Investigation of Response Amplitude Operators for Floating Offshore Wind Turbines Gireesh Ramachandran Amy Robertson Jason Jonkman Marco Masciola 23rd ISOPE - Anchorage, AK - July 3, 2013

Overview FAST, a tool for modeling horizontal-axis wind systems, was recently expanded to include capabilities for modeling offshore systems. Wanted a methodology for verifying the hydrodynamic behavior of an offshore wind system model built in FAST Response amplitude operators (RAOs) are commonly used by offshore companies to assess system behavior. This paper examined the ability to verify a FAST model of an offshore wind system by comparison of its RAOs to those computed from WAMIT. Reviews the process of how to compute RAOs from FAST Highlights the differences between the FAST and WAMIT modeling approaches

FAST Modeling Approach OC4 DeepCwind Semisubmersible Coupled aero-hydro-servo elastic code that computes the loads and responses of both land-based and offshore wind turbines Uses WAMIT output to compute the hydrodynamic loading on the structure This means that FAST models the structural dynamics of an offshore wind system, the influence of the turbine control system, and the forcing from wind, waves, and current. As part of the computation of the hydrodynamic forces, output from the offshore structure code, WAMIT, is needed. RAOs calculated through a nonlinear time-domain simulation approach using white noise wave excitation

WAMIT Modeling Approach OC4 DeepCwind Semisubmersible 3D panel code used to compute wave radiation and diffraction forcing on an offshore structure in the frequency domain Can be used to model offshore wind systems Models only underwater portion of the structure System is considered rigid Influences of turbine and mooring are supplied through external mass, stiffness, and damping matrices (created by FAST) Directly outputs RAOs As you can see there is inter-dependency between FAST and WAMIT for generating offshore wind system RAOs

RAO Computation Flow Chart CG at SWL => WAMIT neglects body gravity term in hydrostatic stiffness in pitch and roll and avoids double-booking in FAST

WAMIT RAO Computation External M, C, K matrices from FAST provide influence of: Mass/inertia of turbine/tower Aerodynamic loading Gyroscopic loading Hydrostatics Mooring stiffness But, does not include: Flexibility of turbine/tower Controller dynamics Nonlinear mooring behavior Turbulent wind

FAST RAO Computation FAST RAOs calculated through a time simulation Wave excitation is a white noise signal – broad-banded Only linear excitation of system, and does not allow for second-order hydrodynamics Can use narrow-banded white noise signal to only provide excitation at wave frequencies Wind excitation can be varied Six simulations run for 8000 seconds System flexibility Platform is rigid Turbine/tower can be flexible and controller enabled (not possible in WAMIT) RAOs computed by dividing averaged cross-spectral density (waves*output response) by auto-spectral density of waves 𝑅𝐴𝑂= 𝐻 𝜔 = 𝑆 𝑥𝑦 𝜔 𝑆 𝑥𝑥 𝜔

Case Study: OC3-Hywind Spar Buoy Rigid Turbine (FAST and WAMIT): No wind (no aerodynamic loads) Below-rated steady wind, V = 8 m/s Rated steady wind, V = 11.4 m/s Above-rated wind, V = 18 m/s Flexible Turbine with Control (only in FAST): The next step is to examine how these RAOs change due to both wind and flexibility of the turbine or tower OC3 Hywind Spar

RAO comparison (no-wind, rigid turbine) Only motion in-line with waves shown since little off-axis motion Platform natural frequencies evident Frequency shift present between FAST/WAMIT in heave/pitch could be due to slight stiffening of mooring lines in FAST Mooring force linearized in WAMIT, but not FAST Surge Pitch Heave Pitch Surge

RAO comparison (all cases): Surge Response Surge response similar at surge natural frequency Less response with rated and just below wind speeds Surge/Heave coupling (not seen in V0 case) Surge/Pitch coupling WAMIT again a bit higher frequency for pitch Larger response for no wind due to absence of aerodynamic damping Surge/heave coupling – why is not seen for no wind? Displaced surge offset creating more coupling to heave

RAO comparison: Sway Response Sway natural freq. Roll natural freq. No sway response when no wind present (V0) Increase in response for increased wind speed due to increased torque Sway minimal with no wind, since response is excited by rotor torque, which is not present Roll natural frequency shifted for WAMIT result Rated (green) shows largest response, except for the FAST rigid – strange large results for the FAST rigid, V18 Torque highest at highest wind speeds, which is why you get largest response at 18

RAO comparison: Heave Response Heave response not affected significantly by wind or modeling approach Anti resonance at surge natural frequency – not present without wind due to surge/heave coupling What is the cause of the anti-resonance? Don’t see a peak??

RAO comparison: Roll Response No roll response when no wind present (V0) Increase in response for increased wind speed due to increased torque

RAO comparison: Pitch Response Pitch motion heavily damped by wind Slightly less response for flexible case Heave/pitch coupling apparent for all but no-wind case 0.47 Hz peak due to fore/aft tower bending frequency – visible in flexible case (out of range on this plot)

RAO comparison: Yaw Response No yaw response for non wind cases – gyroscopic loading from rotating rotor induces yaw motion Roll natural frequency Yaw natural frequency Why no yaw nat freq response for WAMIT? Rotor induced response (3P) for flexible system

Conclusions Presented a methodology for computing RAOs within FAST Used RAOs to verify offshore solution between FAST/WAMIT Presence of platform DOF coupling Influence of aerodynamic damping and gyroscopic loading WAMIT solution does not capture: Flexible turbine and control properties –> extra frequencies Non-linear behavior, especially mooring lines –> shifted freq. Turbulent wind (not demonstrated here) Results are presented for just a spar system, it is suspected that the lack of flexible properties will have more of an impact on other platform designs, such as a TLP (strong tower bending / platform pitch coupling) Aerodynamic damping decreased surge/pitch responses Gyroscopic loading increased yaw response Flexible turbine properties – didn’t see certain frequencies excited Non-linear mooring behavior – shift in frequency for WAMIT

Thank You! Amy.Robertson@nrel.gov