Comparison of Analyses for Moored Systems in Random Waves

1987 ◽  
Vol 109 (2) ◽  
pp. 133-141
Author(s):  
R. Eatock Taylor ◽  
P. Sincock
Keyword(s):  
Transfer Functions ◽  
Probability Distributions ◽  
Low Frequency ◽  
Response Probability ◽  
Random Waves ◽  
Frequency Spectra ◽  
Frequency Wave ◽  
Strongly Nonlinear ◽  
Motion Responses ◽  
Wave Drift Forces

This paper investigates methods of simulating the combined wave frequency and low-frequency wave drift forces and motion responses of floating systems. This is motivated by the requirement for estimates of response statistics for systems on nonlinear moorings. Results are given for a linear system for which experimental data are available (an articulated column model); and for a moored barge on mildly and strongly nonlinear moorings. Estimates are obtained for low-frequency spectra, linear and quadratic transfer functions, response probability distributions, and peak distributions.

scholarly journals Calibration of a Time-Domain Numerical Hydrodynamic Model for Mooring Analysis of a Semi-Submersible

2018 ◽  
Author(s):  
Nuno Fonseca ◽  
Carl Trygve Stansberg
Keyword(s):  
Test Data ◽  
Time Domain ◽  
Transfer Functions ◽  
Numerical Models ◽  
Low Frequency ◽  
Added Mass ◽  
Frequency Wave ◽  
Wave Drift ◽  
Wave Drift Forces ◽  
Drift Forces

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.

The Effect of Wave Directionality on Low Frequency Motions and Mooring Forces

2009 ◽  
Author(s):  
Olaf J. Waals
Keyword(s):  
Water Depth ◽  
Transfer Functions ◽  
Low Frequency ◽  
Sensitivity Study ◽  
Wave Loads ◽  
Offshore Structure ◽  
Frequency Wave ◽  
Drift Theory ◽  
Mooring Forces ◽  
Drift Forces

Operability of offshore moored ships can be affected by low frequency wave loads. The low frequency motions of a moored ship may limit the uptime of an offshore structure such as an LNG offloading terminal. The wave loads that cause the main excitation of these low frequency motions are usually computed using second order wave drift theory for long crested waves, which assumes that the low frequency components are only related to waves coming from the same direction. In this method short crested seas are dealt with as a summation of long crested seas, but no interaction between the wave components traveling in different directions is usually taken into account. This paper describes the results of a study to the effect of 2nd order low frequency wave loads in directional seas. For this study the drift forces related to the interaction between waves coming from different directions is also included. This is done by computing the quadratic transfer functions (QTF) for all possible combinations of wave components (frequencies and directions). Time traces of drift forces are generated and compared to the results without wave directional interaction after which the motions of an LNG carrier are simulated. A sensitivity study is carried out towards the number of direction steps and the water depth. Finally the motions of an LNG carrier in shallow water (15m water depth) are simulated and mooring forces are compared for various amounts of wave spreading.

scholarly journals Bayesian Experimental Design of Cyber-Physical Tests for Hydrodynamic Model Calibration

2021 ◽  
Author(s):  
Giuseppe Abbiati ◽  
Thomas Sauder
Keyword(s):  
Experimental Design ◽  
Transfer Functions ◽  
Low Frequency ◽  
Mooring System ◽  
Empirical Estimation ◽  
Design Algorithm ◽  
Frequency Wave ◽  
Laboratory Setup ◽  
Hydrodynamic Damping ◽  
Physical Tests

An application of cyber-physical testing to the empirical estimation of difference-frequency quadratic transfer functions is presented. As an alternative to today's procedure based on hydrodynamic tests with broad-banded or realistic (e.g., JONSWAP) wave spectra, tests in bichromatic waves are considered. The laboratory setup is the one developed by Sauder \& Tahchiev (2020) that enables magnifying the sensitivity of the floater response to the low-frequency wave loading by adjusting the stiffness and damping parameters of a virtual soft mooring system. Bayesian experimental design is proposed to optimize the selection of the control variables (frequencies in the bichromatic wave and properties of the virtual mooring system) for a batch of cyber-physical tests. The experimental design algorithm is based on the recent work of Huan \& Marzouk (2013). In a virtual yet realistic case study using an uncertain parametric quadratic transfer function, we demonstrate how the uncertainty of its describing parameters and other calibration parameters (low-frequency added mass and hydrodynamic damping) can be reduced. Results indicate that the proposed procedure has the potential for reducing experimental cost for calibration of hydrodynamic models.

scholarly journals Low Frequency Excitation and Damping of Four MODUs in Severe Seastates With Current

2018 ◽  
Author(s):  
Nuno Fonseca ◽  
Carl Trygve Stansberg ◽  
Kjell Larsen ◽  
Rune Bjørkli ◽  
Tjerand Vigesdal ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Low Frequency ◽  
Irregular Waves ◽  
Experimental Program ◽  
Peak Period ◽  
Numerical Predictions ◽  
Analysis Technique ◽  
Wave Drift Forces ◽  
Drift Forces

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.

