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.

scholarly journals Did the Draupner wave occur in a crossing sea?

2011 ◽  
Vol 467 (2134) ◽  
pp. 3004-3021 ◽  
Author(s):  
T. A. A. Adcock ◽  
P. H. Taylor ◽  
S. Yan ◽  
Q. W. Ma ◽  
P. A. E. M. Janssen
Keyword(s):  
Low Frequency ◽  
Quality Measurement ◽  
Order Theory ◽  
Second Order ◽  
Flow Solver ◽  
The North ◽  
Highly Nonlinear ◽  
Nonlinear Potential ◽  
Wind Sea ◽  
Set Up

The ‘New Year Wave’ was recorded at the Draupner platform in the North Sea and is a rare high-quality measurement of a ‘freak’ or ‘rogue’ wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information that was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave's directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90 ° or more. This result has been deduced from a set-up of the low-frequency second-order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second-order theory is satisfactory for such a highly nonlinear event, we have run numerical simulations using a fully nonlinear potential flow solver, which confirm the conclusion deduced from the second-order theory. This is backed up by a hindcast from European Centre for Medium-Range Weather Forecasts that shows swell waves propagating at approximately 80 ° to the wind sea. Other evidence that supports our conclusion are the measured forces on the structure, the magnitude of the second-order sum waves and some other instances of freak waves occurring in crossing sea states.

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.

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.

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.

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.

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.

Effect of Air Fraction on Force Coefficients in Oscillatory Flow

2021 ◽  
Author(s):  
Malene Hovgaard Vested ◽  
Erik Damgaard Christensen
Keyword(s):  
High Speed ◽  
Offshore Structures ◽  
Air Injection ◽  
Wave Loads ◽  
Morison Equation ◽  
Force Coefficients ◽  
Air Content ◽  
Set Up ◽  
High Level ◽  
Spilling Breakers

Abstract The forces on marine and offshore structures are often affected by spilling breakers. The spilling breaker is characterized by a roller of mixed air and water with a forward speed approximately equal to the wave celerity. This high speed in the top of the wave has the potential to induce high wave loads on upper parts of the structures. This study analyzed the effect of the air content on the forces. The analyses used the Morison equation to examine the effect of the percentage of air on the forces. An experimental set-up was developed to include the injection of air into an otherwise calm water body. The air-injection did introduce a high level a turbulence. It was possible to assess the amount of air content in the water for different amounts of air-injection. In the mixture of air and water the force on an oscillating square cylinder was measured for different levels of air-content, — also in the case without air. The measurements indicated that force coefficients for clear water could be use in the Morison equation as long as the density for water was replaced by the density for the mixture of air and water.

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

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.

Analysis on the Performance of Deckwetness of Sandglass-type and Cylindrical Floating Bodies

2016 ◽  
Vol 60 (03) ◽  
pp. 145-155
Author(s):  
Ya-zhen Du ◽  
Wen-hua Wang ◽  
Lin-lin Wang ◽  
Yu-xin Yao ◽  
Hao Gao ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Linear Response Theory ◽  
Second Order ◽  
Irregular Waves ◽  
Wave Loads ◽  
Floating Bodies ◽  
Drift Motion ◽  
First Order ◽  
Series Of Experiments ◽  
Deck Wetness

In this paper, the influence of the second-order slowly varying loads on the estimation of deck wetness is studied. A series of experiments related to classic cylindrical and new sandglass-type Floating Production, Storage, and Offloading Unit (FPSO) models are conducted. Due to the distinctive configuration design, the sand glass type FPSO model exhibits more excellent deck wetness performance than the cylindrical one in irregular waves. Based on wave potential theory, the first-order wave loads and the full quadratic transfer functions of second-order slowly varying loads are obtained by the frequency-domain numerical boundary element method. On this basis, the traditional spectral analysis only accounting for the first-order wave loads and time-domain numerical simulation considering both the first-order wave loads and nonlinear second-order slowly varying wave loads are employed to predict the numbers of occurrence of deck wetness per hour of the two floating models, respectively. By comparing the results of the two methods with experimental data, the shortcomings of traditional method based on linear response theory emerge and it is of great significance to consider the second-order slowly drift motion response in the analysis of deck wetness of the new sandglass-type FPSO.

scholarly journals FIELD MEASUREMENTS AND MODELLING OF NEARSHORE CURRENTS AT A HIGH-ENERGY GEOLOGICALLY-CONSTRAINED BEACH

2020 ◽  
pp. 18
Author(s):  
Arthur Mouragues ◽  
Philippe Bonneton ◽  
Bruno Castelle ◽  
Vincent Marieu
Keyword(s):  
Surf Zone ◽  
Low Frequency ◽  
Field Measurements ◽  
High Energy ◽  
Oblique Wave ◽  
Wave Forcing ◽  
Circulation Patterns ◽  
Wave Conditions ◽  
Nearshore Currents ◽  
Set Up

We present field measurements of nearshore currents at a high-energy mesotidal beach with the presence of a 500-m headland and a submerged reef. Small changes in wave forcing and tide elevation were found to largely impact circulation patterns. In particular, under 4-m oblique wave conditions, our measurements indicate the presence of an intense low-frequency fluctuating deflection rip flowing against the headland and extending well beyond the surf zone. An XBeach model is further set up to hindcast such flow patterns.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/EiqnjBIkWJE

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