The document presents a study on the unsteady aerodynamics of floating wind turbines (FOWT) and the dynamics influenced by large motions due to wave interactions. The authors emphasize the need for a numerical model calibration using experimental results from imposed motion tests, and they outline the analytical formulations used to describe system dynamics. Key findings include the significance of wake reduced velocity in capturing aerodynamics under varying operating conditions, with further research deemed necessary for comprehensive modeling.

1. Firma convenzione
Politecnico di Milano e Veneranda Fabbrica
del Duomo di Milano
Aula Magna – Rettorato
Mercoledì 27 maggio 2015
A formulation for the unsteady aerodynamics of
floating wind turbines, with focus on the global
system dynamics
I. Bayati, M. Belloli, L. Bernini, A. Zasso
Politecnico di Milano, Department of Mechanical Engineering

2. I. Bayati, M. Belloli, L. Bernini, A. Zasso
• Motivations and goals
• The proposed formulation
• Observations on unsteady aerodynamics
• Experimental results form imposed motion tests
• Conclusions
Presentation outline

3. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Ocean Basin/HIL Wind Tunnel/HIL
Hydro validation
Aero validation
Motivation and Goals

4. I. Bayati, M. Belloli, L. Bernini, A. Zasso
• FOWT are subjected to large motion induced by the interaction with
the waves
• A calibration of the numerical model in strong unsteady conditions
is needed for FOWT modelling
• Imposed motion tests represent a good solution to understand how
the wind turbine aerodynamics is influenced by these large motion
• Our focus is on the dynamics of the whole mechanical system
Motivation and goals

5. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Dynamics of the system as a whole
Mooring
Waves
Radiation
Viscosity
Diffraction 1°ord
Diffraction 2°ord
Aero
Control

6. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Experimental wind turbine model and experiments
• 1/75 model of the DTU 10 MW RWT
• 1/3 scale factor for the wind velocity

7. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Very good matching below rated
(Torque & Thrust)
Optimized pitch above rated
- Thrust easily matched
- Torque needing higher pitch
Experimental results: steady state conditions

8. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Wind Tunnel Tests: Imposed Surge and Pitch results
Experiments
• Operational conditions:
• Below rated /
• Rated
• Above Rated
• Wave:
Low Frequency motion
Wave frequency motion

9. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Analytical formulation 1
Torque
Thrust
Effective velocity

10. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Analytical formulation 2
Our focus is on the dynamic behaviour of the whole system and we want to describe
the forces as function of the state space
Let’s try to linearize at fixed TSR and hence and fixed pitch angle
@
Unsteady coefficients

11. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Analytical formulation 3
We can do the same exercise also for the torque and then go for a matricial
representation
Unsteady coefficients This matrix contains the direct
and cross terms of the
aerodynamic sensitivity to
imposed motion at the tower
base

12. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Imposed Motion: Surge frequency in the wake
Freq. 1 Hz
Amp. 30 mm
• Same operational
conditions
• Normalization of
the FFT by the
maximum peak
amplitude
• Clear evidence of
the surge motion
frequency f
• Rotational
frequency still
evident (where
present from no
motion)
NO MOTION SURGE MOTION
RATED
ABOVE R.
RATED
ABOVE R.

13. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Wake reduced velocity (1)
Non dimensional number to describe the unsteady interaction
 WAKE REDUCED VELOCITY
N of rotor diameters D ‘‘travelled ’’ by the air with a drift (mean)
velocity V within one cycle of platform motion of frequency 𝑓
From wake measurements tests we observed that the wake is very distorted when the
the platform is moving and the frequency of the motion is very visible in the wake
spectra
When is high, the wind speed is much higher than the speed due to the imposed
motion  QUASI STEADY BEHAVIOUR
When is low, the wind speed is comparable to the speed due to the imposed
motion  STRONG NON LINEARITIES THE ROTOR REENTER ITS WAKE

14. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Wake reduced velocity (2) (WRV)
Introducing the wake reduced
velocity and considering a pure
sinusoidal motion
The quantities that describes the induced velocity can be rewritten as
Thus the aerodynamic sensitivity matrix is
It is a function of TSR and WRV

15. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Physical meaning of a direct term of the matrix
_x [m /s]
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
"T[N]
-4
-3
-2
-1
0
1
2
3
4
Im posed Surge,6v = 3,U = 2:33[m =s]

16. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Experimental verification

17. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Experimental verification: Thrust over Surge

18. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Numerical verification: Thrust over Surge
• FAST8/AeroDyn14 Simulations
• Custom version for imposed motion
• Generalized Dynamic Wake
• Wind turbine rigid model
• Lift and Drag measured on a 2D
sectional model of the blade profile

19. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Conclusions
• Unsteady aerodynamics has been proven to be significant in FOWT when the
system is subjected to large motions
• Wake measurement suggests that Wake Reduced Velocity could be a
significant parameter to describe the unsteadiness
• Focussing on the dynamic of the system as a whole we propose a formulation
to describe the forces as function of TSR and WRV
• For low WRV the unsteady behaviour is clear
• For high WRV the values of the aerodynamic parameters are going towards
Quasi steady values
• A lot of work is still needed to have a complete model
• IRPWIND Unaflow Joint Experiment is dedicated to this purpose

20. I. Bayati, M. Belloli, L. Bernini, A. Zasso
Numerical verification: Thrust over Pitch