Overview of the ElastoDyn Structural-Dynamics Module
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.
NREL Wind Turbine Modeling Workshop September 11-12, 2014 Bergen, Norway Jason Jonkman, Ph.D. Senior Engineer, NREL
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Outline
• Introduction & Background: – ElastoDyn – What Is It? – Inputs, Outputs, States, &
Parameters – Turbine Configurations
• Theory Basis: – Degrees of Freedom – Overview – Kane’s Method – Blade & Tower Modeling
Assumptions – Rotations
• Input Geometry – Turbine Parameterizations
• Structural Features of FAST v8 Compared to v7
• Modeling Guidance • Recent Work • Current & Planned Work • Future Opportunities
Introduction & Background ElastoDyn – What Is It?
• Structural-dynamic module for horizontal-axis wind turbines: – Used to be a fundamental part of FAST – Now split out as a callable module in the FAST framework with
separate input files & source code – Includes structural models of the
rotor, drivetrain, nacelle, tower, & platform
• Latest version: – v1.01.06b-bjj (July 2014)
• User’s Guide: – Sections of Jonkman & Buhl (2005)
& Addendum (2013)
• Theory Manual (unofficial): – Jonkman (2005)
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Continuous States: • Displacements • Velocities
Parameters: • Geometry • Mass/inertia • Stiffness coefficients • Damping coefficients • Gravity
Outputs: • Displacements • Velocities • Accelerations • Reaction loads
Introduction & Background Inputs, Outputs, States, & Parameters
Inputs: • Aerodynamic loads • Hydrodynamic loads • Controller commands • Substructure reactions
@ transition piece
ElastoDyn
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Introduction & Background Turbine Configurations
• Horizontal-axis (HAWT) • 2- or 3-bladed rotor • Upwind or downwind rotor • Rigid or teetering hub • Conventional configuration or
inclusion of rotor- &/or tail-furling
• Support structure that includes a tower atop a platform
• Land- or offshore-based (via HydroDyn)
• Offshore fixed-bottom (via SubDyn) or floating (via MAP)
1st & 2nd Blade Flap Mode
1st & 2nd Tower Fore-Aft Mode
1st & 2nd Tower Side-toSide Mode
1st Blade Edge Mode
Nacelle Yaw
Generator Azimuth
Shaft Torsion
Platform Yaw
Platform Roll
Platform Pitch
Platform Heave
Platform Sway
Platform Surge
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Theory Basis Degrees of Freedom
Blades: 2 flap modes per blade 1 edge mode per blade
Teeter: 1 rotor teeter hinge with optional δ3 (2-blader only)
Drivetrain: 1 generator azimuth 1 shaft torsion
Furl*: 1 rotor-furl hinge of arbitrary orientation & location between the nacelle & rotor 1 tail-furl hinge of arbitrary orientation & location between the nacelle & tail Nacelle: 1 yaw bearing Tower: 2 fore-aft modes
2 side-to-side modes Platform: 3 translation (surge, sway, heave)
3 rotation (roll, pitch, yaw) __________________________________________________________________________________________
Total: 24 DOFs available for 3-blader 22 DOFs available for 2-blader
*Available in FAST v7, but not yet in v8
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Theory Basis Overview
(any questions? )
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Theory Basis Overview (cont)
• Combined multi-body- & modal-dynamics formulation: – Modal: blades, tower – Multi-body: platform, nacelle, generator, gears, hub, tail
• Utilizes relative DOFs: – No constraint equations – ODEs instead of DAEs
• Nonlinear equations of motion (EoMs) are derived & implemented using Kane’s Method (not an energy method)
• EoM form:
• Time integration using one of several options: – 4th-order Runge-Kutta (RK4) explicit – 4th-order Adams-Bashforth (AB4) multi-step explicit (init. with RK4) – 4th-order Adams-Bashforth-Moulton (ABM4) multi-step predictor-
corrector (PC) (init. With RK4)
( ) ( )dM q,u,t q f q,q,u,u ,t 0+ =
( ) ( ) ( )d r t dOutData Y q,q,u,u ,t Y q,u,t q Y q,q,u,u ,t= = +
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Theory Basis Kane’s Method
( )*r rF F 0 r 1,2, ,NDOF+ = =
= ⋅ + × ⋅i i i i i iN N N N N NE E E EH I α ω I ω
( ) ( ) ( )NDOF
rr 1
q,q,t q,t q q,t=
= + ∑i i iN N NE E E
r tω ω ω
( ) ( ) ( )NDOF
rr 1
q,q,t q,t q q,t=
= + ∑i i iX X XE E E
r tv v v
• Kane’s EoM for MBS without constraints:
