Aerodynamic Optimization of Contra-Rotating VAWT
Honors Thesis Proposal
Student: David Olson
Advisor: Dr. Kenneth Visser
Objective:
The objective of this thesis is to evaluate the possibility of a self-starting, lift-driven, contra-rotating,
vertical axis wind turbine (CR-VAWT) for use in a home heating system. A numerical model will be
utilized to predict the performance and design the turbine. The feasibility of a drag driven CR-VAWT has
been demonstrated but the potential of a lift driven, Darrieus turbine, is much greater; the problem is
Darrieus turbines are not self-starting. The primary goals are: development of suitable computational
performance and annual energy production prediction model for the CR-VAWT, the design and
optimization of the blade design for the CR-VAWT, and the construction of a ¼ scale prototype to
demonstrate the concept in the upcoming heating season.
Motivation:
Global energy demand is predicted to continually increase as fossil fuels are rising in price and are
known to have adverse effects on the environment. Renewable energy is however the alternative to
match energy demand and while remaining environmentally conscious. In general, renewable energy
production costs more than traditional power sources such as coal and natural gas. Renewable energy is
also hindered by relatively larger initial capital costs. If renewable energy sources can be financially
competitive to traditional power sources then it will overtake much of the market.
One type of renewable energy source is the wind. Wind is simply air moving from areas of high pressure
to areas of lower pressure. These pressure differences are created by the cyclic heating and cooling of
the planet by the sun. (Johnson, 2001) It is sufficient to understand that the wind will exist as long as the
earth is heated by the sun and that the complexities involved in its prediction dictate the use of statistics
to determine the mean and distribution of the wind. The wind is also an attractive power source due to
its magnitude, since less than 20% of the available power in the wind is required to meet world energy
demand purposes. (Archer, et al., 2005)
Wind Energy Basics
General Characteristics of Wind Power
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]
(Johnson, 2001)
Power is defined as the time-rate of kinetic energy and by relating mass to the density, , and the crosssectional area, A it may be written as:
[Watts]
(Johnson, 2001)
From linear momentum theory the theoretical maximum power extraction from an actuator disk, or
specifically a wind turbine, is
or 0.593. (Johnson, 2001) (Burton, et al., 2001) 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. (Miller, et al., 2003) 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:
(Archer, et al., 2005) (Burton, et al., 2001)
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, utilitygrade 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:
(Rector, et al., 2006)
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 (Miller, et al., 2003)
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. (Burton, et al., 2001)
Weibull Probability Density
(Devore, et al., 2005)
0.18
K=2|=5
The Weibull distribution is a function of
two parameters: the shape parameter,
k, and the scale factor, . These two
The scale parameter, , corresponds to
K = 2 |  = 10
K = 1.5 |  = 5
0.14
K = 1.5 |  = 10
0.12
Probability
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
0
the average wind speed for the site.
0
5
10
15
20
25
30
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.
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 2 – HAWT (2006)
Figure 3 – VAWT (Sandia National Laboratories)
Two distinct VAWT designs currently exist: lift driven Darrieus turbines (pictured in figure 3), 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. (Burton, et al., 2001) 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. (Sandia National Laboratories)
Contra Rotating Concept
All of the wind turbines discussed thus far rotate in only one direction at a time. The contra-rotating (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.
A combination lift and drag driven turbine, the Lenz turbine, is of particular interest. The Lenz turbine is
both lift and drag driven. The goal is to be self starting and capable of achieving higher tip speed ratios.
The Lenz turbine was designed by Ed Lenz and is currently used by PacWind in several small, 1-10kw
turbines. (Lenz, 2005) (Pac08) The designs utilize innovative airfoil designs which have drastically
different characteristics based on angle of attack.
Figure 4 – CR-VAWT (Czajkowski, 2008)
Figure 5 – Lenz Turbine (Lenz, 2005)
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 6, 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 6 - Results of CR-VAWT (Czajkowski, 2008)
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. (Czajkowski, 2008)
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 7 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 7 - Cyclic-averaged mean streamlines for a VAWT (Bertenyi, et al., 2007)
VAWT Airfoil Selection
Symmetric airfoils have been used primarily for the lift-driven Darrieus turbines. Extensive
computational and experimental work has been done analyzing these symmetric airfoils, particularly the
NACA 0012 (Sheldahl, et al., 1981) (Strickland, 1975).
