Nwtc seminar overview of the impact of turbulence on turbine dynamics and their simulation, september 21, 2011

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.
The Atmospheric Dynamics Associated with Turbine
Dynamic Response and Their Simulation
NWTC Seminar
Neil D. Kelley
September 21, 2011
Innovation for Our Energy Future

Outline
2
• What we learned from the first seminar
• Role of atmospheric buoyancy and stability on turbine dynamic
response
• What atmospheric process is responsible for the observed
turbine response?
• Identification of a critical stability range, the atmospheric
dynamics associated with it, and the resulting turbine response
• Extending our research to the Great Plains turbine operating
environment
• The development of the TurbSim simulation code
• Conclusions and recommendations

What We Learned From the First Lecture
3
• The ingestion of coherent turbulent structures by the turbine rotors
was responsible for the large, damaging fatigue loads observed but
not modeled by the SNLWIND-3D simulation code
• The greatest turbine dynamic response occurs in a narrow, weakly
stable range of the turbine layer Richardson number stability
parameter: +0.01 ≤ RiTL < +0.05 can also contain significant levels of
coherent turbulent kinetic energy Ecoh.
RiTL
-0.3 -0.2 -0.1 0.0 0.1 0.2
HubPeakEcoh(m2
s-2
)
20
30
40
50
60
6
8
10
12
14
16
18
20
22
24
26
kNm
FBM
DEL
Peak
Response
@ RiTL = +0.02

Significant Turbulence Activity Occurs at RiTL = +0.02
 Maximum Turbine Dynamic Response
4
RiTL
-0.2 -0.1 0.0 0.1 0.2
w'T'(o
K-ms-1
)
0
2
4
6
8
10
12
u'w'(m2
s-2
)
-5
-4
-3
-2
-1
0
w'T'
u'w'
RiTL
-0.2 -0.1 0.0 0.1 0.2
PositivePeakw'Ecoh(m3
s-3
)
-300
-200
-100
0
100
200
300
400
NegativePeakw'Ecoh(m3
s-3
)
-600
-400
-200
0
200
400
RiTL
-0.2 -0.1 0.0 0.1 0.2
Ecoh
(m2
s-2
)
2
3
4
5
cohEσ
Intense downward momentum flux u′w′ (shear stress)
Rapid decrease in mean buoyancy, w′ T′
Rapid suppression of peak vertical fluxes of Ecoh
Rapid suppression of vertical velocity fluctuations, σw

Conclusion . . .
5
Atmospheric Buoyancy Is a Major Player as
Revealed by RiTL!

Remembering this demonstration from the first
lecture . . .
Time
An example of dynamic instability
The right combination of vertical temperature
stratification and wind speed shear (Ri ) can
produce an vertical oscillatory or resonant
response in the wind field
Height
warm air
cold air

Define Buoyancy Length Scale, Lb
7
Lb = σw /Nbuoy
where Nbuoy = buoyancy or Brunt-Väisälä frequency
=
and
σw = vertical velocity standard deviation
Relationship between Ri and Nbuoy
2 2
/ ( / )buoyRi N u z= ∂ ∂
Lb is a measure of the maximum buoyant displacement of air
parcels and is the wavelength of the dominant instability mode.
1/2
[( / )( / )]g T T z∂ ∂

Scaling Lb
8
If we scale Lb with respect to the turbine rotor dimensions
by normalizing it by its diameter or
Lb /D
then Lb /D = 1 equates the dominant wavelength of the
flow instability is the same as the rotor diameter.
We will see that helps us explain the physics
behind the highest turbine dynamic response
in the critical +0.01 ≤ RiTL < +0.05 range

Lb /D is an indicator of the degree turbulent eddies are being
damped by negative buoyancy as seen on the ART Turbine
9
PeakFlapwiseStressCycle(kNm)
0
100
200
300
400
500
600
TurblinelayerRi
0.001
0.01
0.1
1
TL Ri vs TL Lb/D
Turbine layer lb/D
0.1 1 10
HubPeakCTKE(m2
/s2
)
1
10
100
Turbine layer Ri
0.0001 0.001 0.01 0.1 1
TurbineLayerlb/D
0.1
1
10
moderate
buoyancy
damping
Buoyancy Damping
Limits Coherent Structure
Size & Intensity and
Reduces Induced Stress
Cycle Magnitude
Lb= buoyancy length scale,
D = rotor diameter
/b w buoyL Nσ=
Turbine layer Lb /D
zero to
very low
buoyancy
damping
critical
RiTL
range
highest
buoyancy
damping

Influence of Increasing Stability and its Damping Effects
on Turbulent Eddies . . .
10
As the air flow becomes more stable; i.e., the Ri increases
due to the air cooling near the ground which
• increases the temperature gradient (∆T/∆z) across the turbine
rotor disk
• the rising air contained in the turbulent eddies then sees more
resistance due to negative buoyancy
• the largest turbulent eddies are affected first limiting their
maximum size.

