Effect of Blade Torsion on Modeling Results for the Small Wind Research
Turbine (SWRT)

Dave Corbus

National Wind Technology Center

National Renewable Energy Laboratory

1617 Cole Boulevard

Golden, Colorado 80401-3393 (USA)

> A. Craig Hansen, Jeff Minnema
>
> Windward Engineering LLC
>
> 2225 East Murray Holladay Road #201A
>
> Salt Lake City, Utah 84117 (USA)

The Small Wind Research Turbine (SWRT) testing project was initiated
with the goal of better characterizing both small wind turbine loads and
dynamic behavior. The main purpose of the testing was to produce high
quality data sets for model development and validation and to help the
wind industry further their understanding of small wind turbine
behavior, including furling. Previous papers have discussed modeling
results for the SWRT using the FAST aeroelastic simulator. This paper
summarizes modeling results from both the FAST and ADAMS aeroelastic
simulators. The ADAMS model allows for blade torsional stiffness to be
modeled, which is shown to significantly improve the agreement between
model and test results for rotor speed and explain variances in previous
comparisons between the SWRT FAST modeling results and the SWRT test
data. The ADAMS model results also show that the aerodynamic pitching
moment impacts the blade torsion more than the inertial forces.

# Introduction

Small wind turbines provide unique challenges to researchers trying to
model their performance because they have higher RPMs than large wind
turbines and often operate with large yaw errors and high yaw rates.
Furthermore, many small wind turbines incorporate furling, whereby the
rotor either tilts and/or yaws out of the wind to protect itself from
overspeed during very high winds, and this can add further complications
to modeling their performance. Because of these operating conditions,
modeling the performance of small wind turbines is particularly
challenging.

The Small Wind Research Turbine (SWRT) project was initiated with the
goal of providing reliable data for a small furling wind turbine for
model development, furthering the understanding of small wind turbine
aerodynamics and furling, and model validation. The test was the most
extensive loads test ever conducted for a small wind turbine ^1^, and
included measurements of turbine furling and thrust, as well as many
other loads measurements.

The SWRT was modeled using the FAST ^2,^^3^ (Fatigue, Aerodynamics,
Structures, and Turbulence) code with the AeroDyn aerodynamic subroutine
package developed by Windward Engineering LLC ^4^ to calculate
aerodynamic forces. FAST, which was developed and is distributed by the
National Renewable Energy Laboratory's (NREL's) National Wind Technology
Center (NWTC), is the primary aeroelastic simulator used by the U.S.
wind industry to model small wind turbines. The recent upgrades to FAST
allow users to simulate lateral offset and skew angle of the rotor shaft
from the yaw axis, rotor-furling and tail-furling degrees-of-freedom
(DOFs), up- and down-furl stops, and tail inertia and tail fin
aerodynamic effects ^5^. Because the location and orientation of the
furling DOFs are user-specified, the simulator is flexible enough to
model virtually any furling wind turbine configuration. FAST's built-in
features allow for the determination of full-system modes, including
furling, of an operating or stationary turbine.

Extensive modeling of the SWRT turbine, using FAST, showed that rotor
RPM was always over predicted, whereas the predicted and measured thrust
were well correlated. This error in the rotor RPM was found for
different airfoils and increased with wind speed ^6^. Various approaches
were tried to understand why the FAST model predicted rotor speeds much
higher than measured in high winds. In low winds, the predictions were
quite good. Both the airfoil tables and the alternator torque-speed
curve were adjusted in various ways. Unrealistically large changes were
required to improve the agreement in high winds, but then the accuracy
in low winds was compromised. The reason for the discrepancy was finally
discovered to be the elastic twist of the blade, which increases with
rotor speed (or wind speed).

Subsequent modeling with ADAMS^®^ (Automatic Dynamic Analysis of
Mechanical Systems, "ADAMS" is used to imply "ADAMS^®^" throughout this
paper) ^7^, allowed blade torsion to be modeled. ADAMS is a general
purpose, multibody-dynamics code from the MSC.Software Corporation for
calculating multi-body dynamic forces that is adaptable for modeling
wind turbines. FAST cannot currently model blade torsion.

