IEEE ISIE 2006, July 9-12, 2006, Montreal, Quebec, Canada

Design Considerations of a Straight Bladed

Darrieus Rotor for River Current Turbines
M. J. Khan*,M. T. Iqbal,and J. E. Quaicoe
Faculty of Engineering and Applied Science
Memorial University of Newfoundland, St. John's, NL, AlB3X5
*Email: mjakhan@engr.mun.ca
Telephone: (709) 737-2049, Fax: (709) 737-8975

Abstract- Hydrokinetic turbines convert kinetic energy of bearing, electrical generator, power conditioning, and end
moving river or tide water into electrical energy. In this load unit (Fig.l(a)). The prime objective of the system is
work, design considerations of river current turbines are dis- to convert mechanical energy into electrical form. Therefore,
cussed with emphasis on straight bladed Darrieus rotors. Fluid
dynamic analysis is carried out to predict the performance investigation of the rotor's performance is of great importance
of the rotor. Discussions on a broad range of physical and and this aspect is emphasized here in this discussion.
operational conditions that may impact the design scenario are
also presented. In addition, a systematic design procedure along Generator Load Power,
Generator Power, Pge
with supporting information that would aid various decision Pout
making steps are outlined and illustrated by a design example. ZII
Finally, the scope for further work is highlighted.
Load
I. INTRODUCTION
Among various types of vertical axis wind and hydroki-
netic turbines, the Darrieus rotor configuration has gained Hydrokinetic
significant attention owing to its unique performance, opera- Power, Ph,d h Airfoil section
tional and design features. French inventor G. J. M Darrieus
patented this concept in 1931 with the U.S. Patent Office,
V
I/
-- C------
which employs a set of curved blades approximating the I
(a) (b)
shape of a perfectly flexible cable, namely the Troposkien
shape. Later vertical axis designs comprising straight blades Fig. 1. Turbine system components
appeared under names such as, 'H-Darrieus' or 'Squirrel
Cage Darrieus' turbines [1], [2]. The hydrokinetic power input Phyd (W) can be related
Although most vertical axis turbines were studied for wind to the rotor's mechanical power capture Prot (W) by a term
energy conversion, these concepts can be equally imparted in commonly know as power coefficient Cp, which is a measure
hydro applications. River Current Turbines (RCT) and tidal of the turbine's hydrodynamic efficiency.
energy converters are examples of such hydrokinetic turbines Prot = CPPhyd (1)
where kinetic energy of moving water is converted into usable For a turbine with an effective swept area of A (m2)
forms of electrical or mechanical energy. Research efforts in placed in a fluid body having velocity V (m/is) and density
this field of energy engineering, especially in River Current
p (kg/m3), this expression can be re-written as
Turbine technology, are rather scarce and the knowledgebase
is quite deficient. Prot = Cp2pAV3 (2)
In this work,analysis and streamtube modeling of this 2
turbine are carried out with a view to bringing insight into In most literature, the two dimensionless quantities: power
its performance. As the prime focus of this article, various coefficient Cp and the tip speed ratio A are used for illus-
design considerations based on a set of general criteria as well trating the effectiveness of a turbine's power extraction at
as fluid dynamic factors are presented. Available information various rotational conditions. Here, tip speed ratio A is an
in wind, tidal, and river energy engineering has been used in index of rotor's rotational speed w (rad/s) against the fluid
formulating the understanding of various subjacent issues. velocity V. This is defined as
wr
II. CONSIDERATIONS FOR FLUID DYNAMIC ANALYSIS A (3)
V
Performance analysis of a straight bladed Darrieus type where, r is the rotor's radius in meters. Another term,
hydrokinetic rotor can be carried out by utilizing the conven- torque coefficient CT is equally important in indicating the
tional methods of wind and tidal energy studies. A typical performance of a turbine. This is defined as
turbine unit employed in electricity generation may consist Cp
of a rotor structure along with components such as, gearing, CT A (4)