Definition of Stability Classes
11
Stability Class Designation Range
Moderate to Weakly Unstable
Class, STC02
-1 < RiTL ≤ 0
Weakly Stable Critical Range,
CRR
+0.01 ≤ RiTL < +0.05
Weakly Stable High Range Critical,
CRRH
+0.05 ≤ RiTL < +0.10
Moderately Stable Range,
STC04
+0.10 ≤ RiTL < +0.25
Very Stable Range,
STC05
+0.25 ≤ RiTL < +1.0
Based on Turbine Layer Gradient Richardson Number, RiTL

Mean and Peak Root Flapwise Bending Fatigue Load
Distributions by Stability Class Comparisons
12
Peak FBM Load
Stability class
STC02 CRR CRRH STC04
100
200
300
400
500
600
700
Root FBM DEL Distributions
50
100
150
200
250
300
NWTC ART Turbine Response
NREL Rotor Root FBM 3-Blade Mean DELs
kNm
4
8
12
16
20
24
NREL Rotor Peak Root FBM
Stability Class
4
8
12
16
20
24
28
32
36
San Gorgonio Micon 65 Turbine Response
STC02 CRR CRRH STC04 STC02 CRR CRRH STC04
San Gorgonio Micon 65 NWTC ART
kNm
Stability class
Means
Peaks

Lb /D Relationships to Turbine Response DELs
13
Peak
Response
Micon 65s NWTC ART
Peak
Response
CRR CRRHSTC02 STC04 CRR CRRHSTC02 STC04

If we now look at the observed distributions of Lb /D by
stability class
14
San Gor NREL Rotor
Lb/D
0.0
0.5
1.0
1.5
2.0
2.5
not defined
ART Turbine
Stability class
Lb/D
0.0
0.5
1.0
1.5
2.0
2.5
not defined
Stability class
San Gorgonio Micon 65
NWTC ART
Lb/D
1.0
1.0
The largest turbine dynamic loads
that occur in the CRR stability
class correspond to Lb /D = 1
or a buoyant wavelength of the
same approximate dimension
as the turbine rotor diameter!
not defined
not defined

The Buoyancy Damping Present Influences the Nature
of the Transient Loads Seen on Wind Turbines
Turbine layer Ri
0.0001 0.001 0.01 0.1 1
TurbineLayerlb/D
0.1
1
10
moderate
buoyancy
damping
Ri =+0.034Ri = +0.007
Upwind array
inflow CTKE
m
2
/s
2
0
20
40
60
80
100
120
0
20
40
60
80
100
120
rotor top (58m)
rotor hub (37m)
rotor left (37m)
rotor right (37m)
rotor bottom (15m)
IMU velocity components
0 2 4 6 8 10 12
mm/s
-20
-10
0
10
20
-20
-10
0
10
20
Time (s)
492 494 496 498 500 502 504
vertical (Z)
side-to-side (Y)
fore-aft (X)
zero-mean
root flap
bending
moment
kNm
-400
-300
-200
-100
0
100
200
300
400
-400
-300
-200
-100
0
100
200
300
400
Blade 1
Blade 2
Ri = +0.015
critical
buoyancy
damping
high
buoyancy
damping
Micon 65/13 Micon 65/13
ART

Innovation for Our Energy Future16
What Atmospheric Process is Responsible ?

