Computational Studies of Horizontal Axis Wind Turbines
Quarterly Progress Report
Covering the period
April 1, 2004 –June 30, 2004
Contract No. XCX-2-32227-02
Submitted to the
National Renewable Energy Laboratory
Attn: Dr. Scott Schreck
1617 Cole Boulevard
Golden, CO 80401-3393
Prepared by
Lakshmi N. Sankar
Sarun Benjanirat
Chanin Tongchitpakdee
School of Aerospace Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0150
June 30, 2004
I. INTRODUCTION
A computational research program is underway at Georgia Institute of Technology
(Georgia Tech), Atlanta, Georgia, in the area of horizontal axis wind turbine (HAWT)
aerodynamics. The research focuses on (a) improving and calibrating a hybrid solution
methodology previously developed under NREL support for non-axial and non-uniform
inflow, (b) improve the capabilities of a companion Navier-Stokes methodology, and
apply it to a rotor-tower configuration for a range of downwind and yaw conditions, and
(c) explore passive and active control concepts for extending the useful operating range
of horizontal axis wind turbines.
The mathematical and numerical formulation used in this study divides the flow field
around a HAWT into three distinct entities: a thin viscous region surrounding the
individual blades, a potential flow region that transfer the disturbances generated by the
rotor to the far field, and a helical wake structure (vorticity) that includes the tip vortices
shed by the rotor blades.
The computational effort focuses on the extension of a three-dimensional (3-D) hybrid
Navier-Stokes/Potential Flow solver that has been developed at Georgia Tech for
helicopter rotor, propeller and HAWTs. In this approach, 3-D unsteady, compressible
Navier-Stokes equations are solved in the thin viscous region on a body-fitted grid
surrounding the rotor blade. Away from the blades in the potential flow region, the 3-D
unsteady compressible potential flow equations shall be solved. The vorticity shed by
the blades as a result of dynamic stall and spanwise and azimuthal variations of
circulation are captured by vortex filaments that are freely convected by the local flow.
Since the costly Navier-Stokes calculations are done only in regions close to the wind
turbine blades, and because much of the vorticity is tracked using Lagrangean
techniques, the method is an order of magnitude more efficient than the full blown
Navier-Stokes methods.
SUMMARY OF ACTIVITIES DURING THE RESEARCH PERIOD
It may be recalled that the previous progress report (Jan 1, 2004 – March 31, 2004)
described the development of a C-O grid topology based analysis, and preliminary
results for axial flow conditions. In this report, we are summarizing additional work that
has been done for yawed flow conditions. These calculations were done on a C-O grid.
There were 140 points in the C- or wraparound direction, 95 points in radial direction
including 70 stations on the rotor blade, and 60 points in the normal direction. The first
point of the wall was placed at 0.0005 chords. The baseline Baldwin-Lomax model was
used in this study. A prescribed wake model was used to account for the inflow from the
vortices that were not captured by the computations. Because many of the calculations
involved extensive flow separation, Navier-Stokes equations were solved over the entire
C-O grid, and no potential flow zone was used.
These calculations were done in a time accurate manner. The computed loads were
averaged over the last revolution. Figure 1 shows typical results for the instantaneous
toque values over an entire rotor revolution, and comparison with measurements.
On Figures 2 and 3 we show the radial variation of normal and chordwise pressure
forces, at several wind speeds and yaw angles. The results were in reasonable
agreement with experiments only at low wind speeds (~ 7 m/sec to 10 m/sec) and low
yaw angles (below 30 degrees). At higher wind speeds and/or high yaw angles, where
extensive flow separation was present, considerable discrepancies were found with this
baseline grid, and baseline turbulence model. Sarun Benjanirat, a Ph D student working
on this project is studying the effects of a higher order turbulence model (k-omega) on
these simulations (for zero yaw conditions) while Chanin Tongchitpakdee, another
student working on this project under school support is studying the effects of grid
spacing on these simulations.
Figure 4 shows the chordwise distribution of pressures for several wind and yaw
conditions. At very low wind speeds, particularly near the inboard stations, the
compressible flow formulation produced very high local pressure coefficients (higher
than the expected value around 1). Because of the low prevalent dynamic pressures,
this discrepancy did not affect the integrated loads (e.g. torque, bending moments, etc).
A low Mach number (incompressible) formulation would help improve the predictions at
these stations, but is not planned at this time.
Figures 5 and 6 show the torque generated by the rotor, and the bending moments as a
function of yaw angle at several wind speeds. As before, at lower wind speeds (7 m/sec
and 10 m/sec) these values are in reasonable agreement with measurements. The
agreement is good for these “integrated” loads even at high yaw angles even though the
sectional loads and flow details differ somewhat from measurements, demonstrating
that the algorithm preserves the global conservation of mass, momentum, and energy.
