1) The document presents a free-form design method for optimizing the shape of wind turbine rotors where airfoil shapes are directly included as design variables.
2) Several applications of the method are shown including optimizing a 2MW rotor with carbon fiber and comparing glass and carbon designs for a 10MW rotor.
3) The effect of carbon fiber price on the 10MW design is also analyzed, showing that a price of $10/kg makes carbon competitive with glass.
4) Rotor sizing studies show that optimal rotor radius depends on constraints like thrust, and flatback airfoils can emerge for larger rotors.
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Background:
• Modern optimization tools for wind turbines assume frozen airfoils.
• This assumption can limit the optimal solution.
• The designer is forced to decide the airfoils in advance.
Goal:
• Develop a free-form design method for the aero-structural design of rotors
• Airfoil shapes are directly included in the optimization problem
• Investigate the ability of the program to handle multi-disciplinary design challenges.
Applications:
• Airfoil tailoring
• Preliminary rotor design
• Cost-oriented trade-off studies
• Low Induction Rotors (11° EAWE PhD Seminar, Stuttgart, 2015)
• Impact of different materials
Formulation
Background and motivations
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Formulation
Design variables
Chord, Twist, Airfoils
(Bézier curves) Structural elements
(Spar Caps)
Rotor
Radius
Aero-structural
Design Variables
• Geometrical constraints
• Automatic checks on regularity
• Spar-box section is assumed
• PS and SS spar are identical
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Formulation
Aero-structural design
2D-Aerodynamics:
• XFOIL + free/forced transition
• Viterna-Corrigan extrapolation
• (possibly) 3D correction
3D-Aerodynamics:
• Classic static BEM method
• Hub/Tip losses correction
Structure:
• 1D exact beam model
• 2D sectional analysis based on
the anisotropic beam theory
Optimization:
• Gradient-based SQP method
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Merit function:
• Levelized Cost of Energy (NREL model) + different blade cost models:
o Scaling laws (NREL) ------> Blade cost as a function of mass
o Detailed industrial model (SANDIA) ------> Materials, Labour & Equipment
Constraints (IEC-inspired, all optional):
• 1° flap frequency ≥ 3P
• Ultimate stress ≤ Admittable
• Max Tip Disp ≤ Tower clearance
• Max thrust ≤ Specified value
• CL ≤ CL_MAX for each airfoil
• Maximum tip speed (acoustic constraint for onshore)
DLC:
• Simplified set of static conditions including storm and power production.
• This set will be dramatically extended in future devs.
Formulation
Optimization framework
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• Carbon fiber is assumed in the spar cap
• Two blade cost models: scaling laws (NREL)
and detailed material cost (SANDIA)
• Differences in the optimal designs are investigated
Applications
1. Carbon-based design of a 2 MW rotor
Wind Turbine
Class IEC IIIA
Number of blades 3
Wind speed 3 - 25 m/s
Rated Power 2.0 MW
Rotor Radius 46.2 m
Hub Radius 1.2 m
Tilt angle 5 deg
Cone angle 1.0 deg
Materials
Properties Units UD Glass UD Carbon
E11 [Gpa] 38.24 115
E22 [Gpa] 8.62 7.56
ν12 [-] 0.26 0.3
G12 [Gpa] 3.5 3.96
ρ [kg/m3] 1901 1578
σ11_max [Mpa] 688 1317
σ11_min [Mpa] 478 625
cost [$/kg] 2.97 26.4
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Both design achieve same mass
NREL: low-solidity/thick-spar
SANDIA: thin spar (to lower cost of carbon)
Aerodynamics is penalized with SANDIA
COE is higher due to higher blade cost
Applications
1. Carbon-based design of a 2 MW rotor
Performance Units NREL SANDIA Delta
Cp [-] 0.491 0.483 -1.63 %
AEP [GWh/yr] 8.12 8.06 - 0.73 %
Blade Mass [kg] 5522 5512 - 0.17 %
Blade Cost [k$] 75.8 77.8 + 2.61 %
Spar Mass [kg] 1412 1098 - 22.2 %
Spar Cost [k$] 37.28 28.9 -22.5 %
COE [$/MWh] 41.7 42.08 + 0.8 %
Chord[m]
Radial position [m]
SparCapthickness[m]
Radial position [m]
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Applications
