Second-Order Wave Loads on a LNG Carrier in Multi-Directional Waves

2008 ◽  
Author(s):  
Mathieu Renaud ◽  
Fla´via Rezende ◽  
Olaf Waals ◽  
Xiao-Bo Chen ◽  
Radboud van Dijk
Keyword(s):  
Low Frequency ◽  
Model Tests ◽  
Second Order ◽  
Wave Loads ◽  
Wave Kinematics ◽  
Directional Waves ◽  
Slow Drift ◽  
Wave Directionality ◽  
Offshore Industry ◽  
Cross Waves

Due to the installation of LNG terminals moored in proximity to the coast, the wave kinematics in shallow water and the consequence on the behavior of those terminals have recently became a major concern of the offshore industry. One key issue is the accurate simulation of the low-frequency motions of LNG carriers, specially the surge, for which the vessel presents low damping, in order to perform the design of the mooring system. The present paper focuses on the effect of wave directionality on second-order slow-drift loads and the related response of the vessel. The paper describes results of model tests in regular cross waves — monochromatic but coming from two directions separated by 90 degrees, as well as bichromatic cross waves. The new “middle field” formulation extended to the case of cross waves, is used to compute the wave drift loads and low-frequency Quadratic Transfer Function (QTF). The results are compared with those from the model tests.

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.

Drift Motions of a Floating Barge in Random Multi-Directional Waves

1991 ◽  
Vol 113 (1) ◽  
pp. 37-42 ◽  
Author(s):  
O. Nwogu ◽  
M. Isaacson
Keyword(s):  
Standard Deviation ◽  
Laboratory Tests ◽  
Low Frequency ◽  
Mooring Line ◽  
Floating Structures ◽  
Directional Waves ◽  
Slow Drift ◽  
Wave Directionality ◽  
The Mean ◽  
Directional Sea States

This paper presents results of a numerical and laboratory investigation into the mooring line forces and slow drift oscillations of large floating structures in multidirectional waves. A procedure for computing the spectral density of the second-order forces in random multi-directional waves based on the concept of a bidirectional, bifrequency quadratic transfer function is presented. Laboratory tests were carried out with a floating barge model, restrained horizontally by soft linear springs. The barge was subjected to random multi-directional waves with different degrees of directional spreading. The influence of wave directionality on the mooring line forces and low frequency motions is investigated by comparing results in unidirectional and multi-directional sea states with an identical frequency spectrum. The results indicate a significant reduction of the mean and standard deviation of the surge response, and an increased sway and yaw response. The mooring line forces were affected by wave directionality in a similar manner as the surge response.

Second Order Loads on LNG Terminals in Multi-Directional Sea in Water of Finite Depth

2007 ◽  
Author(s):  
Fla´via Rezende ◽  
Xin Li ◽  
Xiao-Bo Chen
Keyword(s):  
Near Field ◽  
Low Frequency ◽  
Finite Depth ◽  
Accurate Method ◽  
Second Order ◽  
Wave Loading ◽  
Storage Tanks ◽  
Offshore Area ◽  
Directional Waves ◽  
Poor Convergence

Large LNG terminals are designed to be installed in an offshore area approximate to harbors where the water is of finite depth and waves are multi-directional. The terminal can be of a barge type LNG/FRSU including accommodations, gas preconditioning and liquefied plant, a number of storage tanks and offloading facilities. It serves also as a support to moor a LNG carrier during offloading operations. In the design of such mooring system of LNG/FRSU and LNG carriers in a zone of shallow water, one key issue is the accurate simulation of low-frequency motions of the system to which the second-order wave loading is well known as the main source of excitation. The computation of second-order wave loading in multi-directional waves of finite waterdepth is considered here. New formulations obtained recently in [1] for the computation of second-order loads in mono-directional waves are extended to the case of multi-directional waves. Both the classical near-field formulation and the new middle-field formulation developed in [1] are used and numerical results are compared. Unlike the usual near-field formulation giving results of second-order loads with poor convergence, the middle-field formulation provides an accurate method for the computation of vertical components.

Slow-Drift Pitch Motions and Air-Gap Observed From Model Testing With Moored Semisubmersibles

2007 ◽  
Author(s):  
Carl Trygve Stansberg
Keyword(s):  
Numerical Analysis ◽  
Water Depth ◽  
Low Frequency ◽  
Model Testing ◽  
Model Tests ◽  
Air Gap ◽  
Wave Drift ◽  
Slow Drift ◽  
Gap Data ◽  
Good Agreement

