Bottom Fixed Substructure Analysis, Model Testing and Design for Harsh Environment
Abstract
The aim of this chapter is to study the various hydrodynamic loads important for the design process of offshore wind turbines foundations. A numerical study on weakly nonlinear waves was conducted, using the commercial code StarCCM++. Opensource codes OpenFoam and OceanWave3D were used for the simulation of breaking waves. Existing analytical and empirical formulations, and the results and conclusions from the current numerical study are presented.
Keywords
Wave Height Wind Turbine Impact Force Breaking Wave Regular Wave13.1 Introduction
The main objective of this study is load analysis on fixed bottom support structures of offshore wind turbines suitable for shallow waters and transitional depths (up to 60 m). Usually, hydrodynamic loads cause lower impact on the tower deflection than the wind loads, however for some conditions hydrodynamic loads excite the structure more severely. Hydrodynamic loads are subject of the study in this research, with the primary focus on impulse forces from the breaking waves.
Quantitative data collection from model tests in the AQUILO^{1} project is used for the study on wave propagation and wave loads in the numerical wave tank, by using commercial code StarCCM++. Furthermore, empirical solutions from the Morison equation (Morison et al. 1950) are compared with experimental data as well. Experiments were conducted on support structures installed in the intermediate water depths (d = 40–60 m).
Collaboration with Deltares/Delft within the framework of WiFi^{2}, allowed for an insight into comprehensive experimental data for validation of numerical opensource codes—OpenFoam and OceanWave3D. Experiments were conducted on a monopile structure installed in relatively shallow water (d = 30 m). A series of impulse loadings from breaking waves were observed. It is expected that more comprehensive results will be published after completion of the research. In this chapter, a part of the numerical study is presented.
In short, the purpose of this paper is to present the types of hydrodynamic loads important for the design process of offshore wind turbines foundations, to give a note on existing analytical and empirical formulations and to present results and conclusions from the numerical study.
13.2 Determination of Design Wave
Regular wave profiles in deep water, or intermediate water depth that is not too steep, follow a sinusoidal shape and are well described by linear wave theory. As wave height increases and water depth decreases the wave crest tends to become more narrow and steep, whereas the wave trough becomes long and flat. This happens as the wave starts to sense the bottom. Nonlinearity of wave increases with increased steepness of the wave. Weakly nonlinear, undisturbed waves are in general well understood, and higher order perturbation solutions—such as Stokes 3rd, Stokes 5th, and fully nonlinear stream function theories—exist for regular waves.
Sea states are approximated by wave spectra. The PiersonMoskowitz (Pierson and Moskowitz 1964) and JONSWAP spectrum are commonly used in practice. Generally, the point of interest is the maximum wave elevation in a 3 h storm duration which may occur once in 50years. Within that duration, the maximum expected wave height can be estimated as H_{max} = 1.86H_{s} (DNV 2014), where H_{s} is significant wave height.
Marked positions on Fig. 13.1 correspond to representative cases from experiments in the AQUILO and WiFi projects. Figure 13.2 presents comparison between experimentally observed wave elevation just before wave breaking and theoritical estimations.
13.3 Hydrodynamic Loads
The rotor thrust reaction to wind loads acts on a larger lever arm than loads from the waves. Usually, hydrodynamic loads cause a smaller impact on the tower deflection than wind loads. Wind loads are a dominant source of fatigue loading; however in cases when wind and waves are misaligned, there is no influence of aerodynamic damping, and fatigue from hydrodynamic loads has to be taken into consideration as well.
The extreme and fatigue response stresses depend strongly on the dynamic behavior of the wind turbine structure. When harmonics of the wave frequency coincide with the natural frequency of the structure, the resonance of the structure may result in an amplification of the response. The foundations of fixed bottom wind turbines are designed such that the natural frequency of the structure is out of the range of wave spectrum frequencies. However, higher harmonics of wave excitation can excite structures in resonance and thus amplify the total response. In literature, the phenomena of “ringing” and “springing” are associated with higher harmonic excitations from the incident wave (Faltinsen 1993).
13.4 Analytical and Empirical Formulations
13.4.1 Morison Equation
13.4.2 Higher Harmonic Forces
An amplification of the structural response can be expected when higher harmonics of nonlinear waves coincide with the 1st structural natural frequency. The “Ringing” phenomenon is usually associated with third harmonic excitations from incident waves. The reason why the third harmonic force and “ringing” responses are often associated is that f_{tower}/3 is close to typical peak frequencies of storm waves (Paulsen 2013). When a “ringing” phenomenon is expected, it has to be considered in the design process of wind turbine foundations (DNV 2014).
A comprehensive literature review and a study on higher harmonic loads can be found in the work of (Paulsen 2013). Paulsen (2013) studied higher harmonic loads numerically and compared the obtained results with third order perturbation theories from Faltinsen (1993) and Malenica and Molin (1995). The study by Paulsen (2013) also compared results with the Morison equation with an additional term proposed by Rainey (1989).
13.4.3 Impulse (Slam) Forces from Breaking Waves
Overview on wave impact studies
Author  Max inline force (ρRc^{2})  Max press (ρc^{2})  