1. Carbon-based design of a 2 MW rotor
DU – 30%
CL/CD
*
*
CL
DU – 21%
CL/CD
*
*
CL
Radial position [m]
Thickness%
XFOIL Data @ Re = 1.5 millions
CL/CD
Radial position [m]
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• Blade cost estimated with SANDIA model
• Baseline is a glass design with frozen airfoils
Applications
2. Glass vs Carbon design of a 10 MW rotor
Wind Turbine
Class IEC 1A
Number of blades 3
Wind speed 4 - 25 m/s
Rated Power 10.0 MW
Rotor Radius 89.17 m
Hub Radius 2.8 m
Tilt angle 5 deg
Cone angle 2.5 deg
Materials
Properties Units UD Glass UD Carbon
E11 [Gpa] 41.63 115
E22 [Gpa] 14.93 7.56
ν12 [-] 0.241 0.3
G12 [Gpa] 5.04 3.96
ρ [kg/m3] 1915 1578
σ11_max [Mpa] 876 1317
σ11_min [Mpa] 625 625
cost [$/kg] 2.97 26.4
StressConstraintSparCap
BladeConstraint
Frequency TipDisp
Glass is constrained by
Frequency/TipDisp requirements
Carbon is constrained by
stress/strain requirements
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Carbon has lower solidity (lower TipDisp)
However, airfoil efficiency is penalized
Glass is more convenient than Carbon
Applications
2. Glass vs Carbon design of a 10 MW rotor
Performance Units Baseline Glass Carbon
Cp [-]
0.479
-
0.49
+ 2.3 %
0.49
+ 2.3 %
AEP [GWh/yr]
49.87
-
50.24
+ 0.75 %
50.26
+ 0.78 %
Blade Mass [kg]
40958
-
39077
- 4.59 %
33720
- 17.67 %
Blade Cost [k$]
280.5
-
274.5
- 2.11 %
451.5
+ 60.98 %
Spar Mass [kg]
15317
-
13626
- 11.4 %
8730
- 43 %
Spar Cost [k$]
57.64
-
51.27
- 11.1 %
230.5
+ 315 %
COE [$/MWh]
71.88
-
71.31
- 0.79 %
72.44
+ 0.78 % Chord[m]
Radial position [m]
Sparcapthickness[m]
Radial position [m]
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Applications
2. Glass vs Carbon design of a 10 MW rotor
Radial position [m]
Thickness%
CL/CD
Radial position [m]
• Both designs achieve higher efficiency
• Carbon airfoils are globally thicker
FFA – 24 % (tip)
FFA – 24 %
FFA – 30 %
FFA – 36 %
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The unit price of Carbon is gradually changed
A cost of 10 $/kg makes COE ~ to Glass
Applications
3. Parametric Carbon design of a 10 MW rotor
Glass
35
$/kg
26.4
$/kg
18
$/kg
10
$/kg
AEP [GWh/yr] 50.24 50.15 50.26 50.21 50.36
Solidity [%] 4.94 4.8 4.57 4.54 4.54
Spar Mass [kg] 13626 8136 8729 7978 10139
COE [$/MWh] 71.31 73.05 72.44 71.86 71.31
Increasing
Carbon price
Sparcapthickness[m]
Radial position [m]
Thickness%
Increasing
Carbon price
Increasing
Carbon price
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Applications
4. Rotor sizing of a 10 MW wind turbine
Radius is added to the
design variables
Aero-structural properties
are scaled along η
No constraints on max
chord/solidity
• Thrust constraint:
𝑻𝒊 − 𝑻 𝟎
𝑻 𝟎
≤ 𝜺
Flatback airfoils emerge as R increases
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Applications
4. Rotor sizing of a 10 MW wind turbine
Fixed R Optimal R R + Thrust
Radius [m] 89.17 97.4 93.07
AEP [GWh/yr] 50.24 53.09 51.60
Cp 0.49 0.487 0.487
Blade Mass [kg] 39077 45413 39964
Thrust [kN] 1508 1572 1523
COE [$/MWh]
71.31 70.16
- 1.62 %
70.6
- 0.99 %
Thrust limits
max chord!
Chord[m]
Radial position [m]
Thrust is an active constraintTipDisp is an active constraint
Drop of efficiency
here
Thickness%
Radial position [m]
Constraints
Frequency TipDisp Thrust
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Scope:
• A free-form method has been developed for optimzation of WTs.
• In this approach, airfoils are designed with the blade.
• This offer improvements against frozen-airfoils methodologies.
Results:
• The free-form has been used in a variety of applications
• Although simple formulation, results are encouraging
• The method is very sensitive upon the chosen blade cost model
• An accurate description of the constraints is paramount in the framework of a well-posed optimization
Outlook:
• Main liability is the simplicity of the models
• XFOIL gives biased data which can lead to overestimation of performance
• Future developments will embed the free-form within a complex design environment (Cp-Max)
Remarks