Loads, dynamics and structural design

Transcription

1 Loads, dynamics and structural design Offshore Wind Farm Design Michiel Zaaijer DUWIND

2 Overview Introduction Modelling offshore wind turbines Types of analysis and tools Loads and dynamics in design

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4 Introduction Loads, dynamics and structural design

5 Harmonic loading Loading 1 0 Simple Harmonic Loading F ˆ ( t) = F sin( ω t +ϕ ) Time - Gravity loads on blades - Mass imbalance rotor (1P) - Aerodynamic imbalance (1P) - Small regular waves 27 RPM = 0.45 Hz

6 Loading Non-harmonic periodic loading Complex Cyclic Loading 1st Signal (0.5 Hz) F 0 ( t) = 0 Loading Loading Time nd Signal (1 Hz) Time 0 + k + k a a Fˆ sin k t ( ω ϕ ) k Time Loading rd Signal (1.5 Hz) - Wind-shear - Yaw misalignment - Tower shadow - Rotational sampling of turbulence Time (all 2P or 3P and multiples) 3P

7 Non-periodic random loading 1 Random Load Loading Time - Turbulence (small scale) - Random waves

8 Other (non-periodic) loading Transients Short events Step Load Impulsive Load 1 1 Loading 0 Loading Time Time - Start/stop - Turbine failures - Storm front - Extreme gust - Extreme waves

9 Introduction Loads, dynamics and structural design

10 The effect of dynamics 2 1 Force [N] k k = 1 [N/m] m F x ? Response [m]

11 The effect of dynamics Force [N] -1-2 m = [kg] 2 1 (Static) m = 0 [kg] -1-2 m = 0.1 [kg]

12 The effect of dynamics F System k m Force [N] F intern = k x Internal forces external forces due to dynamics Response [m] Internal forces drive the design, not external forces! m = [kg]

13 Dynamic amplification factor 5 DAF = Dynamic amplitude Static deformation Dynamic Amplification Factor (DAF) Resonance Frequency Ratio damping ratio = 0.1 damping ratio = 0.2 damping ratio = 0.5 f excitation f natural Note: the DAF is defined for harmonic excitation

14 Character of resonance Excitation frequency natural frequency Large oscillations Fatigue damage (due to severe cyclic loading) Generally not destructive (anticipated in design) Natural frequencies of wind turbine (-components) are close to several excitation frequencies

15 Classification for wind turbines DAF soft-soft soft-stiff stiff-stiff Excitation 1 Response 1P 3P f

16 Soft-stiff example 1P = 0.45 Hz f natural = 0.55 Hz 3P = 1.35 Hz

17 Reduced response to loading DAF 1 soft-soft structure Alleviation of (wind) loading by shedding loads through motion Typical rotor loading frequencies Typical wave loading frequencies 1P 3P f 0

18 Increased response to loading Quasi-static or amplified response to wave loading 1-P *-P

19 Single degree of freedom system k c m x F F = m & x +k x + c x&

20 Wind turbine characteristics Stiffness Material properties / soil properties Buoyancy of a floating structure Damping Material properties / soil properties Aerodynamic loading Control (Viscosity of water / radiation in soil) Inertia Material properties Hydrodynamic loading (water added mass) Entrained water mass

21 Linear / non-linear systems Linear system: x(t) y(t) Initial condition x 0 : a x 1 (t) + b x 2 (t) a y 1 (t) + b y 2 (t) x(t) + x 0 y(t) + y 0 Non-linear system: No superposition possible Possible dependency on initial conditions Possible variation in output statistics for the same input (statistics)

22 Non-linearities for wind turbines Aerodynamic loading Hydrodynamic loading extreme waves waves and currents Speed and pitch control some algorithms settings for various wind speeds Extreme deformations (2 nd order effects)

23 Introduction Loads, dynamics and structural design

24 Lifelong response signal Response (loading + dynamics) Extreme events Lifelong variations Time

25 Effects of loads and dynamics Ultimate limit state (ULS) (maximum load carrying resistance) Yield and buckling Loss of bearing / overturning Failure of critical components Fatigue limit state (FLS) (effect of cyclic loading) Repeated wind and wave loading Repeated gravity loading on blade

