Report

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 Installed wind capacity map as of Jan 2011 United States National Seismic Hazard Map 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 mx + cst x + kx = Fx 1 = ρ 2 2 [ ∅ + ∅ ] + [ + + ] + = ( + ) (1 − ) A= r rhub ρ ∙ Vw ∙ (1 − a) CL cos ∅ + CD sin ∅ c r dr 1 = ∙ ∙ (1 + ′) ( + ) ∅ + ( − ) ∅ ℎ 2 , = ( + ) 2 Aerodynamic Damping of HAWTs in the Side-to-Side Direction 1 Fy = ρ 2 Nb rtip i=1 rhub 2 Vrel CL sin ϕ − CD cos ϕ c r ∙ cos(γi t )dr B ′ − A′ my + cST + Nb y + ky = 0 2 1 = 1 − ℎ 2 ′ ′ = ℎ + sin ∅ + − cos ∅ Ω 1 + ′ sin ∅ − cos ∅ , = (′ − ′ ) 4 Numerical Example – 1.5 MW Baseline Turbine by NREL Nacelle 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 Rotor Tower Foundation [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 77 66 55 44 33 22 11 00 -1 -1 -2 -2 7 6 AD,x(%) (%) AD,x AD,x(%) 5 4 3 2 1 0 5 10 15 20 25 Vw(m/s) , = ( + ) 2 A= r rhub 55 10 10 15 15 Vw(m/s) Vw(m/s) 2020 2525 ρ ∙ Vw ∙ (1 − a) CL cos ∅ + CD sin ∅ c r dr 1 = ∙ ∙ (1 + ′) ( + ) ∅ + ( − ) ∅ ℎ 2 Numerical Example – 1.5 MW Baseline Turbine by NREL 2 2 1.5 1.5 1 1 0.5 0.5 AD,y(%) AD,y(%) Aerodynamic damping in the side-to-side direction with W=20 rpm and b=7.5ᵒ 0 -0.5 0 -0.5 -1 -1 -1.5 -1.5 -2 -2 5 , = 10 ′ ( 15 Vw(m/s) − ′ ) 4 20 25 1 = 1 − ℎ 2 ′ ′ = ℎ 5 10 15 Vw(m/s) 20 25 + sin ∅ + − cos ∅ Ω 1 + ′ sin ∅ − cos ∅ Numerical Example – 1.5 MW Baseline Turbine by NREL 7 7 6 6 5 5 4 4 AD,x(%) AD,x(%) Aerodynamic damping in the fore-aft direction with b=7.5ᵒ (left) and W=20 rpm (right) 3 2 W=20 W=15 W=10 1 0 3 5 7 9 b=0˚ b=5˚ b=7.5˚ b=10˚ b=15˚ 3 2 1 11 13 15 17 19 0 3 5 7 9 11 13 15 17 19 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) 1 W=20 W=15 W=10 0.8 0.6 0.4 0.2 0 b=0˚ b=5˚ b=7.5˚ b=10˚ b=15˚ 0.8 0.6 AD,y(%) AD,y(%) 1 0.4 0.2 0 -0.2 -0.2 -0.4 -0.4 3 5 7 9 11 13 15 17 19 3 5 7 9 11 13 15 17 19 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 8 FAST FAST 7 Derivation Equation #15. AD,x(%) 6 5 4 3 2 1 0 10 15 Vw(m/s) 20 25 Numerical Example – 1.5 MW Baseline Turbine by NREL Effect of aerodynamic damping on the seismic response with W=20 rpm 0.9 0.8 0.7 0.6 0.5 Side to Side Fore-Aft b = 0 b = 0 b = 5 b = 5 b = 7.5 b = 7.5 b = 10 b = 10 b = 15 b = 15 0.4 0.3 0.2 0.1 0 3 5 7 9 11 13 15 17 19 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