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What every blade designer should know

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Wind turbine aeroelasticity, some explanation

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What every blade designer should know

  1. 1. JEHO BV Why you SHOULD perhaps, maybe possibly design a blade with edgewise frequency at 6P… J.G. Holierhoek © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  2. 2. Slide 2 • Wind turbine aeroelasticity is more than doing load set calculations using Bladed or FAST or PHATAS or … • Knowing more about specific aeroelastic phenomena that can occur can save you a lot of time and a lot of money • Therefore several of these phenomena will be shortly addressed • Whirling modes: why are some frequencies measured in rotating blade different from the same vibrations measured in the tower??? • Is an instability not just related to resonance? NO IT IS NOT!! • Why are multiples of P actually excited on the wind turbine? • Bring this all together: edgewise frequency is best close to 6P… WHAT??? • These questions will all be answered, even though we have one certainty in aeroelasticity: nothing is for certain… Aeroelasticity © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  3. 3. Whirling modes… what just happened? © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  4. 4. Slide 4 • A wind turbine blade will have a first flapwise mode, first edgewise mode, first torsion mode, second flapwise mode,… till infinity • Higher modes are less relevant due to structural damping: there is so much damping that you will not have to take these modes into account • The lower modes are very important for resonance as well as for aeroelastic stability • On a rotating turbine, some frequencies are measured at different values in the tower then in the blade, why? Turbine whirling frequencies © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  5. 5. Slide 5 • First, what happens to the blade modes if we put three blades on one turbine? • We find three different rotor mode shapes for one blade mode shape: • For example first edgewise: • And a similar combination for flapwise Turbine whirling modes © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  6. 6. Slide 6 The blades start vibrating in one of the edgewise modes as indicated. Now you can assume the reaction force to be (in a rotating frame): • 𝑭 𝒙𝑹 = 𝑨 𝐬𝐢𝐧 𝝎𝒕 ; 𝑭 𝒚𝑹 = 𝟎 So the force will increase and decrease at edgewise frequency ω, but the direction rotates with the blades Now use graph bottom right and find expression for the force FxR in rotating non-rotating frame (XNR,YNR,ZNR): 𝑨 𝐬𝐢𝐧 𝝎𝒕 Ω 𝑭 𝒙𝑹 = 𝑨 𝐬𝐢𝐧 𝝎 𝒆𝒅𝒈𝒆 𝒕 Ψ=Ωt XNR XR YR YNR ZNR=ZR 𝑭 𝒙𝑹 = 𝑨 𝐬𝐢𝐧 𝝎 𝒆𝒅𝒈𝒆 𝒕 This gives the following expressions in stand still frame: 𝑭 𝒙𝑵𝑹 = 𝑨 𝐬𝐢𝐧 𝝎𝒕 𝐜𝐨𝐬 𝛀𝒕 𝑭 𝒚𝑵𝑹= 𝑨 𝐬𝐢𝐧 𝝎𝒕 𝐬𝐢𝐧 𝛀𝒕 © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  7. 7. Slide 7 Using basic mathematics: • 𝑭 𝒙𝑵𝑹 = 𝟏 𝟐 𝑨 𝐬𝐢𝐧((𝝎 − 𝛀)𝒕) + 𝟏 𝟐 𝑨 𝐬𝐢𝐧((𝝎 + 𝛀)𝒕) • 𝑭 𝒚𝑵𝑹= 𝟏 𝟐 𝑨 𝐜𝐨𝐬((𝝎 − 𝛀)𝒕) − 𝟏 𝟐 𝑨 𝐜𝐨𝐬((𝝎 + 𝛀)𝒕) So no longer at frequency ω, but at (ω-Ω) and (ω+Ω)! This change in frequency occurs only if the reaction force or moment is in-plane What does this mean? If the force or moment due to the combined modes of the two or three blades are in-plane the frequency of the vibration will be measured in the tower at (ω-Ω) and (ω+Ω) and at ω in the blades… Ψ=Ωt XNR XR YR YNR ZNR=ZR 𝑭 𝒙𝑹 = 𝑨 𝐬𝐢𝐧 𝝎 𝒆𝒅𝒈𝒆 𝒕 Some basic mathematics: sin(a)cos(b) = 0.5(sin(a+b) + sin(a-b)) sin(a)(sin(b) = 0.5(cos(a-b)-cos(a+b)) cos(a)cos(b)= 0.5(cos(a+b)+cos(a-b)) So we had: 𝑭 𝒙𝑵𝑹 = 𝑨 𝐬𝐢𝐧 𝝎𝒕 𝐜𝐨𝐬 𝛀𝒕 𝑭 𝒚𝑵𝑹= 𝑨 𝐬𝐢𝐧 𝝎𝒕 𝐬𝐢𝐧 𝛀𝒕 𝑭 𝒙𝑵𝑹 𝑭 𝒚𝑵𝑹 © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  8. 8. Slide 8 • Recall there were three modes for each blade mode • Two asymmetric, one is symmetrical (all blades same deformation) • Reaction force or moment symmetric mode is out-of-plane, therefore not resulting in whirling mode • Therefore the symmetric mode does not change in frequency if measured in stand still frame • But there is significant interaction with tower (flapwise) and drive train (edgewise). • This interaction influences the frequency and the damping Summary: © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  9. 