1-4244-0497-5/06/$20.00 © 2006 IEEE 1 750

 A set of Cp vs. A curves is shown in Fig.2, which motion against the water flow. For a well-designed system
illustrates the superiority of horizontal axis propeller type the drag force generated during the process is typically
and Darrieus turbines against other rotor options in terms of smaller than the lift component. For a given blade shape and
efficiency. However, drag type turbines (such as, Savonious Reynold's number, the lift/drag coefficient data is commonly
and Multiblade types) have better starting capabilities. available in chart/graphical forms tabulated/plotted against
angle of attack information [1], [3]. The cumulative effect
ALi Betz Limit (0.59)
of these forces can be further separated along the normal and
0.6 -

Ideal Propel
tangential axes of the blade, where the tangential component
065
~~~~~~~High speed Propeller is responsible for rotating the rotor. With a given rotational
4 speed w, and upstream velocity V, the rotor blades develop
c) Dariu
varying levels of attack angles a with changing azimuth angle
042
0.3
3/American Multiblade
<
\
\
0 (Fig.4(a)).

v~~~~~~~~~uc kur Arrnm

0.1
Tangential) V
axis \
1 2 3 4 5 6 7 8
Tip Speed Ratio,

Fig. 2. Performance of various rotors

The theoretical maximum value of the power coefficient -30 .. . .. .... ........

Cp is known as the Betz limit, which has a numerical value

------------

-50
0 60 120 180 240 300 360
of 0.59. The use of augmentation channels or ducts around Azimuth angle, 0

a turbine may increase this theoretical limit by concentrating (b)

the incoming energy flux toward the rotor.

In order to develop an insight into the working principle of Fig. 4. Blade-flow interaction
a turbine, the pressure and velocity distribution around a rotor
and their subsequent effects on the blades need to be studied The expression given in (6) can be used to determine the
using the principles of fluid dynamics. As an approaching angle of attack developed in the blade as it travels along
stream of fluid interacts with the rotor disk, the pressure right the circular periphery of the rotating disk. Such variation in
before and after the rotor becomes equal in magnitude but angle of attack along the blade's traveling path is shown in
opposite in sign compared to the surrounding pressure. The Fig.4(b).ine the angle of attack developed in the blade as it
boundary of the stream tube also diverges from the turbine travels along the circular periphery of the rotating disk. Such
in the wake of the rotating body. The upstream velocity V variation in angle of attack along the blade's traveling path
reduces to Vrot at the rotor disk, which reduces further to is shown in Fig.4(b).
downstream velocity Vdwn as shown in Fig.3. Under such
-(1-a) sin 0A
circumstances, the term induction factor, a is defined as, a
og~~(
tn(1a) sinO +
tan-
= (6)
A)
1 Vrot (5) The tangential force component, which effectively deter-
V
mines the cumulative affect that cause the rotor to rotate, can
be expressed in terms of an associated force coefficient Ctang

-u-
Ctang CL sin a- CD cos a (7)
Distance
where, CL and CD are lift and drag coefficients of the airfoil
blade. These two parameters solely depend on the blade shape
and Reynolds number under a given operating condition,
and need to be accessed using proper set of tabulated data.
Commonly available data sets such as in, [1], [3] are not
readily usable for analysis of Darrieus turbines that are used
Usram --__
,>V Rotor
in hydro applications. These tables typically contain lift/drag
information for high Reynolds number, low angle of attack
and infinite blade aspect ratio. Suitable corrective measures
Distance
need to be performed on available data sets in order to use
Fig. 3. Pressure and velocity distribution around a turbine them in further fluid dynamic analysis. These three issues are
briefly addressed in the discussions below:
Darrieus turbines employ airfoil shaped blades, which * Reynold's Number modification: Reynolds number is an
primarily utilize the lift force generated due to the blade's index of turbulence created by a body placed in fluid

1751
 [1], [4]. This can be expressed as
=Vv
Re RV.d (8)
where, v = 1.1 x 10-6 is the kinematic viscosity of v).
water [4]. For a given rotor diameter d and wsater .2

velocity V, an estimate of Re can be found. For tthis

work, Re is taken to be 1.5 x 106, which is in Iline
with similar reported works [5]. However, most air foil
data are not readily tabulated for this particular Reync )1ds
Angle of attack, a
number and corrective measures need to undertalken
before using such data [2].
Aspect ratio modification: Aspect ratio of a blade iiR11!
