48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2010, Orlando, Florida
AIAA 2010-1585
Experimental and Numerical Studies of a
High Solidity, Low Tip Speed Ratio DAWT
Michael M. Moeller, Jr.1 and Kenneth Visser2
Clarkson University, Potsdam, NY, 13699
A numerical and experimental investigation of a Diffuser Augmented Wind Turbine
(DAWT) has been conducted. Historically, the advantages of DAWT concept have been
negated by higher material cost and less than stellar real world performance. The current
configuration combines a duct augmentation concept with an optimized, high solidity,
twisted flat plate rotor, a relatively low tip speed ratio, and a tailless configuration to work
towards a turbine with a lower cost per kilowatt than other similar sized machines. The
experimental data of the initial test concept was compared with a numerical blade element
momentum analysis and turbine efficiencies of 0.23–0.25 were observed. An optimized flat
plate blade geometry design was then developed, with Cp values of approaching 0.4, and
when combined with the diffuser, exhibited experimental system efficiencies greater than
0.60. An additional benefit is the possibility of higher annual energy outputs as the turbine
appears to self regulate at higher wind speeds, negating the need for a furling mechanism.
Nomenclature
c
r hub
CL
CD
CP
CPS
P
R
Vo
!
!
!g
"
#
$
T
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
blade cross section chord length
hub radius
lift coefficient
drag coefficient
aerodynamic power coefficient
overall turbine power coefficient. !gCP
power produced
turbine radius
velocity wind speed
tip pitch angle
augmentation ratio
generator efficiency
tip speed ratio
solidity
angular velocity
I. Introduction
he Diffuser Augmented Wind Turbine (DAWT) is a strategy used to augment a conventional Horizontal Axis
Wind Turbine (HAWT) by surrounding the rotor blades with a duct that increases in area in the downstream
direction. DAWTs have been measured to perform with efficiencies greater than the Betz limit of 59.3% when
based on the swept rotor area, and a short review of studies in the field is included below. The purpose is to
increase the mass flow through the blades and hence increase the power extracted for a given rotor size. Certain
researchers have indicated the efficiency increase is caused, in part, by the diffuser enabling a greater pressure drop
across the rotor blade.1 Others feel the larger stream tube captured, increases the mass flow rate and hence the
1
2
Undergraduate, Department of Mechanical and Aeronautical Engineering, Box 5725, Student Member AIAA.
Associate Professor, Department of Mechanical and Aeronautical Engineering, Box 5725, Senior Member AIAA.
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American Institute of Aeronautics and Astronautics
Copyright © 2010 by Ken Visser. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
momentum exchange to the rotor. DAWTs can offer additional advantages including minimizing tip losses,
reducing the noise signature, and being less yaw sensitive than HAWTs. However, there are many issues with
DAWTs that need to be addressed before their full potential can be realized, the foremost being the trade off in the
increased use of material to performance, which usually results in a higher cost. The focus of this study was to
analyze a high solidity DAWT design developed by the WindTamerTM Corporation of Geneseo, NY using both
numerical and experimental methods. It was hoped to experimentally confirm the performance predictions outlined
in the literature and validate the numerical blade element model (BEM), mRotor, developed at Clarkson University.
The WindTamerTM turbine concept is illustrated in Figures 1 and 2. The initial concept was delivered to
Clarkson in the summer of 2008 for testing at the university wind turbine test site. Subsequent design changes to the
blades and diffuser led to the current design blade design in Figure 2 and the current experimental prototype.
Figure 1. Initial WindTamerTM Configurations a) Turbine b) Rotor c) Experimental Prototype
Figure 2. Current WindTamerTM Configurations a) Optimized Rotor b) Experimental Prototype
II. Background
Several studies have been conducted in the past on the feasibility and potential efficiency gains that DAWTs
could provide.1-11 Wilson and Lissaman 2 discussed the physical effects of the presence of a duct, namely that being
to increase the wake expansion, and the possibilities of exceeding a free rotor power coefficient level of 0.593.