An abstract based on these results has been submitted to the 2005 ASME Wind Energy
Symposium, and has been accepted for publication. The next progress report will
include a draft version of our paper, and results for the k-omega simulations.
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Figure 1. The variation of the torque as a function of time (azimuth) for 10 m/s with 100 yaw
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Figure 3d CT Distribution at 15 m/s under several yaw conditions
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Figure4a. Cp Distribution at 7 m/s with 100 yaw angle on several span wise stations
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Figure 4b. Cp Distribution at 7 m/s with 300 yaw angle on several span wise stations
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Figure 4c. Cp Distribution at 7 m/s with 450 yaw angle on several span wise stations
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Figure 4d. Cp Distribution at 7 m/s with 600 yaw angle on several span wise stations
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-6
-6
Cp Distribution at r/R=0.63
Cp Distribution at r/R=0.80
NREL
Code
-5
NREL
Code
-5
-4
-3
-3
-2
-2
Cp
Cp
-4
-1
-1
0
0
1
1
2
2
3
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
x/C
-6
Cp Distribution at r/R=0.95
NREL
Code
-5
-4
-3
Cp
-2
-1
0
1
2
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4f. Cp Distribution at 10 m/s with 300 yaw angle on several span wise stations
0.8
0.9
1
-4
-4
Cp Distribution at r/R=0.30
Cp Distribution at r/R=0.47
NREL
Code
NREL
Code
-3
-2
-2
-1
-1
Cp
Cp
-3
0
0
1
1
2
2
3
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
x/C
0.5
0.6
0.7
0.8
0.9
1
x/C
-4
-4
Cp Distribution at r/R=0.63
Cp Distribution at r/R=0.80
NREL
Code
NREL
Code
-3
-2
-2
-1
-1
Cp
Cp
-3
0
0
1
1
2
2
3
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
x/C
-4
Cp Distribution at r/R=0.95
NREL
Code
-3
-2
Cp
-1
0
1
2
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4g. Cp Distribution at 10 m/s with 450 yaw angle on several span wise stations
0.8
0.9
1
-2
-2
Cp Distribution at r/R=0.30
Cp Distribution at r/R=0.47
NREL
Code
NREL
Code
-1.5
-1
-1
-0.5
-0.5
Cp
Cp
-1.5
0
0
0.5
0.5
1
1
1.5
1.5
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
x/C
-2
0.6
0.7
0.9
1
Cp Distribution at r/R=0.80
NREL
Code
-1.5
NREL
Code
-1.5
-1
-0.5
-0.5
Cp
-1
0
0
0.5
0.5
1
1
1.5
1.5
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
-2
Cp Distribution at r/R=0.95
NREL
Code
-1.5
-1
-0.5
Cp
0.8
-2
Cp Distribution at r/R=0.63
Cp
0.5
x/C
0
0.5
1
1.5
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4h. Cp Distribution at 10 m/s with 600 yaw angle on several span wise stations
0.8
0.9
1
-12
-12
Cp Distribution at r/R=0.30
Cp Distribution at r/R=0.47
NREL
Code
NREL
Code
-10
-8
-8
-6
-6
Cp
Cp
-10
-4
-4
-2
-2
0
0
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
0.1
0.2
0.3
0.4
x/C
0.5
0.6
0.7
0.8
0.9
1
x/C
-12
-12
Cp Distribution at r/R=0.63
Cp Distribution at r/R=0.80
NREL
Code
NREL
Code
-10
-8
-8
-6
-6
Cp
Cp
-10
-4
-4
-2
-2
0
0
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
-12
Cp Distribution at r/R=0.95
NREL
Code
-10
-8
Cp
-6
-4
-2
0
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4i. Cp Distribution at 13 m/s with 100 yaw angle on several span wise stations
0.8
0.9
1
-10
-10
Cp Distribution at r/R=0.30
Cp Distribution at r/R=0.47
NREL
Code
-8
-8
-6
-6
Cp
Cp
NREL
Code
-4
-4
-2
-2
0
0
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
x/C
0.5
0.6
0.7
0.8
0.9
-10
-10
Cp Distribution at r/R=0.63
Cp Distribution at r/R=0.80
NREL
Code
-8
-8
-6
-6
Cp
Cp
NREL
Code
-4
-4
-2
-2
0
0
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
-10
Cp Distribution at r/R=0.95
NREL
Code
-8
-6
Cp
1
x/C
-4
-2
0
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4j. Cp Distribution at 13 m/s with 300 yaw angle on several span wise stations
