European Wind Energy Conference and Exhibition 2010 Warsaw, Poland EWEC 2010 Warsaw 20-23 April 2010 Aeroelastic Analysis of Pre-Curved Rotor Blades V.A.Riziotis,S.G.Voutsinas

European Wind Energy Conference and Exhibition

2010Warsaw, Poland

EWEC 2010 Warsaw 20-23 April 2010

Aeroelastic Analysis of Pre-Curved Rotor Blades

V.A.Riziotis ,S.G.Voutsinas and D.I. Manolas

National Technical University of Athens School of Mechanical Engineering

Fluids Section

E.S. Politis and P. K. Chaviaropoulos

Centre for Renewable Energy Sources Wind Energy Section

EWEC 2010 Warsaw 20-23 April 2010 2/19

Outline

• Rationale of pre-curving rotor blades• Objectives of the work• Alternative structural modeling of pre-curved blades

– 2nd order beam theory– Multi-body formulation

• Comparative results for the 5MW reference wind turbine• Conclusions• Outlook


Rationale of pre-curving

• Fore pre-bending has been originally introduced in order to increase the blade-tower clearance

• However analysis has shown that pre-curving the rotor blades activates flap-torsion coupling which can be very beneficial in mitigating loads

• Flap-torsion coupling can be also achieved by structural tailoring as indicated in recent research at Sandia Laboratories

• The underlying mechanism is that as the outer part of the blade bends; it also twists so that the angles of attack get lower and therefore the aerodynamic loads decrease

• Load reduction is always important due to its direct impact on the cost of energy (e.g. lowering the loads allows the increase of rotor diameter for the same given strength)


• Formulation of suitable formulations based on existing structural models, namely: – Hodges’ 2nd order beam theory and

– multi-body modelling

• Identification of the additional coupling terms in the structural loads

• Comparative analysis of aeroelastic simulations

• Assessment of the various pre-curved blade concepts

Objectives of the work


Alternative structural formulations

• Pre-curvature will generate a distributed change of the orientation of the beam sections which should be taken into account in the kinematics

• Stresses will be re-orientated resulting in a modification of the blade loading including additional couplings which allow load mitigation

• The structural formulation becomes non-linear even though the material properties remain linear


2nd order beam model

x

z

y

η0, s

ξ0

ξ

ζ0

ζη, s

ze(s)

v(s)

u(s)

w(s)+ze(s)

undeformed

deformed

x

z

w(s)+ze(s)

u(s)

ξ

ζ

θt+θ(s)O

O1

O’

0 u(s)

y(s) v(s) u , w , 0

0 w(s)

r = E( )

ez s non-linear

Ze: the pre-bendings

e

0

ˆ(s) (s) u (s) (w (s) z (s)) ds


Multi-body modelling has been introduced in order to take into account non-linear dynamics

The same approach can be also used in order to approximate large displacements along the blade

To this end the blade (major body) is divided into “sub-bodies” each considered as an independent component

Non-linear matching of loading and kinematics is assumed at the connection points

Multi-body modelling

x

y

ξ

ζ η

ρ(q)

sub-body

major body

ξ

ζ η

communicates loads to the

previous sub-body

receives rotations and translations

A(q)

u

v u , w , 0

w

k lr E


Coupling terms

Bending-torsion coupling on pre-bent blades

2 2t

t

1 ÊI EI sin(2 ( )) u w2

ÊI EI cos(2 ( )) u w

2t e

2t t t t e

t e

t t t t e

t

1 ÊI EI sin(2 ( )) z2

ˆ ÊI cos sin( ) EI sin cos( ) z

ÊI EI cos(2 ( )) u z

ˆ ÊI cos cos( ) EI sin sin( ) u z

ÊI EI sin(2 ( )) w

e

t t t t e

z

ˆ ÊI cos sin( ) EI sin cos( ) w z

In case of large bending deflections additional non-linear terms will become significant:


first edgewise second edgewise

fore pre-bent blade (4.5 m tip deflection)

Results


Results

first flapwise second flapwise

aft swept blade (4.5 m tip deflection)


Results

flapwise deflection torsion angle pre-bent – Uwind=8m/s


Results

flapwise deflection torsion angle pre swept blade – Uwind=8m/s


Results

flapwise deflection torsion angle pre-bent 3m – Uwind=8m/s


Results

Equivalent loads


Results

aft pre-bend 3mflapwise mom. (%) power (%)

wind speed (m/s)8 -4.4 -0.6

11 -4.5 -0.8

fore pre-bend 3mflapwise mom. (%) power (%)

wind speed (m/s)8 4.5 -0.4

11 4.5 -0.4

aft sweep 3mflapwise mom. (%) power (%)

wind speed (m/s)8 -7.7 -1.7

11 -11.7 -3.6

fore sweep 3mflapwise mom. (%) power (%)

wind speed (m/s)8 8.9 -0.8

11 14.0 -1.2


• The aeroelastic behaviour of pre-curved blades is analysed using two models: a 2nd order beam model and a multi-body model

• The 2nd order model is formulated with respect to the pre-curved blade geometry while the second is based on multi-body modelling

• Both models take into account the orientation changes along the blade. In the 2nd order model however the additional terms will appear explicitly while in the multi-body model the modifications are implicitly seen only in the results

• Comparison of the two models indicates the consistency of the ordering scheme followed in the 2nd order model

Conclusions


• Fore pre-bend besides increasing the blade-tower clearance, reduces torsion loads and increases blade stability

• Aft pre-bend is meaningless because it reduces the clearance of upwind rotors but also reduces the damping of the low damped edgewise modes.

• Pre-sweep of blades drives flapwise bending/torsion coupling.

• Aft pre-sweep gives rise to nose down torsion deformation and leads to reduced fatigue loads.

• The opposite effect is obtained for forward sweep.

Conclusions


This work was partly funded by the European Commission and by the Greek Secretariat for Research and Technology under contract SES6

019945 (UpWind Integrated Project).

Acknowledgements


Thanks for your attention

END

Documents

European Wind Energy Conference and Exhibition 2010 Warsaw, Poland EWEC 2010 Warsaw 20-23 April 2010 Aeroelastic Analysis of Pre-Curved Rotor Blades V.A.Riziotis,S.G.Voutsinas