2014 wind turbine blade workshop- bottasso

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Aero-Structural Design of Rotors

Carlo L. Bottasso

P. Bortolotti, A. Croce, F. Gualdoni, L. Sartori Technische Universität München & Politecnico di Milano

Sandia Wind Turbine Blade Workshop August 26-28, 2014

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Presentation Outline

• Introduction and motivation: the need for an integrated aero-structural design approach

• Aero-structural design algorithms

• Free-form design: towards a genuine 3D optimization of rotor blades

• Applications and results, including the design of Low Induction Rotors (LIRs)

• Conclusions and outlook

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Pitch-torque control laws: - Regulating the machine at different set points depending on wind conditions - Reacting to gusts - Reacting to wind turbulence - Keeping actuator duty-cycles within admissible limits - Handling transients: run-up, normal and emergency shut-down procedures - …

- Annual Energy Production (AEP) - Noise - …

- Loads: envelope computed from large number of Design Load Cases (DLCs, IEC-61400) - Fatigue (25 year life), Damage Equivalent Loads (DELs) - Maximum blade tip deflections - Placement of natural frequencies wrt rev harmonics - Stability: flutter, LCOs, low damping of certain modes, local buckling - Complex couplings among rotor/drive-train/tower/foundations (off-shore: hydro loads, floating & moored platforms) - Weight: massive size, composite materials (but shear quantity is an issue, fiberglass, wood, clever use of carbon fiber) - Manufacturing technology, constraints

- Generator (RPM, weight, torque, drive-train, …) - Pitch and yaw actuators - Brakes - …

GE wind turbine (from inhabitat.com)

Wind Turbine Design

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Motivation: the Need for Combined Aero-Structural Design

Cost model (Fingersh at al., 2006):

𝑪𝒐𝑬 = 𝑭𝒊𝒙𝒆𝒅𝑪𝒉𝒂𝒏𝒈𝒆𝑹𝒂𝒕𝒆 ∗ 𝑰𝒏𝒊𝒕𝒊𝒂𝒍𝑪𝒂𝒑𝒊𝒕𝒂𝒍𝑪𝒐𝒔𝒕 𝒑

𝑨𝑬𝑷 𝒑+ 𝑨𝒏𝒏𝒖𝒂𝒍𝑶𝒑𝒆𝒓𝒂𝒕𝒊𝒏𝒈𝑬𝒙𝒑𝒆𝒏𝒔𝒆𝒔 𝒑

where 𝒑 = design parameters

Strong couplings between aerodynamic shape (AEP) and structural sizing (blade cost)

Example:

Spar cap thickness ⇧

Blade thickness ⇩

Reduce solidity to increase efficiency (AEP ⇧)

Consequence: effect on weight ⇧

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Increase solidity

Consequence: effect on weight ⇧


Cost model (Fingersh at al., 2006):

𝑪𝒐𝑬 = 𝑭𝒊𝒙𝒆𝒅𝑪𝒉𝒂𝒏𝒈𝒆𝑹𝒂𝒕𝒆 ∗ 𝑰𝒏𝒊𝒕𝒊𝒂𝒍𝑪𝒂𝒑𝒊𝒕𝒂𝒍𝑪𝒐𝒔𝒕 𝒑

𝑨𝑬𝑷 𝒑+ 𝑨𝒏𝒏𝒖𝒂𝒍𝑶𝒑𝒆𝒓𝒂𝒕𝒊𝒏𝒈𝑬𝒙𝒑𝒆𝒏𝒔𝒆𝒔 𝒑

where 𝒑 = design parameters

Strong couplings between aerodynamic shape (AEP) and structural sizing (blade cost)

Example:

Skin buckling critical load ⇩

Skin core thickness ⇧

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Example: INNWIND 10 MW HAWT (class 1A, D=178.3, H=119m)

Baseline design by INNWIND consortium

1. Perform purely aerodynamic optimization for max(AEP)

2. Follow with structural optimization for minimum weight

Dramatic reduction in solidity to improve AEP leads to large increase in weight

Spar cap ▼ Chord ▼

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Standard blade design process: select collection of existing suitable airfoils

Exploration is limited to pre-assumed airfoils

Airfoil shape: strong influence on aero performance but also on structural sizing

Issues with current approach:

• Incomplete exploration of design space

• Suboptimal solutions

Free-form optimization (Bottasso et al. 2014, with ECN):

1) Genuine 3D optimization:

• Airfoils are designed together with the rest of the blade • More complete exploration of the design space