0.8
0.9
1
-14
-10
Cp Distribution at r/R=0.30
Cp Distribution at r/R=0.47
NREL
Code
NREL
Code
-12
-8
-10
-6
Cp
Cp
-8
-6
-4
-4
-2
-2
0
0
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
x/C
0.5
0.6
0.7
0.8
0.9
-10
-10
Cp Distribution at r/R=0.80
Cp Distribution at r/R=0.63
NREL
Code
-8
-8
-6
-6
Cp
Cp
NREL
Code
-4
-4
-2
-2
0
0
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
-10
Cp Distribution at r/R=0.95
NREL
Code
-8
-6
Cp
1
x/C
-4
-2
0
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4k. Cp Distribution at 15 m/s with 100 yaw angle on several span wise stations
0.8
0.9
1
-10
-10
Cp Distribution at r/R=0.30
Cp Distribution at r/R=0.47
NREL
Code
-8
-8
-6
-6
Cp
Cp
NREL
Code
-4
-4
-2
-2
0
0
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
x/C
0.5
0.6
0.7
0.8
0.9
-10
-10
Cp Distribution at r/R=0.63
Cp Distribution at r/R=0.80
NREL
Code
-8
-8
-6
-6
Cp
Cp
NREL
Code
-4
-4
-2
-2
0
0
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
-10
Cp Distribution at r/R=0.95
NREL
Code
-8
-6
Cp
1
x/C
-4
-2
0
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4l. Cp Distribution at 15 m/s with 300 yaw angle on several span wise stations
0.8
0.9
1
-7
-7
Cp Distribution at r/R=0.30
Cp Distribution at r/R=0.47
NREL
Code
-6
NREL
Code
-6
-5
-4
-4
-3
-3
Cp
Cp
-5
-2
-2
-1
-1
0
0
1
1
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
x/C
0.5
0.6
0.7
0.8
0.9
1
x/C
-7
-7
Cp Distribution at r/R=0.63
Cp Distribution at r/R=0.80
NREL
Code
-6
NREL
Code
-6
-4
-4
-3
-3
Cp
-5
Cp
-5
-2
-2
-1
-1
0
0
1
1
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
-7
Cp Distribution at r/R=0.95
NREL
Code
-6
-5
-4
Cp
-3
-2
-1
0
1
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4m. Cp Distribution at 15 m/s with 450 yaw angle on several span wise stations
0.8
0.9
1
-4
-4
Cp Distribution at r/R=0.30
Cp Distribution at r/R=0.47
NREL
Code
-3
-3
-2
-2
Cp
Cp
NREL
Code
-1
-1
0
0
1
1
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
x/C
0.5
0.6
0.7
0.8
0.9
-4
-4
Cp Distribution at r/R=0.63
Cp Distribution at r/R=0.80
NREL
Code
-3
-3
-2
-2
Cp
Cp
NREL
Code
-1
-1
0
0
1
1
2
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x/C
-4
Cp Distribution at r/R=0.95
NREL
Code
-3
-2
Cp
1
x/C
-1
0
1
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x/C
Figure 4n. Cp Distribution at 15 m/s with 600 yaw angle on several span wise stations
0.8
0.9
1
1000
2000
Torque variation with yaw angle (7 m/s)
Torque variation with yaw angle (10 m/s)
NREL
Code
NREL
Code
1800
800
1600
700
1400
600
1200
Torque (Nm)
Torque (Nm)
900
500
400
1000
800
300
600
200
400
100
200
0
0
0
10
20
30
40
50
60
70
0
10
20
Yaw Angle (deg)
30
40
50
60
3000
3000
Torque variation with yaw angle (13 m/s)
Torque variation with yaw angle (15 m/s)
NREL
Code
NREL
Code
2500
2500
2000
2000
Torque (Nm)
Torque (Nm)
70
Yaw Angle (deg)
1500
1500
1000
1000
500
500
0
0
0
10
20
30
40
Yaw Angle (deg)
50
60
70
0
10
20
30
40
50
60
70
Yaw Angle (deg)
Figure 5a. The variation of the torque generated by the rotor as a function of yaw angle at several wind speeds
3000
4000
Root bending moment variation with yaw angle (7 m/s)
Root bending moment variation with yaw angle (10 m/s)
NREL
Code
NREL
Code
3500
3000
Root Bending Moment (Nm)
Root Bending Moment (Nm)
2500
2000
1500
1000
2500
2000
1500
1000
500
500
0
0
0
10
20
30
40
50
60
70
0
10
20
Yaw Angle (deg)
5000
40
50
60
70
5000
Root bending moment variation with yaw angle (13 m/s)
Root bending moment variation with yaw angle (15 m/s)
NREL
Code
NREL
Code
4000
4000
Root Bending Moment (Nm)
Root Bending Moment (Nm)
30
Yaw Angle (deg)
3000
2000
1000
3000
2000
1000
0
0
0
10
20
30
40
Yaw Angle (deg)
50
60
70
0
10
20
30
40
50
60
Yaw Angle (deg)
Figure 6. The variation of the root bending moment as a function of yaw angle at several wind speeds
70