• Generalized active forces: • Generalized inertia forces:
( )
w
ri 1
F
r 1,2, ,NDOF=
= ⋅ + ⋅
=
∑ i i i iX X N NE Er rv F ω M
( ) ( )( )
i
wN*
ri 1
F m
r 1,2, ,NDOF=
= ⋅ − + ⋅ −
=
∑ i i i iX X N NE E E Er rv a ω H
• Partial angular velocities:
• Partial linear velocities: iN
iX
w = # of rigid bodies = rigid body i = mass center of rigid body i
0
0
• EoMs are written in terms of reaction loads between bodies
[ ]( )( )
Mass Matrix 3,r
r 1,2, ,NDOF
= − ⋅
=r
E H L@P3 Rotorω M
FAST Theory Basis Kane’s Method (cont)
( ) ( )( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( )
10H
i 15i 3
6
i 15i 3
0 0
0 0 0 0
d dm q q gdt dt
d dq qdt dt
=
=
= +
+ + × + + ×
− + × + +
− ⋅ + − × ⋅
∑
∑
t t t
t t
L@P H HRotor B1 B2
PQ QS1 S1 PQ QS2 S2B1 B2
PQ QC E C E Ci 15 2
H E H E H E H H E Hi 15
M M M
r r F r r F
r r v v a
I ω ω ω I ω
( ) ( ) ( )NDOF
rr 1
q,q,q,t q,t q q,q,t=
= + ∑ r t
L@P L@P L@PRotor Rotor RotorM M M
• Moments at the shaft from rotor loads:
( ) ( )( ) ( )( ) ( )
( )H
0 0
0 0
0 0
m
= +
+ + × + + ×
− + × − ⋅
r r r
r
r
L@P H HRotor B1 B2
PQ QS1 S1B1
PQ QS2 S2B2
PQ QC E C H E Hr r
M M M
r r F
r r F
r r v I ω
( )r 1,2, ,NDOF=
• Teeter DOF (3rd) EoM in terms of these partial moments: [ ]{ } { }Mass Matrix Accelerations Forcing Function=
{ }( )Forcing Function 3 = ⋅t
E H L@P3 Rotorω M
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Theory Basis Blade & Tower Modeling Assumptions
• Bernoulli-Euler beams under bending:
– No axial or torsional DOFs – No shear deformation
• Straight beams of isotropic material & no mass/elastic offsets: – Blade pretwist induces flap & edge coupling
• Small to moderate deflections: – Superposition of lowest modes:
• Mode shapes specified as polynomial coefficients • Mode shapes not calculated internally:
– Found from e.g. BModes or modal test
• Shapes should represent modes, but orthogonality not required: – No diagonalization employed
– Bending assumes small strains: • Small-angle approximations employed
with nonlinear corrections for coordinate system orthogonality
1st mode 2nd mode
Modal Representation
2
2u
hκ ∂≈∂
uh
θ ∂≈∂
( ) ( ) ( ) ( )2 TFA2 TFATwrFlexL
jiTFA TFAij 2 2
0
d hd hk EI h dh i, j 1,2
dh dhφφ
= =∫
( ) ( ) ( ) ( )2 TSS2 TSSTwrFlexL
jiTSS TSSij 2 2
0
d hd hk EI h dh i, j 1,2
dh dhφφ
= =∫
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Theory Basis Blade & Tower Modeling Assumptions (cont)
• Otherwise, all terms include full nonlinearity:
– Mode shapes used as shape functions in a nonlinear beam model (Rayleigh-Ritz method)
– Motions include radial shortening effect (geometric nonlinearity), important for centrifugal stiffening
– Inertial loads include nonlinear centrifugal, Coriolis, & gyroscopic terms
dh
dh u(h,t)
w(h,t)
u(h+dh,t) w(h+dh,t) g
h
h=0
h=H u(h,t)
w(h,t)
( ) ( ) 2
0
',1, '2 '
h u h tw h t dh
h ∂
= ∂ ∫
Radial Shortening Effect
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Theory Basis Rotations
• Support platform pitch, roll, & yaw rotations; blade deflections; & tower deflections employ small-angle approximations (no sequence) with nonlinear correction for orthogonality: – Transformations loose considerable accuracy for angles >> 20˚
• All other DOFs may exhibit large motions w/o loss of accuracy
3 2
3 1
2 1
11
1
θ θθ θθ θ
− ≈ − −
1 1
2
3
2
3
XXX
xxx
1X
2X
3X
1θ
1x
2x
3x
2θ
3θ
1
2θ3θ
1
1θ2θ
1 3θ
1θ
Correction for Orthogonality
( ) ( ) ( ) ( )( ) ( ) ( ) ( )
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 1 2 3 2 3 3 1 2 3 1 2 1 2 3 2 1 2 3 1 3 1 2 3
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 23 1 2 3 1 2 1 2 3 1 2 1 2 3 3 1 1 2 3 2 3 1 2 3
1 1 1 1 1
1 1 1 1 1
θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ
θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ
θ
+ + + + + + + + + + + − − + + + + + + − − + + + + + + − + + + + + + + + + + + −=
1
2
3
xxx ( ) ( ) ( ) ( )
( )
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 1 2 3 1 3 1 2 3 1 1 2 3 2 3 1 2 3 1 2 3 1 2 3
2 2 2 2 2 21 2 3 1 2 3
1 1 1 1 1
1
θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ
θ θ θ θ θ θ
+ + + + + + − − + + + + + + − + + + + +
+ + + + +
1
2
3
XXX
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Input Geometry Turbine Parameterization – Upwind, 3-Blader
Wind
Rotor Axis
Yaw Axis
TipRad
Precone(negative as shown)
Apex of Coneof Rotation
ShftTilt(negative as shown)
OverHang
Nacelle C.M.
