MudlineMSL

Fixed Base Coupled Springs Distributed SpringsApparent Fixity

Foundation Models for Offshore Wind Turbines

Erica Bush and Lance Manuel University of Texas at Austin

Problem Overview

Characteristic loads for reliability-based design of offshore wind turbines can be derived from time-domain aeroelastic-hydrodynamic response simulations

Design load = Load Factor × Characteristic Load

Accuracy of derived characteristic loads depends on number of simulations run accuracy of critical sea state selection (when using

Inverse FORM) accuracy of the simulation models used

ObjectiveCompare loads derived from alternative foundation model using simulations

5 MW baseline offshore wind turbine developed at the National Renewable Energy Laboratory (NREL)

11.5 m/s rated wind speed

FAST is used to simulate waves and turbine response; TurbSim is used to simulate wind

126 m

90 m

20 m

36 m

Mudline

Hub

MSL

Tapers linearly upward

Outer diameter = 3.87 mWall thickness = 1.9 cm

Outer diameter = 6 mWall thickness = 2.7 cm

Outer diameter = 6 mWall thickness = 6 cm

not to scale

Wind Turbine Model

MudlineMSL

Fixed Base Coupled Springs Distributed SpringsApparent Fixity

Foundation Models Different properties and dimensions need to be specified for each model These properties and dimensions depend on the sea state considered We discuss how they are computed and then used in FAST

STEP 1 STEP 2 STEP 3

36 m

AFL, EI

MFF

M

Ѳ

w w

Ѳ

MF

Apparent Fixity Model

From a fixed base simulation, obtain shear, F, and moment, M, values at the mudline in the fore-aft direction

STEP 1 STEP 2 STEP 3

36 m

AFL, EI

MFF

M

Ѳ

w w

Ѳ

MF

Apparent Fixity Model

Determine the corresponding deflection, w, and rotation, Ѳ, for the real pile

STEP 1 STEP 2 STEP 3

36 m

AFL, EI

MFF

M

Ѳ

w w

Ѳ

MF

Apparent Fixity Model

Calculate the length and stiffness of a cantilever that would produce the same deflection and rotation for the given shear and moment

For each sea state, 50 contemporaneous shear (F) and moment (M) pairs at the tower base in the fore-aft direction are randomly selected from a single fixed base simulation idea: to calibrate flexible foundation model for anticipated loads from what’s above the mudline

Are 50 random pairs selected from one fixed-base simulation representative?

Step 1: Shear and Moment Values

Sea State 1Simulation A Simulation B

μF (kN)

μM (kN-m)

ρF,MμF (kN)

μM (kN-m)

ρF,M

50 Random Pairs 555 63210 0.86 615 64374 0.73

Time Series 576 64809 0.80 572 64709 0.78

Sea State 2Simulation A Simulation B

μF (kN)

μM (kN-m)

ρF,MμF (kN)

μM (kN-m)

ρF,M

50 Random Pairs 315 33448 0.80 157 33041 0.92

Time Series 306 34652 0.88 322 35567 0.88

We use LPILE to perform lateral pile analysis (with p-y curves) in order to determine the deflections and rotations of the real pile based on each of the shear and moment pairs

The p-y curves for the lateral force-displacement relationships are based on API guidelines

A pile length of 36 m below the mudline and this sand profile were chosen based on previous work (Passon, 2006; Jonkman et al., 2007)

γ = 10 kN/m3

Ф’ = 38.5°k = 35288 kN/m3

22 m

Sand 1γ = 10 kN/m3

Ф’ = 33°k = 16287 kN/m3

5 m

Sand 2γ = 10 kN/m3

Ф’ = 35°k = 24430 kN/m3

9 m

Sand 3

Soil Profile Considered

Step 2: Deflections and Rotations

FM

L, EI L, EI

L = AFLEI = Stiffness

Step 3: Equivalent Length and Stiffness

L and EI are calculated for each of the 50 randomly selected shear and moment pairs

The average L and EI is then used in the model

Coupled Springs Model

Spring stiffnesses are calculated from the AFL and EI

Flexibility Matrix Stiffness Matrix

Coupled Springs Model

Note that the AFL and EI were calculated from shear and moment in the fore-aft direction

But the translational and rotational springs will be attached in both horizontal directions (totaling four coupled springs)

Heave and yaw DOF are turned off FAST must be recompiled with this platform stiffness matrix

surge

roll

yaw pitch

heave

sway

wind

The sea state must be represented by a single shear and moment pair

The shear and moment pair that has an AFL closest to the average AFL is selected from the 50 contemporaneous pairs

Distributed Springs Model

Shear Moment Deflection RotationAFL EI

F M w θ

(kN) (kN-m) (cm) × 10-3 (rad) (m) (kN-m2)

1 1417 69170 1.16 0.001255 17.63 1.15E+09

2 61.7 54860 0.72 0.000848 16.97 1.11E+09

: : : : : : :

8 298.3 46890 0.66 0.000756 17.13 1.12E+09

: : : : : : :

48 850.5 87100 1.30 0.001462 17.40 1.12E+09

49 739.4 70640 1.06 0.001185 17.34 1.13E+09

50 -413 43990 0.50 0.000619 16.49 1.08E+09

Average 17.13 1.12E+09

Note: V = 12 m/s is shown in table

.