Atmospheric Dynamics Associated with CRR Stability
Range
17
Atmospheric Conditions . . .
 Narrow, weakly stable Ri range of +0.01 to +0.05
 High mean shear stress across rotor disk layer, u*
 Highest values of coherent turbulent kinetic
energy (Ecoh)
 Buoyancy length scale, Lb ≅ rotor disk diameter
 Evidence of significant increase in buoyancy damping
for Ri > +0.05 (CRRH range)
Conclusion: Some form of shear instability or instabilities present
• Kelvin-Helmholtz Instability (KHI)?
• internal gravity wave instability (GWI)?
RiTL
-0.3 -0.2 -0.1 0.0 0.1 0.2
Hublocalu*(ms-1
)
1.6
1.8
2.0
2.2
2.4
2.6
2.8
8
10
12
14
16
FBM DEL
(kNm)
NREL rotor
Micon 65/13 Dynamic Response
CRRCRRH

Comparisons of KHI and GWI Shear Instabilities
18
Kelvin-Helmholtz Instability (KHI) attributes that impact turbine dynamics . . .
 Turbulent perturbations in the flow initiate KHI that extract energy out of the mean flow to
create intense three-dimensional coherent turbulent filling the shear layer
 Majority of turbulent Ecoh is contained within the shear layer and decays rapidly away from it
 Formations of coherent turbulent structures or “patches” have a typical life span of 15-30
minutes which includes the initial rollup, rollover or breaking, and then decay.
 The life cycle of an individual KH billow or turbulent patch is the order of tens of seconds
Internal Gravity Waves (GWI) have different attributes . . .
 GWI turbulent structures are much thinner that those associated with KHI
 KE propagates away both upwards and downward from the shear layer in which it was formed
 GWI turbulent structures grow much slower than KHI and can persist for many hours
 May form at the conclusion of a KHI formation life cycle
CONCLUSION: KHI is the dominant atmospheric instability that affects the
dynamic response of turbines

KHI as revealed in a cloud formation
19
Growing billows
Initial
Shear
Layer
Roll Over &
Breakdown
(Turbulence
Phase)
Source: Adapted from “Kelvin-Helmholtz Clouds” (DI00152) by Terry Robinson, copyright University Corporation for Atmospheric Research
flow direction
2-D vortex
braid

KHI Dynamics
20
• The initial stages of KH billows growing within a stably stratified atmospheric
layer from a turbulent perturbation can be analyzed as an eigenvalue problem
• The billow can be represented as a spectral superposition of temporally
growing oscillatory velocity normal modes of the form
exp[ik(x-ct)]
where k is the wavenumber (or equivalently the wavelength) ,
c is the complex phase speed c = cr + ici
t is time.
cr is the speed of the perturbation in the direction of the background flow
kci is its rate of growth; i.e., growing modes are characterized by ci > 0.
• A necessary but not sufficient condition for KH billows or perturbations to grow
within the shear layer is
Ri < +0.25

If we have the vertical profiles of wind speed and
temperature which include a turbine rotor disk
21
U(z)
Height(z)
T(z)
U = tanh(z)
T = tanh(z)
→
→
↑
}Drotor
= shear layer depthRi

Relationships between Fastest Growing K-H Modes, Buoyancy
Length Scale, and Turbine Dynamic Response
22
K-H Mode
Fastest
Growth Rate
Adapted from: Rosenthal, A.J.;
Lindzen, R.S. Journal of the
Atmospheric Sciences (40:3)
Ri
Turbine layer Ri
Disk-Diameter Normalized
Buoyancy Length Scale, Lb /D
Micon 65/13 Turbine Dynamic
Responses (DEL)
CRR CRRH STCO4
max turbine
dynamic
response

Relationship Between KH Billow and Turbine Structural
Vibratory Modes
23
Variation of Range of K-H Mode Growth Rate
With Shear Layer Depth in Rotor Diameters
Adapted from Hogg and Ivey. Journal of Fluid Mechanics (477)
K-H Mode
Growth
Rates
Adapted from: Rosenthal, A.J.; Lindzen, R.S. Journal of the Atmospheric Sciences (40:3)
fastest
growing
K-H modes
• widest range of K-H mode wavelengths
matches up with the most structural modes
• narrower range of K-H mode wavelengths
matches up with fewer structural modes
slowest
growing
K-H modes
• narrowest range of K-H mode wavelengths
matches up with the fewest structural modes
fastest growing K-H modes
occur at Ri = +0.02 and
the shear layer depth
= buoyancy length scale
Lb /D =1; the rotor diameter!
Variation of Range of K-H Mode Wavenumbers
(Wavelengths) with Growth Rate
Corresponds to maximum
turbine dynamic response!
Mode wavenumbers (2π/λ) →

Summary of What We Have Found . . .
24
• Buoyancy length scale Lb coincides closely with the
fastest growing (most unstable) K-H mode.
• If Lb /D = 1, then it is a good predictor of significant
turbine dynamic response.
• If Lb = D then the equivalent wavelength of the fastest
growing or unstable mode is approximately the same
as the rotor diameter.
• This allows for the coupling of the coherent K.E.
contained in the higher order K-H modes into the
corresponding turbine structural modes.

