2.2.1. Preliminary/concept design

It is an iterative process which begins with concept selection or preliminary design. This is followed by a more detailed design and analysis of the loads and system's response to ensure the structural strength is sufficient to withstand the load effects (DNVGL-ST-0119, 2018).

As discussed in Borg and Collu (2015), Kolja Müller and Simon Tiedemann (2017) and Lefebvre and Collu (2012), the preliminary design of a floating substructure is divided into two stages, which are the preliminary sizing of the support structure's concept, and the design for further development and refinement. The main requirements to fulfil when sizing is the hydrostatic stability requirements which are:

• •

  Support structure must ensure floatability

• •

  A maximum pitch/roll angle of 5° for static equilibrium and 5° combined with ± 15 degrees of dynamic amplitude imposed in order not to substantially compromise the performance of the FOWT (Borg and Collu, 2015). As mentioned in Borg and Collu (2015), this is only a guideline.

• •

  Maximum floater offset or floater excursion in surge including static, first and second order loads is less than 50% of the water depth (Kolja Müller and Simon Tiedemann, 2017).

Other drivers to consider when sizing are the site conditions/metocean data designed for extreme driven ultimate limit state (ULS), turbine weight and inertias and the thrust force on the turbine (Friedemann Borisade et al., 2016).

The preliminary sizing is based on two equations which are the buoyancy force equation detailed in Lefebvre and Collu (2012) and the restoring moment equation detailed in Collu and Borg (2016). The buoyancy force acting on the FOWT system is equivalent to the weight of the turbine and weight of the support structures (tower, platform and mooring lines) while the restoring moment in roll/pitch is a summation of water plane stabilization parameters, ballast stabilization parameters and mooring stiffness discussed in Section 2.1.

An iterative method is used to solve the set of buoyancy force equation and restoring moment equation based on the substructure's geometry to select the concept for detailed design. The iterative method can also be in the form of optimizers to explore the design space based on design objectives like platform's motion response and platform's mass to select the optimal design concept.

2.2.2. Detailed design

For a detailed design assessment, the preliminary design is refined to ensure the structural strength has been improved in intact conditions (Lefebvre and Collu, 2012). Due to the complexity of FOWT as an engineering system, its design must be governed by adequate industry's technical standards and guidelines. The most widely used design standards for FOWTs are Det Norske Veritas (DNV) (DNV-OS-J101, 2013; DNVGL-RP-0286, 2019; DNVGL-SE-0422, 2018; DNVGL-ST-0119, 2018; DNVGL Oslo, 2018; DNVGLAS, 2016), American Bureau for Shipping (ABS) (ABS, 2014, Updated July 2020.), Bureau Veritas (BV) (Veritas, 2010, 2015, Updated, 2019), Class NK (Kyokai, 2012) and the International Electrochemical Commission (IEC) (IEC-61400-1, 2014; IEC-61400-3-2, 2019; IEC-61400-3, 2009). The methodology used for most of the design standards highlighted is the “load and resistance factor design”. The aim of this approach is to obtain design within the adequate safety level by considering safety factors to account for uncertainties in both structural load and structural resistance (Bachynski and Collu, 2019; DNV-OS-C105, 2008). In their work, Collu and Borg (2016) discussed the classifications criteria of the support structures based on existing codes and standards verification societies: BV (Veritas, 2010), ABS (ABS, 2015, Updated March 2018, 2020) and DNV (DNV-OS-J101, 2013).

BV (Veritas, 2010) adopts the classification criterion based on the floating platform's stability mechanisms i.e., ballast stabilized floating platforms (spar-buoy), buoyancy stabilized floating platforms (semi-submersibles and barges), and tensioned stabilized platform classes (TLP).

ABS (ABS, 2015; Updated March 2018; 2020) adopts the classification criterion based on the structural elements of the different floating substructure, without expressly defining the stabilizing mechanism.

For the DNV offshore standard, the criteria are based on whether a structure is restrained (displaced in the order of centimetres) or compliant (displaced in the order of meters or more).

Overview of the analysis approach for detailed design are discussed in Jonkman and Matha (2011) and highlighted below:

• 1.

