Harmonic structure of wave loads on a surface piercing column in directionally spread and unidirectional random seas

Abstract

We investigate the harmonic structure of wave-induced loads on vertical cylinders with dimensions comparable to those used to support offshore wind turbines. Many offshore wind turbines are designed, so the structural resonance is two or three times the fundamental wave loading period, which may be excited by higher harmonics of wave loading. The suitability of a ‘Stokes-type’ model for force is examined. We analyse experimental data for unidirectional and directionally spread sea-states. We demonstrate that approximate harmonic components may be extracted from a random time series, using a novel signal processing method. The extracted harmonics are shown to follow a ‘Stokes-like’ model, where the higher harmonics in frequency are proportional to the n-th power of the linear inline force component and its Hilbert transform. Results show that the third harmonic component of force is fitted less well by this model, which is consistent with the literature. A key new result is that the harmonic coefficients for spread and unidirectional seas are nearly identical when fitted as powers of the linear inline force and its Hilbert transform. This finding has the potential to greatly simplify the process of generating harmonic data for new wavelength to cylinder and wavelength to depth ratios. This also implies that the size of the inline component of the $$n\textrm{th}$$ n th harmonic for force in a directional sea relative to the same component in a unidirectional sea scales as $$\cos ^n \sigma _\theta $$ cos n σ θ , where $$\sigma _\theta $$ σ θ is the rms directional spreading angle of the incident wave field. Hence, higher harmonics will be of less importance in directionally spread seas than unidirectional ones. We show that the computationally fast harmonic decomposition approach taken here can reproduce the shape and magnitude of the loading from non-breaking waves waves in a wide range of realistic unidirectional and directionally spread sea-states. The proposed force model has potential as an engineering tool for computationally fast prediction of nonlinear wave loads.

Influence of wave spreading on offshore wind turbine design: IEA 15-MW scenario

“…The origin of this reduction comes from the decrease in loading magnitude associated with directionally spread seas. Where the reduction is proportional to inline wave kinematic factor to the power of the harmonic order [23]. However, the fatigue analysis also demonstrates that it is non-conservative in operating load cases to assume that sea states are uni-directional, despite being a common design assumption.…”

“…This factor is commonly used to reduce the in-line kinematics (velocities and accelerations) of uni-directional wave theories to account for directionality. Results from [23] has shown that for inertia dominated surface piercing columns, the harmonic components of the force signal scale with this inline wave kinematic factor to the power of n-th harmonic as given below:…”

Data Informed Model Test Design With Machine Learning–An Example in Nonlinear Wave Load on a Vertical Cylinder

“…Datasets obtained from the previous three experiments are used as the prior information for guiding the design of this new experimental campaign (details are given in [11][12][13]). Similar focused wave group profiles were generated during these experiments with the same JONSWAP spectrum (𝛾 = 3.3) but with different peak periods and amplitudes.…”

“…All the experiments including the previous and current cases are primarily focused on the unidirectional wave conditions (except for [11] where spreading sea states are also considered), which is different for the directionally spread waves in the open ocean [29].…”

“…Various theoretical works have looked at these higher order harmonics [5][6][7][8]. Experiments and numerical simulations [9,10] are also used to further explore the underlying physics of these higherorder harmonics, including our recent work, where a phase decomposition method is applied to further separate the higher frequency components from the linear loading and Stokes type force expansion is used to predict the higher frequency forces as a nonlinear function of the linear loading in time [11][12][13].…”