Wave- and drag-driven subharmonic responses of a floating wind turbine

Abstract

The nonlinear hydrodynamic responses of a novel spar-type soft-moored floating offshore wind turbine are investigated via analysis of motion measurements from a wave-basin campaign. A prototype of the TetraSpar floater, supporting a $1:60$ scale model of the DTU 10 MW reference wind turbine, was subjected to irregular wave forcing (with no wind) and shown to exhibit subharmonic resonant motions, which greatly exceeded the wave-frequency motions. These slow-drift responses are excited nonlinearly, since the rigid-body natural frequencies of the system lie below the incident-wave frequency range. Pitch motion is examined in detail, allowing for identification of different hydrodynamic forcing mechanisms. The resonant response is found to contain odd-harmonic components, in addition to the even harmonics expected a priori and excited by second-order difference-frequency hydrodynamic interactions. Data analysis utilising harmonic separation and signal conditioning suggests that Morison drag excitation or third-order subharmonic potential flow forcing could be at play. In the extreme survival-conditions sea state, the odd resonant responses are identified to be drag-driven. Their importance for the tested floater is appreciable, as their magnitude is comparable to the second-order potential flow effects. Under such severe conditions, the turbine would not be operating, and as such neglecting aerodynamic forcing and motion damping is likely to be reasonable. Additionally, other possible drivers of the resonant pitch response are explored. Both Mathieu-type parametric excitation and wavemaker-driven second-order error waves are found to have negligible influence. However, we note slight contamination of the measurements arising from wave-basin sloshing.

Non-hydrostatic modelling of the wave-induced response of moored floating structures

“…To distinguish between the first-and second-order wave motion, excitation loads and body motions predicted by SWASH; we employ the phase separation method (e.g., Fitzgerald et al, 2014). This methodology assumes that the nonlinear wave-driven processes can be described by a Stokes-type perturbation expansion, and has been successfully applied to study both nonlinear wave processes (e.g., Orszaghova et al, 2014;Whittaker et al, 2017;Zhao et al, 2017) and nonlinear wave dynamics of fixed and moving structures (e.g., Fitzgerald et al, 2014;Chen et al, 2021;Orszaghova et al, 2021). To separate the primary and secondorder contributions with this methodology, we ran a simulation with two different wavemaker signals that are out of phase (i.e., all wave frequencies of the second wavemaker signal are phase shifted by 180 • relative to the first wavemaker signal).…”

Resonant response of a flexible semi-submersible floating structure: experimental analysis and second-order modelling

“…(2017) and Orszaghova et al. (2021), where EC3 has been used for conditions below rated wind speeds ( m s in full scale for the DTU 10 MW reference wind turbine) and EC6 has been used above the rated wind speed. We will denote these states as ‘mild’ and ‘intermediate’, although the significant wave height is quite large for both.…”

“…However, due to the -term, where u is the local horizontal fluid velocity for drag, resulting in a squared amplitude dependence, amplitude analysis can be applied to separate and identify the driving forces behind the first- and third-harmonic responses, as done in Orszaghova et al. (2021).…”

“…(2021) for four-phase separation on fixed structures and Orszaghova et al. (2021) for two-phase separation for a floating structure. In the present paper, time series-based four-phase separation is applied for the first time to a floating structure.…”

“…Odd-harmonic inertia and drag loads, however, can be separated by analysis of amplitude scaling, which was used for the first time by Pierella, Bredmose & Dixen (2021) and Orszaghova et al. (2021). In the latter paper, harmonic separation and amplitude analysis was applied to the response of a laboratory scale floating wind turbine.…”