Free-form design of rotors - An overview
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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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Free-form design of rotors - An overview
- 1. POLI diMI tecnico lano tecnico lano Free-form design of rotors L. Sartori, A. Croce, C. L. Bottasso 12°EAWE PhD Seminar, 25-27 May 2016, Copenhagen
- 2. Free-formdesignofrotors 2 of 20 • Formulation: • Background and motivations • Aero-structural design • Design variables • Optimization framework • Applications: • 1. Carbon-based design of a 2 MW rotor • 2. Glass vs Carbon design of a 10 MW rotor • 3. Parametric Carbon design of a 10 MW rotor • 4. Rotor sizing of a 10 MW wind turbine • Conclusions: • Remarks and outlook Summary
- 4. Free-formdesignofrotors 4 of 20 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
- 5. Free-formdesignofrotors 5 of 20 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
- 6. Free-formdesignofrotors 6 of 20 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
- 7. Free-formdesignofrotors 7 of 20 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
- 9. Free-formdesignofrotors 9 of 20 • 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
- 10. Free-formdesignofrotors 10 of 20 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 [$/MWh] 41.7 42.08 + 0.8 % Chord[m] Radial position [m] SparCapthickness[m] Radial position [m]
- 11. Free-formdesignofrotors 11 of 20 Applications 1. Carbon-based design of a 2 MW rotor DU – 30% CL/CD * * CL DU – 21% CL/CD * * CL Radial position [m] Thickness% XFOIL Data @ Re = 1.5 millions CL/CD Radial position [m]
- 12. Free-formdesignofrotors 12 of 20 • Blade cost estimated with SANDIA model • Baseline is a glass design with frozen airfoils Applications 2. Glass vs Carbon design of a 10 MW rotor Wind Turbine Class IEC 1A Number of blades 3 Wind speed 4 - 25 m/s Rated Power 10.0 MW Rotor Radius 89.17 m Hub Radius 2.8 m Tilt angle 5 deg Cone angle 2.5 deg Materials Properties Units UD Glass UD Carbon E11 [Gpa] 41.63 115 E22 [Gpa] 14.93 7.56 ν12 [-] 0.241 0.3 G12 [Gpa] 5.04 3.96 ρ [kg/m3] 1915 1578 σ11_max [Mpa] 876 1317 σ11_min [Mpa] 625 625 cost [$/kg] 2.97 26.4 StressConstraintSparCap BladeConstraint Frequency TipDisp Glass is constrained by Frequency/TipDisp requirements Carbon is constrained by stress/strain requirements
- 13. Free-formdesignofrotors 13 of 20 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]
- 14. Free-formdesignofrotors 14 of 20 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 %
- 15. Free-formdesignofrotors 15 of 20 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
- 16. Free-formdesignofrotors 16 of 20 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
- 17. Free-formdesignofrotors 17 of 20 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
- 19. Free-formdesignofrotors 19 of 20 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
- 20. Free-formdesignofrotors 20 of 20 Thank you for your attention.