Self-Starting Contra-Rotating Vertical Axis
Wind Turbine for Home Heating Applications
David Olson1 and Ken Visser2
Department of Mechanical and Aeronautical Engineering
The Darrieus turbine has been proven for commercial grid connected utility scale operations; it has not
however been fully adapted to small scale stand-alone applications. The market for small scale
commercially viable wind turbines is expanding from an economic standpoint and the social “going green”
phenomena. The Contra-rotating concept has been previously determined to be feasible and a new analysis
yields a higher theoretical maximum efficiency than a normal VAWT or HAWT. The objectives of the project
will design, build and test a self-starting contra-rotating vertical axis wind turbine in the Clarkson University
High Speed Wind Tunnel.
Introduction
The wind is comprised of a homogenous fluid moving with some velocity. Air, although
transparent and light has mass and therefore, kinetic energy. The kinetic energy of a parcel of
air, with mass m and speed of u in the x-direction is:
[Joules]
(1)
Power is defined as the time-rate of kinetic energy and by relating mass to the density,
the cross-sectional area, A it may be written as:
[Watts]
, and
(1)
From linear momentum theory the theoretical maximum power extraction from an actuator
disk, or specifically a wind turbine, is
or 0.593. (1) (2) This value is known as the Betz limit
which is reduced to the statement: no more than 59.3% of the available power in the wind can
be extracted. No turbine to date has exceeded this limit. (3) It is convenient to correlate turbine
output to available power in terms of Cp or the Power Coefficient; the following convention will
be used to define this value:
1
2
Student, Aeronautical Engineering 2009, Honors Program
Advisor, Department of Mechanical and Aeronautical Engineering
(4) (2)
Where Pm is the mechanical power extracted. The Power Coefficient is not constant, varying
widely across with wind speed due to aerodynamic complexities of blade designs; typical peak
values (or Cp rated) are between 30% and 45% with the upper bounds found in highly
sophisticated, variable pitch,
utility-grade turbines. A typical Cp
versus
(tip speed ratio) curve
for multiple blade pitch angles ( )
is shown in Figure 1. Tip speed
ratio,
, is defined as:
(5)
Where r is the rotor radius,
is
the angular velocity of the turbine
and u is the wind velocity
upstream. The Cp- has a specific
trend with design implications:
there exists an optimum tip speed
ratio for a given pitch angle.
Figure 1 (3)
Annual Energy Production
Although the power production capabilities of the turbine are emphasized for design and
marketing, the most important aspect is the total energy output. The net energy production of a
turbine is a function of the specific turbine characteristics, the wind speed and duration.
Incorporating both the turbine characteristics and wind statistics a turbine’s annual energy
production can be estimated. The annual energy production is a primary evaluation method for
turbines and will be utilized for comparisons.
The specific characteristics of a turbine, when combined with the wind speed distribution will
yield a more accurate evaluation of the effectiveness of a turbine. Certain turbines may be
optimized to efficiently produce energy at low to moderate wind speeds whereas others may be
optimized for higher wind speeds. Utilizing statistical distributions of wind speeds the annual
energy production may be quantized and evaluated for various optimization schemes to
produce a solid basis for comparing turbine outputs and determining economic feasibilities.
Wind Statistics
The highly dependent nature of power production on wind speed necessitates accurate
predictions for wind speeds in any proposed location. However, the wind is not highly
predictable and a simple average wind speed for a location does not suffice in providing enough
information for determining the annual energy production of a turbine. It is important to know
both the average speed and the distribution of wind speeds for a location for an accurate energy
production calculation.
The Weibull density distribution is a commonly applied statistical distribution to model wind
speed distributions. The Weibull curve is a probability density function and indicates both the
frequency and magnitude of a given
wind speed over a period of time. (2)
Weibull Probability Density
(6)
0.18
K=2|=5
The Weibull distribution is a function of
two parameters: the shape parameter,
K = 2 |  = 10
K = 1.5 |  = 5
0.14
K = 1.5 |  = 10
0.12
Probability
k, and the scale factor, . These two
parameters define the shape or
steepness of the curve and the mean
value of the distribution. For modeling
wind, typical k values range from 1 to
2.5 and can vary drastically form site to
site.
0.16
0.1
0.08
0.06
0.04
0.02
The scale parameter, , corresponds
0
0
5
10
15
20
25
to the average wind speed for the site.