The approach to modeling the SWRT consisted of the following: (1)
upgrading the FAST model to include furling; (2) validating the FAST
model by constructing an ADAMS model of the SWRT and comparing the two
results for furling cases; (3) running simulations with the FAST model
and comparing them to the SWRT test data; and finally, (4) including
torsional blade stiffness in the ADAMs model and re-running the
simulations performed in step (3) in ADAMs. This last step, which is the
topic of this paper, was necessary because after lengthy data analysis
and comparisons between FAST SWRT simulations and test data, it was
determined that the "live twist" of the blade was having a significant
impact on rotor performance. Torsional stiffness cannot currently be
modeled in FAST, so the ADAMS model was used for the final simulations
and the torsional stiffness of the blade was input into the model.

The ADAMS modeling with blade torsion as an input resulted in a
significantly improved correlation between modeled and measured rotor
RPM as discussed in this paper and revealed that blade torsion, referred
to herein as "live twist", can have a very significant effect in wind
turbine modeling.

# Test Turbine Description

The SWRT is a modified Bergey EXCEL 10-kW turbine that furls
horizontally out of the wind. The tail boom attaches with a hinge and
bumper arrangement to the rotor/generator/main-frame assembly, and there
is a lateral offset between the yaw axis and the rotor axis. The axis of
the hinge pivot joint is inclined laterally at a small angle to the
vertical yaw axis and produces a gravity restoring moment. A main-frame
stop keeps the tail boom from furling more than about 68 degrees. As the
wind speed increases, so do the thrust and aerodynamic normal force on
the nominally aligned vertical tail at the end of the tail boom. Furling
occurs when the rotor moments exceed the gravity restoring moment. The
furl damper provides very little resistance to furling but a high
resistance to unfurling ^1^.

The Bergey EXCEL is a three-bladed upwind turbine with a rated output of
10 kW at 13.0 m/s. The EXCEL uses a permanent magnet alternator to
produce three-phase variable frequency output at a nominal 240-volts.
The three-phase output is then rectified to DC power and converted to
single-phase 240-volt 60-hz AC power by the Gridtek inverter. The
turbine blades are constant chord and made from pultruded fiberglass,
and the direction of rotation is counter-clockwise. The experimental
data in this paper are from Configuration C of the SWRT, which has
constant chord blades with the SH3055 airfoil, a swept area of 35.3
m^2^, and a rotor diameter of 6.7 m. The turbine nacelle and shaft have
an eight-degree tilt, and the SWRT is installed on a Rohn SSV, 24.4 m.
(80 ft.), freestanding lattice tower.

The SWRT was modified in several ways to allow for the installation of
test instrumentation. One significant modification was the turbine main
shaft was shortened approximately 0.18 m. (7 in.) to allow for
installation of a 0.18 m (7 in.) load fixture in-line with the
non-rotating shaft to measure shaft loads. It should be noted that
because the SWRT was modified, the test results in this report are not
necessarily representative of the Bergey EXCEL turbine.

# Modeling Approach

To supply inputs for aeroelastic models of the SWRT, the turbine tail
assembly and mainframe were weighed and centers of gravity (Cgs) were
determined. Tests were also conducted to calculate the inertia about the
tail axis and the yaw axis. Tail damper properties were measured and all
turbine geometries noted. A modal test was conducted for a blade to
determine mode shapes for flap and edge. This data, as well as all
turbine related parameters, including airfoil data, was input into the
FAST and ADAMS models of the SWRT. To measure the blade torsion, 182.3
N-m of torque was applied about the 0.25 chord of the blade. This was
applied 2.74 m from the outboard edge of the rootpad (twisting 2.74 m of
blade) and the measured angular deflection was 4.1 degrees or .022
degrees/N-m over 2.74 m of blade. Based on this data the torsional
stiffness of the SH3055 blade is 6500 Nm. The c.g. offset is 0.017 m
(towards the trailing edge) from the quarter chord.

