Paul D. Sclavounos

Development of Fully Coupled Aeroelastic and Hydrodynamic Models for Offshore Wind Turbines

Aeroelastic simulation tools are routinely used to design and analyze onshore wind turbines, in order to obtain cost effective machines that achieve favorable performance while maintaining structural integrity. These tools employ sophisticated models of wind-inflow; aerodynamic, gravitational, and inertial loading of the rotor, nacelle, and tower; elastic effects within and between components; and mechanical actuation and electrical responses of the generator and of control and protection systems. For offshore wind turbines, additional models of the hydrodynamic loading in regular and irregular seas, the dynamic coupling between the support platform motions and wind turbine motions, and the dynamic characterization of mooring systems for compliant floating platforms are also important. Hydrodynamic loading includes contributions from hydrostatics, wave radiation, and wave scattering, including free surface memory effects. The integration of all of these models into comprehensive simulation tools, capable of modeling the fully coupled aeroelastic and hydrodynamic responses of floating offshore wind turbines, is presented.

Removing the irregular frequencies from integral equations in wave-body interactions

The paper presents a method that removes the effects of all irregular frequencies in boundary-integral equations governing the interaction of regular waves with floating bodies of general geometry. A modified integral equation is obtained by the linear superposition of the classical Green equation and its normal derivative with respect to the field point.

THE SLOW-DRIFT MOTION OF ARRAYS OF VERTICAL CYLINDERS

The large-amplitude rectilinear ‘slow-drift’ oscillation of a floating body constrained by a weak restoring force in random waves is considered. The free-surface flow is approximated by a perturbation series expansion for a small slow-drift velocity and wave steepness. A model slow-drift equation of motion is derived, the time-dependent slow-drift excitation force and wave damping coefficient are defined and the complete series of free-surface problems governing their magnitude are formulated. The free-surface problem governing the wave-drift damping coefficient in monochromatic waves is studied and an explicit solution is obtained for a vertical circular cylinder of infinite draught. This solution is extended for arrays of vertical circular cylinders by employing an exact interaction theory. The wave-drift damping coefficient is evaluated for configurations of interest in practice and an expression is derived for the steady drifting velocity of an unconstrained body in regular waves.

On Steady and Unsteady Ship Wave Patterns

The properties of steady and unsteady ship waves propagating on a free surface discretised with panels are studied. The wave propagation is characterised by an explicit discrete dispersion relation which allows the systematic analysis of the distortion of the wave pattern due to discretisation and the derivation of a stability criterion to be met by the numerical algorithm. The conclusions of the study are applied to a panel method used for the computation of steady and time-harmonic free-surface flows past elementary singularities and a ship hull.

Three-dimensional nonlinear solitary waves in shallow water generated by an advancing disturbance

The nonlinear long waves generated by a disturbance moving at subcritical, critical and supercritical speed in unbounded shallow water are investigated. The problem is formulated by a new modified generalized Boussinesq equation and solved numerically by an implicit finite-difference algorithm. Three-dimensional upstream solitary waves with significant amplitude are generated with a periodicity by a pressure distribution or slender strut advancing on the free surface. The crestlines of these solitons are almost perfect parabolas with decreasing curvature with respect to time. Behind the disturbance, a complicated, divergent Kelvin-like wave pattern is formed. It is found that, unlike the wave breaking phenomena in a narrow channel at F h [ges ] 1.2, the three- dimensional upstream solitons form several parabolic water humps and are blocked ahead of the disturbance at supercritical speed in an unbounded domain for large time.

Floating Offshore Wind Turbines: Responses in a Seastate Pareto Optimal Designs and Economic Assessment

