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

Determination of the Effect of Second Order Motions of Moored MODU on Wellhead Fatigue

2014 ◽  
Author(s):  
Dara Williams ◽  
Patrick Ashton
Keyword(s):  
Fatigue Damage ◽  
Water Depth ◽  
Low Frequency ◽  
Fatigue Analysis ◽  
Second Order ◽  
First Order ◽  
Analysis Techniques ◽  
Wave Drift ◽  
Wave Drift Forces ◽  
Drift Forces

As has been noted in industry publications and conferences in the recent past the use of more modern deepwater capable 5th and 6th generation semisubmersible drilling rigs in relatively shallow water applications (when compared to design water depth) is likely to become more commonplace. Water depths of 500m or less will necessitate the use of mooring systems in order to maintain position close to the well centre whilst drilling. For fatigue assessments of moored MODUs, the current industry practice to estimate fatigue damage in the drilling riser and the wellhead, using global riser analysis techniques, is to consider both wave and VIV fatigue effects. Standard wave fatigue analysis considers two key response parameters, firstly the impact of the hydrodynamic loading on the riser joints due to drag forces, inertia and added mass effects, and secondly the effects of vessel motions on the riser system and wellhead loading. Standard practice for wave fatigue analysis is to consider only first order motion effects as described by the vessel RAO (response amplitude operator). However, for a moored MODU low frequency (100s-200s period) vessel response can have a significant impact on the overall vessel motions. The actual response and magnitude of MODU motion will be influenced by the size and displacement of the vessel in addition to the configuration of the mooring system. First order lateral motions for a semisubmersible tend to increase as wave period is increased and therefore at lower periods first order motions can be quite low. However, the opposite can be said of wave drift forces that contribute to second order response. Although the wave drift forces are largest for lower wave periods, these low period drift forces have a significant influence on the resulting long period second order response of a moored MODU. This has important implications for drilling riser and wellhead fatigue analysis as in many cases the critical seastates for fatigue damage are low period seastates with a large number of occurrences. Thus the current global analysis techniques for fatigue calculations may lead to an underestimation of fatigue damage contribution from low period seastates. The purpose of this paper is to present the key conclusions and findings of a study carried out in order to determine the effects of low frequency moored MODU motions on wellhead fatigue. These results are derived from a case study of a moored 6th generation semi-submersible drilling vessel in 500m water depth.

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.

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

Wave Drift Forces and Low Frequency Damping on the Exwave FPSO

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

A method is followed in the present analysis to estimate realistic surge and sway wave drift force coefficients for the Exwave FPSO. 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 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 linearized low frequency damping. The paper presents results from a few cases selected from the Exwave JIP test matrix. Empirical mean wave drift coefficients are compared to potential flow predictions. It is shown that the latter underestimate the wave drift forces, especially at the lower frequency range where severe seastates have most of the energy. The sources for the discrepancies are discussed.

Real Time Prediction of Second Order Wave Drift Forces for Wave Force Feed Forward in DP

2010 ◽  
Author(s):  
P. Naaijen ◽  
R. H. M. Huijsmans
Keyword(s):  
Wave Field ◽  
Prediction Error ◽  
Wave Force ◽  
Second Order ◽  
First Order ◽  
Wave Drift ◽  
Wave Elevation ◽  
X Band ◽  
Wave Drift Forces ◽  
Drift Forces

The presented research is an extension of the development of an onboard wave and motion estimation system that aims to predict wave elevation and wave frequent vessel motions some 60–120 s ahead, using remote measurements of short crested waves. The main aim is to provide decision support during motion critical offshore operations. As an addition to this, an attempt is made to predict second order wave drift forces. This can be useful for condition monitoring of a Dynamic Positioning (DP) system [18] or for feed forward of wave drift forces into the control of DP systems. The paper describes the techniques used to predict second order wave drift forces real time from remote wave measurements. For validation, measurement data is used from model experiments during which wave elevation in irregular short crested seas was recorded by a large number of probes simultaneously. A method is described to obtain a 3D representation of a wave field in such a way that it can be used to predict both first order waves and motions and second order forces. The second order forces resulting from the wave field description as obtained from remote probe measurements can be compared to those that have been derived from the probes in the proximity of the prediction location, thus providing insight in the sensitivity of the 2nd order wave force prediction error with respect to the first order wave prediction error. In a full scale field situation, remote wave sensing can be provided by X-band radar. Possibilities for application of the developed method with the WAMOS II X-band radar system is considered.

