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Investigation of Stability Issues for an Adaptive Trailing Edge System Leonardo Bergami MSc + PhD student, Risø DTU, Denmark Mac Gaunaa Senior Scientist, Risø DTU, Denmark Morten Hartvig Hansen Senior Scientist, Risø DTU, Denmark AIAA Orlando Jan 6.th 2009

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Outline Motivation & Introduction ”why?” Simplifying the Problem & Making things doable ”how?” Preliminary study ”justifying assumptions in modelling later on” Theory ”how? #2 more specifically & under what conditions” –Structural model –Aerodynamic model –Control model –Time lag model –Coupling everything & solving it Validation ”does it work?” Results ”so what are the implications, then?” Conclusion ”what have we learned?”

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Motivation & Introduction Main driver of fatigue loading on a wind turbine: unsteady flow conditions (Wind turbulence, Shear, Tower shadow, Yaw/tilt misalignment, etc.)

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Motivation & Introduction Main driver of fatigue loading on a wind turbine: unsteady flow conditions (Wind turbulence, Shear, Tower shadow, Yaw/tilt misalignment, etc)

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Motivation & Introduction Main driver of fatigue loading on a wind turbine: unsteady flow conditions (Wind turbulence, Shear, Tower shadow, Yaw/tilt misalignment, etc) Fluctuations in aerodynamic loads Fatigue on WT blade REMEDY Control for active fatigue load reduction –Using blade pitch (Up to 28% load reductions reported) Not especially fast, harder for flexible blades, expensive –Using local flow control Fast and ”local” control possible for instance by changing airfoil shape at TE

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Motivation & Introduction Fatigue loads may be alleviated by compensating locally on the blade for effects of flow fluctuations

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Motivation & Introduction Why is the Trailing Edge a good place to change the shape of an airfoil? Potential flow thin-airfoil theory #1: Maximize bang for bucks #2: Low loads at TE… Both steady and unsteady

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Motivation & Introduction Why not a plain rigid-body trailing edge flap? Surface discontinuity triggers stall Noise issues Bad L/D leading to loss in power production Flap losing it’s potential load reducing effect Go for the continuously deforming one (smooth deformation shape)!

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Motivation & Introduction Fatigue load reduction potential much higher than for pitching the blade alone –Pitching: Up to 28% –Pitching and TE flap: Up to 48% A BIG POTENTIAL! But… How is aeroelastic/aeroservoelastic stability affected when TE flaps are added?

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Aeroelastic Phenomena in Attached Flow Flutter Dynamic phenomenon: coupling of two or more DOF Time series: Exponentially growing amplitude: ”Trumpet” Modal Analysis: Neg. damped mode Limited by non-linear effects, approx 2*rot speed on WT’s Divergence Static phenomenon: pitching moment equilibrium Time series: Exponential growth Modal Analysis: Neg. damped static mode Easy to predict, usually limit higher than flutter limit Aeroservoelastic phenomenon: Control reversal

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Outline Motivation Simplifying the Problem & Making things doable Preliminary study Theory –Structural model –Aerodynamic model –Control model –Time lag model –Coupling & Solving Validation Results Conclusion

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Reduce 3D problem to analysis of 2D section: Qualitatively representative –Flutter computation and experiment: Theodorsen and Garrick (1940) –Load reduction capabilities: Buhl et.al. (2005) & Andersen et.al. (2008) –Results and mechanisms easier understandable Fully attached 2D thin airfoil potential flow –Viscous and thickness effects neglected, Small AOA, Small flap deflection –Good approximation to outer sections on a PRVS turbine In plane (2D) motion with linear springs and dampers, small AOA and flap deflections Flap actuation and deformation mode same (same generalised coordinate) Control delay modelled as a simple first order filter Simple control algorithms tested (As in Buhl et.al. J.Solar Energ. Eng. 2005) Simplifying the Problem

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Outline Motivation Simplifying the Problem & Making things doable Preliminary study Theory –Structural model –Aerodynamic model –Control model –Time lag model –Coupling & Solving Validation Results Conclusion

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Preliminary study: 3 DOF system (x, y, ) No deformation or control of TE x-dof Non-linear aerodyn eq’s, linearized Validated using the classic work of Theodorsen and Garrick Main result: x-dof Negligible influence on aeroelastic stability The streamwise dof can be neglected! Basic important properties for stability for sections with low heave-torsion frequence ratios –Not important: Structural damping, Elastic axis position –Important: Mass, Moment of inertia, Torsion stiffness, Heave stiffness, Position of centre of gravity (aft CG reduces flutter onset vel)

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Outline Motivation Simplifying the Problem & Making things doable Preliminary study Theory –Structural model –Aerodynamic model –Control model –Time lag model –Coupling & Solving Validation Results Conclusion

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Theory: Structural Dynamics Structural dynamics, 3 dof: y, and (generalised coordinate)

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Theory: Structural Dynamics Structural dynamics, 3 dof: y, and (generalised coordinate) Equations of motion –Eq. y and α. suspended airfoil + flap inertial coupling. Small α –Eq. flap. Generalized coordinates according to deflection shape –Eq. flap. Control term ctrl as additional elastic term –Laed, Maed, GFaed. Aerodynamic forces Coupling with aerodynamic model

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Theory: Aerodynamics Gaunaa’s model. –Unsteady 2D aerodynamic forces and distribution –Arbitrary motion and camberline deformation. Assumptions: –Thin Airfoil Camberline –Potential flow Fully attached Neglect x-streamwise dof linear model