The FAST and ADAMs models of the SWRT were developed using geometric,
aerodynamic, and mass properties for the SWRT. The models include blade
flexibility, a variable-speed generator with a torque-speed look-up
table, tail furling with nonlinear user-defined springs and dampers, and
free yaw.

Modeling data was compared to experimental data taken for the SWRT
turbine ^1^. Data were sampled at 160 hz, and a 40-hz, 6-pole low-pass
Butterworth filter was used to filter the data. Records of 10 minutes in
length were stored.

# SWRT Modeling 

##  Blade Torsion

Because the FAST program cannot model blade elastic torsion motion, an
ADAMS model was created from the FAST model that includes the blade
torsion degrees of freedom (DOF). The torsional stiffness of the blades
was measured and input into the ADAMS model. The aerodynamic pitching
moment was added to the airfoil tables so the ADAMS model includes both
aerodynamic and inertial causes of blade twisting. There were no other
changes to the model. Therefore, the only substantial reason for
differences between the FAST and ADAMS predictions is live blade twist.
(Previous work has shown that FAST and ADAMS predictions are nearly
identical when blade torsion stiffness is very high ^5^).

ADAMS and Fast predict blade motions differently. ADAMS uses 6 DOF per
blade element, and there are 15 elements per blade for a total of 90 DOF
per blade. Fast has 3 DOF per blade ( 2 flapwise and 1 edgewise) plus a
polynomial mode shape for each DOF. ADAMS also requires blade torsional
stiffness values, chordwise center of gravity (Cg) offsets, and the
option of using the center of mass (Cm) values in the airfoil tables.
Fast does not allow for any of these.

## Modeling Results for Summary Statistics

Direct comparison of time series data is useful in that it provides a
highly detailed view of a small amount of data. Comparisons of 10-minute
average, maximum, and minimum summary statistics are valuable because
they provide a view of a large quantity of data, albeit in much less
detail. Figures 1-6 show the results of the summary statistics for SWRT
Configuration C using the ADAMS model. These results were generated
using the original 'untuned' airfoil and alternator data. They therefore
represent the accuracy of predictions that would be done during a design
if airfoil and alternator properties were available from wind tunnel or
bench testing and blade elastic properties were known from Finite
Element Analysis (FEA) or testing.

The statistics were compared by running the ADAMS model with simulated
turbulent wind conditions generated by SNWind v1.22. An 8 x 8 grid of
points was used across the rotor disc and three components of
time-varying wind were generated at each grid point. The turbulence was
generated with statistics that match the IEC Category-A conditions.
Site-specific turbulent inputs were not used in this analysis. Figure 1
shows a plot of the actual turbulence intensity from the SWRT tests and
the IEC Category A turbulence.

![](media/image1.wmf){width="2.7423611111111112in"
height="1.6284722222222223in"}

![](media/image2.wmf){width="2.86875in"
height="1.7097222222222221in"}![](media/image3.wmf){width="2.7423611111111112in"
height="1.6284722222222223in"}

![](media/image4.wmf){width="2.7423611111111112in"
height="1.6284722222222223in"}![](media/image5.wmf){width="2.7423611111111112in"
height="1.6284722222222223in"}![](media/image6.wmf){width="2.7423611111111112in"
height="1.6284722222222223in"}![](media/image7.wmf){width="2.7423611111111112in"
height="1.6284722222222223in"}

## Time Series Modeling Results

Time series comparisons are made by driving the ADAMS model with
measured wind data. Measurements of the hub-height horizontal and
vertical wind speeds and the wind direction are used for the
comparisons. Measurements of instantaneous horizontal wind shear were
not available. Horizontal wind shear is known to be an important driver
of yaw and furling motions ^8^, but it is difficult to measure. Driving
a model with "hub-height" wind data misses small-scale turbulence
effects but captures the large-scale, slow variations in wind
characteristics.

