Chungwook Sim1

Sukanta Basu2

Lance Manuel1

1University of Texas at Austin2Texas Tech University

Paper No. AIAA-2009-140528th ASME Wind Energy Symposium

Held in conjunction with the 47th AIAA Aerospace Sciences Meeting and Exhibition, Orlando, FL

January 8, 2009

The Influence of Stable Boundary Layer

Flows on Wind Turbine Fatigue Loads

MotivationNeutral atmospheric stability conditions form the basis for turbine design. However, near-neutral conditions occur only twice per day (sunrise and sunset).

Stable conditions occur generally at night – turbulence is generated by shear then, while negative buoyancy limits turbulence.

Stable BL flows are often accompanied by low-level jets (LLJs); wind shear is different from what is assumed in neutral conditions. These LLJs can be low enough to impact today’s large utility-scale turbines.

We compare turbulence, turbine loads, and accumulated fatigue damage for a utility-scale wind turbine for stable versus neutral atmospheric conditions.

Outline

Introduction Large-Eddy Simulation Fractal Interpolation

Turbine Response Simulations Blade & Tower Loads

Fatigue

Sensitivity Study on Stable BL Flow Parameters Geostrophic wind speed Surface temperature cooling rate

Conclusions

Introduction – Large-Eddy Simulation (LES)

Reynolds-Averaged Navier-Stokes (RANS)

model just ensemble statistics

Direct Numerical Simulation (DNS)

resolve all eddies

Large-Eddy Simulation (LES)

resolve larger eddies & model smaller ones

Computational

Boundary

Complexity (Re, geometry)

Res

olut

ion

DNS

LES

RANS

DNS of ABL turbulence over a domain of 10 km x 10 km x 1 km would require:

1020 grid points!!!

NOT yet computationally feasible

Introduction – Large-Eddy Simulation (LES)

Resolved

Log(k)

Log(

Ek)

kc = /f

Subgrid iu iu

Subgrid

iu

iu

Resolved

Physical Space Fourier Space

Introduction – Large-Eddy Simulation (LES)

DNS

LES

Unknown subgrid-scale (SGS) term due to the nonlinear term in the original SBE equation

1-D Example: Stochastic Burgers Equation (SBE)

filter

Introduction – Large-Eddy Simulation (LES)

Need to model:

Unknown: either prescribe or determine empirically (Germano’s dynamic modeling approach)

Smagorinsky SGS Model:

Introduction – Large-Eddy Simulation (LES)

DNS (8192 grid points)

LES (512 grid points)

1-D Example: Stochastic Burgers Equation (SBE)

Introduction – Large-Eddy Simulation (LES)

DNS (8192 grid points)

LES (512 grid points)

LES is not simulating these high-wavenumbers. A good SGS model tries to account for these wavenumbers effectively.

1-D Example: Stochastic Burgers Equation (SBE)

Introduction – Large-Eddy Simulation (LES)

3-D Example: Atmospheric Boundary Layer Turbulence

Introduction – Large-Eddy Simulation (LES)

where

where

Smagorinsky SGS Model:

CHALLENGE: How do we specify/determine CS,

PrSGS ?Locally Averaged Scale-Dependent Dynamic Model (Basu and Porté-Agel,

2006)

Introduction – Large-Eddy Simulation (LES)

Domain of size: 800 m × 800 m × 1280 m

Phase 1:Simulation time: 12 hours Time step: 0.2 sGrid spacing: 20 m in each direction

Phase 2:Simulation time: 30 minutesTime step: 0.1 sGrid spacing: 13.3 or 20 m in each direction

Full-field wind files for 3-D velocity components are output from the last 15 minutes of these 30-minute phase II simulations at a frequency of 2.5 Hz.

Introduction – Large-Eddy Simulation (LES)

Introduction – Fractal Interpolation

XDomain of size: 800 m × 800 m × 1280 m

Phase 1:Simulation time: 12 hours Time step: 0.2 sGrid spacing: 20 m in each direction

Phase 2:Use fractal interpolation to (synthetically) generate small-scale turbulence

Turbine Response Simulations

Parameters Values

Hub Height 90 m

GeostrophicWind Speed

5 m/s, 10 m/s, 15 m/s

Cooling rate 0.01, 0.25, and 0.5 K/hr

Grid Spacing 20 m, 13.33 m

Surface Roughness 0.1 m

TurbSim (Jonkman and Buhl, 2008) for neutral BL flows

LES (Basu and Porte-Agel 2006) for stable BL flows

Aeroelastic Simulation using FAST (Jonkman and Buhl, 2005) for rotor and tower loads

