Computational performance analysis of a two-slotted bucket Savonius
rotor
CHASIOTIS VASILEIOS1, TACHOS NIKOLAOS2, FILIOS ANDRONIKOS1
1Department of Mechanical Engineering, University of West Attica, GR12244 Egaleo
GREECE
2Department of Materials Science and Engineering, University of Ioannina, GR45110 Ioannina
GREECE
Abstract: - The objective of the current computational study is to predict the performance output of a modified
two-bucket Savonius rotor. Each bucket consists of three arc-type blades of different radius which is determined
by the slot width ratio, in the range of 0.05 to 0.15 and the slot central angle, in the range of 0 to 20 deg. Nine
configurations are designed with a fixed rotor diameter and a variable slot width and slot central angle, aiming to
resolve the performance output and investigate the effect of the two previous parameters on the power and the
static torque coefficients. The commercial CFD package Fluent® is used to solve the unsteady Reynolds-
Averaged Navier-Stokes equations, along with Spalart-Allmaras turbulence model. Initially, a standard Savonius
rotor, was used to validate the computational procedure using experimental results available in literature. Next,
the same validated model is used to resolve the designed slotted bucket configurations. The performance of the
examined slotted bucket configurations indicates improved self-starting characteristics, but a lower power
coefficient compared with the solid bucket Savonius rotor. Lower values of slot width ratio have improved output
performance while the slot central angle, does not greatly affect the overall performance of slotted bucket rotor.
Key-Words: - Vertical Axis Wind Turbines; Savonius rotor; Slotted bucket rotor; Computational Fluid Dynamics
(CFD)
Received: May 12, 2021. Revised: January 20, 2022. Accepted: February 17, 2022. Published: March 24 2022.
Nomenclature
A0 Wind turbine rotor swept area (m2)
b Radial interspace between two overlapping
blades or slot width (m)
c Rotor gap distance (m)
CP Power coefficient,
CT Static torque coefficient,
D Wind turbine rotor diameter (m)
bgr Bucket gap width ratio
N Number of buckets
q∞ Freestream dynamic pressure (Pa)
Rr Wind turbine rotor radius (m)
R Wind turbine bucket radius (m)
Re Reynolds number per unit length,
s Length of the overlapping part of the blade
or slot length (m)
T Turbine rotor torque (N·m)
V∞ Freestream wind speed (m/s)
θ Central angle of the overlapping blade arc or
circular arc slot central angle (deg)
Θ Rotor’s angular position (deg)
λ Tip speed ratio, λ=ωRr/V∞
μ∞ Freestream air viscosity (Pa·s)
ρ∞ Freestream air density (kg/m3)
φ Slot’s angular position (deg)
Φ Bucket arc (deg)
ω Angular velocity (rad/s)
1 Introduction
In recent years, numerical and experimental
validations of ‘S’ type or Savonius rotor wind
turbines have been added in the published literature.
A series of studies conducted by different researchers
have been presented, regarding the behaviour and the
performance output of Savonius wind turbines as it is
expressed by the power and torque coefficients, in
relation with the blade geometry. Savonius wind
rotors with improved performance characteristics
could lead to a rise of utilization of Savonius wind
turbines as they have several advantages compared
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with the horizontal axis wind turbines i.e. the simpler
and the cheaper construction, better initial torque at
lower wind speeds, lower noise levels, less wear on
rotating parts, more rotor configuration options,
smaller footprint occupation and the omnidirectional
nature negating the need for a yawing mechanism [1].
Consequently, Savonius wind rotors could have a
wider range of use and utilization in additional
applications, particularly in the electricity needs of
rural areas or covering partial loads in remote regions
and the low cost decentralized power production [2].
Advanced blade configurations with improved
performance characteristics, would be of much
importance as they could extent the wind energy
electricity generation by utilizing urban resources,
where the present classic horizontal axis wind
turbines would not be an appropriate selection since
they are best performed in flat-terrain regions without
obstacles [3]. A variety of models have been tested to
determine the connection between the Savonius wind
turbine performance and the different geometry
design parameters. These configuration design
parameters relate to the number of buckets, the rotor
aspect ratio, the separation gap of rotor buckets, the
profile change of the bucket cross-section, the
overlap, the presence or absence of rotor endplates,
the influence of bucket stacking and the presence of
valves or gaps in the blades’ midpoint, aiming to
reduce the drug for the retreating blade [4-6].