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Theory: Aerodynamics Indicial Response Function approximation: Lift Deficiency Function approx. with series of time-lag terms. Ai and bi coefficients define step response. Time-lag terms: first order differential equations Introduce additional state variables z to the system. Effective downwash speed computed as:

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Theory: Control model Input/Output –Input: Measurements. Describing the state of the aeroelastic system. –Output: angle that modifies flap actuator deflection Control Algorithm –Linear equations, relating input to desired flap deflection –2 kinds investigated: y and

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Theory: Control model y, Heave displacement: , Angle of Attack:

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Theory: Time lag model Delay in control system: first order filter. Additional first order differential equation (and variable) For zero time lag

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Theory: Coupling & solving Set of equations describing the system –Linear equations (non linear with x dof) –Substitution of second order variables State space formulation –Set of 3 + 3 + 3 + 1 Equations. –First order matrix equation

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Solution: set of complex eigenvalues corresponding to the modes describing the system –Imaginary part: mode frequency. –Real part: stability parameter Mode damping Stability: given condition and flow speed –ALL the modes positively damped –To determine stability limit: solution at increasing flow speed. –(Modal Assurance Criterion) Theory: Coupling & solving Eigenvalue approach: –Time marching unpractical and inefficient for stability investigation. –Linear (linearized) system. Assume harmonic solution –Generalized eigenvalue problem.

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Examples of time stepping results Classical flutter:

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Examples of time stepping results Control flutter:

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Examples of time stepping results Control divergence:

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Outline Motivation Simplifying the Problem & Making things doable Preliminary study Theory –Aerodynamic model –Structural model –Control model –Time lag model –Coupling & Solving Validation Results Conclusion

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Validation Using Theodorsen and Garrick (1940) results (elastic flat flap, no control)

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Validation Against time-stepping version of the tool: –Good agreement using controlled non-elastic flap Hereby Validated!

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Outline Motivation Simplifying the Problem & Making things doable Preliminary study Theory –Aerodynamic model –Structural model –Control model –Time lag model –Coupling & Solving Validation Results Conclusion

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The standard TE controlled section As in Buhl et.al. (2005)

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Results No flap control. Influence of flap stiffness Flutter limits are affected by the flap Reasonable stiff flap (ref. case): flutter limit is increased relative to rigid flap case Converging to rigid flap case as stiffness is increased Soft flap: Flutter limit is lowered. flap deflection mode becomes unstable. The effect of the elastic flap on flutter velocity is not straightforward

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Results Controlled flap. Influence of flap stiffness and control method Flutter limits are generally decreased when fatigue load reduction control algorithms (60m/s) are used There is a big influence of the choice of control algorithm AOA-control behaves better than y-control y-control stability limit critically low The effect of the controlled elastic flap on flutter velocity is not straightforward

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Results Controlled flap. Influence of control system time lag Very different effect of time lag on the two different control methods AOA-control behaves better than y-control y-control stability limit critically low The effect of the controlled elastic flap on flutter velocity is not straightforward

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Outline Motivation Simplifying the Problem & Making things doable Preliminary study Theory –Aerodynamic model –Structural model –Control model –Time lag model –Coupling & Solving Validation Results Conclusion

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Conclusions Streamwise dof has negligible effect on stability limits for an airfoil without a flap it is reasonable to neglect the streamwise dof in 2D investigations of aeroelastic and aeroservoelastic stability A 2D aeroservoelastic stability tool for an trailing edge control system is formulated and implemented Validation with a reimplementation of Theodorsen and Garricks method show excellent agreement Basic important properties for stability for sections with low heave-torsion frequence ratios –Not important: Structural damping, Elastic axis position –Important: Mass, Moment of inertia, Torsion stiffness, Heave stiffness, Position of centre of gravity (aft CG reduces flutter onset vel) Apart from the above, the prescence of the flap, either actively controlled or not, significantly modifies the stability limits of the section. The two control algorithms investigated have a very different impact on stability limits

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Conclusions The AOA control is superior to the y control with regards to stability in all cases investigated At overspeeding situations: turn off smart controls! The effect of the controlled elastic flap on flutter velocity is not straightforward, so a tool like the one presented can come in handy

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Thank You!

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OLD SLIDES OF INTEREST AFTER THIS ONE Blablabla..

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Risø DTU, Technical University of Denmark09.03.2008Presentation42 5MW reference turbine (UPWIND)

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Risø DTU, Technical University of Denmark09.03.2008Presentation43 3D results (HAWC2)

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Risø DTU, Technical University of Denmark09.03.2008Presentation44 3D results (HAWC2) Reduction / Pitch / Power 7m/s11m/s18m/s 10 min. max blade1, flapwise root moment 11.8%16.0%24.0% 10 min. max tower, flowwise root moment 8.8%6.5%15.9% Blade1, equivalent flapwise root moment 38.1%45.5%47.9% Tower, equivalent flowwise root moment 33.2%20.8%33.3% Pitch rate, standard deviation n/a10.9%19.0% Mean power prod. (+loss) without DTEF 1375KW4694KW5291KW Mean power prod. (+loss) with DTEF 1364KW4682KW5300KW Percent change in power production -0.8%-0.2%+0.2%

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Risø DTU, Technical University of Denmark09.03.2008Presentation45 Rubber Flap

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Risø DTU, Technical University of Denmark09.03.2008Presentation46 Rubber Flap (Movie)

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