Wind Speed
The main inaccuracy of the Weibull
Figure 2 - Weibull Curve
distribution is that it always has a zero
probability of zero wind speed, which is not the case, since there are frequently times in which
no wind is blowing. However, the fault is virtually without consequence because most turbines
will not operate in speeds below 3 m/s and the distribution is more accurate, compared to
measured data, within the zone most used by turbines: 8 to 14 m/s.
Figure 2 shows four different distributions. The higher the k value, the sharper the increasing
part of the curve is. The higher
values correspond to a shorter and fatter distribution, with a
higher mean value. Ideally the mean value would correlate with the rated wind speed of the
turbine: producing rated power for the greatest period of time annually.
30
The availability of high quality wind speed distributions is crucial to accurate forecasts of annual
energy production for a wind turbine. Statistical distributions suffice for early estimations,
however actual wind speed measurements are necessary for accurate predictions.
Wind Turbine Classification
Wind turbines have two main classes, named for the axis in which the shaft rotates: horizontal
and vertical axis. The horizontal axis is the more common type; it is the main type both General
Electric and Siemens manufacture for utility grade electricity production. The vertical axis wind
turbines (VAWT) tend to be of a smaller scale, and are popular in California. VAWTs will be
discussed in further detail.
Figure 3– HAWT (7)
Figure 4 – VAWT (8)
Two distinct VAWT designs currently exist: lift driven Darrieus turbines (pictured in figure 4), and
drag driven Savonius turbines. The lift driven Darrieus turbines are typically not self-starting but
are capable of achieving higher tip speed ratios and higher efficiencies. (2) The Savonius turbines
are typically self-starting but are limited to lower tip speed ratios. The lift driven, Darrieus
turbines were researched in great depth by Sandia after the 1973 Arab oil embargo. (8)
Contra Rotating Concept
All of the wind turbines discussed thus far rotate in only one direction at a time. The contrarotating (CR) type has two sets of blades which rotate in opposite directions at the same time.
Both horizontal and vertical axis contra-rotating turbines have been designed and tested at
Clarkson University.
The contra-rotating turbine has been researched by Curtis M. Rector and Mark Czajkowski under
Dr. Kenneth Visser at Clarkson University. Curtis’s dissertation, “Feasibility Study of a Small
Contra-Rotating Horizontal-Axis Wind Turbine” utilized the HAWT design with a specially
designed contra-rotating generator. Mark’s Honors Thesis, “Feasibility of a Unique Wind
Powered Home Heating System” evaluated the CR concept applied to a VAWT. The feasibility
studies previously conducted provides sufficient evidence to look closer at the concept to
eventually produce quantifiable comparisons to other turbines. Figure 5, a plot of power output
versus wind tunnel velocity demonstrates some of the supporting evidence for the CR-VAWT.
The plot shows a large difference between the power output of the CR-VAWT operating in
contra-mode and the sum of the power produced by the individual rotors operating
independent of one another.
Wind Speed vs Power Output - Outide Rotor: 5in
0.7
0.6
Sum of Both Spinning in Contra Mode
Outside Rotor Only
Inside Rotor Only
Sum of Inside and Outside Rotors
Power Output (W)
0.5
0.4
0.3
0.2
0.1
0
13
14
15
16
17
18
Wind Tunnel Velocity (m/s)
19
20
21
Figure 5 - Results of CR-VAWT (9)
The contra-rotation concept has been used for other applications. The Fairey Gannet, Kamov
helicopter, Azimuth Propeller, and RC helicopters employ contra-rotating propulsion systems.
(9) The torque produced by each set of blades of the helicopters cancel one another out,
producing a stable flight without requiring a tail rotor, (simplified controls and ease of use for
the RC beginner).
Aerodynamic advantages to contra-rotating turbines have been studied previously for HAWTs at
Clarkson. No known previous work has been done on CR-VAWTs. The advantages for VAWT are
currently not known. Figure 6 shows the cyclic-average mean streamlines for a VAWT with a
solidity of 2.8, and operating at a tip speed ratio of 4.5 with a counter-clockwise rotation. The
streamlines are skewed with a counter-clockwise rotation off the downwind section of the
turbine. A clockwise rotating turbine would produce an opposite skew. The combination of the
two, the formulation of a CR-VAWT, is hypothesized to cancel one another out: straightening
out the streamlines. This straightening affect would have positive aerodynamic benefits in terms
of overall turbine performance.