Slotted bucket configurations of Savonius
wind turbines have been sparsely explored by some
researchers. Limited information is found in
literature on exploring further the slot concept that
Alaimo et al. [3, 7] presented in his work. A bucket
configuration of the Savonius rotor was presented,
implicating slots which have been examined with the
Computational Fluid Dynamics (CFD) commercial
software. Steady state CFD studies were performed
aiming to explore the new configuration’s behaviour
regarding the starting torque and a parametrical
analysis was conducted by changing the slot position
on the bucket’s running length. It was indicated that
the placement of a slot in the bucket, towards the
rotor’s center, would improve the performance of the
Savonius wind turbine only at lower tip speed ratios
and would enhance the self-starting capability of the
turbine. The slot’s angle was investigated by testing
different configurations with a constant slot position
and a variable angle ranging only on the best
performance configuration. There were no significant
changes in the moment and the power coefficients,
concluding that the slot angle is not a crucial factor in
the overall turbine performance.
An implementation of a single slot was also
attempted by Rahai [8] for optimizing a modified
blade for Savonius wind turbine. The slotted
geometry design investigated, was not adopted since
the introduced slot would not contribute to the overall
improvement in the power performance. Rahai and
Hefazi [8-9] introduced a complex blade shape that
was finalized after an iteration process, using the
NASA INS2D CFD software involving torque
maximization algorithms with a modified version of
the transfinite interpolation method. The slot
placement was examined in the region where a flow
separation was observed by the flow velocity-
pressure contours at high angles of attack. The slot
action was connected with the momentum injection
to the other side of the blade, increasing the flow
separation of the upper side for both upstream and
downstream of the placed slot, thus, the amount of
flow separation of the concave side was reduced, but
the overall net effect of slot resulted in a loss of
momentum, lower performances and a decrease of
the efficiency.
In current research, the wind tunnel performance
data of a two-bucket Savonius rotor [10] are
compared with numerical results from slotted bucket
rotors derived through the modification of the wind
tunnel model bucket geometry. The solid buckets of
the Savonius rotor model are replaced with slotted
buckets consisting of partially overlapping blades
that are placed in position, in order to utilize and take
advantage of the lift forces applied on the blades,
apart from the drag forces that a standard Savonius
rotor relies for its rotation resulting to poor
performance. Thus, the main objective of the current
research is the CFD study of slotted bucket
configurations of Savonius rotors and the prediction
of their performance that are compared with the
experimental data for the solid two bucket rotor [10].
The unsteady Reynolds-Averaged Navier-Stokes
(RANS) equations are solved, using Fluent® [11]
commercial code. A total of nine configurations of
slotted bucket rotors are examined by introducing a
geometry of a double slot bucket profile and the flow
around the new wind turbine rotor is simulated to
predict the performance output and the self-starting
ability. Additionally, a parametrical study of
geometry settings is included, aiming to investigate
the central angle of the overlapping blade arc and the
radial interspace between two overlapping blades.
2 Geometry aspects of the slotted
bucket rotor
The conventional Savonius model rotor Config. No.
11, presented by Blackwell et al. [10] was used as the
reference geometry for replacing the solid buckets
with slotted. Each slotted bucket consists of three
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partially overlapping circular arc blades forming two
slots with the length and the width of the slots being
the parameters of the configuration. Outline
dimensions such as the rotor diameter and gap ratio,
remain the same with the wind tunnel rotor Config.
No. 11. A schematic view of Config. No. 11 rotor and
a dimension summary is included in Fig. 1 (a) and
Table 1 respectively.
Fig. 1. Wind tunnel Savonius rotor - Configuration
No. 11 (a) and the modified slotted bucket rotor (b).
Table 1 Geometry of Config. No. 11 Savonius rotor
(Blackwell et al. 1978)
Description Symbol Value Units
Number of
buckets N 2 -
Bucket arc Φ 180 degress
Rotor’s
diameter D=4R-c 950 mm
Bucket’s radius R 250 mm
Bucket gap
width c 50 mm
Bucket gap
width ratio c/2R 0.1 -
Fig. 2. Definition of the studied slotted bucket
geometry and examined configurations.
Based on the reference rotor model, two slots
between overlapping circular arc blades were placed
at 60 deg and at 120 deg with the bucket coordinate
system, (x,y), located on bucket’s arc center. The new
bucket geometry contains three new subsections,
named Blade 1, Blade 2, Blade 3 with the prefix “R”
for the right bucket and “L” prefix for the left bucket.