measure of its length and slenderness. For a blade M ith Fig. 6. Modified airfoil data (NACA 63-018 with AR = 10, Re = 2 x 106)
chord length c and height h (Fig. 1), the aspect rati( D is
defined as Two common methods applied in this regard are: simple
AR h (9) momentum (single or multiple streamtube) modeling and
c
Typical airfoil data is given for infinite aspect ratio complex vortex modeling [1], [2]. As the name implies, in
whereas a true blade is of finite length. This calls f single streamtube modeling, the performance of the complete
rotor is determined on the basis of computations done on
a modification of available data for a given applicat ion
one single tube of streaming fluid. On the other hand, in
case.
Angle of attack modification: Lift and drag data are multiple streamtube analysis, a series of equal streamtubes
11 are assumed to pass through the rotor. For each tube, the
normally available for low angle of attacks (typica
10 -20), as shown in Fig. 5. However, for a Darri
eu
llyu momentum equations are computed and the effects of all the
streamtubes are integrated in order to determine the forces
turbine, this angle may vary widely depending oi a

blade's position and speed (Fig.4(b)). Performance ar al- acting on a rotor blade. Although, single streamtube modeling
has proven to be sufficiently accurate for most applications,
ysis of such a turbine will fail unless data modificat ion
this method fails to explain the flow fields around the
for high angle of attack instances is incorporated.
rotor. On the other extreme, methods such as vortex models
I.,
and double-multiple streamtube models are more accurate
only when proper assumptions and inputs are incorporated.
Therefore, in this work, multiple streamtube modeling has
11 .. .. ... ...

been adopted in order to maintain reasonable accuracy and

simplicity by utilizing the computing capabilities of modern
.u

v 0.5 day computers.

Under such modeling approach, the torque coefficient of a
ov0 2 4 6 8 10 12 14 16 18L 2(.o
straight bladed Darrieus turbine is given as [2]
Angle of attack, a m 2
0.02
(a)
E( V ) Ctang
i=l
CT = 0- m
(10)
Q 0.015- where, m is the number of streamtubes and a is the rotor
solidity, defined as
0.01 ... / NC
o. 07 (1 1)
d
.005 L5 -- here, N is the number of blades, c is the blade chord
0 1 2 3 4 6 7 8 9 1(0
Angle of attack, a
length and d is the rotor diameter. Integrating the torque
(b) contributions of each streamtube, the torque coefficient CT
can be determined using (10). The power coefficient Cp can
then be evaluated using (4).
Fig. 5. Typical airfoil data (NACA 63-018) Following the aforementioned steps for multiple stream-
tube modeling, a set of performance curves for the straight
A procedure detailed in [2] can be utilized to obtain corrected bladed Darrieus (solidity 25%, NACA 63-018 blades) is
airfoil data. Employing these computations in Matlab [6], obtained and is plotted in Fig.7.
significantly divergent plots for the airfoil NACA 63-018 is As seen in this figure, the power and torque capabilities of
found (Fig.5, Fig.6). the Darrieus rotor are poor in the low tip speed conditions.
Fluid dynamic performance prediction of Darrieus rotors Although varying levels of rotor solidity may shift these
can be approached through detailed mathematical modeling. curves right or left, the starting problem remains. The starting

1752
 TABLE I
TYPICAL EFFICIENCY VALUES

Efficiency term Typical value Ref.

0.4 .. ~~~ Hydrodynamic,Cp 0.45 [7], [12], [131
t~~~~~
Gearing-bearing,?7dr0 0.90 [9]
0.3 .. .. Generator,71gen 0.875 [9]
Power Converter,'7con 0.875 [9]

0.1
The input value of water density may vary significantly
for a given site (river and ocean), which may further relate
0 1 2 3 4 5 6
Tip Speed Ratio, A to annual average temperature and geographical location.
Decision on this parameter can be made through the chart
Fig. 7. Performance plot of a Darrieus turbine (solidity 25%, NACA 63-018 shown in Fig. 8(a)
blades)

torque depends on the rotor's angular position as shown in

Fig.4(b). The turbine may self-start if a blade is held securely
in the optimum position where the generated tangential
force exceeds the starting requirements. This problem may
also be approached by external mechanical, electrical or
electromechanical means. 2.0 3.0 4.0 20 40 60
(a) Salinity (%) (b) Percentage time
III. DESIGN OF STRAIGHT BLADED DARRIEUS ROTOR
Fig. 8. (a)Water density variations (b) Velocity duration curves and resource
The design problem of straight bladed Darrieus rotor is classification
essentially an optimization problem where decision on the
rotor's structure, dimension and blade design is sought. For A decision on water velocity, which may also be termed
a given application (river or tidal energy), resource dependent as rated velocity from design point of view, is an unsolved