Figure 7 is a plot of blade elastic twist versus rotor RPM. The twist
can be up to 4 deg. at higher RPMs. Figure 8 is a time series plot of
blade elastic twist for the SWRT that shows the large amount of live
twist during one 10-minute time series file with an average wind speed
of 16.2 m/s. Figures 9-12 show the same time series file for RPM, furl,
thrust, and yaw error. The FAST modeling results without torsional
stiffness are also shown in addition to the ADAMS results with torsional
stiffness. The agreement between the ADAMS model data and test data is
good, whereas the FAST model severely over predicts rotor RPM, and furl
and yaw error agreement are also poor. The results demonstrate the
importance of blade live twist to modeling, especially for the RPM.

![](media/image8.wmf){width="2.7472222222222222in"
height="2.3743055555555554in"}![](media/image9.wmf){width="3.122916666666667in"
height="2.671527777777778in"}

![](media/image10.wmf){width="2.8743055555555554in"
height="2.3465277777777778in"}![](media/image11.wmf){width="3.0in"
height="2.6069444444444443in"}

![](media/image12.wmf){width="3.123611111111111in"
height="2.670138888888889in"}

## Effect of Aerodynamic Pitching Moment and Wake Model Algorithm on ADAMS Results![](media/image13.wmf){width="3.1222222222222222in" height="2.716666666666667in"}

Modeled sensitivity analyses with ADAMS show the importance of the
aerodynamic pitching moment to the blade live twist. Figure 14 shows a
plot of rotor speed versus time for the same 10-minute data series shown
previously with the aerodynamic pitching moment turned both on (i.e. Cm)
and off (i.e. No Cm). The data show aerodynamic forces have a large
impact on "live" blade twist. Live blade twist has a big impact on RPM
and hence power. Figure 14 shows a plot of electric power output versus
time for the same 10-minute data set.

Figures 13 and 14 also show the effect of changing the dynamic inflow
option in ADAMS. When the value is DYNIN ^4^, a generalized dynamic wake
(GDW) inflow model is used to calculate the induction factor. A value of
EQUIL ^4^ assumes that the wake is always in equilibrium with the forces
on a blade element (the "quasi-steady" or equilibrium wake assumption).
For EQUIL, the BEM theory with skewed wake and tip loss corrections is
used. The GDW model was developed as an expanded version of the Pitt and
Peters model. It uses a series solution to describe the induced velocity
field in the rotor plane, which includes Legendre functions in the
radial direction and trigonometric functions in the tangential
direction. The current GDW model in AeroDyn employs 0P, 1P, 2P and 3P
terms ^4^. The dynamic inflow effect is often insignificant, so results
in most cases should not differ from the BEM results. The exception is
cases with rapid changes in blade angle-of-attack, where the dynamic
inflow effect can be significant, as is the case with the SWRT turbine.
Yaw oscillation resulting from the GDW model has also been observed
while modeling a small, upwind, tail-vane turbine, though the reasons
for this are not yet known ^4^.

## Comparison of Rotor RPM between ADAMS and SWRT Data ![](media/image13.wmf){width="3.1222222222222222in" height="2.716666666666667in"}

Comparisons between predicted rotor RPM for the ADAMS model and measured
rotor RPM from the SWRT data show some interesting trends depending on
if the GDW or BEM wake model is used. Figure 15 shows summary statistics
for rotor RPM versus wind speed for the ADAMS model results with the two
different wake models and the SWRT data for Configuration C. The
aerodynamic pitching moment is turned on in these ADAMS plots.