Source: R. Banta, NOAA/ESRL
Horizontal distance (km)
Height(km)
NOAA HRDL LIDAR Observation of Wave
Motions in Stable Boundary Layer
in Southern Kansas
22:34 LST
Generation of Coherent Turbulence by Atmospheric
Wave Motions in Nocturnal Stable Boundary Layer
low-level
jet organized
turbulent air
motions from
waves
height of
wind speed
maximum
high vertical
shear
region
SCHEMATIC OF COHERENT
TURBULENCE GENERATION
waves
25

Role of Shear Layer Instability and Turbine Loads
Intense vertical shear
within rotor disk layer
provides
the catalyst for
developing
atmospheric wave
motions
Breaking KHI
atmospheric
wave motions
produce bursts
of coherent
turbulence
Transient loads
are induced when
turbine rotors
encounter
coherent
turbulent
regions
26

LIDAR Observations of Coherent Turbulent Structures In Stable
Nocturnal Boundary Layer
Buoyancy & vertical shear play a major role in shaping the
impact of coherent turbulent structures within shear layers in
the stable boundary layer and the subsequent impact on wind
turbine components
Height
Time
wind
turbines
Coherent turbulent structures observed in stable boundary layer by NOAA/ESRL HRDL Lidar in
southeast Colorado during NREL/NOAA Lamar Low-Level Jet Project, September 2003.
wind
speed profile
intense vertical shear
bursts of coherent
turbulent energy
27

Details of Coherent Turbulence Episode at Great Plains
Site Using LIDAR, SODAR, & Tower Measurements
28
wind
turbines
LIDAR
wind
profile
SODAR
wind
profile
SODAR
σw
profile
tower
measured
Ecoh
strong vertical motions

Turbulent Buoyancy and Coherent Events
29
coherent
structures
negative
buoyant
damping
buoyancy (w′ T′ )
Coh TKE (Ecoh)

How Does a Wind Turbine Respond to a KH Billow?
30
• Peter Sullivan and Ned Patton of NCAR/MMM created an non-
dimensionalized LES simulation of the life cycle of a stationary KH billow
turbulence structure for a shear layer Ri of +0.05.
• Marshall Buhl of the NWTC interfaced the NCAR KH billow simulation into
the NREL aerodynamics routine AeroDyn that is used to drive the NWTC
turbine dynamics simulations (FAST and MSC.ADAMS).
• The NCAR KH billow simulation was used to excite the dynamic simulation of
the 1.5 MW WindPACT virtual turbine using the MSC.ADAMS multi-body
code.
• We examined the turbine dynamic response to the KH billow simulation.

The Dominant Atmospheric Dynamics Associated with
the Critical Stability (CRR) Range
31
• Is weakly stable with the RiTL covering the range of +0.01 to +0.05
• Vertical shear exists
• The majority of the hub-height mean wind speeds are at or below rated,
however the highest mean wind speeds also occur within this range
• In the San Gorgonio wind farm a persistent downward buoyancy flux exists
that damps the largest turbulent eddy sizes
• The highest values of Ecoh occur within this range suggesting the frequent
appearance of coherent turbulent structures
• The buoyancy length scale is the same as the diameter of the Micon and ART
turbine rotor disks at least 50% of the time; i.e. Lb = Drotor
Atmospheric Flow Characteristics Associated with the
CRR Stability Classification . . .