9. Slide 9 • Flapwise whirling modes: resulting moments that are in-plane (yawing / tilting => vector description of moment will be in-plane!). • So flapwise asymmetric modes also have different frequency in non-rotating reference frame than in rotating frame • Note that turbine is rotating in all situations, we only define different reference frames (e.g. measuring at blade root versus in tower) • Symmetric modes are also called collective modes • The generator will have significant effect on frequency of symmetric edgewise mode • The rotor shaft stiffness will also affect the symmetric edgewise mode frequency • Sometimes we see a symmetric flap mode with counteracting tower motions, depends on the mass distributions. • Tower will have effect on frequency of symmetric flapwise modes. Summary: © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  10. 10. Instability ≠ resonance © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  11. 11. Slide 11 • This is an answer we often get when we suggest to someone that a course on wind turbine aeroelasticity could be of great help for their situation • Aeroelasticity is about much much more than resonance • Avoiding resonance seems rather simple, but avoiding aeroelastic instabilities is a much more complicated problem • Resonance: some external excitation occurring at a certain frequency will excite one of the natural modes which has a natural frequency close to this excitation frequency • Instability: vibrating in the natural mode (at natural frequency) results in aerodynamic forces ADDING energy to the vibration Aeroelasticity: we know, we avoid resonance.. © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  12. 12. Slide 12 • Mode shape is much more important than frequency in case of instability • The external force does not have some forcing frequency, its frequency is purely caused by the vibration of the structure, the deformation and deformation velocities of the structure change the aerodynamic forces • So assume we know the mode shape, we can calculate the work done by the force during one cycle. If this work is positive: energy is added to the vibration => instability Aeroelastic instability © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  13. 13. Slide 13 • In general: • Aerodynamic damping flapwise modes is high • Aerodynamic damping edgewise modes is low • Going close or into stall reduces aerodynamic damping flap & edge • Structural damping is higher for higher modes, therefore only the lower modes (1st, 2nd, 3rd flap and edge & 1st torsion) are thought to be relevant. • Using our code WAF1C we can determine the damping of a prescribed mode shape. • Mostly for gaining insight, seeing effect of certain mode shape changes, not for evaluating actual blade designs. Damping of a mode © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  14. 14. Slide 14 • Example for a predefined mode shape, wind speed, rotor speed Calculation WAF1C Torsion motion, flapwise motion: positive damping. Torsion motion significantly less damping than flap. Edgewise motion is unstable for this prescribed mode shape © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  15. 15. All those excitations.. where do they come from? © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  16. 16. Slide 16 • Two types: 1. reoccurring at a frequency, 2. not or randomly reoccurring. • Whenever you analyse the results of a time simulation for a wind turbine and perform an FFT you will notice that there are frequencies present at 1 times the rotor speed (1P), 2 times (2P), 3 times (3P), etc. • This happens if you include e.g. tower shadow and/or turbulence. • You can probably imagine why 1P, perhaps also why 3P, but why the others? • For turbulence we know this as ‘rotational sampling’. Even though the turbulent wind field does not have any peaks in the FFT, the turbulent wind field seen from a rotating blade will have peaks at nP. Excitations on wind turbine © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  17. 17. Slide 17 • A continuous turbulent wind field will flow through the rotor plane • Assume that there is a certain disturbance at a certain location, than you can imagine that a similar disturbance will still be there the next time the blade passes the same location. • Therefore there will be a 1P frequency in the wind speed that is seen. • But why also 2P, 3P etc.? Rotational sampling © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  18. 