They concluded that a simple analysis requires an assumption on the duct exit pressure and that the entire flow needs
to be modeled to determine the potential performance levels. However, if the flow could be expanded to a value
greater than the optimal free rotor expansion, while still maintaining an ideal axial induction of the flow, the
increased mass flow rate would improve the power output beyond that of an open rotor.
Gilbert and Foreman 3,4 indicated that the overall Cp values could actually be greater than the Betz limit by as
much as a factor of 2.65. They defined this in terms of an augmentation ratio,
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namely the ratio of Cp obtained with the ducted rotor to that of the traditional open rotor Betz limit translating into
an equivalent Cp of about 1.57 for ! = 2.65.
Phillips et al. 5 reported optimized designs with a Cp = 1.9, corresponding to " > 3 and their experimental results
showed Cp values of about 2. Ingra 6,7 has published experimental results of augmentation factors > 2 and indicated
3 could be achievable. However the effects of tunnel blockage are ignored from the wind tunnel tests and this can
cause significant error. Hansen 8 has reported viscous CFD results that predicted ideal Cp values approaching 0.94,
corresponding to an augmentation factor of " = 1.6. He indicated this as a practical upper limit, but also indicated
that theoretically the augmentation factor could be increased if the duct geometry could be made to keep the flow
attached.
Werle and Presz 9, using fundamental momentum principles, concluded, along with Hansen, that augmentation
factors approaching 2 are possible corresponding to ideal Cp values >1 as seen in Figure 3. They also comment that
earlier studies used incorrect assumptions in their derivations, leading to overly optimistic predictions. Note that
Hansen’s calculations lead to values of Cp = 0.94 as shown by the black filled circles in Figure 1b.
a)
b)
Figure 3. Theoretical and Numerical DAWT Predictions 9 a) Augmentation Ratio
b)Power Coefficient
A recent article by van Bussel 10 substantiates the above arguments regarding mass flow and indicates that the
increase of the mass flow, and thus the augmentation ratio, is proportionate to the ratio of the diffuser area to the
rotor area, as suggested in Figure
3a. Discussion by van Bussel
concludes that the amount of
energy extracted per unit volume of
air with a DAWT remains the
same as for a bare rotor, but since
the volume of air has increased, so
has the total energy extracted. As
can be seen in Figure 4, extracted
from his paper, Cp values above 1,
corresponding to augmentation
ratios on the order of 1.7, are
achievable with diffuser area ratios
on the order of 2.5. In addition to
the experimental data, he has
plotted the effect of reducing the
10
Figure 4. Theoretical and Experimental DAWT Performance
back pressure, which can also have
a beneficial effect on performance.
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One of the few large constructed DAWTs was the Vortec 7, shown
below in Figure 5 11. This DAWT had a 7.3 m diameter rotor with a
design purpose to see the commercial feasibility for a DAWT wind
farm. The anticipated performance to the turbine, however, was not
realized.
The above derivations are, of course, applied to the ideal levels of
power extraction.
One could also use the argument that the
augmentation factor could be applied to any given turbine performance
level, and this represents a potential to increase any rotor power
extraction level by a factor of ! leading to:
Cp Ducted Rotor = ! Cp Bare Rotor
however realizing this practically is another matter.
Figure 5. Vortec 7 DAWT
12
III. Evaluation Methodology
Numerical and experimental methods have been used to examine the current high solidity WindTamerTM
concept. The numerical study used the design tool, mRotor,13,14 developed at Clarkson University, as well as the
publicly available wind turbine analysis tool WT_Perf, developed by the National Renewable Energy Laboratory
(NREL). An experimental test of two of the first generation prototype turbines was conducted at the Clarkson
University Wind Turbine Test Site. The test site is located at the Potsdam airport, approximately 2 miles from
campus and connected via a line of sight wireless communication system. Additional data was acquired on the
second generation designs at Geneseo and Perry, NY. The second generation turbines are scheduled to be tested at
Clarkson in the upcoming months.