Estimating Second Order Wave Drift Forces and Moments for Calculating DP Capability Plots

2019 ◽  
Author(s):  
Saeed Barzegar Valikchali ◽  
Mitchell Anderson ◽  
David Molyneux ◽  
Dean Steinke
Keyword(s):  
Wind Waves ◽  
Low Frequency ◽  
Offshore Structures ◽  
Second Order ◽  
Design Stage ◽  
Wave Direction ◽  
Dynamic Positioning System ◽  
Wave Drift ◽  
Wave Drift Forces ◽  
Drift Forces

Abstract The DP capability plot is a useful tool to show the limitations of a dynamic positioning system for ships or offshore structures under loading from wind, waves and ocean currents. At the preliminary design stage, it is desirable to use fast methods for calculating the forces and moments caused by the environment, preferably without the need for CFD simulations or model experiments. Empirical methods are available for predicting aerodynamic forces and moments, and hydrodynamic forces and moments from currents, but little is published for second order wave drift forces. Wave drift forces and moment calculations have been carried out using WAMIT, for a series of ship hulls from OSVs to VLCCs and the effects of wave direction and frequency on the Surge, Sway, and Yaw forces and moment have been studied. The presentation of the results allows the user to interpolate the resulting drift forces and moments as a function of wave direction for a given ship size. In terms of wave drift loads calculation, it is found that the very large vessels are dominant in the low frequency waves, while smaller size ships are in high frequencies. The wave frequency and direction in which maximum drift load occurs depends on the ship size.

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.

Analysis of Semi-Submersible Under Combined High Waves and Current Conditions Compared With Model Tests

2018 ◽  
Author(s):  
Limin Yang ◽  
Arne Nestegård ◽  
Erik Falkenberg
Keyword(s):  
Simulation Model ◽  
Low Frequency ◽  
Model Tests ◽  
Wave Forces ◽  
Viscous Effects ◽  
Numerical Predictions ◽  
Wave Drift ◽  
Zero Current ◽  
Frequency Excitation ◽  
Wave Drift Forces

Viscous effects on the low-frequency excitation force on column based platforms are significant in extreme waves. The wave drift force as calculated by a zero-current potential flow radiation/diffraction code becomes negligible for such waves. In the present study, the effect of current and viscous contributions on the slowly varying wave forces are adjusted by a formula developed in the Exwave JIP, see e.g. [1], which is validated against model test results. This paper presents numerical predictions of low frequency horizontal motions of a semi-submersible in combined high waves and current condition. In the simulation model, frequency dependent wave drift forces from radiation/diffraction code are modified by the formula. Static current forces and viscous damping are modelled by the drag term in Morison load formula using relative velocity between current and floater and with force coefficients as recommended by DNVGL-RP-C205 [2]. Low frequency surge responses calculated by the simulation model are compared with model tests for waves only and for combined collinear and noncollinear wave and current conditions.

Motion Prediction of a Single-Point Moored Tanker Subjected to Current, Wind and Waves

1990 ◽  
Vol 112 (1) ◽  
pp. 83-90 ◽  
Author(s):  
T. Jiang ◽  
T. E. Schellin
Keyword(s):  
Digital Simulation ◽  
Single Point ◽  
Wave Spectrum ◽  
Memory Effects ◽  
Wave Forces ◽  
Restoring Force ◽  
Low Frequencies ◽  
Frequency Wave ◽  
First Order ◽  
Drift Forces

Horizontal motions of a tanker attached to a single-point mooring (SPM) terminal were predicted using digital simulation in the time domain. Excitations from steady current, gusting wind, and irregular seaway were included. Hydrodynamic forces generated by the ship’s motion and the action of its propeller and rudder were calculated in accordance with a previously validated, nonlinear quasi-steady four-quadrant maneuvering model, extended to include linear memory effects due to waves generated by the moving ship. Memory effects were approximated by a vectorial recursive state space model corresponding to a set of higher order differential equations. A nonlinear relationship of the force in the mooring hawser was assumed to represent restoring force characteristics of the SPM system. Wave excitation forces comprised first-order forces at wave frequencies and second-order drift forces at low frequencies. First-order wave forces were obtained by superposition of force components corresponding to regular wave components comprising the wave spectrum. Based on the low-frequency wave envelope, drift forces were calculated using mean drift force coefficients in regular waves. Selected sample simulations are presented to illustrate the use of this digital simulation method.

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