2) Relieve the designer from a priori choices

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Blade Design Environment

Cost: AEP Aerodynamic parameters: chord, twist

Cost: Blade weight (or cost model if available) Structural parameters: thickness of shell and spar caps, width and location of shear webs

Cost: Physics-based CoE Parameters: Aerodynamic and structural

Controls: model-based (self-adjusting to changing design)

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Combined

Aero-Structural

Optimization

Structural

Optimization +

Controls

Aerodynamic

Optimization

• SQP optimization of chord and twist for max AEP

• Constraints on max chord, tip speed, geometry

• SQP optimization of rotor (and possibly tower)

• Load freezing for reduced computational time and handling of solution space roughness

• Multi-level coarse-fine iterations

• Multiple algorithms (complexity/cost trade-offs)

• Free-form design (genuine 3D optimization)

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Blade: - Geometrically exact beam model - Span-wise interpolation

Blade: - ANBA 2D FEM sectional analysis - Compute 6x6 stiffness matrices

Blade: definition of structural design parameters

Blade constraints: - Maximum tip deflection - Natural frequencies - Max stresses/strains (ANBA) - Fatigue (ANBA)

▶ Update blade mass & cost

Tower constraints: - Natural frequencies - Max stresses/strains - Fatigue

▶ Update tower mass & cost

Tower: - Geom. exact beam model - Height-wise interpolation

Tower: - Compute stiffness matrices

Tower: definition of structural design parameters

SQP optimizer

min cost subject to constraints

Update complete HAWT Cp-Lambda multibody model - DLCs simulation - Campbell diagram - AEP DLC post-processing: load envelope, DELs, Markov, max tip deflection

Coarse-Level Structural Optimization

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Multi-Level Structural Optimization

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Structural Optimization

Use gradient based SQP because of the many constraints that need to be enforced

Issues:

• Large cost of recomputing DLCs

• Possible non-smoothness of the solution space

Solution: temporary load freezing (Bottasso et al 2012 and 2014a)

Structural design parameters: 𝒑𝑠; aerodynamic design parameters: 𝒑𝒂

Typically converges in 2-3 iterations (starting from reasonable guess)

As long as it converges, freezing will not negatively affect the solution accuracy


min𝒑𝑠

𝐶𝑂𝐸

subject to constraints

DLCs update Aero-shape (𝒑𝒂) Design (𝒑𝒂)

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The Importance of Multi-Level Blade Design

Stress/strain/fatigue: - Fatigue constraint not satisfied at

first iteration on 3D FEM model - Modify constraint based on 3D

FEM analysis - Converged at 2nd iteration

Fatigue damage constraint satisfied

Buckling: - Buckling constraint not satisfied at first iteration - Update skin core thickness - Update trailing edge reinforcement strip - Converged at 2nd iteration

Peak stress on initial model

Increased trailing edge strip

ITERATION 1 ITERATION 0




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Increased skin core thickness

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Combined

Aero-Structural

Optimization

Structural

Optimization +

Controls

Aerodynamic

Optimization

• SQP optimization of chord and twist for max AEP

• Constraints on max chord, tip speed, geometry

• SQP optimization of rotor (and possibly tower)

• Load freezing for reduced computational time and handling of solution space roughness

• Multi-level coarse-fine iterations

• Multiple algorithms (complexity/cost trade-offs)

• Free-form design (genuine 3D optimization)

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Aero-Structural Optimization

Monolithic with Load Update (MLU) (Bottasso et al 2014b):

Pre-Assumed Aerodynamic Shapes (PAAS) (Bottasso et al 2012):

External Aerodynamic Internal Structure (EAIS) (Bottasso et al 2014b):


min𝒑𝑎𝒑𝑠

𝐶𝑂𝐸


DLCs update


min𝒑𝑠

𝐶𝑂𝐸


DLCs update Assumed

aero-shapes (𝒑𝒂) Designs (𝒑𝒂)

Optimization

min𝒑𝑎

𝐶𝑂𝐸


min𝒑𝑠

𝐶𝑂𝐸



Optimization

min𝒑𝑎

𝐶𝑂𝐸

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Monolithic with Load Update (MLU) (Bottasso et al 2014b):

Structural 𝒑𝑠 and aerodynamic 𝒑𝒂 design parameters are optimized simultaneously

Conceptually, a straightforward generalization of the structural sizing problem

Frozen loads must be approximatively updated during optimization (because of change of aerodynamic shape):