von Karman (1929)  π  T  
Wagner (1932)  2π  T  
Goda et al. (1966)  π  T  
Sawaragi and Nochino (1984)  3π  E  
Tanimoto et al. (1987)  1.1π–1.8π  E  
Zhou et al. (1991)  4–13  E  
Chaplin (1993)  2π–4π  E  
Chan et al. (1995)  16–47  E  
Wienke and Oumeraci (2005)  2π  T  40  E 
Ros (2011)  1.1π–1.4π  E  
Hildebrandt and Schlurmann (2012)  0.8π–1.1π  N  4–12.5  E 
For the calculation of impact forces due to plunging wave breakers on offshore wind turbines, a reference is usually made to the model developed by Wienke and Oumeraci (2005). The theoretical description of their model is based on Wagner’s (1932) 2Dmodel; to account for the temporal development of the impact they compute the nonlinear velocity term in Bernoulli’s equation.
Comprehensive experimental studies have been conducted to study impact forces of breaking waves. High fluctuations and scattering from the point of view of local line forces and local pressures are observed. Table 13.1 gives an overview on wave impact studies.
13.5 Numerical Analysis
13.5.1 Star CCM++
 The domain should be refined in the free surface zone (around 25 cells per wave height and 115 cells per wave length); the aspect ratio should be dx/dz ≤ 4 (Fig. 13.6)

Second order time discretization should be used with at least five iterations per time step; in the equation for volume fraction of water, the convection flux was discretized using a special highresolution interfacecapturing (HRIC) scheme which is designed to keep the interface sharp. To use the HRIC scheme propagation, the wave should be less than half a cell per time step

kε turbulence models introduce significant generation of eddy viscosity at the free surface interface; significant numerical diffusion was observed. After wave propagation of few wave lengths, wave height was reduced up to the 20 % compared with the initialized wave height.

Better results were obtained by using an inviscid model. After wave propagation of 20 wave lengths, the wave height was reduced up to the 6 % compared to the initialized wave height

The structure under analysis must not be placed too close to the inlet boundary because of the reflected waves that propagate upstream toward the inlet boundary and changing inlet values.

In a case where the linear wave propagating in the numerical tank is influenced by the sea bed, the obtained wave height at the position of interest was around 20 % lower than theoretically expected.

It was found that the propagation of a wave, influenced by the sea bed, suffers from significant damping. It is suggested that parameters of initialised wave be close to the characteristics of the specific wave of interest.
In this technique, waves that are reflected off the structure and propagate upstream towards inlet boundary can be reduced and their influence on results can be eliminated; additionally, the necessary wave damping towards the outlet can be achieved more progressively, and the domain size can be reduced so that the speed of computation is increased.
13.5.2 OceanWave3D: OpenFoam
To correctly predict the nonlinearity of the incident waves, bathymetry changes have to be taken into account as soon as the wave starts to get influenced by the bottom. To simulate the propagation of a wave with a strong influence of the sea bed (very steep, near breaking or breaking waves) the computation domain should be very long—however, the solution would be significantly influenced by numerical diffusion. To reduce the influence of numerical diffusion, and to reduce the time of the computation, one can solve the Navier–Stokes/VOF equations in a very small “inner” region of interest, while wave propagation up to the “inner” region of interest is solved by existing wave theories. A fully nonlinear domain decomposed solver is presented by Paulsen et al. (2014). The fully nonlinear potential flow solver is combined with a fully nonlinear Navier–Stokes/VOF solver via generalized coupling zones of arbitrary shape.
The Navier–Stokes/VOF governing equations are solved using an opensource computational fluid dynamics toolbox, OpenFoam®. The equations are discretized using a finite volume approximation with a collocated variable arrangement on generally unstructured grids. For the current investigation, OpenFoam® version 2.3.0 is combined with the opensource wave generation toolbox, waves2Foam.
13.6 Results
13.6.1 Stokes 5th Order
13.6.2 Breaking Wave
13.7 Conclusions
A series of computations for hydrodynamic forces on fixed bottom support structures for offshore wind turbines have been carried out. It can be conclusively stated that the Morison equation is an adequate and fast engineering tool for the estimation of inline forces on the slender structures installed in relatively deep water, where strongly nonlinear waves are not expected. CFD tools are important for studies related to local flow around the structure, wave runups, higher harmonic forces, and impact forces from waves.
It is also noted that simulations of wave propagation (analyses with StarCCM++) suffer from artificial numerical diffusion, especially when kε turbulence models are included in the computations. CFD simulations are too expensive and diffusive for simulation of undisturbed wave propagation—which can instead be computed with the potential wave tools, such as OceanWave3D.
Footnotes
 1.
AQUILO—Development of the selection method of the offshore wind turbine support structure for Polish maritime areas, project cofounded by NCBiR; www.morcekoaquilo.pl
 2.
WiFi—joint industry project, Wave Impact on Fixed turbines; secondment at Deltares/Delft.
Notes
Acknowledgments
The presented work was realized within the framework of AQUILO project (PBS1/A6/8/2012), cofunded by The National Centre for Research and Development and MareWint project under research area FP7PEOPLE2012ITN MarieCurie Action : “Initial Training Networks”. Secondment in Deltares was realized under the framework of the joint industry project WiFi (Wave Impacts on Fixed Turbies).
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