A. Numerical Strategy
Both mRotor and WT_Perf are based on blade element momentum theory, BEM, which has demonstrated fairly
good reliability for a fast turn around time in analyzing the performance of HAWTs.14 The blade is divided into
spanwise elements according to, say, a cosine distribution. The forces acting on the elements, which are calculated
from the airfoil lift and drag coefficients, are depicted in Figure 6.
In the current version of mRotor, CL and CD are found through bi-linear interpolation of tabulated CL and CD data
vs. # for a range of Re for a specific airfoil. The Reynolds number on each element will change as a function of
radial location, chord length, and rotational speeds. For elements where the calculated Reynolds number is above or
below the available range of aerodynamic data, mRotor takes the closest available point. Extrapolation of data was
not performed at low Reynolds numbers (below 100,000) due to the difficulty caused by laminar separation
effects.15,16
To insure consistency between the two BEM programs,
identical correction methods, airfoil data, and other inputs
were used. The airfoil data was formatted to be compatible
with WT_Perf using the NREL-created spreadsheet called
AirfoilPrep. This formatting consists of post-stall data
addition according to methods of Viterna and Corrigan,17
and was implemented as a new airfoil data
correction/formatting routine in mRotor. Additionally,
mRotor was updated with routines that can create WT_Perf
input files, execute WT_Perf, and create an output file
which can then be read for plotting in mRotor. This can all
be done from the mRotor graphical user interface, allowing
for quick comparison. An optimum blade geometry design
routine function is also available in mRotor based on Figure 6. Blade Element Forces and Velocities.
general momentum theory by Glauert.18
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In the single design point mode, mRotor can analyze the efficiency of a turbine with the given parameters of
number of blade elements, radius of rotor tip and hub, design ", design #, the number of blades, the wind speed
regime, pitch angles, Reynolds number, tip loss corrections, twist distribution, and chord distribution. In the
optimum design mode of mRotor, the program can construct the optimized design for a wind turbine blade with an
optimized twist and chord distributions. The flat plate lift and drag data used in the current study was obtained from
McCormick.19
B. Experimental Methods
All measurements were taken at the Clarkson University Wind Turbine Test Site, located at the Potsdam airport.
The test site includes a test silo and a meteorological tower and resides on relatively flat terrain at an elevation of
approximately 474 feet. The northern and western borders are open and free of obstruction. The southern and eastern
borders bare deciduous and evergreen tree lines approximately 150 feet and 300 feet, respectively, from the test
turbines. Figure 7 illustrates the layout of the
test site. The meteorological tower, pictured
on the far right, is located approximately 20
meters upwind of the two pictured 1 kW
turbines.
The test silo houses the data acquisition
system running Labview 7.1i and uses two
National Instruments PCI-6024e DAQ boards
with a BNC-2120 interface. Power is
determined from the product of the
measurements of current and voltage
transducers at the connection point of the
resistive load bank. RPM is determined from
the frequency of the rectified voltage signal.
Wind speed is measured at heights of 6, 12
and 18 m with NRG Type 40 anemometers
on a meteorological tower. Wind direction is
measured at 6 and 18 m with 2 NRG 200
series wind vanes. Pressure, temperature and
Figure 7. Clarkson University Wind Turbine Test Site
humidity are collected at 3 m and corrected
to the height of both turbine hubs.
Two identical resistive load banks have been constructed, instead of a battery bank, to eliminate effects of the
charging and discharging rates of the batteries. Resistance values can be varied from 1 to 25 ohms, in 1 ohm
increments.
Power and meteorological measurements are continuously obtained at the test site at a rate of one hertz. The data
is stored in the local system and transferred daily to the campus computer where it is checked for errors and usable
data. Analysis procedures have followed the NREL performance test plans and the data is processed in two steps.
Step one sorts the data by load case, applies hub height corrections, calculates the air density and theoretical power
output, and performs a one and ten-minute average. The second step sorts all the data into bins according to wind
speed, 0.5 m/s wide with bin centers located at multiples of 0.5 m/s. The range of wind speeds is dependant on the
load case, but generally extends from 2 m/s to 13 m/s. The power curve is created from the averaged bins.
Performance coefficients, CP, versus tip speed ratio, ", curves, and total energy capture can be created and
compared to analyze the overall performance of the prototype.