- Ultimate loads: scaled by chord-radius changes

- Fatigue loads: updated with reduced aeroelastic model

Cons: load updating is a possible weakness/fragility


min𝒑𝑎𝒑𝑠

𝐶𝑂𝐸


DLCs update

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Pre-Assumed Aerodynamic Shapes (PAAS) (Bottasso et al 2012):

Assumed aero shapes optimized by max(AEP)

Family indexed in terms of suitable parameters: solidity, tapering, …

Example: indexing by solidity 𝝈 ▶

Pros: trivial implementation, potentially fast

Cons: limited by goodness of family of assumed shapes


min𝒑𝑠

𝐶𝑂𝐸


DLCs update Assumed

aero-shapes (𝒑𝒂) Designs (𝒑𝒂)

Optimization

min𝒑𝑎

𝐶𝑂𝐸

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External Aerodynamic Internal Structure (EAIS) (Bottasso et al 2014b):

External optimizer handles only chord design parameters

Twist design parameters have modest effect on COE ⇨ handled by aero optimization for max(CP)

Pros: general, robust, potential for global optimization (depending on external optimization algorithm)

Cons: possibly high computational cost


min𝒑𝑠

𝐶𝑂𝐸



Optimization

min𝒑𝑎

𝐶𝑂𝐸

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Comparison of algorithms on the INNWIND 10 MW (class 1A, D=178.3, H=119m)

MLU: limited set of DLCs to simplify updating

PAAS: assumed shapes parameterized for solidity ▶

EAIS: external pattern search optimizer (matlab opt toolbox)

Similar solutions in terms of COE, AEP and mass for EAIS, MLU, PAAS(3)

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Comparison of algorithms on the INNWIND 10 MW (class 1A, D=178.3, H=119m)

Aerodynamic and structural solutions are also similar:

Computational cost: PAAS=1, MLU=1.25, EAIS=3

Chord ▼

Spar cap ▼

◀ Skin

◀ Shear webs

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POLITECNICO di MILANO POLI-Wind Research Lab

Case Study Results: Optimal blade 3D

Three-dimensional view with detail of thick trailing edge and flatback airfoils.

Free-Form 3D Aero-Structural Optimization (with ECN)

Design airfoils together with blade:

• Bezier airfoil parameterization

• Airfoil aerodynamics by Xfoil + Viterna extrapolation

Simplified implementation for proof of concept:

• Min(COE)

• Constraints: frequency, max stress (storm load), CL max (margin to stall), max thrust, geometry

Automatic appearance of flatback airfoil!

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Application to Low Induction Rotors

Objective function: max(AEP) (as in Chaviaropoulos et al. 2014), or min(COE)

Design variables: radius, chord, twist, airfoils (about 100 dofs)

Constraints: thrust (not to exceed baseline), 1st flap frequency, CL max (margin to

stall), ultimate stress (vstorm=50 m/s)

LIR appears only for max(AEP),

not min(COE)

max(AEP) min(COE) min(COE) free-form

CP 0.434 (LIR) 0.473 0.483

Radius +15.60 % +3.97 % +3.34 %

Limiting constr. Frequency Stress Stress

AEP + 7.83 % +2.68 % +2.95 %

Blade mass +16.17 % -25.10 % -27.60 %

COE -1.14 % -2.40 % -2.91 %

min(AEP) min(COE) min(COE) free-form

CP 0.466 (LIR) 0.480 0.480

Radius + 6.54 % +2.64 % +2.48 %

Limiting constr. Frequency Stress Stress

AEP + 4.93 % +2.62 % +2.56 %

Blade mass +6.60 % -12.40 % -15.13 %

COE +0.22 % -1.89 % -2.20 %

◀ INNWIND 10MW ▼ 2MW

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Application to Low Induction Rotors

INNWIND 10 MW

Slight adjustment of airfoils:

• Small increase in camber

• Improved efficiency

Diameter growth limited

by spar stress allowable

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Conclusions

• Strong couplings between aero and structural design variables

• Various algorithms differ in complexity/generality/robustness: EAIS is costlier, but probably the best candidate for wide applicability

• Free-form design further enlarges the solution space Open issues/outlook: • COE: solutions are sensitive to cost model, need detailed reliable

models that truly account for all significant effects

• Free-from: need higher fidelity tools (CFD) for airfoil design (multi-level Xfoil-CFD?)

• Freeing of additional parameters: prebend, precone, sweep, BTC, …

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Acknowledgements

Research funded in part from the European Union through the FP7 INNWIND project, through the Politecnico di Milano

2014 wind turbine blade workshop- bottasso

Engineering