26 Effects of loads and dynamics Accidental limit state (ALS) (accidental event or operational failure, local damage or large displacements allowed) Ship impact Serviceability limit state (SLS) (deformations/motion, tolerance for normal use) Blade tip tower clearance Vibrations that may damage equipment Tilt of turbine due to differential settlement

27 Design drivers of wind turbines Component Design drivers Ultimate Fatigue Tower top top mass - Tower - wind/wave Submerged wind/wave/current wind/wave tower Foundation wind/wave/current

28 Importance of dynamics in design Increase or decrease of maximum load Affects Ultimate Limit State conditions Increase or decrease of number of load cycles and their amplitudes Affects Fatigue Limit State / Lifetime

29 Effect on structural design Support structure cost Soft-stiff monopile 100 % Soft-soft monopile 80 % Monopile soft-stiff Monopile soft-soft Energy cost Soft-stiff monopile 100 % Soft-soft monopile 95 %

30 Use of dynamic models Analyse system properties Avoid resonance and instabilities Reduce internal loads and match resistance Make lightest and cheapest structural design Assess lifelong loading Validate reliability and technical lifetime

31 Modelling of offshore wind turbines Structural models of rotor, nacelle and support structure

32 Flexibility of wind turbines Rotor Drive train - Torsion Blades Tower - Rotation - Flapwise bending - Edgewise bending - Torsion - Bending - Torsion Foundation - Rotation - Horizontal - Vertical

33 Integrated dynamic model Offshore wind turbine Controllers Wind Wave Rotor Drive train Generator Support structure Grid

34 Rotor model Aerodynamic properties Distributed mass-stiffness Beam theory FEM Tables C l α C d α µ, EI x,y,p

35 Drive train model Transmission ratio I hub+low speed shaft I generator Stiffness torsion in transmission and main shaft; main shaft bending Damping transmission suspension and generator torque control

36 Generator model synchronous generator: T k,g generator 0 0 n 0 n motor T k,g induction generator: Slip generator 0 0 n 0 2n 0 n motor

37 Tower model Distributed mass-stiffness Modal representation Beam theory FEM + = µ, EI x,y,p Deflection 1 st mode Deflection 2 nd mode Total deformation Effective reduction of DOFs

38 Foundation model H M = k k x x θx k k xθ θθ u θ

39 Modelling of offshore wind turbines Deriving parameters for foundation models

40 Importance of foundation model 40.0m 5.0m 15.0m 21.0m MSL Flange Tower Boat Landing Pile Scour Protection 3.5m Rotor/nacelle mass 130,000 kg x Ø x m J-Tube 2800Ø x Ø x Ø x Ø x m 4.6m 6.0m 12.0m 12.0m 12.0m 15.4m 2500Ø x 100 x Ø x 75 (25.0m Penetration) 6.0m 3.0m 37.0m First natural frequency (Hz) without foundation with foundation with scour Second natural frequency (Hz) without foundation with foundation with scour

41 Enhanced foundation model External shaft friction (t-z curves) Use: Standards (API/DNV) Existing software (In exercise: ANSYS Macro s) Pile plug resistence (Q-z curves) Lateral resistance (p-y curves) Internal shaft friction (t-z curves) Pile point resistance (Q-z curves)

42 Scour Pile 0 Vertical effective soil pressure Seabed General scour depth Local scour depth Typically times pile diameter No scour condition General scour only Local scour condition Overburden reduction depth Typically 6 times pile diameter

43 Effective fixity length Seabed Effective fixity length Configuration Stiff clay Very soft silt General calculations Effective fixity length 3.5 D 4.5 D 7 D 8 D 6 D Experience with offshore turbines 3.3 D 3.7 D

44 Uncoupled springs Tower Rotation Seabed Forced displacement/rotation u F Ignore M θ M Method A Ignore F In exercise: Use ANSYS Macro s and method B for a monopile Applied force/moment F u M θ Method B Translations Ignore θ Ignore u