18. Slide 18 Turbulence and rotational sampling Mathematical background: • The Fourier transform of a Dirac comb III a ( x ) is another Dirac comb ( 1/a ) III1 / a( p ) • In rotational field one single disturbance is like a Dirac comb 20-Mar-19 1P 2P 3P ….. Source: Wind energy handbook, Burton et al. © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  19. 19. Slide 19 • Another way to think about this • A mass spring system • Assume two types of excitation: • Impulses at frequency P (= Ω) • F=sin(Ωt), so continuous • To keep simple: look at what happens to energy in one cycle of Impulse or F Excitations at nP © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  20. 20. Slide 20 Similar: if you push someone on the swing, if you push every other or every three times, the push will still have the effect you are looking for: excitation of the swinging frequency which is 2 or 3 times higher than your pushing frequency. © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED F: 1 Hz, nat freq. 1 Hz F: 1 Hz, nat freq. 2 Hz: also excited!
  21. 21. Slide 21 • An impulse occurring at same phase every time will increase energy • So the excitation at P will excite also vibrations at 2P, 3P,… • This is another way of understanding why e.g. turbulence excites nP • Similar idea results in tower shadow resulting in 1P, 2P, 3P,… excitations on the blades. • In stand still frame 3P, 6P,... will be dominant when looking at effect of tower shadow (for 3 bladed turbine). Excitations at nP © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  22. 22. Slide 22 • Now, assume continuous force • F=sin(Ωt) • If natural frequency is also Ω, then resonance. Energy will rapidly increase • If natural frequency is nP, e.g. 2P or 3P the energy added in one full cycle of the force is 0! (orthogonal functions) • Therefore wind shear / gravity /… does not excite at nP, with n>1. Only at P. Excitations at nP © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  23. 23. Put edgewise frequency close to 6P…. Are you sure??? © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  24. 24. Slide 24 • No, I am never 100% sure, I am an aeroelasticity expert, but… • Edgewise modes: little to no aerodynamic damping (or even negative) • If the edgewise frequency is close to 5P => FW whirling in stand still frame close to 6P => very significant excitation due to tower passing • If the edgewise frequency is close to 7P => BW whirling in stand still frame close to 6P=> very significant excitation due to tower passing • Symmetric or collective edgewise mode will get significant damping from generator, therefore being close to excitation frequency is less relevant. • Investigations have shown that if edgewise frequency is in range 5-5.4 P fatigue loads are increased due to FW whirl mode excitation. Edgewise frequency close to 6P… © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  25. 25. Relevant aeroelasticity subjects © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
  26. 26. Slide 26 • Current size wind turbines can suffer from different instabilities • Most important ones are: • Classical flutter (overspeed) • Damping of edgewise mode (shape edgewise mode becomes more and more complicated with coupling to e.g. torsion) • Parked/Idling instabilities • It would be wise to perform a full aeroelastic evaluation of the design: • Check aerodynamic damping in constant settings, different values around supposed operating conditions, excite the modes and see what happens. • Check when overspeed instabilities occur • Check for resonances • Check idling situations • Interested in knowing more about this? See next slides! Interested in having an expert perform this check of your design? Contact us, we can discuss the different possibilities (info @ jeho . nl ) More to find out in this wonderful field… © 2019 J.G. HOLIERHOEK ALL RIGHTS RESERVED
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  29. 29. Slide 29 Get to know everything about this and much much more in this course. Info: www.jeho.nl

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