Loads, dynamics and structural design Offshore Wind Farm Design Michiel Zaaijer 2007-2008 1 DUWIND
Overview Introduction Modelling offshore wind turbines Types of analysis and tools Loads and dynamics in design 2007-2008 2
2007-2008 3
Introduction Loads, dynamics and structural design 2007-2008 4
Harmonic loading Loading 1 0 Simple Harmonic Loading F ˆ ( t) = F sin( ω t +ϕ ) 1 0 1 2 3 4 5 6 Time - Gravity loads on blades - Mass imbalance rotor (1P) - Aerodynamic imbalance (1P) - Small regular waves 27 RPM = 0.45 Hz 2007-2008 5
Loading Non-harmonic periodic loading Complex Cyclic Loading 1st Signal (0.5 Hz) 0.5 1 F 0 ( t) = 0 Loading Loading 0.5 0 1 2 3 4 5 6 Time 0.5 0 2nd Signal (1 Hz) 0.5 0 1 2 3 4 5 6 Time 0 + k + k a a Fˆ sin k t ( ω ϕ ) k 1 0 1 2 3 4 5 6 Time Loading 0.5 0 3rd Signal (1.5 Hz) - Wind-shear - Yaw misalignment - Tower shadow - Rotational sampling of turbulence 0.5 0 1 2 3 4 5 6 Time (all 2P or 3P and multiples) 3P 2007-2008 6
Non-periodic random loading 1 Random Load Loading 0 1 0 1 2 3 4 5 6 Time - Turbulence (small scale) - Random waves 2007-2008 7
Other (non-periodic) loading Transients Short events Step Load Impulsive Load 1 1 Loading 0 Loading 0 1 0 1 2 3 4 5 6 1 0 1 2 3 4 5 6 Time Time - Start/stop - Turbine failures - Storm front - Extreme gust - Extreme waves 2007-2008 8
Introduction Loads, dynamics and structural design 2007-2008 9
The effect of dynamics 2 1 Force [N] k k = 1 [N/m] m F x 0-1 -2 2 1 0 1 1? Response [m] -1-2 2007-2008 10
The effect of dynamics 2 2 1 1 0 1 0 1-1 -2 Force [N] -1-2 m = 0.0005 [kg] 2 1 (Static) 2 1 0 1 0 1-1 -2 m = 0 [kg] -1-2 m = 0.1 [kg] 2007-2008 11
The effect of dynamics F System k m 2 1 0-1 1 Force [N] F intern = k x Internal forces external forces due to dynamics -2 2 1 0 1 Response [m] Internal forces drive the design, not external forces! 2007-2008 12-1 -2 m = 0.0005 [kg]
Dynamic amplification factor 5 DAF = Dynamic amplitude Static deformation Dynamic Amplification Factor (DAF) 4 3 2 1 Resonance 0 0 1 2 3 4 5 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 2007-2008 13
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 2007-2008 14
Classification for wind turbines DAF soft-soft soft-stiff stiff-stiff Excitation 1 Response 1P 3P f 0 2007-2008 15
Soft-stiff example 1P = 0.45 Hz f natural = 0.55 Hz 3P = 1.35 Hz 2007-2008 16
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 2007-2008 17 f 0
Increased response to loading Quasi-static or amplified response to wave loading 1-P *-P 2007-2008 18
Single degree of freedom system k c m x F F = m & x +k x + c x& 2007-2008 19
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 2007-2008 20
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) 2007-2008 21
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) 2007-2008 22
Introduction Loads, dynamics and structural design 2007-2008 23
Lifelong response signal Response (loading + dynamics) Extreme events Lifelong variations Time 2007-2008 24
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 2007-2008 25
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 2007-2008 26
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 - 2007-2008 27
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 2007-2008 28
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 % 2007-2008 29
Use of dynamic models 1. 2. 3. 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 2007-2008 30
Modelling of offshore wind turbines Structural models of rotor, nacelle and support structure 2007-2008 31
Flexibility of wind turbines Rotor Drive train - Torsion Blades Tower - Rotation - Flapwise bending - Edgewise bending - Torsion - Bending - Torsion Foundation - Rotation - Horizontal - Vertical 2007-2008 32
Integrated dynamic model Offshore wind turbine Controllers Wind Wave Rotor Drive train Generator Support structure Grid 2007-2008 33