Simulated 1.5 MW WindPACT Turbine Response to
Ingestion of NCAR LES KH Billow
32
m/s
15
16
17
18
UH
m/s
-2
-1
0
1
2
u'
v'
w'
m
2
/s
2
-2
-1
0
1
2
u'w'
u'v'
v'w'
Time (s)
0 50 100 150 200 250
m
2
/s
2
0.0
0.5
1.0
1.5
2.0
2.5
E
Ecoh
Simulated Hub-Height Inflow Wind & Turbulence
horizontal
wind speed
u′, v′, & w′
components
Reynolds
stresses
ET and Ecoh
billowbreakdown
1.5 MW WindPACT Turbine Inflow & Response
flapwise bending moment
continuous wavelet transform scalogram
discrete wavelet transform detail bands
reduction in root stresses from
mixing out of vertical shear

WindPACT Turbine Response to Coherent Structures in
Billow Breakdown
33
-30 -20 -10 0 10 20 30
Time Record 566
60
80
100
-30 -20 -10 0 10 20 30
Time Record 2500
60
80
100
-30 -20 -10 0 10 20 30
Time Record 4000
60
80
100
z(m)
-30 -20 -10 0 10 20 30
Time Record 5000
60
80
100
-30 -20 -10 0 10 20 30
x (m)
Time Record 6000
60
80
100
t = 0 s
t =
91.5 s
t =
166.2 s
t =
217.7 s
t =
271.7 s
rotor
plane
x (m)
z(m)
Billow breakdown beginning with
max 2-D structure
scalogram
of
continuous
wavelet
transform
detail
bands of
discrete
wavelet
transform
Root Flapwise Bending Load
Spectral Stress Distribution
phase coherent responses

Conclusions from Simulation
34
1. The turbine aeroelastic response prior to the KH billow breaking down was
dominated in the high blade cyclic root stresses as a result of the strong
shear across the rotor
2. The greatest transient loading takes place during and after the billow
breakdown when intense coherent turbulent structures are created in the
flow
3. Wavelet analysis shows that these loading transients contain significant
levels of coherent turbulent kinetic energy that induce phase coherent
dynamic responses in the blade root bending loads
4. These results are consistent with our previous discussions and underscore
the role of turbulence generated in a weakly stable boundary layer when the
Ri = +0.05 which corresponds with the fastest growing KH instability modes.

Reasons for Extending Our Research to the Great
Plains Operating Environment
35
• The greatest wind resource in U.S. resides in the western Great Plains
• Best winds often occur during the stable nighttime hours
• Nocturnal low-level jet streams occur frequently, particularly during
warmer months
• Intense vertical wind shears occur beneath in the stratified flows
beneath the jets
• We found that coherent turbulent motions often form within these
stratified layers
• We have shown that coherent turbulence can induce significant loading
on wind turbine rotors and structures

Typical Diurnal Variation in Wind Speed and
Vertical Shear on the Great Plains
observed
wind
shear
design
wind
shear
Emick Ranch
South of
Lamar, Colorado
(Colorado Green Wind Farm)
36

LLJ Source: Bonner, W. D., December 1968,
“Climatology of the low-level jet,”
Monthly Weather Review, 96(12), 833-850.
Strong Correlation Between Wind
Resource and Jet Bi-annual Frequency
The Nocturnal Low-Level Jet and Its Geographic
Frequency
Eventual
Potential
Turbine
Heights
p
4 6 8 10 12 14 16 18 20 22
Height(m)
0
100
200
300
400
500
Typical Vertical Wind
Profiles Associated
With Low-Level Jets
Colorado Green Wind Farm, Colorado
Low-Level Jet
GE 1.5S
Turbine
Layer
10-min mean wind speed (m/s)
Colorado
Green
Wind Farm
37

Annual Diurnal Turbine Fault and Wind Shear Patterns
Observed at Big Spring, Texas
0
100
200
300
400
500
600
700
12 AM 4 AM 8 AM 12 PM 4 PM 8 PM 12 AM
Time
FaultTime(hours)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
WindShearExponent
Fault Time
Shear
Source: DNV Global Energy Concepts
Evidence of Possible Turbine Availability
Relationship to Great Plains Low-Level Jet
peak low-
level jet
activity
38

Lamar Low-Level Jet Project
39
• Joint effort of DOE/NREL & Enron Wind
(October 2001 through September 2003)
• Collaboration with NOAA/ESRL
• Project Objectives
• Process and analyze 1 year record of
multi-level turbulence data from 120-m
tower on high plains of southeast
Colorado
• Assess potential impact of KH instability
associated with LLJs on turbine response
dynamics
• Collaborate with NOAA using HRDL
LIDAR to measure LLJ characteristics
• Use data to incorporate low-level jet
profiles, turbulence characteristics, and
coherent turbulent structures into
TurbSim turbulence simulation code