Hub C.M.
HubCM(negative as shown)
Pitch Axis
HubRad
TowerHt
(negative as shown) Twr2Shft
Yaw BearingC.M.
NacCMzn
NacCMxn
NcIMUzn
NcIMUxn
Nacelle IMU
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Input Geometry Turbine Parameterization – Downwind, 2-Blader
Wind
Teeter Pin
UndSling
HubCM
OverHang
Teeter Pin
HubRadPitch Axis
Rotor Axis
TipRad
TowerHtApex of Cone
of Rotation
Hub C.M.
Nacelle C.M.
PreCone
Teeter
Apex of Coneof Rotation
Yaw Axis
Rotor Axis
Twr2ShftNacCMzn
NacCMxn
ShftTilt
Yaw BearingC.M.
NcIMUzn
NcIMUxn
Nacelle IMU
TeeterAxis
LookingDownwind
+δ3
Directionof
Rotation
Leading Edge
Structural Features of FAST v8 Compared to v7
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FAST Features v7.02 v8.08 • Blade-bending DOFs • Rotor-teeter DOF • Generator azimuth and drivetrain torsion DOFs • Nacelle-yaw DOF • Tower-bending DOFs • Rigid-body platform DOFs • Furling DOFs • Fixed-bottom multi-member substructure DOFs • Gravitational loading • Gearbox friction • System of independent mooring lines solved quasi-statically • System of multi-segmented mooring lines solved quasi-statically • Mooring dynamics • Earthquake excitation
• This workshop will apply FAST v8 • All new features are being added to the new framework • Until all features of v7 are included in v8, both will be supported
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Modeling Guidance
• Integration method & time step: – Method = 3 – ABM4 – DT = 1/(10*highest frequency in Hz)
• Initial conditions – to minimize start-up transients: – RotSpeed = nominal speed for given mean wind speed – BldPitch = nominal angle for given mean wind speed
• Disable DOFs to debug problems • Disabling a DOF means that acceleration will be zero, velocity
will be constant, & displacement will vary linearly (if constant velocity is nonzero), regardless of loads applied: – Inside ElastoDyn, EoM for disabled DOFs are not formulated, resulting
in no acceleration of those DOF
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Modeling Guidance (cont)
• Blade & tower mode shapes: – Tower mode shapes depend on substructure mass/stiffness & tower-
top mass/inertia – Recompute with change to substructure or tower-top – Blade mode shapes depend on rotational speed & blade-pitch angle –
Typically fine to use rated conditions – Structural pretwist in blades leads to coupling between flap & edge – Use BModes & ModeShapePolyFitting.xls to derive mode shapes – Use mass & stiffness tuning factors for minor adjustments to match
known data (e.g. natural frequencies or overall mass/centers)
• Blade & tower discretization: – TwrNodes ~ 20 – Tower discretization in ElastoDyn is currently used by AeroDyn – BldNodes ~ 20 (in AeroDyn) – Blade discretization in AeroDyn is currently used by ElastoDyn
• Use different blade files to model rotor mass imbalances
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Recent Work & Current & Planned Work
• Recent work: – Split out ElastoDyn as a
callable module in the FAST framework with separate input files & source code
• Current & planned work: – Address current limitations
of FAST v8 relative to v7 – Reorganize ElastoDyn
source code for improved computational speed
– Add nacelle-based mass-damper DOFs (with UMass)
Nacelle-Based Mass-Damper
Lackner & Rotea (2011)
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Current & Planned Work (cont)
G. Bir, NREL
Blade Twist Induced By Anisotropic Layup
Thomsen (2013)
Advancement in Blade Design from 1990s to Today
• Incorporate higher-fidelity modeling of blades (BeamDyn): – Based on Geometrically Exact Beam
Theory (GEBT): • Linearly elastic material • Full geometric nonlinearity
– Bending, torsion, shear, & extensional DOFs
– Anisotropic material couplings (full 6x6 mass & stiffness matrices from PreComp, NuMAD, or VABS)
– Sectional mass & elastic offsets – Built-in curvature & sweep – Phase I - Spectral finite element (FE) – Phase II – Improved modal method
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Future Opportunities
• Publish ElastoDyn Theory Manual • Introduce built-in foundation models • Add blade-pitch DOFs • Add drivetrain dynamics
& shaft deflection DOFs • Improve friction models
for yaw, teeter, & furling • Develop a nonlinear beam
FE with fewer than 6 DOFs per node
• Develop general capability for hinged & segmented blades
SIMPACK Gearbox
Simplified Models of a Monopile with Flexible Foundation
Apparent Fixity Model
Coupled Springs Model
Distributed Springs Model
Questions?
Jason Jonkman, Ph.D. +1 (303) 384 – 7026 [email protected]
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.