Rotor model Aerodynamic properties Distributed mass-stiffness Beam theory FEM Tables C l α C d α µ, EI x,y,p 2007-2008 34
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 2007-2008 35
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 2007-2008 36
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 2007-2008 37
Foundation model H M = k k x x θx k k xθ θθ u θ 2007-2008 38
Modelling of offshore wind turbines Deriving parameters for foundation models 2007-2008 39
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 30 2800Ø x 20 5.0m J-Tube 2800Ø x 60 2800Ø x 60 2800Ø x 32 2800Ø x 25 3.0m 4.6m 6.0m 12.0m 12.0m 12.0m 15.4m 2500Ø x 100 x 100 3500Ø x 75 (25.0m Penetration) 6.0m 3.0m 37.0m First natural frequency (Hz) without foundation 0.34627 with foundation 0.29055 with scour 0.28219 Second natural frequency (Hz) without foundation 2.2006 with foundation 1.3328 with scour 1.2508 2007-2008 40
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) 2007-2008 41
Scour Pile 0 Vertical effective soil pressure Seabed General scour depth Local scour depth Typically 1-1.5 times pile diameter No scour condition General scour only Local scour condition Overburden reduction depth Typically 6 times pile diameter 2007-2008 42
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 2007-2008 43
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 2007-2008 44
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 2007-2008 45
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 2007-2008 46
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) 2007-2008 47
Documented GBS model parameters GBS Rocking Spring stiffness G D 3 3 ( 1 ν ) Viscous damping 4 D 0.65 32 ρ G ( 1 ν ) Inertia ρ D 0.64 32 5 ( 1 ν ) Lumped springs and dashpots for: - Horizontal - Vertical - Rocking Horizontal 16G D 7 8ν ( 1 ν ) 2 D 4.6 4 ρ G ( 2 ν ) ρ D 0.76 8 3 ( 2 ν ) Vertical 2G D 1 ν 2 D 3.4 4 ρ G ( 1 ν ) ρ D 1.08 8 3 ( 1 ν ) 2007-2008 48
Types of analysis and tools Natural frequency and mode analysis 2007-2008 49
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 2007-2008 50
Natural frequencies Natural frequencies 3.5 3 2.5 2 1.5 1 0.5 0 Monopile Monopod Tripod Truss 2007-2008 51
Modes of the support structure Monopile 1 st mode 2 nd mode 2007-2008 52
Rayleigh's method Ẑ Velocity: SDOF : V max = 1 2 k ( xˆ ) 2 SDOF : T max 1 2 1 2 mω (( x) ) = m & = 0 2 2 ( ) 2 xˆ v ( x, t) = Ψ( x) Zˆ sin( ωt) Maximum strain energy ˆ 2 ~ Z 2007-2008 53 = Maximum kinetic energy ˆ 2 2 ~ Z ω
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) 2007-2008 54
Rayleigh s method for stepped tower T 2 ( m + ) 2 2 3 4π 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 2007-2008 55
2007-2008 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, 2 2 1 4 1 4 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
Types of analysis and tools Response analysis 2007-2008 57
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) 2007-2008 58
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 1.2-1.5 Superimpose results (including partial safety factors per loading type) 2007-2008 59
Superposition of forces Gravity Thrust Wind on tower Waves + current Superposition 2007-2008 60
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. 2007-2008 61
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 ) 1 2 1 2 2007-2008 62
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 2007-2008 63
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 2007-2008 64
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 2007-2008 65
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 2007-2008 66
Aerodynamic damping aerodyn. damping as frac. of crit. damp. [%] 6 5 4 3 2 1 0 soft-soft monopile soft-stiff monotower stiff-stiff lattice tower Function of wind speed, turbine design (aerodynamic and control) and support structure! 5 10 15 20 25 wind speed at hub height [m/s] 2007-2008 67
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 2007-2008 68
