The development of a frequency-domain Multi-Unit Floating Platform model for design optimization

Abstract

The report summarises the development of a frequency domain Multi-Unit Floating Platform (MUFP) model and a parametric design optimization using the model. The model returns the response statistics of a MUFP due to environmental wind and wave loading using input variables of column separation, column diameter and draft. The model is developed with careful consideration to ensure compatibility with gradient-based optimizers. The low fidelity tool is capable of quickly traversing a design space to land on optimal substructure dimensions. The program uses the input variables to calculate the geometry, buoyancy, mass and stiffness matrices of the MUFP. The design of a mooring system is considered outside the scope of this report. As a result, the stiffnesses in surge, sway and yaw are filled with placeholder stiffnesses. The hydrodynamic coefficients of the three MUFP columns are calculated in HydroD. Smaller drag components such as bracing are assumed to be less influential and are therefore ignored. To maintain computational efficiency during the optimization, the hydrodynamic coefficients are interpolated using surrogate models. The rated power of the MUFP is 10 MW, this is generated using two 5 MW turbines. The aerodynamic loading is accounted for by taking the Power Spectral Density (PSD) of a thrust force time series generated for the NREL 5 MW reference turbine in SIMA. The thrust force time series is taken as the sum of two individual SIMA simulations run in a 280m x 200m wind field. The response statistics of the MUFP are calculated in the frequency domain. This is done by assuming the MUFP motion can be modelled by a Gaussian distribution. The Gaussian distribution is used to derive the zero-crossing periods and the expected number of cycles in a 3-hour timeseries. These values are used to calculate the probability of the maximum wave amplitude. The Most Probable Maxima (MPM) is then found by equating this probability to a Rayleigh distribution. The MUFP is tested against two load cases at rated wind speeds. The first load case includes uni-directional head-on wind and wave loading. The second load case is designed to test the MUFP weathervaning properties. This is done by simulating head-on wind loading, a 90 degree wave heading and a 3 degree yaw misalignment. The optimization is run using the SciPy SLSQP Minimize function. The objective function is the total steel mass and constraints are set on the static heave displacement in addition to the MPM pitch and roll rotations expected in a 3-hour timeseries. The optimization was run three times. Two solutions were found at the global minimum while the third was found at a less optimal local minimum. A comparison of the MUFP optimized dimensions is made against a 10 MW WindFloat design. The comparison revealed the optimization solution was considerably smaller than the WindFloat. Although the physical properties of the MUFP do provide benefits such as a reduction in the aerodynamic pitching moment arm, it is concluded that the reduction in size is a result of the calculation process underestimating the MUFP response statistics.