena Associated With Vessels Moored at Sea

1975 ◽  
Vol 15 (06) ◽  
pp. 487-494 ◽  
Author(s):  
J.A. Pinkster
Keyword(s):  
Wave Height ◽  
Low Frequency ◽  
Second Order ◽  
Irregular Waves ◽  
Ship Motions ◽  
Wave Forces ◽  
Mooring System ◽  
Frequency Wave ◽  
First Order ◽  
The Mean

Abstract The influence of the low-frequency-wave-drifting force on the motions of moored vessels and the loads in the mooring system is demonstrated from results of model tests in irregular waves. The origin of the wave drifting force is discussed and methods for calculating the mean drifting force are reviewed. To facilitate calculation of the low-frequency-wave drifting force on an object in irregular waves, an existing method using the mean drifting force in regular waves is generalized. The results of calculations using the method introduced in this paper are compared with previously published test results. Finally, some remarks are added concerning effects that have not been accounted for in existing calculation methods. Introduction A vessel moored at sea in stationary conditions with regard to waves, wind, and current is subjected to forces that tend to shift it from the desired position. For a given vessel and position in the position. For a given vessel and position in the horizontal plane, the motions depend on both the mooring system and the external forces acting on the vessel. In steady conditions, the forces caused by a constant wind and current are constant quantities for a given heading angle of the vessel. The forces caused by a stationary irregular sea are of an irregular nature and may be split into two parts: first-order oscillatory forces with wave parts: first-order oscillatory forces with wave frequency, and second-order, slowly varying forces with frequencies much lower than the wave frequency.The first-order oscillatory wave forces on a vessel cause the well known ship motions whose frequencies equal the frequencies present in the spectrum of the irregular waves. These are the linear motions of surge, sway, and heave and the three angular motions of roll, pitch, and yaw. In general, the first-order wave forces are proportional to the wave height, as are the ensuing motions. The magnitude of the linear oscillatory motions is in the order of the height of the waves.The second-order wave forces, perhaps better known as the wave drifting forces, have been shown to be proportional to the square of the wave height. These forces, though small in magnitude, are the cause of the low-frequency, large-amplitude, horizontal motions sometimes observed in large vessels moored in irregular waves. Tests run in irregular waves in wave tanks of the Netherlands Ship Model Basin revealed a number of properties and effects of the low-frequency-wave properties and effects of the low-frequency-wave drifting force that are discussed here using the results of two test programs.The first of these programs concerns tests run with the model of a 125,000-cu m LNG carrier moored in head seas with an ideal linear mooring system. The second program deals with a 300,000-DWT VLCC moored with a realistic nonlinear bow hawser to a single-buoy mooring in waves, wind, and current coming from different directions.The results of the tests with the LNG carrier are shown in Figs. 1 through 3, while the results of the tests with the 300,000-DWT VLCC are shown in Fig. 4. All results are given in full-scale values. Fig. 1 shows the wave trace and the surge motion of the LNG carrier to a base of time. SPEJ P. 487

Second-Order Responses of a 10 MW Floating Wind Turbine, Considering the Full QTF

2019 ◽  
Author(s):  
Qun Cao ◽  
Longfei Xiao ◽  
Xiaoxian Guo ◽  
Mingyue Liu
Keyword(s):  
Wind Turbine ◽  
Natural Frequencies ◽  
Second Order ◽  
Operating Conditions ◽  
Wave Loads ◽  
Random Waves ◽  
Frequency Wave ◽  
First Order ◽  
Frequency Responses ◽  
Floating Wind Turbine

Abstract Second-order components of wave loads acting on the floating foundation for wind turbines may induce severe resonance and lead to fatigue damage at natural frequencies of structures. In this study, the INNWIND.EU Triple-Spar and the DTU 10 MW Reference Wind Turbine were simulated by utilizing software FAST to obtain the second-order responses of the floating wind turbine under selected steady winds with collinear random waves. Low-frequency responses at surge and pitch natural frequencies dominated the response spectra, which were underestimated by the first-order numerical model. A response peak appeared in tower-top motion spectrum in vicinity of the first-order fore-aft vibration frequency of the tower when the sum-frequency wave effects were considered. The second-order high-frequency responses arose when the full QTF was utilized, compared to results with Newman approximation. Different operating conditions with varying wind speeds, wave periods, significant wave heights and wave directions were selected to conduct the sensitivity study of the second-order responses.

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