The experimental testing of the WindTamerTM consisted of two phases. First, the original design provided by the
WindTamerTM Corporation was erected at the Clarkson University Wind Turbine Test Site. The prototypes were
mounted on a pole to place the center of the hub at a height of 6m. The base of the pole was bolted to a 4’ diameter
concrete base, extending 8’ below ground level. The geometry was shown in Figure 1 previously.
The second portion of the experimental testing at Clarkson will be used to verify the optimization design from
mRotor. An optimized blade design geometry was developed using a flat plate blade, shown in Figure 2. Two units
will be brought to the Clarkson University Wind Turbine Test Site for the second portion of the experimental
testing in the beginning of 2010. The prototype in Figure 2b, which utilizes an updated diffuser design to
eliminate the need for a tail, coupled with the new rotor design, and has also been set up on a farm in Perry, NY,
near the company headquarters.
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IV. Results and Discussion
A. Numerical Analysis
The design code mRotor was run in the single design point and optimized geometry modes, to analyze the 12bladed design baseline design supplied by the company, determine the range of Cp for the original design and to
compare the numerical to field test results. mRotor was then run in the optimized geometry design mode to
determine the optimal design ", and other optimal design parameters. The Cp vs. " results for the baseline prototype
of Figure 6 are shown in Figures 8 and 9. As a result of the constraint of using a flat plate for the airfoil, intended to
reduce the total cost of the turbine, the numerical results indicated that a lower tip speed ratio produced a greater Cp,
or higher efficiency, than what might be expected at a higher value of ". It was also determined that more efficient
airfoils, such as a NACA 2414 and SG6043 blade profiles, produced results favoring higher tip speed ratios. Figures
8 and 9 show Cp vs. " and Cp vs. wind speed at a design point of " = 2.1 for a flat plate blade profile, with their
comparative geometries shown in Figure 10. Although the Cp values tended to oscillate as a function of wind speed,
the trend was approximately constant. The oscillation is due to the discrete nature of the experimental lookup data
trying to match Reynolds number along the blade and the interpolation scheme is presently being updated.
a)
b)
Figure 8. Power Coefficients for the Original Wind Tamer design as a function of a) tip speed ratio b) wind speed.
a)
b)
Figure 9. Power Coefficients for the Optimized Wind Tamer geometry as a function of: a) tip speed ratio for
mRotor and WT-Perf and b) wind speed
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a)
b)
Figure 10. mRotor geometries for the Wind Tamer with a) the original design b) the optimized geometry
B. Experimental Analysis – First Generation Prototype
Typically, wind turbine performance is examined as time averaged quantity. Large utility turbines use 10 minute
averaging, but smaller turbines tend to use less, such as 1 minute averaging. The data is then first averaged into 1
minute values and then this data is sorted into “bins” of specified wind speeds. The data presented here has been
sorted into 0.5 m/s (1.1 mph) bins, meaning the value of 2 m/s, for instance, accounts for all the data from 1.75 m/s
to 2.25 m/s. Gipe explains the reason for this in his Article “Testing the Power Curves of Small Wind Turbines (©
2000) 20:
The reason the data points are scattered is due to differences between the anemometer's and the wind
turbine's inertia. When a gust strikes a lightweight Maximum cup anemometer it begins speeding up
almost instantly. However, there is a longer lag between the time a gust strikes a wind turbine rotor and
when it begins to respond because of the mass in the blades, hub, generator, and transmission if one is
used. The reverse is also true. The anemometer responds more quickly than the wind turbine in lulls.
The wind turbine, because of its rotational inertia, will continue spinning and putting out power for a
few seconds or more after the gust has passed. This lag, or hysteresis as the engineers call it, makes it
difficult to accurately measure a wind turbine's performance without averaging.
The decision on how long to average is also not clear cut. As Gipe reports:
The amount of time over which the data is collected and, hence, the total amount of resulting data affects
the accuracy of the results. The American Wind Energy Association’s standard requires a minimum of
60 samples for wind speed bins less than 28 mph (12.5 m/s), 20 samples for bins from 28 mph to 35
mph (12.5-15.6 m/s), and 10 samples for bins greater than 35 mph (15.6 m/s). [Other people are] …
recommending that the proposed European standard require 30 1-minute samples or one-half hour of
data for each wind speed bin.