Wind is the fastest growing renewable energy source, increasing at an annual rate of 25% with a worldwide installed capacity of 74 GW in 2007. The vast majority of wind power is generated from onshore wind farms. Their growth is however limited by the lack of inexpensive land near major population centers and the visual pollution caused by large wind turbines. Wind energy generated from offshore wind farms is the next frontier. Large sea areas with stronger and steadier winds are available for wind farm development and 5MW wind turbine towers located 20 miles from the coastline are invisible. Current offshore wind turbines are supported by monopoles driven into the seafloor at coastal sites a few miles from shore and in water depths of 10–15m. The primary impediment to their growth is visual pollution and the prohibitive cost of seafloor mounted monopoles in larger water depths. This paper presents a fully coupled dynamic analysis of floating wind turbines that enables a parametric design study of floating wind turbine concepts and mooring systems. Pareto optimal designs are presented that possess a favorable combination of nacelle acceleration, mooring system tension and displacement of the floating structure supporting a five megawatt wind turbine. All concepts are selected so that they float stably while in tow to the offshore wind farm site and prior to their connection to the mooring system. A fully coupled dynamic analysis is carried out of the wind turbine, floater and mooring system in wind and a sea state based on standard computer programs used by the offshore and wind industries. The results of the parametric study are designs that show Pareto fronts for mean square acceleration of the turbine versus key cost drivers for the offshore structure that include the weight of the floating structure and the static plus dynamic mooring line tension. Pareto optimal structures are generally either a narrow deep drafted spar, or a shallow drafted barge ballasted with concrete. The mooring systems include both tension leg and catenary mooring systems. In some of the designs, the RMS acceleration of the wind turbine nacelle can be as low as 0.03 g in a sea state with a significant wave height of ten meters and water depths of up to 200 meters. These structures meet design requirements while possessing a favorable combination of nacelle accleration, total mooring system tension and weight of the floating structure. Their economic assessment is also discussed drawing upon a recent financial analysis of a proposed offshore wind farm.Copyright

Floating Offshore Wind Turbines

Increasing at a rate of 30% annually, wind is a renewable energy source that is rapidly growing, with onshore wind farms generating the vast majority of wind power. The visual impact large wind turbines cause and lack of inexpensive land near major population centers limit the growth of these facilities, however. The next frontier is floating offshore wind farm-generated wind energy. Wind turbine towers are invisible, even at 5 MW, when they are located 20 miles from the coastline, and there is availability of vast sea areas with stronger and steadier winds for wind farm development. Bottom mounted structures, including monopoles driven into the seafloor, in water depths of 10-15 m and coastal sites a few miles from shore, currently support offshore wind turbines. As water depths increase, their prohibitive cost is their primary growth impediment. The author discusses motion resistant floating offshore wind turbine development-associated technologies and economics, drawing on a seven-year Massachusetts Institute of Technology research effort. There is discussion of two floater concept families, inspired by oil and gas industry development for deep water hydrocarbon reservoir exploration. Severe weather floater response dynamics interaction with wind turbine system dynamics is addressed, as is such couplings impact on new multi-megawatt wind turbines generation design for offshore deployment. There is also discussion of utility scale floating offshore wind farm developments primary economic drivers.

Radiation and diffraction of second-order surface waves by floating bodies

The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of initial-value problems that ensure they satisfy the proper radiation condition at infinity. The second-order velocity potential is expressed as the sum of a particular and a homogeneous component. The former satisfies the non-homogeneous free-surface condition and is expressed explicitly in terms of the second-order Green functions. The latter is subject to the homogeneous free-surface condition and enforces the body boundary condition by the solution of a linear problem. An analysis is carried out of the singular behaviour of the second-order potential near the intersection of the body boundary with the free surface.

An unsteady lifting-line theory

A lifting-line theory is developed for wings of large aspect ratio undergoing time-harmonic oscillations, uniformly from high to low frequencies. The method of matched asymptotic expansions is used to enforce the compatibility of two approximate solutions valid far from and near the wing surface. The far-field velocity potential is expressed as a distribution of normal dipoles on the wake, and its expansion near the wing span leads to an expression for the oscillatory downwash. The near-field flow is two-dimensional. A particular solution is obtained from strip theory and a homogeneous component is added to account for the spanwise hydrodynamic interactions. The compatibility of the inner and outer solutions leads to an integral equation for the distribution of circulation along the wing span. In the zero-frequency limit it reduces to that in Prandtls lifting-line theory, and for high frequencies it tends to the two-dimensional strip theory. Lift computations are presented for an elliptic and a rectangular wing of aspect ratio A = 4.

Karhunen-Loeve representation of stochastic ocean waves

A new stochastic representation of a seastate is developed based on the Karhunen–Loeve spectral decomposition of stochastic signals and the use of Slepian prolate spheroidal wave functions with a tunable bandwidth parameter. The new representation allows the description of stochastic ocean waves in terms of a few independent sources of uncertainty when the traditional representation of a seastate in terms of Fourier series requires an order of magnitude more independent components. The new representation leads to parsimonious stochastic models of the ambient wave kinematics and of the nonlinear loads and responses of ships and offshore platforms. The use of the new representation is discussed for the derivation of critical wave episodes, the derivation of up-crossing rates of nonlinear loads and responses and the joint stochastic representation of correlated wave and wind profiles for use in the design of fixed or floating offshore wind turbines. The forecasting is also discussed of wave elevation records and vessel responses for use in energy yield enhancement of compliant floating wind turbines.