The Influence of Aerodynamic Damping in the Seismic Response of HAWTs Andrew T. Myers, PhD, PE, Assistant Professor Vahid Valamanesh, Graduate Student Department of Civil and Environmental Engineering Northeastern University

Presentation Outline Motivation Dimensions of utility-scale HAWTs Vulnerability to earthquakes Derivation of aerodynamic damping Fore-aft direction Side-to-side direction Numerical example – 1.5 MW NREL baseline turbine Conclusions

Motivation: Exposure of HAWTs to Earthquakes United States National Seismic Hazard Map Installed wind capacity map as of Jan 2011

Dimensions and Period of HAWTs Approximate dimensions of a utility-scale HAWT First Period ~ 3 s

Vulnerability to Earthquakes No redundancy in the support structure Slender hollow sections (D/t as high as 280) Farms consisting of many nearly identical structures Large directional affect due to aerodynamic damping Side-to-side Fore-aft

Aerodynamic Damping of HAWTs in the Fore-Aft Direction Forces based on blade element momentum theory (BEM) Flexibility of rotor is omitted Wind direction is along fore-aft direction Steady wind First mode of vibration is considered m x + c st x +kx= 𝑑F x 𝐹 𝑥 = 1 2 ρ𝑁 𝑏 [𝑉 𝑟𝑒𝑙 2 𝐶 𝐿 𝑐𝑜𝑠 ∅ + 𝐶 𝐷 𝑠𝑖𝑛 ∅ 𝑐 𝑟 ]𝑑𝑟 𝑚 𝑥 +[ 𝑐 𝑆𝑇 + 𝑁 𝑏 𝐴+𝐵 ] 𝑥 +𝑘𝑥= 𝑁 𝑏 (𝐴+𝐵) 𝑉 𝑤 (1−𝑎) A= r hub r 𝑡𝑖𝑝 ρ∙ V w ∙(1−a) C L cos ∅ + C D sin ∅ c r dr 𝐵= 𝑟 ℎ𝑢𝑏 𝑟 𝑡𝑖𝑝 1 2 𝜌∙𝛺𝑟∙(1+𝑎′) (𝐶 𝐿𝛼 + 𝐶 𝐷 ) 𝑐𝑜𝑠 ∅ + (𝐶 𝐷𝛼 − 𝐶 𝐿 ) 𝑠𝑖𝑛 ∅ 𝑐 𝑟 𝑑𝑟 𝜉 𝐴𝐷,𝑥 = 𝑁 𝑏 (𝐴+𝐵) 2 𝑘𝑚

Aerodynamic Damping of HAWTs in the Side-to-Side Direction F y = 1 2 ρ i=1 N b r hub r tip V rel 2 C L sin ϕ − C D cos ϕ c r ∙cos⁡( γ i t )dr m y + c ST + N b B ′ − A ′ 2 y +ky=0 𝐴 ′ = 𝑟 ℎ𝑢𝑏 𝑟 𝑡𝑖𝑝 1 2 𝜌 𝑉 𝑤 1−𝑎 𝐶 𝐿𝛼 + 𝐶 𝐷 sin ∅ + 𝐶 𝐿 − 𝐶 𝐷𝛼 cos ∅ 𝑐 𝑟 𝑑𝑟 𝜉 𝐴𝐷,𝑦 = 𝑁 𝑏 ( 𝐵 ′ − 𝐴 ′ ) 4 𝑘𝑚 𝐵 ′ = 𝑟 ℎ𝑢𝑏 𝑟 𝑡𝑖𝑝 𝜌Ω𝑟 1+𝑎′ 𝐶 𝐿 sin ∅ − 𝐶 𝐷 cos ∅ 𝑐 𝑟 𝑑𝑟

Numerical Example – 1.5 MW Baseline Turbine by NREL Power output 1.5 MW Hub Height 84 m Rotor Diameter 70 m Number of Blades 3 Max Rotational Speed 20 rpm Cut in wind speed 5 m/s Cut out wind speed 25 m/s Nacelle Mass 51 Ton Hub Mass 15 Ton Tower Mass 123 Ton Rotor Mass 11 Ton Active Pitch Control Yes [Base image from Nuta, 2010]

Numerical Example – 1.5 MW Baseline Turbine by NREL Aerodynamic damping in the fore-aft direction with W=20 rpm and b=7.5ᵒ A= r hub r 𝑡𝑖𝑝 ρ∙ V w ∙(1−a) C L cos ∅ + C D sin ∅ c r dr 𝜉 𝐴𝐷,𝑥 = 𝑁 𝑏 (𝐴+𝐵) 2 𝑘𝑚 𝐵= 𝑟 ℎ𝑢𝑏 𝑟 𝑡𝑖𝑝 1 2 𝜌∙𝛺𝑟∙(1+𝑎′) (𝐶 𝐿𝛼 + 𝐶 𝐷 ) 𝑐𝑜𝑠 ∅ + (𝐶 𝐷𝛼 − 𝐶 𝐿 ) 𝑠𝑖𝑛 ∅ 𝑐 𝑟 𝑑𝑟

Numerical Example – 1.5 MW Baseline Turbine by NREL Aerodynamic damping in the side-to-side direction with W=20 rpm and b=7.5ᵒ 𝐴 ′ = 𝑟 ℎ𝑢𝑏 𝑟 𝑡𝑖𝑝 1 2 𝜌 𝑉 𝑤 1−𝑎 𝐶 𝐿𝛼 + 𝐶 𝐷 sin ∅ + 𝐶 𝐿 − 𝐶 𝐷𝛼 cos ∅ 𝑐 𝑟 𝑑𝑟 𝜉 𝐴𝐷,𝑦 = 𝑁 𝑏 ( 𝐵 ′ − 𝐴 ′ ) 4 𝑘𝑚 𝐵 ′ = 𝑟 ℎ𝑢𝑏 𝑟 𝑡𝑖𝑝 𝜌Ω𝑟 1+𝑎′ 𝐶 𝐿 sin ∅ − 𝐶 𝐷 cos ∅ 𝑐 𝑟 𝑑𝑟

Numerical Example – 1.5 MW Baseline Turbine by NREL Aerodynamic damping in the fore-aft direction with b=7.5ᵒ (left) and W=20 rpm (right)

Numerical Example – 1.5 MW Baseline Turbine by NREL Aerodynamic damping in the side-to-side direction with b=7.5ᵒ (left) and W=20 rpm (right)

Numerical Example – 1.5 MW Baseline Turbine by NREL Validation with FAST in the fore-aft direction with b=7.5ᵒ and W=20 rpm FAST Derivation

Numerical Example – 1.5 MW Baseline Turbine by NREL Effect of aerodynamic damping on the seismic response with W=20 rpm

Conclusions Aerodynamic damping of operational wind turbines strongly depends on wind speed. For the considered example (1.5 MW turbine, W = 20 rpm, b = 7.5˚, wind speed between cut-in and cut-out): The fore-aft aerodynamic damping varies between 2.6% and 6.4% The side-to-side aerodynamic damping varies between -0.1% and 0.9% For this same operational case, the derivative of the lift coefficient with respect to the angle of attack is the most influential parameter in aerodynamic damping in the fore-aft direction The blade pitch angle and rotational speed also influence the aerodynamic damping in both the fore-aft and side-to-side directions The directional effect strongly influences the seismic response, with median spectral drift predicted to be as much as 70% larger in the side-to-side direction than in the fore-aft direction