The impact of different time averages can be quite substantial as will be indicated in the preliminary
results section below. This is especially true with the Wind Tamer, which has a large “flywheel“ effect. A typical
series of daily data is now presented, as an example of the data and to help understand the analysis process. This is
followed by preliminary data for the baseline prototype.
September 18, 2008 was picked as a typical days worth of data and the output from the turbine with a 4 ohm load
is presented in various forms below. Time traces of the data are presented in Figures 11-14. The velocity profile in
Figure 11 illustrates various periods of calm and winds which reach a maximum up to 18 mph during the 10 AM to
4PM. The associated power in the wind is also displayed in Figure 11. Figure 12 illustrates the voltage and current
output for the turbine during the day and the resulting power output is shown in Figure 13.
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Figure 11. Velocity and Total Wind Power of September 20, 2008
Figure 12. Voltage and Current Output of September 20, 2008
Figure 13. Prototype Turbine Power Output on September 20, 2008
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In order to determine the turbine power as a function of wind speed, ie the power curve, the raw data was
then processed into 1 minute averages and the power output as a function of velocity is presented below in Figure
14. Note that, as expected for a given day, at higher wind speeds there are substantially less points.. Each red circle
represents a 1 minute average. The data is then further processed into “bins” of wind speeds. In this case, the
bin width is 0.5 m/s (1.1mph) so that at 2 m/s, for instance, all the 1 minute averages with wind speeds ranging
from 1.75 m/s to 2.25 m/s are averaged together to arrive at the point defining the line in the Figure 14a. The data
can be compared to the total power in the wind as well as the theoretical extraction limit, or Betz limit, in Figure
14b.
a)
b)
Figure 14. Prototype Turbine Power Curve (September 20, 2008) a) 1 minute averages b) Power Curve, Betz Curve and
Total Wind Power
Data for a weeks worth of testing, from September 17-23, 2008, is illustrated in Figure 15a. Note that the line
drops back to zero if there are not more than 30 1 min averages in a given bin, however one can follow the trend by
eye for a reasonable estimate.
a)
b)
Figure 15. First Prototype Turbine Power Curve (September 17-23) a) Power Curve, Betz Curve and Total Wind Power
(1 min averages binned) b) System Efficiency, CPS
It is interesting to note that there are red data circles that indicate not only a higher power extraction than
the Betz limit, but even higher than the total wind power limit! The reason for this is the response time of the
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turbine to changes in the wind speed, as was described earlier by Gipe, and thus the need for time averaging. In the
case of the Wind Tamer, the hysteresis or “flywheel” effect is very large and thus there are a lot of points that
appear to be producing more power than the wind has available. This has both positive and negative
implications. The pros associated with a larger flywheel effect is that if the wind speed drops off momentarily, the
turbine is still producing power and thus the sensitivity to small, short period gusting and directional
changes is minimized. The downside is that if the wind speed spikes momentarily, the Wind Tamer will not
respond as quickly and thus will be unable to capture the peak power point.
The power coefficient values for the system, CPS, which includes the generator efficiency, are plotted in Figure
15b. The ideal open rotor Betz limit is represented by a value of Cp=0.593, and CPS will, of course, be lower, but
there are many points that “exceed” this value. These are a result of the flywheel effect and once the time
averaged values in each bin are averaged, the black line results.
Interestingly, the performance of the Wind Tamer compares favorably to the numerical predictions of mRotor in
Figure 8b. The efficiency is approaching 20% by the time wind speeds reach about 5 m/s (11 mph). Although this
is the un-optimized configuration of Figure 10a, it indicates that the diffuser for this configuration is not really
effective at all. Another look at Figure 1c indicates that the ratio of exit to inlet ratio is very small and in retrospect,
one can acknowledge this not to be effective.