![](media/image14.wmf){width="4.622916666666667in" height="4.225in"}

![](media/image15.wmf){width="4.504166666666666in"
height="3.8881944444444443in"}

![](media/image16.wmf){width="4.355555555555555in"
height="2.9944444444444445in"}

# Conclusion

The SWRT test has provided the small wind turbine and research community
with a unique set of data for validating aerodynamic models for a
turbine that operates at a significant yaw error, has high yaw rates, is
in and out of stall quickly, and operates at higher RPMs. Analysis and
comparison of FAST and ADAMS model simulations and test data for the
SWRT has resulted in a better understanding of small wind turbine
modeling, as well as a FAST furling model that can be used by engineers
to better design small furling wind turbines. However, comparison of
FAST and ADAMS results has shown the importance of including blade
torsion in the SWRT model, which can only be done with the ADAMS model
at this time. The SWRT blade is quite soft in torsion; hence it is
doubtful that live twist will be as important for many other turbines.
It was shown with the ADAMS model that the aerodynamic pitch moment has
more of an effect on blade torsion than do inertial forces. Future
near-term changes to the FAST model will include adding the ability to
model blade torsion.

# Acknowledgments {#acknowledgments .unnumbered}

The authors would like to thank Mark Meadors of NREL for his technical
help in conducting the SWRT testing, Jason Jonkman of NREL for his help
in upgrading the FAST model to include the effects of furling, and Kathy
O'Dell of NREL for her help in making this document more readable. We
would also like to thank Todd Hanley of Bergey Windpower for his
continuous help during both the testing and modeling phase of the
project.

# References {#references .unnumbered}

^1^ Corbus, D. and Prascher, D. "Analysis and Comparison of Test Results
from the Small Wind Research Turbine Test Project," *Collection of the
2005 ASME Wind Energy Symposium Technical Papers Presented at the 43^rd^
AIAA Aerospace Sciences Meeting and Exhibit, 10-13 January 2005, Reno,
NV.,* Washington, D.C.: American Institute of Aeronautics and
Astronautics, January 2005, NREL/CP-500-36891.

^2^ Jonkman, J.M. and Buhl, M.L. (March 2004). *"FAST User's Guide".* 
NREL/EL-500-29798. Golden, CO: National Renewable Energy Laboratory, 105
pp.

^3^ Jonkman, J.M. and Buhl, M.L. (January 2004). "New Developments for
the NWTC\'s FAST Aeroelastic HAWT Simulator," *Collection of the 2004
ASME Wind Energy Symposium Technical Papers Presented at the 42^rd^ AIAA
Aerospace Sciences Meeting and Exhibit, 5-8 January 2004, Reno, NV*.
Washington, D.C.: American Institute of Aeronautics and Astronautics,
pp. 181-191; NREL/CP-500-35077.

^4^ David J.and Hansen, A. Craig. (September 2001). *User\'s Guide to
the Computer Software Routines AeroDyn Interface for ADAMS^®^*. Salt
Lake City, UT: Windward Engineering LLC, Prepared for the National
Renewable Energy Laboratory under Subcontract No. TCX-9-29209-01, 24 pp.

^5^ Jonkman, J.M. and Hansen, A.C., "Development and Validation of an
Aeroelastic Model of a Small Furling Wind Turbine," *Collection of the
2005 ASME Wind Energy Symposium Technical Papers Presented at the 43^rd^
AIAA Aerospace Sciences Meeting and Exhibit, 10-13 January 2005, Reno,
NV*. Washington, D.C.: American Institute of Aeronautics and
Astronautics, January 2005, NREL/CP-500-36776.

^6^ Corbus, D. and Hansen, C. (2005). \"Test Results from the Small Wind
Research Turbine (SWRT) Test Project.\" Prepared for the *WindPower 2005
Conference Proceedings, May 2005*. NREL/CP-500-38224. Golden, CO:
National Renewable Energy Laboratory, 14 pp.

^7^ Laino, David J.and Hansen, A. Craig. (September 2001). *User\'s
Guide to the Computer Software Routines AeroDyn Interface for ADAMS^®^*.
Salt Lake City, UT: Windward Engineering LLC, Prepared for the National
Renewable Energy Laboratory under Subcontract No. TCX-9-29209-01, 24 pp.

^8^ Hansen, A.C. (May 1992). Yaw Dynamics of Horizontal Axis Wind
Turbines, Final Report. NREL/TP-442-4822. Golden, CO: National Renewable
Energy Laboratory.