.

.

LPILE is run with the chosen shear and moment pair

We discretize the embedded pile at 252 points; LPILE gives the distributed lateral resistance and deflection at each point

The lateral spring stiffness is calculated at each point by dividing the distributed resistance (kN/m) by the deflection (m) and, then, multiplying by the tributary length (m) for that point result: spring stiffness for each point in kN/m

We reduce the number of springs to 37 at 1-meter spacing by adding stiffnesses at points within the tributary length of each discrete spring

FAST is recompiled with these spring stiffnesses for each simulation with the distributed springs model

Distributed Springs Model

.

.

.

Random wind loading 3-D Inflow turbulence random field

over a 2-D rotor plane uses Kaimal power spectrum and exponential coherence spectrum

Random wave loading Irregular long-crested waves are

simulated using a JONSWAP spectrum, Airy wave kinematics, and Morison’s equation

Structural response Combine modal and multi-body

dynamics formulation (includes control systems)

Wind load

Wave load

u

v

w

Loading Models

Rosenblatt Transformation

vFu V1Φ

hFu VH |2Φ

= Reliability index 22

221 βuu

(-) = PT = Target Failure Probability

U2

U1

V (m/s) Hs (m) Tp (s)

10 5.5 5.8

12 6.2 6.2

14 6.9 6.5

16 7.5 6.8

18 8.1 7.1

20 8.6 7.3

22 9.0 7.5

Selecting Critical Sea States

20-year return period considered (T = 20 yrs)

PT = 1/(20 × 365.25 × 24 × 6) = 9.51 × 10-7 (load exceedance probability in 10 mins) = 4.76

2D Inverse FORM (Environmental Contour Method)

V (m/s)

Mean (MN-m)

Std. Dev. (MN-m)

Max (MN-m)

12 66.0 16.2 119.2

22 34.8 18.7 105.5% Inc.

12-22 m/s -47 15 -11

PF (max)

Skewness KurtosisUpcrossing

Rate (s-1)

3.27 0.01 2.89 0.29

3.78 0.03 3.25 0.36

16 n/a 12 24

Mean + (Std. Dev.)(PF) = Max

+ x =

Fore-Aft Tower Bending Moment at the Mudline for Fixed Base Model (150 sims)

Summary Statistics ( V = 12 vs. 22 m/s)

V (m/s)

Mean (MN-m)

Std. Dev. (MN-m)

Max (MN-m)

12 66.7 19.5 130.1

22 35.2 23.1 112.9% Inc.

12-22 m/s -47 19 -13

PF (max)

Skewness KurtosisUpcrossing

Rate (s-1)

3.25 0.02 2.93 0.21

3.36 -0.07 3.10 0.22

3 n/a 6 3

Fore-Aft Tower Bending Moment at the Mudline for Apparent Fixity Model (150 sims)

Going from 12 to 22 m/s (with either fixed base or AF model)

V (m/s)

Mean (MN-m)

Std. Dev. (MN-m)

Max (MN-m)

12 66.0 16.2 119.2

22 34.8 18.7 105.5

PF (max)

Skewness KurtosisUpcrossing

Rate (s-1)

3.27 0.01 2.89 0.29

3.78 0.03 3.25 0.36

Fore-Aft Tower Bending Moment at the Mudline for Fixed Base Model (150 sims)

Summary Statistics (Fixed vs. Flexible)

V (m/s)

Mean (MN-m)

Std. Dev. (MN-m)

Max (MN-m)

12 66.7 19.5 130.1

22 35.2 23.1 112.9

PF (max)

Skewness KurtosisUpcrossing

Rate (s-1)

3.25 0.02 2.93 0.21

3.36 -0.07 3.10 0.22

Fore-Aft Tower Bending Moment at the Mudline for Apparent Fixity Model (150 sims)

Consider 12 m/s sea state only

With change from fixed-base to flexible model Mean is unchanged; SD increases by ~20%, PF is unchanged;

hence max increases but by only ~10% [since max = mean + SD × PF]

Max = Mean + (Std. Dev.)(PF)

Summary Statistics

ModelMean

(MN-m)Std. Dev.(MN-m)

Max (MN-m)

Fixed 66.0 16.2 119.2

AF 66.7 19.5 130.1

CS 64.6 22.4 138.7

DS 64.5 20.1 132.6

PF (max)

Skewness KurtosisUpcrossing

Rate (s-1)

3.27 0.01 2.89 0.29

3.25 0.02 2.93 0.21

3.30 0.04 2.92 0.20

3.38 0.03 2.91 0.26

Fore-Aft Tower Bending Moment at the Mudline for V = 12 m/s (150 sims)

• Mean trend matches control system’s dependence on mean wind speed

• All models are seeing the same wind and wave time series; so, control system behaves the same way as far as mean load goes

