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

Wind Turbine Modeling Workshop 2 National Renewable Energy Laboratory

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

Wind Turbine Modeling Workshop 16 National Renewable Energy Laboratory

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

Wind Turbine Modeling Workshop 19 National Renewable Energy Laboratory

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)

Wind Turbine Modeling Workshop 20 National Renewable Energy Laboratory

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 jason.jonkman@nrel.gov

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.