The center of each blade arc was maintained on the
initial blade arc axis origin, but each end blade has
different radius defined by the addition or subtraction
of the slot width. In the present design, the slot length
is also investigated since the circular arc slot central
arc can be adjusted. The investigated slotted bucket
rotor geometry is illustrated in Fig. 1 (b) and Fig. 2.
The examined geometric parameters of the slotted-
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bucket rotor models are the slot width ratio (b/R),
expressing the dimensionless radial interspace
between two overlapping blades and ranges from
0.05 to 0.15, and the central angle of the overlapping
blade arc (θ) which defines the slot length (s=Rθ),
ranges from 0 to 20 deg.
On the rotor bucket, each blade arc is described by a
constrained circle equation. The equations used to
export each blade in the (x,y) bucket coordinate
system and the (X,Y) rotor coordinate system, are
summarized as follows:
Left blade i (i=1,2,3):
(1)
Right blade i (i=1,2,3):
(2)
Blade 1:
(3)
Blade 2:
(4)
Blade 3:
(5)
where, R=0.25 m, φ=60 deg, θ=(0, 10 and 20 deg),
b=(12.5, 25.0 and 37.5 mm).
The radial interspace between two overlapping
blades ratio or the slot width ratio, modified within
the range of 5% and 15%, and the central angle of the
overlapping blade arc or the circular arc slot central
angle, modified within the range of 0 to 20 deg, are
investigated for their influence on the power
coefficient and the static torque. The previous
parameters have been selected as variable inputs by
Fig. 3. Definition of the studied slotted bucket
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maintaining constant the rest geometric parameters
for producing the investigated slotted bucket rotor
configurations. Nine selected configurations,
representing each combination of the previous
parameters, are presented in Fig. 2. The prefix M is
used in the configuration code names, followed by
the circular arc slot central angle value and the slot
width ratio value. The schematic views of the
selected configurations are illustrated with the
finalized dimensions in Fig. 3.
3 Numerical calculations
3.1 Computational domain and boundary
settings
The dimensions of the surrounding flow domain of
the studied slotted bucket rotors are expressed in
relation to the rotor’s diameter (D). The origin of the
rectangular shaped flow domain is located on the
rotor’s rotational axis and the length is extended by
6D upwind and 26D downstream in order to allow
wake patterns to be fully deployed (Fig. 4).
Sideways, the distance is 6D allowing the modelling
of the generated vortices at rotor blade tips, which
contribute to the induced drag. Symmetry was set on
The constructed meshes have been designed aiming
an acceptable mesh quality of the appropriate indices.
The two-dimensional mesh, generated in Gambit®
[12], consists of 3.25·104 elements with the 87% of
the total cells concentrated in the rotor’s rotating
mesh region. An unstructured mesh was selected
since it can be adapted better on complex curved
shapes and the generation is more automated and
faster than structured meshes. Grid independence
was studied for the reference model, simulating
further refined meshes that resulted in efficiency
value change below 2%. The mesh was generated
with quadrilateral elements with noticeable cells
converted to paved quadrilaterals. Indices that were
checked for the mesh quality are the aspect ratio,
skewness and the orthogonal quality [13] that were
shaped respectively to accepted values. Mesh
adaption was performed on solver to reduce max y+
value below one, y+≤1 that is recommended for the
selected turbulence model [14]. Mesh details for the
reference non-modified model are shown in Fig. 5.
Fig. 4. Geometry of the computational domain.
Fig. 5. Mesh overview for Savonius reference rotor
and details (a) near the interface, (b) between the
rotor gap, (c) at blade tip.
3.2 Simulations
For the current numerical modelling, two-
dimensional viscous and incompressible flow was
assumed in the computational domain. The unsteady
Reynolds-Averaged Navier-Stokes (RANS)
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equations were solved with Fluent’s pressure-based
solver using the Semi-Implicit Method for Pressure
linked Equations (SIMPLE) algorithm for pressure-
velocity coupling. A second order upwind scheme
was used to discretize in finite-volume formulation
the turbulent quantities and the flow variables.