• Only about 3% difference between largest and smallest mean (among models)

fff

wind structure TBM

Summary Statistics

ModelMean

(MN-m)Std. Dev.(MN-m)

Max (MN-m)

Fixed 66.0 16.2 119.2

AF 66.7 19.5 130.1

CS 64.6 22.4 138.7

DS 64.5 20.1 132.6

PF (max)

Skewness KurtosisUpcrossing

Rate (s-1)

3.27 0.01 2.89 0.29

3.25 0.02 2.93 0.21

3.30 0.04 2.92 0.20

3.38 0.03 2.91 0.26

Fore-Aft Tower Bending Moment at the Mudline for V = 12 m/s (150 sims)

Max = Mean + (Std. Dev.)(PF)

Summary Statistics

ModelMean

(MN-m)Std. Dev.(MN-m)

Max (MN-m)

Fixed 66.0 16.2 119.2

AF 66.7 19.5 130.1

CS 64.6 22.4 138.7

DS 64.5 20.1 132.6

PF (max)

Skewness KurtosisUpcrossing

Rate (s-1)

3.27 0.01 2.89 0.29

3.25 0.02 2.93 0.21

3.30 0.04 2.92 0.20

3.38 0.03 2.91 0.26

Fore-Aft Tower Bending Moment at the Mudline for V = 12 m/s (150 sims)

Max = Mean + (Std. Dev.)(PF)

• PF = f(exposure time, asymmetry, tails, upcrossing rate)

• Only about 4% difference between flexible foundation models

Summary Statistics

PF (max)

Skewness KurtosisUpcrossing

Rate (s-1)

3.27 0.01 2.89 0.29

3.25 0.02 2.93 0.21

3.30 0.04 2.92 0.20

3.38 0.03 2.91 0.26

Fore-Aft Tower Bending Moment at the Mudline for V = 12 m/s (150 sims)

Max = Mean + (Std. Dev.)(PF)

• The variability in maxima for the four models mostly depends on std. dev.

• As std. dev. increases, the max increases

ModelMean

(MN-m)Std. Dev.(MN-m)

Max (MN-m)

Fixed 66.0 16.2 119.2

AF 66.7 19.5 130.1

CS 64.6 22.4 138.7

DS 64.5 20.1 132.6

High frequency peaks shift left as the upcrossing rate for the model decreases

AF and CS have very similar behavior because they tell FAST effectively the same information However, the AF model

has more inertia by design

AF has slightly less power than CS as seen in the smaller std. dev.

Power Spectra

Exceedance Plots

Median of 10-min. extreme can be taken as 20-year characteristic value (Inverse FORM)

20-year loads for the flexible models differ by less than 6% (from each other)

All four models have 90% confidence interval < 4 MN-m (on 20-year load) based on bootstrap estimation

150 simulations are sufficient for 2D Inverse FORM

Tails will be more important for 3D Inverse FORM

Then, more simulations will be necessary

Fixed AF CS DS

119.0 129.6 137.2 132.3

Median of 10-min. Extremes (MN-m)

Medians of 10-min. extremes for this sea state are not associated with 20-year load because they are not the largest on the environmental contour

Medians for the three flexible models differ by less than 1% (from each other)

Statistics and power spectra have similar trends to the 12 m/s case

Fixed AF CS DS

103.9 110.5 110.5 109.6

Median of 10-min. Extremes (MN-m)

Another Sea State

Fore-Aft Tower Bending Moment at the Mudline for V = 22 m/s (150 sims)

Recipe for Use of Flexible Foundation Models

• Each sea state requires the following steps:

STEP 1 Run one fixed base simulation, and select 50 random shear and moment pairs from the time series.

STEP 2 Run LPILE for all 50 load pairs, and calculate the AFL and EI for each pair.

STEP 3 AF model Use the average AFL and EI.

CS model Use the average AFL and EI to calculate the coupled spring constants.

DS model Choose the shear and moment pair that produces an AFL and EI closest to the average. Run LPILE for this pair, and calculate distributed

spring constants from the output.

STEP 4 Run N simulations per model, and extract N 10-min extremes. (N = 150 was used here apply Inverse FORMto get long-term load)

• The three flexible models yield 20-year loads that are within 6% of each other when using 2D Inverse FORM to evaluate critical sea states

• The three flexible models seem fairly interchangeable, but AF may be the easiest to implement because FAST does not need to be recompiled

Conclusions

• The AF and CS models do not have same mass as the original structure

• Evaluate alternative inertia distributions for these

• Verify whether 50 random (F, M) pairs from a single FB simulation are sufficient

• Perform 3D Inverse FORM (a more accurate approach to sea state selection)

• Well-behaved tails are required for acceptable confidence in 20-year loads

• More simulations are necessary to produce well behaved tails

• Study other soil profiles to evaluate flexible foundation models

Future Work

Dr. Jason Jonkman of the National Renewable Energy Laboratory

Dr. Puneet Agarwal, former student of Dr. Lance Manuel

Dr. Shin Tower Wang of Ensoft, Inc.

National Science Foundation

Grant No. CMMI-0449128 (CAREER)

Grant No. CMMI-0727989

Acknowledgments