  Develop a model of each complete system with a comprehensive simulation tool capable of modelling the coupled dynamic response of the system from combined wind and wave loading. This form of modelling requires the application of comprehensive aero-hydro-servo-elastic simulation tools that incorporate integrated models of the wind inflow, aerodynamics, hydrodynamics (offshore systems), control (servo) dynamics and structural (elastic) dynamics in the time domain in a coupled nonlinear simulation environment. Some of the available commercial simulation and modelling tools for FOWT system are: DNV suites (Genie, HydroD, Wadam, SIMA), Ansys Aqwa, Nastran, Orcaflex. An important open source simulation and analysis tool is OpenFAST code, developed by (Jonkman, 2007). It enables high fidelity model analysis and verification in the time domain.

• 2.

  Verify elements of each full system dynamics model from step 1 by checking its response predictions with responses predicted by a simpler model. When modelling a floating wind turbine, it is advantageous to check the sophisticated nonlinear time domain model against a much simpler linear frequency domain model. This kind of check can be made in terms of response amplitude operators of system motions and loads for excitation by regular waves or in terms of probability distributions of system motions and loads for excitation by irregular waves.

• 3.

  Using each full system dynamics model from step 1, a comprehensive loads analysis is performed to identify the ultimate loads and fatigue loads expected over the lifetime of the system. Loads analysis involves running a series of design load cases (DLCs) covering essential design-driving situations, with variations in external conditions and the operational status of the system.

• 4.

  Improve each floating system design through design iteration of the above steps, ensuring that each of the system components is suitably sized through limit-state analyses.

2.3.1. Shape parameterization review

Shape parameterization is an important concept in design. It facilitates the exploration of a conceptual design space and provides informed knowledge to make design decisions. Geometric shape parametric modelling cuts across all areas of design and has been widely researched in the aerospace, automotive, construction, architecture, manufacturing and civil engineering sectors.

Shape parameterization techniques review has been extensively done for aerospace geometric designs and are detailed in the works of Samareh (1999), Samareh (2001) and Kulfan and Bussoletti (2006). For offshore hydrodynamic models, the application of shape parameterization techniques for design, analysis and optimization can be seen in works done by (Birk and Clauss (2002), Birk et al. (2004) and Birk and Clauss (2008)). These techniques are the reviewed techniques from the aerospace sector and are highlighted in this section. Properties of a well conducted parameterization method as discussed in the works of Kulfan and Bussoletti (2006), Samareh (2001) and Zhu (2014)are:

• 1.

  Provide high flexibility to cover the potential solution in the design space;

• 2.

  Give as small number of design variable as possible;

• 3.

  Produce smoothness and reliability of geometric shapes;

• 4.

  Provide correct design parameters for geometric and physical understanding in design space exploration by the engineers.

An overview of some of the shape parameterization techniques are highlighted in Section 2.3.1.1 to 2.3.1.3.

2.3.2. Parameterization work on FOWT

Efficient evaluation of a large number of FOWT designs require adequate parameterization, which can enable the exploration of a rich design space limiting the number of design variables. The design parameterization should ideally cut across more floating platform classes and different geometrical variables for optimization purposes. A detailed parametric study of a FOWT system is presented in (Tracy, 2007), where the optimization leads to the definition of the Pareto fronts for mean square acceleration of the turbine against multiple cost drivers of the offshore structure (simply put – a trade-off between performance and cost). The cost drivers include displacement of the structure and total mooring line tension.

Another work on FOWT parameterization and optimization can be traced to Sclavounos et al. (2008). In this work, they presented a coupled dynamic analysis of floating wind turbines incorporating a parametric design study of floating wind turbine concepts and mooring system. They presented a Pareto optimal design that has a favourable combination of nacelle acceleration, mooring system tension, and displacement of the floating substructure supporting a 5 MW wind turbine. Their results show that, for a fully coupled dynamic analysis conducted for the wind turbine, the floating substructure and the mooring system, considering both wind and sea state environmental conditions, the Pareto optimal structures are generally either a narrow deep drafted spar or a shallow barge ballasted with concrete. The varying parameters for this work are the draft and the diameter of the platform.