45 Stiffness matrix Tower Run two load cases with FEM model with py-curves (See next slide) Seabed H M = k k x x θx k k xθ θθ u θ Stiffness matrix

46 FEM-based pile-head stiffness 1. Solve FEM for F 1, M 1 (F 1, M 1 near loading situation of interest) 2. Solve FEM for F 2, M 2 (F 2, M 2 near loading situation of interest) F M F M 1 = kxx u1 + kxθ θ1 = k u + k 1 θx 1 θθ θ1 2 = kxx u2 + kxθ θ 2 = k u + k 2 θx 2 θθ θ 2 3. Scratch one equation and solve k xx, k xθ, k θθ (k θx = k xθ, assume matrix equal for both loads) 4. Check assumption with another FEM solution

47 Selection of pile foundation models Foundation flexibility significant enough to require close consideration of modelling Effective fixity length model dissuaded Stiffness matrix much more favourable than uncoupled springs For exercise: Monopile in Bladed modeled with uncoupled springs (unfortunately)

48 Documented GBS model parameters GBS Rocking Spring stiffness G D 3 3 ( 1 ν ) Viscous damping 4 D ρ G ( 1 ν ) Inertia ρ D ( 1 ν ) Lumped springs and dashpots for: - Horizontal - Vertical - Rocking Horizontal 16G D 7 8ν ( 1 ν ) 2 D ρ G ( 2 ν ) ρ D ( 2 ν ) Vertical 2G D 1 ν 2 D ρ G ( 1 ν ) ρ D ( 1 ν )

49 Types of analysis and tools Natural frequency and mode analysis

50 FEM modal analysis 1 Z Y X Parametric support structure model generation FEM analysis provides: Natural frequencies Mode shapes (Pre-processed) matrices of structural properties: Mass Stiffness Damping

51 Natural frequencies Natural frequencies Monopile Monopod Tripod Truss

52 Modes of the support structure Monopile 1 st mode 2 nd mode

53 Rayleigh's method Ẑ Velocity: SDOF : V max = 1 2 k ( xˆ ) 2 SDOF : T max mω (( x) ) = m & = ( ) 2 xˆ v ( x, t) = Ψ( x) Zˆ sin( ωt) Maximum strain energy ˆ 2 ~ Z = Maximum kinetic energy ˆ 2 2 ~ Z ω

54 Rayleigh's method To estimate first natural frequency (lowest) Based on energy conservation in undamped, free vibration: Exchange of energy between motion and strain Mode shape must fit boundary conditions Best estimate of mode shape results in lowest estimate of natural frequency (Deflection under static top-load gives educated guess of mode shape)

55 Rayleigh s method for stepped tower T 2 ( m + ) π 4π m L L top eq 48 = + ω 3EI π 2 4 eq C found See document on Blackboard for: Derivation of this equation Explanation of EI eq, m eq, C found

56 Free vibration of cylinder in water ( ) ( ) c w c w D c M w M x v x v D C x D C a D C f & & & & + =,, 2, ρ π ρ π ρ Inertia force Drag force Inertia force due to moving cylinder Still water remaining inertia term is called water added mass With C M 2 water added mass mass of replaced water But related to water surrounding the cylinder! Use water added mass in analysis of natural frequency and modes

57 Types of analysis and tools Response analysis

58 Types of response analysis Static analysis with dynamic response factors Time domain simulation Frequency domain analysis Mixtures All approaches can also be divided in: Integrated combined loading Superposition of effect of load components (wind, wave, current, gravity)

59 Static + dynamic response factors Calculate static response for several loading conditions (separate wind, wave, g) Estimate a dynamic response factor per condition (comparison of characteristic frequencies) Typical Superimpose results (including partial safety factors per loading type)

60 Superposition of forces Gravity Thrust Wind on tower Waves + current Superposition

61 Time domain simulation Generate realisations of external conditions Integrate equations of motion numerically Analyse response (extremes, probability distribution, fatigue, ) Repeat until statistically sound information is obtained The tool used in the exercise to do this is Bladed. See Blackboard item Assignments for a tutorial and manuals