Observation Systems Used
SODAR
(Scintec MFAS)
Mean wind profiles
up to 500 m
LIDAR
(NOAA HRDL)
Vertical profiles and turbulence
spatial structure
Direct turbulence
measurements
from Enron Wind
120-m tower
(sonic anemometers)
High-resolution turbulence
& vertical thermal structure
REMOTE SENSING
40

Innovation for Our Energy Future41
The TurbSim Stochastic Simulator

Development of TurbSim Simulator
42
• The SNLWIND-3D simulator was used as the basis for TurbSim
• Site-specific turbulence spectral models based on the direct measurements
made at the NWTC and the Lamar (Colo. Green) Site were added
• Low-level jet wind and direction profiles were included in the Great Plains
Low-Level Jet Model (GP_LLJ) from SODAR profiles and corresponding tower
data
• Direct measurements of the properties of coherent turbulent structures were
made from the data collected at the three San Gorgonio wind farm sites
(upwind of Row 1, Row 37, and downwind of Row 41), the NWTC, and the
Colorado Green (Lamar) Site.
• Fully 3-D coherent structures based on LES and DNS KH billow simulations
by NCAR and Colorado Research Associates (CoRA) respectively have been
incorporated into each of the site-specific TurbSim spectral models whose
stochastic intensity and temporal distributions are scaled by the direct
measurements.

TurbSim Spectral Models Scaling
43
• Each of the site-specific turbulence models utilize diabatic scaling based on the following the
observed turbine layer Richardson number stability ranges and mean wind speeds in 2 m/s
increments between 3 and 28 m/s.
 STC01 : RiTL ≤ -1
 STC02: -1 < RiTL ≤ 0
 STC03: 0 < RiTL ≤ +0.10
 STC04: +0.10 < RiTL ≤ +0.25
 STC05: +0.25 < RiTL ≤ +1
• Power spectral models incorporating up to two peaks were derived for the u, v, and w turbulent wind
components for each specific site
• Mean hub-height Reynolds stresses were scaled with Ri and other parameters depending the choice
of which depends on the particular site.
• Spatial coherence models were derived and scaled for each specific site
• Parametric random distributions were employed when the scaled residuals were not Gaussian
distributed
• Low-level jet wind speed and direction profiles are scaled with stability and other boundary layer
parameters in the GP_LLJ spectral model
• Coherent structure attributes are scaled with stability and other boundary layer parameters based on
the specific site.

Example of Power Spectral Models Variations with
Stability
44
NWTC
GP_LLJ
Peak turbulent
energies occur
at lower frequencies
(longer wavelengths)
at the NWTC as
compared with the
Great Plains Site

Spatial Coherence U-Component Models
45

Example of Adding Coherent Structures to Background
Flow
46

Example of simulated NWTC inflow wind field with and
without added coherent structures
47
without coherent
structures added
with coherent
structures added
more black
color visible;
structures
more intense

NREL TurbSim Stochastic Inflow Simulator
Documentation
48

Conclusions and Recommendations
49
• We believe the TurbSim site-specific spectral models provide the turbine
designer with a range of realistic emulations of full-field turbulent inflows that
turbines will likely encounter; i.e., downwind of very complex terrain and beneath
low-level jets in the Great Plains.
• We believe that designers should pay particular attention to testing turbine
designs with stabilities in the critical Richardson number range (CRR) because of
the challenging turbulence conditions associated with it.
• At some point in the design process, we strongly suggest that designers use the
TurbSim site-specific inflow models with a multi-body dynamics code in order to
fully assess the impact of turbulence generated with the CRR stability range.
• We also suggest that for a more complete picture of the role of turbulence in the
dynamic response of wind turbines we encourage our colleagues to examine our
full report on this subject that will be available within the next few weeks.

Nwtc seminar overview of the impact of turbulence on turbine dynamics and their simulation, september 21, 2011

Recommended

Recommended

More Related Content

What's hot

What's hot (18)

Similar to Nwtc seminar overview of the impact of turbulence on turbine dynamics and their simulation, september 21, 2011

Similar to Nwtc seminar overview of the impact of turbulence on turbine dynamics and their simulation, september 21, 2011 (20)

More from ndkelley

More from ndkelley (6)

Recently uploaded

Recently uploaded (20)

Nwtc seminar overview of the impact of turbulence on turbine dynamics and their simulation, september 21, 2011