Mathieu instability of a spar platform with mooring and risers
TL;DR: In this article, the authors evaluate damping effects and hull/mooring/riser coupled effects on the principal instability of a spar platform and show that the available damping is important in suppressing the instability.
About: This article is published in Ocean Engineering.The article was published on 2004-12-01. It has received 96 citations till now. The article focuses on the topics: Mathieu function & Spar.
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TL;DR: In this paper, aero-hydro-servo-elastic time-domain simulations of spar-type 5MW wind turbines in harsh and operational environmental conditions are presented.
Abstract: This paper addresses coupled wave and wind-induced motions of spar-type 5-MW wind turbines in harsh and operational environmental conditions. Global dynamic motion responses have been analyzed by aero-hydro-servo-elastic time-domain simulations. The aerodynamics is based on an advanced blade element momentum theory. Panel method and Morison formula accounting for the instantaneous position of the structure are applied for hydrodynamics. Hydrodynamic drag and considering geometrical updating introduce nonlinearities. Hydrodynamic nonlinearities were found to cause excitation of the natural frequencies in the low frequency range more than in the wave frequency range. Extrapolation methods are applied to estimate the maximum responses. A previous study showed that the uncertainty of such an extrapolation for the present concept is less than 2%. In this study it is found that the mean values of the dynamic responses are primarily wind induced and the standard deviations of the responses are primarily wave ind...
125 citations
TL;DR: In this paper, a simplified approach for dynamic response analysis of floating wind turbines that are subjected to wave and wind loads is presented, which is suitable for feasibility and pre-engineering studies of alternative substructures where effects from rotor dynamics are of minor importance.
94 citations
TL;DR: In this article, the dynamic response of a spar-type hollow cylindrical floating substructure moored by three catenary cables to irregular wave excitation was investigated by using the Pierson-Moskowitz spectrum.
88 citations
Cites background from "Mathieu instability of a spar platf..."
..., the vertical distance between the metacenter and the center of mass) (Koo et al., 2004) and the relative distance between the centers of gravity and buoyancy (Karimirad et al....
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...…roll stiffness of spar-type floating substructure which increases in proportional to the metacentric height (i.e., the vertical distance between the metacenter and the center of mass) (Koo et al., 2004) and the relative distance between the centers of gravity and buoyancy (Karimirad et al., 2011)....
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TL;DR: In this paper, the authors proposed three survival modes to ensure the survivability of the spar floating wind turbine under extreme conditions, and the results from the tests and the numerical simulations were compared in the towing tank of MARINTEK, Norway.
87 citations
Cites background from "Mathieu instability of a spar platf..."
...Mathieu-type instability (Haslum and Faltinsen, 1999; Koo et al., 2004) is a kind of instability that occurs when the wave excitation period is half of the pitch natural period, the pitch r esonance is exited....
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...Mathieu-type instability (Haslum and Faltinsen, 1999; Koo et al., 2004) is a kind of instability that occurs when the wave excitation period is half of the pitch natural period, the pitch resonance is exited....
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TL;DR: In this article, the authors studied the drivetrain dynamics of a 750'kW spar-type floating wind turbine (FWT) with a high-speed generator, one-stage planetary, two-stage parallel and three-point support type.
Abstract: This paper studies the drivetrain dynamics of a 750 kW spar-type floating wind turbine (FWT). The drivetrain studied is a high-speed generator, one-stage planetary, two-stage parallel and three-point support type. The response analysis is carried out in two steps. First, global aero-hydro-elastic-servo time-domain analyses are performed using HAWC2. The main shaft loads, which include the axial forces, shear forces and bending moments, are obtained in this integrated wind–wave response analysis. These loads are then used as inputs for the multi-body drivetrain time-domain analyses in SIMPACK. The investigations are largely based on comparisons of the main shaft loads and internal drivetrain responses from 1 h simulations. The tooth contact forces, bearing loads and gear deflections are the internal drivetrain response variables studied. The comparisons are based on the mean values, standard deviations and maximum values extrapolated using a 10 − 5 up-crossing rate. Both operational and parked conditions are considered. The investigation consists of three parts. First, the responses are compared between the FWT and its equivalent land-based version. Second, the contributions from the main shaft loads (shear forces, axial forces and bending moments) and nacelle motions are investigated individually. Third, an improved four-point support (4PT) system is studied and compared against the original three-point support system for the FWT. The results show that there are general increases in the standard deviations of the main shaft loads and internal drivetrain responses in the FWT. In addition, these increases are a result of the increased main shaft loads in the FWT, especially the non-torque loads. Last, the 4PT system, when applied to a FWT drivetrain, significantly reduces the tooth contact forces and bearing loads in the low-speed stage, but this result comes at the expense of increased main bearing radial loads. Copyright © 2013 John Wiley & Sons, Ltd.
61 citations
References
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TL;DR: In this article, a model of an inextensible elastic rod with equal principal stiffnesses is presented, which permits large deflections and finite rotations and accounts for tension variation along its length.
Abstract: A new three-dimensional finite element model of an inextensible elastic rod with equal principal stiffnesses is presented. The model permits large deflections and finite rotations and accounts for tension variation along its length. Its use in static analysis is described and a time integration method for dynamic analysis is developed. Accuracy of the spatial discretization and stability of the time integration method are demonstrated by comparison of numerical results with exact solutions for certain nonlinear problems.
212 citations
01 Jan 1999
97 citations
01 Jan 1986
65 citations
Journal Article•
TL;DR: In this paper, the nonlinear response characteristics of a tethered/moored spar platform in regular and irregular waves are investigated, and a time-domain coupled nonlinear motion analysis computer program is developed to solve both the static and dynamic behaviors of a moored compliant platform as an integrated system.
Abstract: The nonlinear response characteristics of a tethered/moored spar platform in regular and irregular waves are investigated. A series of experiments with a 1:55 scale model was conducted in the OTRC three-dimensional deepwater model basin to observe the motion characteristics of this kind of platform in both survival and operational conditions with and without currents and winds. The spar model presently used is relatively small compared to the large spar studied in Ran et al. (1995). The small spar was supported by a vertical tether and 6 spread mooring lines. In parallel with this experimental program, a time-domain coupled nonlinear motion analysis computer program was developed to solve both the static and dynamic behaviors of a moored compliant platform as an integrated system. In particular, an efficient global-coordinate-based dynamic finite element program was developed to simulate the nonlinear tether/mooring responses. This program was successfully coupled with previously developed time-domain hull motion programs by imposing adequate boundary conditions at the attachment points. Using this program, coupled dynamic analysis results are obtained, and they are compared with uncoupled analysis results to see the effects of tethers and mooring lines on hull motions and vice versa. The numerical results are also compared with the large-scale experiments.
64 citations
01 Jan 2000
50 citations