62 Frequency domain analysis Fourier transforms and linear systems Time domain Frequency domain ( t), y( t) h( t) X ( ω ), Y ( ω ), H ( ω ) x, ( ) = ( τ ) ( τ ) τ = ( )* ( ) Y( ω) = X ( ω) H ( ω ) y t x h t d x t h t a a x1 ( t) + b x2( t) a X1( ω) + b X 2( ω) y ( t) + b y ( t) a Y ( ω) + b Y ( ω )

63 Frequency domain analysis Determine transfer function per load source Linearise system or use small harmonic loads Multiply spectrum of load source with transfer function Superimpose response spectra of different sources Due to non-linearity in the system, this procedure must be repeated for different average wind speeds

64 Time domain - frequency domain Time domain Frequency domain Comprehensive non-linear structural model Very time consuming Careful choice of time signal Able to model control system dynamics Established fatigue prediction tools Simplified linear structural model Very rapid calculation Well documented wind turbulence spectra Able only to model linear control system Fatigue prediction tools relatively new

65 Mixing time- and frequency domain + TD simulation: - Transfer function tower top loading (linearisation) - Aerodynamic damping FD analysis: - Transfer function for wind loading - Aerodynamic damping as extra structural damping - Linear wave loading

66 Aerodynamic damping Tower for-aft motion δl Blade motion Angle of attack decreases/increases Lift/thrust force diminishes/increases U(1-a) δl opposite V blade α V blade -V blade

67 Aerodynamic damping aerodyn. damping as frac. of crit. damp. [%] soft-soft monopile soft-stiff monotower stiff-stiff lattice tower Function of wind speed, turbine design (aerodynamic and control) and support structure! wind speed at hub height [m/s]

68 Some relevant analysis tools ANSYS Sesam Adams WT Phatas Bladed Flex Turbu FEM Time Freq Rotor Offshore X X X X X X X X X X X X X X X X X X X X X X X X X

69 Loads and dynamics in design Overview of the process

70 Suggested steps Choose a limited set of load cases Make preliminary design based on static loads Check for resonance* Check extreme loads with time domain simulations* Check fatigue damage* * Adjust design when necessary

71 Partial safety factor method Apply load and resistance factors to: loads on the structure or load effects in the structure resistance of the structure or strength of materials R γ S S γ Fulfill design criterion: Combined loading with non-linear effects: Apply one safety factor to combined load effect, determined from structural analysis of simultaneous loading R

72 Values for safety factors Importance of structural component w.r.t. consequence of failure considered Typically between 0.7 and for favourable loads! Load factor 1.0 for fatigue (safety in resistance) See e.g. Offshore standard DNV-OS-J101 Design of offshore wind turbine structures

73 Loads and dynamics in design Choose load cases

74 Fundamental problems in evaluation Response (loading + dynamics) What is the true extreme? More realisations at the same site Long time span (20 year) Time

75 Load cases: Combine conditions external conditions normal extreme operational conditions normal conditions stand-by start-up fault conditions power production normal shut-down condition after occurrence of a fault erection The number of combinations that is required in the standards is enormous!

76 Reducing number of load cases (extremes) Select a few independent extreme conditions that might be design driving, e.g.: Extreme loading during normal operation Extreme loading during failure Extreme wind loading above cut-out Extreme wave loading And combine these with reduced conditions for the other aspects (wind, wave, current)

77 Reducing number of load cases (fatigue) Hs \ \ Tz total Idling: V w > V cut_out lumped sea state Normal operation: V cut_in < V w < V cut_out Idling: V w < V cut_in total Lump states in 3D scatter diagram Use normal operation and idling

78 T Knowledge about load case selection: Thrust curves Stall ~V -1 Response to gust/failure ~V 2 Ideal pitch ~V 2 V rated V cut-out V extreme V

79 Extreme and reduced conditions H max 1.86 H s H reduced 1.32 H s V gust,max 1.2 V 10 min V gust,reduced (1.2 / 1.1) V 10 min

80 Loads and dynamics in design Make preliminary design

81 Preliminary support structure design Determine largest loads at several heights Estimate wind, wave, current and gravity loads e.g. C D,AX = 8/9 (Betz) at V rated & linear wave & DAF & safety Superimpose and determine largest at each height Dimension tower (moments / section modulus) Rule of thump D/t 200 tower section ~60 driven foundation pile (see e.g. API on BB) Estimate pile size with Blum s method (See document on Blackboard!)