Sliding mesh model is used to solve the unsteady
flow field. Spalart-Allmaras turbulence model was
used, as numerous studies have used the specific
model for Savonius rotor simulations, proving that
can successfully predict the aerodynamic attributes of
the wind turbine rotor [15-18]. The curved edges of
the rotor blades were set as stationary walls with a
no-slip condition, domain and rotor overlapping
edges were set as contact interfaces, the surface
domains were prescribed as fluid interiors and the
rotor domain was set to moving mesh with different
rotational velocities at a time, for achieving in each
run the desirable tip speed ratio (λ) value. The air
properties were set according to Sandia Laboratory’s
experimental data [10], i.e., 20 °C for the
temperature, 1.204 kg/m3 for the density and
1.7894·10-5 Pa·s for the viscosity, resulting in
Reynolds number per unit length (Re) 4.32·105. A
maximum number of iterations was set, along with
the convergence criterion of six orders of magnitude
residuals drop. For the steady state runs, a maximum
of 3·103 iterations with a drop of 10-5 of all scaled
residuals was set, while for the transient flow runs, a
maximum value of 50 iterations per time step was
selected, before the solver jumps to the next time step
with the same order of magnitude of the residuals
drop.
4 Results and discussion
The numerical simulation performance results of
wind tunnel two-bucket Savonius rotor
Configuration No 11, N=2, bgr=0.1 [10], are
presented in Fig. 6. A good agreement of the selected
Spalart-Allmaras turbulence model results can be
noted up to tip speed ratio λ=1.2. Results for
increased λ values are more overestimated, compared
with lower λ values. A satisfying agreement with the
experimental results is also noted for static torque
(CT), despite the overall slight overestimation in
some regions. Weak validity spots are detected at the
rotor’s angular position of 75 and 125 deg, while the
region of 0 to 55 deg is more overestimated. The final
validation results have been accepted and the Spalart-
Allmaras turbulence model was used to predict the
performance and the flow characteristics for the
slotted bucket-rotors at Re=4.32·105, for 7 m/s
airflow velocity. The simulation results of the power
coefficient (CP) versus the tip speed ratio and the
static torque coefficient versus rotor’s angular
position curves of the different slotted-blade
configurations, are presented in Fig. 7, Fig. 8 and Fig.
9. The results have been organized in groups
according with the blade overlap range group.
The CP - λ curves indicate that all the examined
slotted bucket rotors present a lower power
performance than the reference solid bucket Savonius
rotor. Among the configurations, the geometry
named M00-05 that has a slot width ratio of 5%
without blades overlapping, has the best power
performance (CP=0.19) in the range of λ=0.8~1 for
Re=4.32·105, which is about 20% lower than the
standard Savonius rotor. Blades overlapping is not
noticed to have a significant effect on the
performance output, for the current geometries with
fixed slot positions at 60 and 120 deg. The
configuration groups of the same circular arc slot
central angle and variable slot width ratio indicate a
significant difference on the power coefficient for
each λ solution set and that constitutes the slot width
ratio an important design parameter for the power
output performance of Savonius rotor modifications.
Despite the reduced power performance, the static
torque results indicate an improvement at low
incidence angles compared with the Savonius rotor
reference model. At the rotor’s angular position of 0
to 55 deg and 145 to 165 deg for the most slotted
bucket configurations, an increased average static
torque value about 25% to 190% of the experimental
value is observed. The best configuration (M00-05)
has no negative static torque values and presents an
average CT value of 0.396 at 0 to 180 deg, which is
improved compared to the solid bucket Savonius
rotor that has an average CT value of 0.303. The most
inefficient configuration case is the M00-15 having
15% slot width ratio, which presented the lowest
average CT=0.280 with CT=-0.07 at 55 deg rotor
angular position, along with the M20-15 case, which
had the lowest local CT=-0.188 at 55 deg with an
average CT=0.356.
Next, the flow around the rotor was examined.
Flow characteristics that relate to the performance
output are addressed by visualizing the flow and
examining the contours and the vectors of velocity
around the bucket slots. The transient solution of the
best and worst performed configurations (M00-05
and M20-15) are selected for further examination.
Four selected frames of the last rotation
corresponding to time steps which the rotor’s
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Fig. 6. Experimental and simulation results of power
coefficient (a) and static torque coefficient (b) for
Savonius wind tunnel rotor.
Fig. 7. Computed power coefficient versus tip speed
ratio and static torque coefficient versus rotor angle
for the M00-xx group of the studied slotted bucket
rotors, compared with the corresponding
measurements of solid bucket Savonius rotor.
Fig. 8. Computed power coefficient versus tip speed
ratio and static torque coefficient versus rotor angle
for the M10-xx group of the studied slotted bucket
rotors, compared with the corresponding
measurements of solid bucket Savonius rotor.