Loads and dynamics in design Overview of the process 2007-2008 69
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 2007-2008 70
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 2007-2008 71
Values for safety factors Importance of structural component w.r.t. consequence of failure considered Typically between 0.7 and 1.35 1.0 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 2007-2008 72
Loads and dynamics in design Choose load cases 2007-2008 73
Fundamental problems in evaluation Response (loading + dynamics) What is the true extreme? More realisations at the same site Long time span (20 year) Time 2007-2008 74
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! 2007-2008 75
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) 2007-2008 76
Reducing number of load cases (fatigue) Hs \ \ Tz 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 total 5.5-6 0.0 5-5.5 Idling: V w > V cut_out 0.08 0.1 4.5-5 0.04 0.3 0.3 4-4.5 0.3 0.08 0.4 3.5-4 lumped sea state 0.7 0.7 3-3.5 Normal operation: 0.7 0.7 2.5-3 V cut_in < V w < V cut_out 0.6 0.04 0.7 2-2.5 0.2 0.2 1.5-2 0.0 1-1.5 Idling: V w < V cut_in 3.4 0.4 3.8 0.5-1 19 58 0.7 77.7 0-0.5 0.68 1.0 65 12 0.1 0.11 79.0 total 0.7 0.0 1.0 84.2 73.4 2.0 1.9 0.5 0.0 164 Lump states in 3D scatter diagram Use normal operation and idling 2007-2008 77
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 2007-2008 78
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 2007-2008 79
Loads and dynamics in design Make preliminary design 2007-2008 80
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!) 2007-2008 81
Loads and dynamics in design Check for resonance 2007-2008 82
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- 2007-2008 83
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 2007-2008 84
Loads and dynamics in design Check lifetime fatigue 2007-2008 85
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 2007-2008 86
S-N curves UTS log σ amp 1:20? 1:10 1:3 Steel (Welded) Carbon-Epoxy Glass-Polyester log N 2007-2008 87
Variable amplitude loading Miner s Damage Rule: n N i 1 2 3 4 = + + + + 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 2007-2008 88
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 2007-2008 89
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 2007-2008 90
Rainflow counting Established method Several equivalent algorithms exist Reservoir method Intermediate extremes in groups of 4 Principle based on stress-strain hysteresis loops: 2007-2008 91
Frequency domain approach Rayleigh: Theoretical, narrow band signals: Dirlik: Empirical, wide band signals: Used for spectra of random, Gaussian, stationary processes 2007-2008 92
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 0.0 5-5.5m 0.08 0.1 4.5-5m Idling, high: Vw>=Vcut_out 0.04 0.3 0.3 4-4.5m 0.3 0.08 0.4 3.5-4m lumpedseastate 0.7 0.7 3-3.5m 0.7 0.7 2.5-3m 0.6 0.04 0.7 2-2.5m 0.2 0.2 1.5-2m idling, low: Vw<Vcut_in 0.0 1-1.5m 3.4 0.4 3.8 0.5-1m 19 58 0.7 77.7 0-0.5m 0.68 1.0 65 12 0.1 0.11 79.0 total 0.7 0.0 1.0 84.2 73.4 2.0 1.9 0.5 0.0 164 Determine stress time series or PSD (PSD = Power Spectral Density) σ Determine stress histogram (Rainflow counting Dirlik) σ amp Time log N 2007-2008 93
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 10. 9. 8. 7. 6. 5. 4. 3. 2. 1. Pile 5.5 m below mudline Load case type PP wind & waves II, IP: waves 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0.0 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 3 2007-2008 94 damage for load case with unity probability [-] probability of load case [-] PP: wind PP: waves probability 0.14 0.12 0.10 0.08 0.06 0.04 0.02 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
Integrated system dynamics Equivalent bending moment 50 40 30 20 10 0 wind loading separate analyse wave loading superposition integrated analysis combined loading wind wave combined 2007-2008 95