Skewed streamlines
Figure 6 - Cyclic-averaged mean streamlines for a VAWT (10)
Results / Progress
Maximum Theoretical Efficiency
The maximum theoretical efficiency of a wind turbine, modeled as a uniformly loaded actuator
disk, may be derived using the laws of conservation of mass, momentum and energy (11). The
accepted maximum efficiency for an actuator disk is 59.3%, known as the Lanchester-Betz or
Lanchester-Betz-Joukowsky Limit (12) (13) (14). This limit was shown to be pessimistic for the
VAWT due to the rotor intercepting the fluid twice per rotation (15). The maximum efficiency,
utilizing the same strategy used in the derivation of the Lanchester-Betz-Joukowsky Limit, was
determined to be 64% for two actuator disks in series (11) (13).
A similar derivation as outlined in (11) was applied to the contra-rotating concept. The contrarotating concept has 2 concentric rotors which were modeled as 4 actuator disks in series, two in
the upwind zone and 2 in the downwind zone. The power extracted by the turbine is a function of
the change in axial momentum across each disk:
[Eq. 1]
,
,
,
[Eq. 2-5]
The maximum power extraction was determined by solving Equations 2-5 and subsequent
substitution and simplification. To facilitate further exploration of the maximum theoretically
efficiency a symbolic computational program was formulated to determine the efficiency of an
arbitrary number of actuator disks in series. The computational case study determined:
[Eq. 6]
For the infinite case, this can be visually confirmed in Figure 7.
Figure 7 - Maximum Efficiency of Tandem Actuator Disks
Methods to improve Self-Starting Capabilities
The Darrieus Turbine, a lift-driven VAWT, is, in general, not self starting due to a dead band of
negative torque or power coefficients typically between tip speed ratios of 0.5 and 3.0
depending on the blade airfoil (16) (17). This dead band is due to the blade operating within
stall and post-stall conditions during its rotation. Typically a grid-connected VAWT are powered
up to a sufficiency high tip speed ratio using a motor-generator and then transition to power
production; this is not acceptable for home heating or stand-alone applications. Two primary
areas can be looked at to improve the self-starting capabilities of the Darrieus turbine:
airfoil/blade design and pitch control.
An exhaustive review of all current methods of improving self-starting capabilities may be found
in (18) (16), an abbreviated review is listed here for applicable methods.
Methods of improving self-starting capabilities in the airfoil/blade design section include:
increased thickness, cambered airfoils, flexible or reversible camber airfoils, and increased
solidity. Methods in the pitch control area include passive and active pitch control, where both
attempt to lower the relative angle of attack just below stall to improved aerodynamic
efficiency.
Prototype Design: Airfoil Selection
The simplest methods are the modifications to the blade airfoil, increasing the thickness and
utilizing cambered airfoils. An airfoil was designed in (16) to be self-starting by introducing
camber and thickness to the NACA0018 airfoil, known as the DU-06-W-200, and is shown in
Figure 8. Outlined in (18) the use of the S1210 airfoil section should be self-starting and achieve
comparable efficiencies at lower tip speed ratios than blades with symmetrical sections. The
S1210 airfoil is shown in Figure 9.
Figure 8 - DU 06-W-200 Airfoil
Figure 9 - SG1210 Airfoil
The performance prediction curves for a straight-bladed VAWT with the DU 06-W-200 airfoil and
S1210 airfoils are shown in Figures 10 and 11. The operating tip speed ratios are 3 and 2.75; low
in comparison to symmetrical airfoils but not at a disadvantage for home heating applications.
The low tip speed rations will reduce noise and not be a factor in generator efficiency because
no electrical generator will be used. The maximum efficiencies are 0.47 and 0.33; the DU 06-W200 airfoil will be the first airfoil used in testing.
Figure 10 – Performance Prediction DU 06-W-200 (16)
Figure 11 - Performance Prediction of S1210 Airfoil (18)
Conclusions
The traditional Darrieus Turbine will not suffice for stand-alone home heating applications: it
must be optimized for self-starting capabilities. The contra-rotating concept has proven to have
a theoretically higher maximum efficiency; the controlled testing of the prototype will permit
the confirmation or rejection of the postulated advantages of concentric rotors from and
aerodynamic perspective. The DU 06-W-200 and S1210 airfoil sections will be used in the next
phase of the project: design and manufacturing of the prototype. The prototype will be
manufactured by mid-fall assuming design completion by the begging of the 2008 Fall Semester.
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