As the limited fossil energy sources become empty, new sources for energy need to be exploited. One such renewable energy is wind energy. The wind energy potential is high offshore, and is therefore a beneficial location to place wind power plants. The dimensions of offshore wind turbines are relatively larger than onshore wind turbines. Traditionally, offshore wind turbines are bottom fixed and installed in relatively shallow waters. Europe has very large areas of seabed with a suitable water depth and sea floor. However, shipping lanes, fishing banks, bird migration zones, defense testing grounds and recreational interest all tend to limit the area potentially available for offshore wind farms. Taking these limitations into account, there are not sufficient shallow water areas for large-scale offshore wind farms. One must therefore exploit the possibility of wind turbines at large water depths. Here, floating solutions must be introduced. As it is not possible to perform model tests which comply with the scaling laws for both the aerodynamic and wave forces, the design of floating wind turbines is highly dependent on precise numerical tools to find the optimal technical solutions.
The main loads on an offshore structure come from the environmental, waves, wind and current, with waves as the most important. Thus, it is very important to simulate waves correctly so that their effects on the structures have an adequate degree of accuracy. Fast Fourier Transform (FFT) is normally used for linear analysis when simulating irregular waves. However, the computational requirements will become prohibitive when performing a nonlinear analysis on floating offshore structures, and therefore is an alternative method for representation of the wave spectrum desirable. The purpose of this thesis is to contribute to the verification of an alternative method, the Equal Area Principle (EAP), i.e. the main objective is to compare the Equal Area Principle method against Fast Fourier Transform.
The thesis is divided into two main parts where the first part deals with the adequacy of the equal area method on a single bottom fixed, vertical cylinder. The second part compares the equal area method with FFT on the floating structure, the SWAY turbine. The assessment of the validity of the equal area method is based upon results from the following quantities; the mean, the standard deviation and the extreme values plotted in Gumbel probability papers. 90 percentile estimate of the Gumbel distributions are also used for comparison.
The models are implemented in the nonlinear structural analysis program, USFOS. The accuracy of the USFOS command, SpoolWave employed on SWAY has also been examined, and is found to be satisfactory.
The relevant statistical parameters for the resulting surface elevations have also been investigated. The simulated waves should approach a Gaussian process. The distribution has the following characteristics; a mean value of 0, standard deviation of 3, skewness of 0, and a kurtosis of 3. Both methods produce a good wave profile, i.e. satisfactory parameters, except the kurtosis. FFT produces a kurtosis value less than 3 and less than the equal area method. EAP produces in fact “better” parameters than FFT. The mean extremes of surface elevation from FFT and EAP are respectively lower and higher than the theoretical value. However, the deviations are not significant, and FFT and EAP results in a satisfactory, asymptotically Gaussian distribution.
Considering the results for the fixed cylinder, the equal area method gives both conservative and nonconservative response in comparison to FFT, i.e. the tendency of the equal area method is not predictable. Safety factors are proposed in the conclusions if employing EAP. However, according to present observations the equal area method is not recommended to be used on fixed structures because of the non-consistent trend in the results.
Several response quantities have been studied when checking the adequacy of the equal area method on the SWAY turbine. The equal area method always produces higher responses than FFT, i.e. the equal area method is conservative when employed on the SWAY turbine. However, the difference between the two methods is minor. This suggests that the equal area method is valid when employing a potential correction factor. These are proposed in conclusions.
The simulations have been carried out with a duration of one thousand seconds, and twenty samples from each case are available for comparison. Because of statistical uncertainty, the information basis may be too small to justify firm conclusions. It is therefore recommended to carry out more simulations with longer duration before final conclusions are made.