Fig. 9. Computed power coefficient versus tip speed
ratio and static torque coefficient versus rotor angle
for the M20-xx group of the studied slotted bucket
rotors, compared with the corresponding
measurements of solid bucket Savonius rotor.
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angular position is 0, 45, 90 and 135 degrees, are
included in Fig. 10 to Fig. 13, for λ=0.8. The interval
of 45 degrees is selected in order to represent equally
a semi cycle rotor rotation, along with the 0 deg angle
for which the air incidents perpendicularly the
convex and the concave side of the advancing and
returning blade. At 0 deg angle, the same flow
structure characteristics with the reference Savonius
rotor are observed in terms of the acceleration at the
tip of the advancing blade and the stagnation point on
the convex side of the returning blade. More
boundary layer separation regions are noted on the
Fig. 10. Flow through bucket slots A and C at 0, 45, 90 and 135 degrees rotor position, for M00-05
configuration at
λ=0.8.
Fig. 11. Flow through bucket slots B and D at 0, 45, 90 and 135 degrees rotor position, for M00-05
configuration at λ=0.8.
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walls of the sub-blades of advancing rotor blade. At
the 45 deg angle where the Savonius rotor presents
low CT value, the recirculation of flow behind the
advancing blade gets more intense. The stagnation
zone is displaced on the second slot on the returning
blade where flow is observed to pass to the concave
side of the returning blade, reducing the opposing
torque applied on rotor. This improvement is reduced
by the same event occurring on the advancing blade
where the flow pass from concave to convex side. At
the 135 deg rotor angle where the Savonius presents
a high static torque value, the flow is noted to
Fig. 13. Flow through bucket slots B and D at 0, 45, 90 and 135 degrees rotor position, for M00-05
configuration at λ=0.8.
Fig. 12. Flow through bucket slots A and C at 0, 45, 90 and 135 degrees rotor position, for M20-15
configuration at λ=0.8.
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accelerate towards the wind flow direction on the
convex side of the advancing blade, which is the lift
generation mechanism driving the rotor, apart from
the drag forces exerted on concave side of advancing
blade. The introduced gap between the first and the
second blade amplify this effect by inserting more
airflow from the concave side to the convex side. The
slots on the returning blade that allow the air to pass
through the blade, are also beneficial for the current
angle and the overall torque balance. However, more
stagnation points appear near the increased slot width
space of M20-15 and additional recirculation areas
are observed locally between the gaps, contributing
to the decreased power output performance.
5 Conclusion
It was concluded that all the examined slotted bucket
configurations present a lower average power
coefficient compared with the conventional model of
Savonius rotor. However, the static investigation of
the slotted bucket configurations, revealed improved
static torque coefficients in the configurations with
reduced slot width ratio values. Implementing double
slots in fixed positions resulted in a new way for
modifying the classical Savonius bucket rotor, with a
trade-off between achieving better self-starting
characteristics and reducing slightly the turbine’s
efficiency. Two of the most important parameters
associated with the slot implementation which are the
slot width ratio and the circular arc slot central angle,
have been examined aiming to investigate their effect
on the performance attributes. The slot width ratio
was noticed to have greater influence on the power
output performance, since low values relate to
improved efficiency, while increased values of slot
width ratio lead to reduced power coefficients. The
second examined parameter of the circular arc slot
central angle had the least influence, since no
significant changes were observed at the output
performance characteristics.
The flow structure flow around the rotor had an
increased level of complexity. The implementation of
slots complicates further the flow around the rotor,
since more flow separation points can be observed,
and additional vortices appear behind the rotor and
near the slots. Additional stagnation points and flow
separation regions with flow recirculation, are
spotted in regions where are not reported on classic
Savonius rotors. The previous observation combined
with the unwanted flow passing from concave to
convex side of the advancing blade, are assumed to
be the main causes of inferior power performance.
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Contribution of individual authors to
the creation of a scientific article
Chasiotis Vasileios carried out the simulation,
analysis, data curation, visualisation and writing the
original draft, Tachos Nikolaos carried out the
methodology and simulation and Filios Andronikos
was responsible for the overall supervision.
Sources of funding for research
presented in a scientific article or
scientific article itself
The authors declare that there is no conflict of interest
in this paper. No financial support was received to
carry out this study.
Creative Commons Attribution
License 4.0 (Attribution 4.0
International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2022.17.5
Chasiotis Vasileios, Tachos Nikolaos, Filios Andronikos
E-ISSN: 2224-347X
59
Volume 17, 2022