Fatigue Damage Calculation: Rainflow-Cycle Counting (ASTM, 1985)ASTM, 1985, Standard Practices for Cycle Counting in Fatigue Analysis, American Society for Testing and Materials Standards, E1049-85.Basu, S., Porte-Agel, F. (2006). “Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: a scale-dependent dynamic modeling approach”, Journal of the Atmospheric Sciences, 63, 2074Jonkman, B.J. and Buhl, M.L., Jr. (2008), “TurbSim User’s Guide for Version 1.30,” National Renewable Energy Laboratory.Jonkman, J. M. and Buhl, M. L. Jr. (2005), FAST User’s Guide, National Renewable Energy Laboratory, NREL/EL-500-38230, Golden, CO.

Grid Resolution and Fractal Interpolation

Base Case Inflow: GWS = 15 m/s, CR =0.25 K/hr (20-meter grid spacing)

Neutral vs Stable: Low-frequency energy is similar but high-frequency energy is reduced in stable case with coarse grid (20-meter spacing)

Finer Grid and Fractal Interpolation: Increase in energy at high frequencies is significant, especially for the fractal interpolation case, where the energy is now comparable with neutral case

Power Spectral Densities and cumulative variance plot of Inflow Turbulence

Blade & Tower Loads

Blade loads: Despite differences in turbulence PSDs, rotor load PSDs are remarkably similar

Tower loads: Without fractal interpolation, tower resonant modes are more clearly evident in the stable case since the background energy is absent compared to the neutral BL case. With the interpolation, tower load PSDs are comparable for neutral and stable cases.

Power Spectral Densities and cumulative variance plots of Blade and Tower Loads

Fatigue Loads of Stable vs Neutral BL Flows

Equivalent Fatigue Load and Rainflow Cycle Counting Algorithm

Wohler exponent : m = 3 (steel) Tower loadsm = 10 (Composite) Blade loads

Fatigue Loads of Stable vs Neutral BL Flows

Blade histograms: Fractal interpolation case (magenta) indicates more large-amplitude load cycles (compared to LES cases without interpolation). Equivalent Fatigue Loads (EFLs) are comparable for neutral and stable cases.

Fatigue Loads of Stable vs Neutral BL Flows

Tower histograms: For the stable case, fractal Interpolation leads to almost a 40% increase in EFL (from 3.5 to 5.8). EFL values are still about 10% less than for the neutral case.

Sensitivity Study on Parameters of SBL Flow

Turbulence: In all stable cases, energy at lower frequencies is comparable and similar to that for the neutral case but significantly lower at high frequencies. Consistent with the larger forcing at higher geostrophic wind speeds, variance is largest for GWS = 15 m/s.

Tower Loads: Resonant component (seen at frequencies above ~ 0.3 Hz) grows with decreasing geostrophic wind speed. Possibly because background energy is lowest compared to the neutral case for the lowest geostrophic wind speeds.

PSDs for various Geostrophic Wind Speeds (15 m/s, 10 m/s, 5 m/s)

Sensitivity Study on Parameters of SBL Flow

Turbulence: Power spectral density of the longitudinal velocity component suggests that with decrease in the cooling rate, energy shifts slightly to somewhat higher frequencies.

Tower Loads: Changes in cooling rates do not seem to affect tower loads greatly; a very slight increase in high-frequency energy is evident with lower cooling rates in the tower loads as was the case with the inflow turbulence.

PSDs for various Surface Cooling Rates (0.05 K/hr, 0.25 K/hr, 0.5 K/hr)

Conclusions

Near-neutral atmospheric stability conditions are all that are addressed in today’s wind turbine design guidelines.

It has been suggested that stable BL flows accompanying high wind shears and low-level jets (especially at Great Plains sites with good wind resources) occur at times where a disproportionately higher no. of turbine faults have occurred.

LES offers a means of simulating stable BL flows that can be input in turbine response simulations to assess designs. FIT can help resolve high-frequency turbulence that might influence rotor and tower loads on a turbine.

By varying cooling rates and geostrophic winds, LES, FIT, and turbine load simulations have been studied. Fatigue damage predictions for neutral and stable BL flows have been compared.

Additional work is underway to aid in wind turbine reliability analysis that accounts for different atmospheric stability conditions.

Acknowledgements

Sandia National LaboratoriesContract No. 743358

National Science FoundationGrant No. ATM-0748606

Texas Higher Education Coordinating Board

Grant No. 003658-0100-2007

Paul S. Veers (Sandia National Laboratories)Andy Swift (Texas Tech University)