This paper focuses on the analysis of a floating wind turbine under multidirectional wave loading. Special attention is given to the different methods used to synthesize the multidirectional sea state. This analysis includes the double-sum and single-sum methods, as well as an equal-energy discretization of the directional spectrum. These three methods are compared in detail, including theergodicity of the solution obtained. From the analysis, the equal-energy method proved to be the most computationally efficient while still retaining the ergodicity of the solution. This method was chosen to be implemented in the numerical code FAST. Preliminary results on the influence of these wave loads on a floating wind turbine showed significant additional roll and sway motion of theplatform.
Ocean energy is one of the most important sources of alternative energy and offshore floating wind turbines are considered viable and economical means of harnessing ocean energy. The accurate prediction of nonlinear hydrodynamic wave loads and the resulting nonlinear motion and tether tension is of crucial importance in the design of floating wind turbines. A new theoretical framework is presented for analyzing hydrodynamic forces on floating bodies which is potentially applicable in a wide range of problems in ocean engineering. The total fluid force acting on a floating body is obtained by the time rate of change of the impulse of the velocity potential flow around the body. This new model called Fluid Impulse Theory is used to address the nonlinear hydrodynamic wave loads and the resulting nonlinear responses of floating wind turbine for various wave conditions in a highly efficient and robust manner in time domain. A three-dimensional time domain hydrodynamic wave-body interaction computational solver is developed in the frame work of a boundary element method based on the transient free-surface Green-function. By applying a numerical treatment that takes the free-surface boundary conditions linearized at the incident wave surface and takes the body boundary condition satisfied on the instantaneous underwater surface of the moving body, it simulates a potential flow in conjunction with the Fluid Impulse Theory for nonlinear wave-body interaction problems of large amplitude waves and motions in time domain. Several results are presented from the application of the Fluid Impulse Theory to the extreme and fatigue wave load model: the time domain analysis of nonlinear dynamic response of floating wind turbine for extreme wave events and the time domain analysis of nonlinear wave load for an irregular sea state followed by a power spectral density analysis.
The Unidirectional Hybrid Wave Model (UHWM) predicts irregular wave kinematics and pressure accurately in comparison with its linear counterpart and modification, especially near the free surface. Hence, in using the Morrison equation it has been employed in the computation of wave loads on a moored floating structure, such as Spar or TLP (Tension Leg Platform), which can be approximated by a slender body or a number of slender components. Dr. Jun Zhang, with his former and current graduate students, have developed a numerical code, known as COUPLE, over the past two decades, simulating 6 Degree Of Freedom (DOF) motions of a moored floating structures interacting with waves, current and wind. COUPLE employs UHWM as a module for computing wave loads on a floating structure. However, when the duration of simulating the wave-structure interaction is long, say 3 hours (typically required by the offshore industry for extreme storm cases), the computation time of using UHWM increases significantly in comparisons with the counterpart based upon linear wave theory. This study is to develop a numerical scheme which may significantly reduce the CPU time in the use of UHWM and COUPLE. In simulating irregular (or random) waves following a JONSWAP spectrum of a given cut off frequency, the number of free wave components in general grows linearly with the increase of the simulation duration. The CPU time for using a linear spectral method to simulate irregular waves is roughly proportion to N2, where N is the number of free wave components used in simulating irregular waves, while that for using a nonlinear wave model, such as UHWM, it is roughly proportional to N3. Therefore, to reduce the CPU time, the total simulation duration is divided into a number of segments. However, due to the nature of Fast Fourier Transform (FFT), the connection between the two neighboring surface elevations segments is likely discontinuous. To avoid the discontinuity, an overlapped duration between the two neighboring segments is adopted. For demonstration, a free-wave spectrum is input to COUPLE for simulating the 6 DOF motions of a floating 5-MW wind turbine installed on an OC3 moored Spar and tensions in the mooring lines. It is shown that the CPU time for the above simulation for duration of 2048 seconds is reduced from more than16 hours when the irregular wave elevation and kinematics are calculated without dividing into segments to less than three hours when those are calculated by dividing into five segments. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148395
A procedure is developed for modeling stochastic ocean wave and wind loads as diffusive stochastic differential equations (SDE) in a state space form to derive the response statistics of offshore structures, specifically wind turbines. Often, severe wind and wave systems are highly nonlinear and thus treatment as linear systems is not applicable, leading to computationally expensive Monte Carlo simulations. Using Stratonovich-form diffusive stochastic differential equations, both linear and nonlinear components of the wind thrust can be modeled as 2 state SDE. These processes can be superposed with both the linear and nonlinear (inertial and viscous) wave forces, also modeled as a multi-dimensional state space SDE. Furthermore, upon implementing the ESPRIT algorithm to fit the autocorrelation function of any real sea state spectrum, a simple 2-state space model can be derived to completely describe the wave forces. The resulting compound state-space SDE model forms the input to a multi-dimension state-space Fokker-Planck equation, governing the dynamical response of the wind turbine structure. Its solution yields response, fatigue and failure statistics-information critical to the design of any offshore structure. The resulting Fokker-Planck equation can be solved using existing numerical schemes.