It can be observed from the examples provided that the parametric approach is mainly varying platform diameter and draft. To apply geometric shape parameterization technique, there is need to look at other offshore sectors like the oil and gas and maritime sectors. In their study, Zhang et al. (2008), noted that a successful hydrodynamic optimization of ship hull depends on the geometric variation of hull planer forms. The parametric design of hull forms involves; specifying form parameters, design of a set of longitudinal curves, parametric modelling of sections which forms the body parts and generating hull forms (Zhang et al., 2008). This curve parameterization technique has been successfully used in the design of ship hulls, and can be implemented in the design of FOWT platforms. Another parameterization and optimization work, carried out for oil & gas offshore structures, with an optimization methodology based on linear analysis of wave-body interaction, has been done by Birk and Clauss (2008). This work was started over a decade earlier as hydrodynamic shape optimization of large offshore structures by the same authors (Clauss and Birk, 1996). In Birk and Clauss (2008), a reliable hydrodynamic analysis, using the WAMIT program, has been integrated with a newly developed parametric hull design methodology, which enables the automated generation of hull shapes, without the need for user interaction. The optimization algorithm is used to optimize the shapes with the hull responses. The shape parameterization technique discussed in Section 2.3.1 can be employed in the design, analysis, and optimization of FOWT platforms.

2.4.1. Frequency domain approach

The frequency domain approach has been extensively used in the oil and gas industry, as it enables the assessment of the system's wave response spectrum given the wave spectrum of the site and the response amplitude operator (RAO) of the given system (Journée and Massie, 2001; Patel, 2013). For a FOWT system in regular wave, the resultant system of equations of motion, in the frequency domain is highlighted in Coraddu et al. (2020) and Newman (2018).

The formulation for the radiation and diffraction boundary value problem and the resulting hydrodynamic added mass, damping matrices and wave-excitation force depend on frequency, water depth, and sea current, as well as on the geometric shape of the support platform, its proximity to the free surface, and its forward speed. Additionally, the wave-excitation force depends on the heading direction of the incident waves (Jonkman, 2007). The frequency dependence of the hydrodynamic added mass and damping matrices is of a different nature to that of the wave-excitation force. In the frequency dependence of the hydrodynamic added mass and damping matrices, the matrices depend on the oscillation frequency of the particular mode of support platform motion. However, the frequency dependence of the wave-excitation force means that the force depends on the frequency of the incident wave. Both set of frequencies (added mass and damping frequency and wave excitationfrequency) are identical because the platform is assumed to oscillate at the same frequency as the incident wave.

By definition, the frequency-domain model assumes that the platform motions are at the same frequency as the incident waves and that the incident waves are regular. While this means that the transient response of the system cannot be modelled, the assumption of linearity implies that the responses at different wave frequencies can be superimposed according to a wave spectrum to predict the system behaviour in irregular sea states (Hall et al., 2013). Extensive discussion of these hydrodynamic coefficients can be found in Anaya-Lara et al. (2018) and Journée and Massie (2001). The hydrodynamic coefficients (added mass. radiation damping and first order wave excitation) can be approximated as solution to the linear radiation-diffraction problem using the boundary element method. This is implemented in softwares like WAMIT, detailed in WAMIT-Inc (2020) and WADAM in DNVGL Høvik (2019).

The complex magnitude of the response transfer function between the amplitude of the wave and the amplitude of oscillation in the oscillatory degree of freedom is the RAO highlighted in Eq. (5).(5)${}_{}\underset{\mathrm{}}{\overset{\mathrm{}}{}}\frac{{}_{}}{{}^{\mathrm{}}{}_{}{}_{}{}_{}{}_{}}$Where $$ is the frequency of oscillation of the platform, ${}_{}$ is the total system mass matrix, ${}_{}$ is the hydrodynamic added mass coefficient, ${}_{}$ is the radiation damping coefficient without the consideration of viscous forces and ${}_{}$ is the sum of the hydrostatic and mooring stiffness coefficients. and ${}_{}$ is the first order wave excitation load transfer function (Coraddu et al., 2020; Newman, 2018).

The wave response spectrum should be minimized in order to minimize the displacements and accelerations of the FOWT system. It is important that the natural frequencies (periods) of the FOWT system should be outside the most energetic frequency (period) range of the wave spectrum (Collu and Borg, 2016). This depends on the location, but in general wave spectra are most energetic between the 5s and 25s period (1.25–0.25 rad/s), and therefore the structure should aim at having natural periods above 25s or below 5s in all the DOFs (Collu and Borg, 2016).

The frequency domain analysis approach is mostly used for preliminary design of FOWTs as the RAO concept is strictly valid to estimate the regime response to waves and by definition is a linear approach (Collu and Borg, 2016). To capture the transient behaviour of a FOWT due to non-linear loading from wind and irregular seastate, a more detailed approach is required as in the time domain approach.