parameters such as, water density and mean annual flow need problem by its own merits. This term may comprise several
to be incorporated. Apart from common knowledge of system other factors as given in (14):
designing, fluid dynamic considerations are also brought in
during the design process. V = Vmean faug fecon (14)
Amongst the two types of straight bladed Darrieus turbine, Here, Vmean stands for mean river water velocity. Deciding a
the H-Darrieus rotor is mostly used in larger turbines where value for this term requires study of water velocity patterns
mechanical strength is of great significance [7]. In smaller in various rivers on a global basis. Reasonable values can
turbines, use of H-type structure may cause significant tur- be selected and resource qualities can be tagged against each
bulence, reducing the turbine efficiency. Therefore, squirrel velocity level. In the absence of such a detailed study, a result
cage configuration is suited for low scale power generation as of a micro scale investigation reported in [14] is opted in
exemplified in [8]-[11]. In the discussions to follow, this type this exercise (Fig. 8(b)).
of rotor will be considered, although the design of H-Darrieus The augmentation factor faag in (14) essentially incorpo-
rotors can also be approached using the same technique. rates the effects of adding a channel augmentation device.
A. Basic Dimensioning A moderate value of faag = 1.5 is considered in this work,
whereas reports of even higher value is available in [14],
For the cylindrical shape of the straight-bladed squirrel [15]. The remaining term in the velocity expression,fecon
cage rotor, basic dimensioning implies a decision on the relates the economics of a turbine operating in varying
choice of rotor diameter and height. The design process can velocities around the year. Discussions on optimal choice of
be initiated by modifying the power expression given in (2) rated velocity for variable speed wind turbines can be found
for incorporating overall system efficiency as given in (12). in [16]. Use of this factor is common in wind turbine designs,
where a typical rated wind velocity is around 10 -12 m/rs
Pout =rjSys2pAV3
2
(12) even if the site mean velocity is 7- 8 m/rs. In this work, a
The overall system efficiency rj,y, is defined in terms of more conservative value fecon = 1.5 is chosen.
efficiency contributions of all the cascaded stages (Fig.l(a)) Using the factual values of water density, rated velocity
as given in the equation, and efficiency terms in (12), the swept rotor area A can
be determined for a given level of desired output power.
Tjsys Cp.qTdrv *Tgen* 1con (13) The effective area encountered by the water is essentially
a rectangle, given as:
Rule of thumb values for these efficiency terms are tabu-
lated in Table I. A= h.d (15)

1753
 Even though, different height (h) and diameter (d) combi- to 6 blades is possible, examples of 4 or 5 bladed Darrieus
nations may yield the same rotor area and therefore the same turbines are more common for hydro applications [7], [10].
theoretical power, ultimate performance of the system de- The subsequent problem, which is also an open problem,
pends on several more subtle factors. A qualitative overview is to decide on the shape of airfoil to be used. Since
of these issues is given below: water turbines experience large torque variations as a blade
. Power capture and efficiency: For a given power level rotates along the rotor circumference, symmetric blades are
and rotor area, an increase in diameter implies decrease generally preferred [5], [7], [9], [10], [13], [18], [19]. The
in turbine height. Since, the airfoil shaped blades are most common blade profiles used in Darrieus turbines are:
present in the vertical spacing only, this measure even- NACA 0012, NACA 0015, NACA 0018, and NACA 63-
tually reduces the power output. In a rotor with higher 018. Availability of lift/drag data may become difficult for
diameter the blades can be separated far apart. This some shapes (eg: NACA 63-018) especially for low Reynolds
reduces the mutual effects due to turbulence eventually number as discussed earlier.
elevating the efficiency. Therefore, a trade off need to The dimension of a rotor, number of blades and blade
be reached between rotor efficiency and power output chord length are interrelated through solidity information,
while deciding the height-diameter ratio [9]. as expressed in (11). Water turbines are of higher solidity
. Torque, speed and generator selection: Selection of an than wind turbines and solidity values may range from
electrical generator is heavily dependent on rotor speed 0.15 to 1.6 [2], [5], [10]. Lower solidity implies better
