Investigation of Response Amplitude Operators for Floating Offshore Wind Turbines

1. 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

2. 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

3. 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 • RAOs calculated through a nonlinear time-domain simulation approach using white noise wave excitation

4. 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

5. RAO Computation Flow Chart

6. 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

7. 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

8. 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): • 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 OC3 Hywind Spar

9. RAO comparison (no-wind, rigid turbine) Surge Pitch • 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 Heave Pitch Surge

10. 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

11. 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

12. 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

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

14. 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)

15. 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 Rotor induced response (3P) for flexible system

16. 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)

17. Thank You! Amy.Robertson@nrel.gov