C. Experimental Analysis – Second Generation Prototype
A prototype of the second generation 77” configuration was installed in Perry, NY, in mid 2009. Figure 16
illustrates the configuration. This unit was configured in a grid-connected mode using a Windy Boy inverter and a
custom charge controller. The hub height is approximately 13 feet off the ground
Figure 16: 77” Wind Tamer in Perry, NY
This turbine was used to optimize blade number and test for various blade geometries. Two primary
configurations were tested, the second using a lighter, smaller hub, and lighter thinner blades. These two sets of data
presented below reflect the behavior of the larger and smaller hubs.
Figure 17 illustrates an example data set of the power output acquired on May 31, 2009. Due to the nature of the
controller, the data consists of 5 minute averages acquired from the web box interface to the Windy Boy Inverter.
Hence these data represent conditions where the turbine was generating enough power to connect to the grid. Note
that this configuration, and the following set of data, did not have the optimum blade geometry twist from mRotor.
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Figure 17: Output Power of 77” Wind Tamer in Perry, NY – large hub configuration, May 31, 2009
In order to examine the effectiveness of the unit, the overall power turbine coefficient, CPS, was calculated, based on
the rotor area, and is shown in Figure 18. As can be seen the averaged power being produced is exceeding the
idealized Cp = 0.593 limit for an open rotor, noted by the dashed line at speeds from about 13 to 23 mph. This
indicates the diffuser is working and increasing the mass flow through the turbine, much more effectively than the
previous design.
Figure 18: CPS of 77” Wind Tamer in Perry, NY – large hub configuration, May 31, 2009
In an effort to improve the start up speed and responsiveness to the wind, the hub and blades were lightened on
the test turbine by about 21 lbs. Figure 19 illustrates the performance on June 12, 2009. The wind speed was
considerably lower than Figures 17 and 18.
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The system efficiency, CPS, was calculated, based on the rotor area, and is shown in Figure 19 on the left vertical
axis (blue circles) with power (red triangles) on the right. At speeds above 6 mph, the power being produced was
observed to exceed the Betz limit, based on the rotor area. CPS values reached values > 0.7. Although more data is
required to meet 30, 1 minute samples for each wind speed, the trend was very encouraging and illustrates the
potential of the WindTamerTM concept.
Figure 19: Output Power and Cp of 77” Wind Tamer in Perry, NY – small hub configuration, June 12, 2009
A mobile rig was also designed to be used with resistive loads by WindTamerTM to be used to both in a mobile mode
and towed to locations to obtain parked data. Figure 20 illustrates the setup. The hub height was approximately 13
feet off the ground. Data acquired with the rig parked is illustrated in Figure 21. The data was acquired every
second and the Cp efficiency values are presented in red for the 1 second data. In order to get a more representative
estimate of the efficiency, 1 minute averages were calculated are illustrated in green. It can be seen that CPS, and
hence even higher Cp values, based on the rotor area, are above the Betz efficiency, from about 4 to 8 m/s (about 9
to 18 mph).
Figure 20: WindTamerTM Mobile Test Rig with 52” Rotor
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Figure 21: WindTamerTM Mobile Test Rig Data, Parked, 271 Ohm Resistance, October 13, 2009
These data above appear to indicate that the WindTamerTM is capable of CPS values in the 0.6 to 0.8 range, well
above that of small wind turbines on the market today by almost a factor of 2, and above Cp values of the limit for
an open rotor. Further long term testing will be initiated at Clarkson University in the near future.
D. Preliminary CFD Results
In an effort to understand, and possibly
optimize, the diffuser for this turbine,
FLUENT, a computational fluid dynamics
code, was used to examine the impact of a
diffuser geometry on the rotor blades, modeled
by an axisymmetric fan with a pressure drop.
Figure 22 illustrates the baseline, open rotor
case, with an upstream velocity of 6 m/s and
flow from left to right. Viscous effects are
neglected and hence no boundary layers exist..
As a check on the viability of this type of
simple fan analysis, the open rotor fan results
yielded a Cp = 0.593.