A combination lift and drag driven turbine, the Lenz turbine, is of particular interest to be self starting
and capable of achieving higher tip speed ratios. Such a turbine would combine the strengths of both
the lift driven and drag driven turbines. The Lenz turbine was designed by Ed Lenz and derivatives are
currently used by PacWind in several small, 1-10kw turbines (Lenz, 2005) (Pac08).
The airfoils under consideration to achieve the performance goals are: single-sided airfoils (pictured in
Figures 4 and 5), doubled-sided open airfoils (Figure 8), and derivatives of the Kline-Fogleman stepped
airfoils.
Figure 8 - Double Sided Open Airfoil
Project Details
The thesis project has three primary parts: computational model, prototype construction and prototype
testing. The key contribution to the overall project which constitutes the thesis is the optimization and
design of the turbine blades.
The computational model will analyze the geometry of the problem and allow a simplified performance
model to be evaluated. Pre-existing computational tools, XFOIL and FLUENT, will be utilized for to
estimate the aerodynamic characteristics of new airfoils. The computational tools are necessary to
analyze the airfoils that the turbine will be based off of: no data currently exists for this airfoil design.
The progress made thus far can be seen in Figure 9.
Figure 9 - VAWTSIM Program
The Computational model seeks to provide: visual animations of the velocity and force vectors acting on
the blades, a simplified performance prediction model (determining power output) for airfoils with
known aerodynamic characteristics. The performance model will start will not include blade interaction
effects: it will only be suitable to relatively compare different airfoils and geometric configurations. An
advance model, incorporating blade interactions and flow field interactions would be the next logical
step for continuing the computational tool.
A statistical analysis will be taken into account for the optimization scheme. The performance metric to
be maximized is the net annual energy production (AEP), which is highly depended on the wind speed
and distribution as previously discussed. The AEP will be compared for different airfoils / blade
configurations and this data will provide the basis for blade choice on the prototype.
The prototype construction phase of the project will rely heavily on the design of pre-existing VAWTs ,
the work done by Mark Czajkowski (Clarkson University, Honors Thesis) in 2007-2008, and additional
contra-rotating devices. The prototype will be a joint project with Joseph Cipollina (Clarkson University,
Honors Thesis, Class of 2009) whose thesis is on the design of the generator and gearing for the turbine.
Assistance in construction / design of the prototype will be obtained through additional research
assistants during the summer. The prototype will be designed to produce, at rated conditions, between
1 and 10 kW.
The prototype will be tested to verify the computational work done and to further develop and optimize
the turbine. The planned prototype will not fit inside any of the available wind tunnels. The turbine will
be tested using several large industrial fans. The fans will simulate a constant wind for testing and
evaluating designs.
The prototype will also be used to evaluate different configurations of the turbine. Two of the possible
configurations are: one set of blades inside another, and blades stacked one on top of another.
Additional configurations and designs will become apparent as the project progresses.
Time Table
The first part of the thesis, the computational analysis is to be completed by the end of the 2008 spring
semester. Initial computational experiments utilizing XFOIL and FLUENT will also begin in the spring
semester. This will lay the groundwork for beginning summer research. The summer research, spent
here at Clarkson, will comprise of the design, analysis and optimization of different blade designs. The
turbine structure will be designed and constructed as well.
Experiments will begin in the late summer and continue into the fall. The testing beginning in the late
summer would primarily be for developing a working prototype.
Expected Results
The feasibility of the contra-rotating concept had been determined by the work previously done by
Mark Czajkowski. However, that concept was drag driven and the new prototypes will be optimized
based on a combination lift and drag driven design. It is hypothesized that the turbine will have better
performance than the solely lift-driven turbines at low tip speed ratios and perform better than the
solely drag-driven turbines at high tip speed ratios.
The performance model generated and used for design is expected to provide upper bounds for the
performance of the turbine. The trends seen in the computational model is expected to hold true for the
actual prototype. If this is not the case then re-evaluation of the performance and optimization models
would be warranted to match closer to the experimental data and trends. The re-evaluated model could
then be used in greater confidence to optimize the design.
A highly successful project would result in a prototype that would be advantageous to market as a new
turbine type. The annual energy production of the turbine would be compared to equivalent existing
VAWT’s, if the results are similar then the turbine deign is highly successful and would warrant
additional resources to further research the concept.
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