and torque. With increased diameter and reduced height hydrodynamic performance and higher values generally allow
(for a given power level and rotor area), the rotor speed stronger mechanical structure and increased induced torque
reduces and shaft torque increases. With regard to using [5], [7], [9], [10], [13], [18], [19]. For a given blade shape,
a direct drive generator or low-conversion-ratio gearbox, decision on blade number and blade chord length can be
this measure is not recommended. On the contrary, approached through fluid dynamic performance analysis. The
higher torque may reduce the problem of rotor starting modeling methods discussed in the earlier section can be used
for a vertical axis turbine [11]. in this regard. Multiple streamtube analysis carried out on
. Behavior in skewedflow: Skewed fluid flow is significant a turbine consisting of NACA 63-018 blades is plotted in
in constrained flow channels such as, shallow river or Fig. 9.
built environment. Depending on the skew angle, rotors
with varying height-diameter ratios perform differently.
Such considerations need to be incorporated in the 0.45 U.. 0 15
-E)- U- 0.25
design process when flow patterns are not uniform for 0.4 ... .... U7 0.35
L cT 0.45
a channel [17]. 0.5 5
0.3
.3.
A decision on height-diameter ratio hld, (typical values 0.25 2.3.....
may range from 0.5 to 1.5) would yield values of rotor height 0.2
and diameter from (15). 0.15

B. Blade Design
When basic dimensioning is complete, the subsequent Tip Speed Ratio, A
problem is to select a set of blades with certain shape and
solidity. The blades of a lift type device are of airfoil shape Fig. 9. Performance of Darrieus rotor at various solidity
and the tangential forces induced in the blades are the prime
movers of the rotor. Therefore, fluid dynamic factors dictate As seen in the plot, solidity values around 0.30 deems
its performance and the process of blade designing requires more suitable for the given blade shape (NACA 63-018)
performance predictive modeling and delicate decision mak- and application (hydro). However, practical considerations
ing. such as, model inaccuracy, structural strength, and increased
Probably the foremost and cliched problem in the rotor de- torque induction may require even higher solidity. When a
sign process inquires what number of blades would optimize certain value is decided based on these observations, blade
the performance of a turbine. Although a good number of chord length can be determined using (11) for a rotor
theoretical and experimental studies that attempt this problem with specific number of blades. Additionally, rotor speed
is available [2], [5], [7], [9], [10], [13], [18], [19], there is can be calculated from tip speed ratio data obtained from
no agreed solution. With increasing number of blades, the Fig. 9 and (3). Information on the rotor's rotational speed is
solidity of the turbine increases and induced torque is higher. vital in selecting proper gearing/transmission mechanism and
This reduces the starting problem of Darrieus turbines. On the electrical generator.
contrary, lower number of blades reduces turbulence of fluid
flow and increases the hydrodynamic efficiency. A turbine C. Design example
with lesser blades usually runs on higher rpm, which eases As discussed in the foregoing sections, the design of a
the generator selection problem. Although, incorporating 2 Darrieus rotor involves performance modeling and decision

1754
making based on practical observations. The process of in this article are intended for developing an understanding
designing can be described with a flow chart given in Fig. 10. on how to design a straight bladed Darrieus turbine de novo.
The two major components of this process is to analyze the The subtler issue of finding an optimum rotor configuration
turbine performance and based on the outputs, decide on the (dimension, solidity, blade shape) still remains an open
design parameters. problem. However, the approach presented in this paper may
serve as a good starting point.
Analysis
I / / ModificationI
~~~~~~Data ACKNOWLEDGMENT
I/ ~~~~~(Reynolds Number, StreamtubeI
Start Blade Data, Aspect Ratio, + Modelingn The authors would like to thank the Faculty of Engineering
_ _ _ _ _ Aspect Ratio Angle of attack)
& Applied Science at the Memorial University of Newfound-
| Solidity land, NSERC, and ACOA for their support.
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-

Tidal paper 16-08-03 1. [Online]. Available: http://www.cyberiad.net/

Fig. 9, optimum tip speed ratio for this turbine is A = 2.25. tide.htm
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this article. The procedure, information and example given

1755