Three different models were then analyzed,
to examine the general impact of diffuser shape
and rotor location. These included the baseline
diffuser geometry of the WindTamerTM, the
baseline modified with a straight duct segment
in front of the diffuser and the rotor in the same
location and lastly with the rotor at the forward
Figure 22: Idealized Rotor Modeled as a Fan in FLUENT
end of the duct. Figures 23 – 25 illustrate the
resulting calculated flow fields..
Unfortunately, the results have provided limited insight to date. Figure 23, the baseline WindTamerTM case
indicated a Cp of 0.619, not much better than an open rotor. Adding a straight segment of duct forward of the fan
face, Figure 24, yielded an increase to Cp = 0.66. A similar increase of Cp to 0.66 was also observed with the fan
face moved to the front of the constant area duct extension as shown in Figure 25. Both cases in Figure 24 and 25
were run at freestream speeds of 6 m/s. As can be seen, the velocity tends to increase substantially in the duct, but
the values of Cp did not seem reflect this “benefit” in an appreciable way
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Figure 23: WindTamerTM model
Figure 24: WindTamerTM model, fan at rear of extension
V. Concluding Remarks
Some closing comments on the nature of this type
of turbine might be useful for further reflection. There
are several potential benefits arising from this design
that have been observed by the authors in a
qualitative, rather than quantitative, fashion that
should be mentioned and the use of a proper area to
non-dimensionalize the power has provided some
controversy and so warrants a comment.
First, it appears that the turbine self-regulates
itself at higher wind speeds. It is possible that the
increased number of blades, which would improve
the aerodynamics, combined with the poor L/D of the
flat plate “airfoils” serves to limit the speed of at
turbine at some wind speed, essentially creating a flat
power curve at higher wind speeds. The implications
of this are quite large, that being that the annual
energy output (AEO) would be increased
substantially. While other turbines begin to furl at
Figure 25: WindTamerTM model, fan at front of extension
some speed above their rated speed, eventually falling
off in power production, the present configuration
continues to output power at the limiting rate.
Second, the higher solidity causes the optimum operating point to be at a much lower tip speed ratio, $, than
conventional open rotor designs. In this case it seems to operate best around a $=2. Although this may not be the
most efficient from a generator standpoint, it has been reported that the noise generated by a wind turbine scales
with tip speed ratio as a 5th power 21 and the turbine was observed to be very quiet under all loads in the field. Of
course, this would need to be substantiated with measurements.
Finally, the use of twisted flat plates reduces the cost of the blades to an almost negligible level and allows for an
increased blade number for little extra cost. The current blades are constructed from plate aluminum, however there
are other light weight alternatives that could also be utilized.
The bottom line for a successful product in the market would seem to be the cost of energy produced, namely
$/kWh. The presence of the duct improves the power output and if it can do so at a lower cost than increasing the
rotor size, a benefit would be had.
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Regarding the means, and possible ensuing controversy, by which the measured power data should be nondimensionalized, since the power produced exceeds an open rotor of the same diameter and hence one might be
inclined to conclude the Betz limit has been “broken”, it seems that the use of the power in the captured stream tube
would appears to be the most fundamental approach. The shroud area would not seem to be anymore correct as a
non-dimensionalizing area, representing a more "correct" stream tube, than the area of an open rotor, albeit for
different reasons. It is a different physical process. Even for an open rotor, the captured stream tube is technically
not the rotor diameter, since the upstream tube expands as it nears the rotor and only a certain fraction goes through
the rotor. In fact, if one was to put a duct around a rotor that happened to lie on the expanding streamlines, it would
have no effect at all, and the use of the “duct area” would be meaningless. Thus, the question of whether the "Betz
limit" is even defined appropriately in it’s current use for actual, open rotor flows, being that the rotor lies in the
midst of the expanding stream tube, is a valid one.
Acknowledgments
The authors would like to express their appreciation to the WindTamerTM Corporation for their support of the
project and graduate students Benjamin Kayna, and Daniel Hetzel for their assistance.
References
1
Phillips, D. G. “An Investigation on Diffuser Augmented Wind Turbine Design”. Auckland, New Zealand. Doctoral Thesis
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