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 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.

Extreme Response of Floating Structures in Combined Wind and Waves

2003 ◽  
Vol 125 (2) ◽  
pp. 87-93 ◽  
Author(s):  
P. Teigen ◽  
A. Naess
Keyword(s):  
Numerical Solutions ◽  
Transfer Functions ◽  
Low Frequency ◽  
Water Structure ◽  
Environmental Parameters ◽  
Wave Loads ◽  
Stochastic Loading ◽  
Wide Range ◽  
Extreme Response ◽  
Load Effects

The paper highlights the problem of evaluating the extreme surge response of a floating, deep water structure subjected to stochastic loading from concurrent wind and waves. Additional load effects associated with ocean currents are also briefly discussed. Both long-crested and short-crested waves are considered, whereas the wind field is assumed to be unidirectional. The probability density function (PDF) of the combined wave frequency and low frequency response of the structure, due to waves, is calculated by an eigenvalue analysis and convoluted with the corresponding PDF from the wind loads, to obtain the PDF of the global response. The necessity of employing full, biquadratic transfer functions to evaluate the low frequency part of the wave loads is amply documented. The effect of short-crested versus unidirectional seas on the TLP motion response is discussed at some length, along with various numerical aspects related to the mathematical modelling and to the convergence and accuracy of the obtained solutions. Numerical solutions are presented for a wide range of harsh weather type, environmental parameters.

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.

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.

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.

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.

Study on Influence of Vortex Induced Loads on the Motion of Spar-Type Wind Turbine Based on Aero-Hydro-Vortex-Mooring Coupled Model

2017 ◽  
Author(s):  
Yougang Tang ◽  
Yan Li ◽  
Liqin Liu ◽  
Weichen Jin ◽  
Xiaoqi Qu
Keyword(s):  
Coupled Model ◽  
Numerical Code ◽  
Wave Loads ◽  
Frequency Wave ◽  
Nonlinear Motion ◽  
Restoring Forces ◽  
Mooring Forces ◽  
Vortex Shedding Frequency ◽  
Set Up ◽  
Heave Motion

The coupled nonlinear motion and the influence of vortex induced loads on the motion of Spar type FOWT is studied based on the aero-hydro-vortex-mooring coupled model. The first order and second order difference-frequency wave loads are calculated based on 3D potential theory; the aerodynamic loads on the rotor are calculated based on blade element momentum theory; the vortex induced loads are simulated with CFD approach; the mooring forces are solved by the catenary theory and the nonlinearity of restoring forces are also considered. The nonlinear coupled model is set up and a numerical code is developed for solving the motion of OC3-Hywind Spar-type FOWT in time domain. The responses of FOWT are calculated under different load cases. It is shown that the amplitudes of sway and roll are excited by vortex excited force, and the roll amplitudes can reach to pitch value order in some circumstances. Due to the coupling effects, the heave motion is also influenced by vortex-induced forces. When vortex-shedding frequency is close to roll natural frequency, not only the roll but also the motions in other DOFs are increased and the super-harmonic resonance response occurs in heave motion.

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.

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