Low-frequency pitch motions of a moored semisubmersible in irregular sea states are analyzed. Physical mechanisms and significance to air-gap problems are addressed. Excitation from wave drift and from moorings/risers is primarily considered, Effects from current and wind are also addressed. Related challenges in deepwater model testing of semis with truncated moorings are discussed. Motion and air-gap data from two previously performed model tests are analysed. Catenary moorings in 335m water depth and in 1100m water depth, respectively, are considered. Model scales are 1:55 and 1:150, respectively. Observed slow-drift pitch components are of the same magnitude level as the wave-frequency components. Comparisons to coupled numerical analysis models are made. Wave drift moment coefficients calibrated empirically according to experiments were used, since the original coefficients gave too low results. The final comparisons show good agreement for the 1:55 case. For the 1:150 case, fairly good agreement is found, but some deviations are observed and believed to be due to poorer wave repeatablity. Tests with truncated moorings at half of the two actual depths were also included, for a check of methods for deepwater model tests performed at reduced depths and combine with numerical analysis (hybrid verification). The importance of proper experimental reproduction at reduced depths, of full-depth pitch and air-gap, is addressed. The results show that with the actual truncation designs, reasonable agreements are obtained, but use of the scale 1:150 seems to give too large uncertainties due to the poorer wave repeatability.

Statistical Analysis of Slow-Drift Responses

1983 ◽  
Vol 105 (3) ◽  
pp. 310-317 ◽  
Author(s):  
C. T. Stansberg
Keyword(s):  
Probability Density ◽  
Low Frequency ◽  
Mathematical Expression ◽  
General System ◽  
Analytical Signal ◽  
Second Order ◽  
Induced Response ◽  
Frequency Spectra ◽  
Slow Drift ◽  
Continuous Frequency

The statistical properties of second-order wave-induced response processes are investigated theoretically. Emphasis is placed on the slow-drift components. The assumed forcing waves are irregular with continuous frequency spectra. A spectral analysis of the response of a general system is made. It is shown that the slow-drift components are closely connected to the complex analytical signal and the Hilbert envelope of the wave elevation. A simple mathematical expression exists for the slow-drift components, based on the complex wave signal and the second-order impulse response of the system. By use of this explicit formula, the theoretical probability functions of slow-drift responses are investigated. The analysis is based on the Kac-Siegert method. A similar approach has earlier been applied to study the sum of both the low-frequency and the high-frequency second-order responses. Final calculations of the probability density functions are in general very complicated, but it can be simplified by the use of a simple idealized model for the second-order transfer function. Probability density curves for a few simple cases are presented.

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.

Investigation of the Horizontal Drifting Effects on Ships With Forward Speed

2009 ◽  
Author(s):  
Sheguang Zhang ◽  
Kenneth M. Weems ◽  
Woei-Min Lin
Keyword(s):  
Horizontal Plane ◽  
Mathematical Formulation ◽  
Low Frequency ◽  
Second Order ◽  
Wave Loads ◽  
Forward Speed ◽  
Large Amplitude Motions ◽  
Domain 3 ◽  
Set Up ◽  
Control Surfaces

This paper is concerned with the horizontal drifting effects on ships moving with forward speed in waves. The ship configurations can be a single or multiple ships operating alongside one another. In close-in position (CIP) ship operations, the position of the ships often needs to be maintained relatively steady by means of Dynamic Positioning (DP) systems that incorporate thrusters or control surfaces. In developing such systems, especially those using wave feed-forward (WFF) control algorithms, the mean or low frequency drift force and moment in the horizontal plane are required to set up the control loop. The present study uses the Large Amplitude Motions Program (LAMP), a time domain, 3-D panel code for the prediction of motions and wave loads for a ship or ships in waves, to calculate the drifting forces in the horizontal plane for ships moving with or without forward speed. Since the drifting effects are second order in association with the incident wave amplitude, the formulation in LAMP has been expanded to account for the additional second order terms. This paper presents the mathematical formulation — including the second order drifting effects, its numerical implementation in LAMP, and the results from several validation cases — for a single body with or without forward speed. The analysis of the horizontal drifting effects on two-ship configurations with or without a DP system will be conducted in a future study.

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.

Simulation of Second-Order Roll Motions of a FPSO

2008 ◽  
Author(s):  
Fla´via Rezende ◽  
Xiao-Bo Chen ◽  
Marcos D. Ferreira
Keyword(s):  
Transfer Functions ◽  
Model Tests ◽  
Second Order ◽  
Vertical Position ◽  
Wave Loads ◽  
Natural Period ◽  
New Developments ◽  
Linear Waves ◽  
Instantaneous Position ◽  
Key Parameter

The roll motions are a key parameter on the design of FPSOs that operate in moderate and severe environmental conditions. To reduce the magnitude of roll motions, some techniques based on changing the vertical position of gravity center are used to put the roll natural period outside of the frequency range of the linear waves. However, recent model tests and also numerical calculations have shown that the vessel may still experience large roll motions which are considered to be induced by second-order wave loads. Further to the work in Rezende et al. (2007) to compute the roll response in frequency domain, new developments to perform simulations in time domain are presented here. In this new method, variations of second-order roll moments dependent on the roll and heave motions are taken into account consistently. It is shown that, unlike the horizontal loads, the quadratic transfer functions of the vertical loads depend on the instantaneous position of the vessel. The variation of the roll moment with the heave position of the vessel has been considered more important than the variation obtained only with the inclination of the vessel. Furthermore, numerical results of roll simulations are compared with model tests results and presented in the paper.

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