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.

scholarly journals Bayesian Experimental Design of Cyber-Physical Tests for Hydrodynamic Model Calibration

2021 ◽  
Author(s):  
Giuseppe Abbiati ◽  
Thomas Sauder
Keyword(s):  
Experimental Design ◽  
Transfer Functions ◽  
Low Frequency ◽  
Mooring System ◽  
Empirical Estimation ◽  
Design Algorithm ◽  
Frequency Wave ◽  
Laboratory Setup ◽  
Hydrodynamic Damping ◽  
Physical Tests

Abstract An application of cyber-physical testing to the empirical estimation of difference-frequency quadratic transfer functions is presented. As an alternative to today’s procedure based on hydrodynamic tests with broad-banded or realistic (e.g., JONSWAP) wave spectra, tests in bichromatic waves are considered. The laboratory setup is the one developed by Sauder & Tahchiev (2020) that enables magnifying the sensitivity of the floater response to the low-frequency wave loading by adjusting the stiffness and damping parameters of a virtual soft mooring system. Bayesian experimental design is proposed to optimize the selection of the control variables (frequencies in the bichromatic wave and properties of the virtual mooring system) for a batch of cyber-physical tests. The experimental design algorithm is based on the recent work of Huan & Marzouk (2013). In a virtual yet realistic case study using an uncertain parametric quadratic transfer function, we demonstrate how the uncertainty of its describing parameters and other calibration parameters (low-frequency added mass and hydrodynamic damping) can be reduced. Results indicate that the proposed procedure has the potential for reducing experimental cost for calibration of hydrodynamic models.

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

Hydrodynamic Study and Performance Analysis of the OC4-DeepCWind Platform by CFD Method

2020 ◽  
pp. 2050020
Author(s):  
Yang Huang ◽  
Yuan Zhuang ◽  
Decheng Wan
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Center Of Gravity ◽  
Mooring Line ◽  
Time Step ◽  
Mooring Lines ◽  
Frequency Wave ◽  
Nonlinear Motion ◽  
Motion Responses ◽  
Motion Performance

(1) The RAOs of OC4-DeepCWind platform motions are more sensitive to the low-frequency wave than the high-frequency wave. The nonlinear motion responses for platform heave and pitch motions are comparatively remarkable. (2) The pitch motion of OC4-DeepCWind platform is much more apparently influenced by the height of center of gravity (COG) than surge and heave motions. The lower COG height within a suitable range leads to a smaller fluctuation amplitude of platform pitch motion in waves. (3) A large horizontal displacement abruptly occurs to the OC4-DeepCWind platform when one mooring line is failure. The risk of failure for the other mooring lines significantly increases. To better understand the hydrodynamic performance of a floating support platform in various wave environments, a two-phase CFD solver naoe-FOAM-SJTU based on the open source CFD toolbox OpenFOAM is applied to investigate the hydrodynamic characteristics and motion performance of the OC4-DeepCWind platform. Moreover, the restoring force and moment of mooring lines are simulated using the solver in time domain. The studies of grid sensitivity and time step refinement are first conducted to determine an appropriate time step and mesh size. Then hydrodynamic responses of the floater in free-decay tests are analyzed and compared with experimental data, and the motion performance of the platform in regular waves with different parameters is also investigated. In addition, the platform motion responses with one mooring line broken and different heights of center of gravity are explored. It is shown that simulation results have good agreement with published data, and several conclusions can be drawn through the study. The RAOs of platform motions are found to be more sensitive to the low-frequency wave than the high-frequency wave. Nonlinear motion responses are comparatively remarkable in platform heave and pitch motions. Besides, the lower height of center of gravity within a suitable range is benefit to the stability of floating platform. Survival condition with broken mooring line should be paid enough attention to avoid the failure of other mooring lines.

Wave Drift Forces and Low Frequency Damping on the Exwave Semi-Submersible

2017 ◽  
Author(s):  
Nuno Fonseca ◽  
Carl Trygve Stansberg
Keyword(s):  
Potential Flow ◽  
Low Frequency ◽  
Second Order ◽  
Difference Frequency ◽  
Frequency Wave ◽  
Wave Drift ◽  
The Difference ◽  
Wave Drift Forces ◽  
The Relationship ◽  
Drift Forces

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.

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