82 Loads and dynamics in design Check for resonance

83 Campbell diagram Characteristic frequency margin forbidden area 1 e lead-lag 1 e flap 1 st tower frequency stiff 1 st tower frequency 1 st tower frequency Softsoft Wave-excitation Soft-soft Rotor speed Stiffstiff Soft-stiff 3-P 1-P Soft

84 Design adaptations Change diameters and/or wall thicknesses Shift masses e.g. move transformer from nacelle to platform Adjust rotor speed control e.g. skip resonance in partial load region Change concept e.g. to braced tower / tripod

85 Loads and dynamics in design Check lifetime fatigue

86 Fatigue Fatigue: after a number of cycles of a varying load below static strength failure occurs. F F static σ failure fatigue test time number of cycles

87 S-N curves UTS log σ amp 1:20? 1:10 1:3 Steel (Welded) Carbon-Epoxy Glass-Polyester log N

88 Variable amplitude loading Miner s Damage Rule: n N i = i n N 1 n N 2 n N 3 n N 4 n N 5 5 σ amp Damage < 1.0 n 1 n 2 N 1 N 2 n 3 n 4 n 5 N 3 N 3 N 4 N 5 log N

89 Stochastic loading Stress history can be converted to blocks of constant amplitude loadings (using counting method) Stress history σ σ amp stress histogram Time log N Information about sequence lost

90 Rainflow counting Two parametric method: Range and mean Display series of extremes with vertical time axis Drip rain from each extreme, stop at a larger extreme Start and stop combine to one stress cycle

91 Rainflow counting Established method Several equivalent algorithms exist Reservoir method Intermediate extremes in groups of 4 Principle based on stress-strain hysteresis loops:

92 Frequency domain approach Rayleigh: Theoretical, narrow band signals: Dirlik: Empirical, wide band signals: Used for spectra of random, Gaussian, stationary processes

93 Lifetime fatigue analysis Do the following for all load cases (scatter diagram, operational and idle) Hs\ \ Tz 0-1s 1-2s 2-3s 3-4s 4-5s 5-6s 6-7s 7-8s 8-9s total 5.5-6m m m Idling, high: Vw>=Vcut_out m m lumpedseastate m m m m idling, low: Vw<Vcut_in m m m total Determine stress time series or PSD (PSD = Power Spectral Density) σ Determine stress histogram (Rainflow counting Dirlik) σ amp Time log N

94 Lifetime fatigue analysis i i Apply Miner s rule to histogram (damage per load case) σ amp n 1 N1 D = n N Apply Miner s to all load cases: Damage of each load case (normalised to 1 unit of time) * Probability of load case * Total lifetime log N Pile 5.5 m below mudline Load case type PP wind & waves II, IP: waves Idle,low 1 Idle,low 2 Idle,low 3 prod. 8 m/s prod. 10 m/s prod. 14 m/s prod. 15 m/s prod. 17 m/s prod. 19 m/s prod. 20 m/s prod. 21 m/s Idle, high 1 Idle, high 2 Idle, high 3 Idle,low 1 Idle,low 2 Idle,low 3 prod. 8 m/s prod. 10 m/s prod. 14 m/s prod. 15 m/s prod. 17 m/s prod. 19 m/s prod. 20 m/s prod. 21 m/s Idle, high 1 Idle, high 2 Idle, high damage for load case with unity probability [-] probability of load case [-] PP: wind PP: waves probability Pile 5.5 m below mudline Fatigue analysis type No.1: wind & waves (full avail.) No. 2: waves & no aerodyn. damping No. 4: pure wind No. 5: waves & aerodyn. damping (absolute) damage per load case [-] 0.00

95 Integrated system dynamics Equivalent bending moment wind loading separate analyse wave loading superposition integrated analysis combined loading wind wave combined