Optimization of three-bladed Savonius wind Turbine

7/26/2019 Optimization of three-bladed Savonius wind Turbine

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OPTIMAL PERFORMANCE OF A MODIFIED THREE-BLADE SAVONIUS TURBINEUSING FRONTAL GUIDING PLATES

Mohamed H. Mohamed

[email protected]

GaborJaniga

[email protected]

Elemer Pap

[email protected]

Dominique Thevenin

[email protected]

Laboratory of Fluid Dynamics and Technical Flows

University of Magdeburg Otto von Guericke

Magdeburg, Germany

ABSTRACT

Wind energy is one of the most promising sources of re-

newable energy. It is pollution-free, available locally, and

can help in reducing the dependency on fossil fuels. Al-

though a considerable progress has already been achieved,

the available technical design is not yet adequate to de-

velop reliable wind energy converters for conditions corre-

sponding to low wind speeds and urban areas. The Savo-

nius turbine appears to be particularly promising for such

conditions, but suffers from a poor efficiency. The present

study considers an improved design in order to increase theoutput power and the static torque of the classical three-

blade Savonius turbine, thus obtaining a higher efficiency

and better self-starting capability. To achieve this objec-

tive three geometrical properties are optimized simultane-

ously: 1) the position of an obstacle shielding the return-

ing blade; 2) the position of a deflector guiding the wind

toward the advancing blade; and 3) the blade skeleton line.

As a whole, fifteen free parameters are taken into account

during the automatic optimization process, carried out by

coupling an in-house library (OPAL) relying on Evolu-

tionary Algorithms with an industrial flow simulation code

(ANSYS-Fluent). The output power coefficient is the single

target function and must be maximized. The relative per-

formance improvement amounts to more than 50% at the

design point compared with the classical configuration.

KEYWORDS

Savonius rotor, Wind energy conversion, Optimization,

Evolutionary Algorithms, Turbomachines.

Introduction

Wind power is the conversion of wind energy into a

useful form of energy, such as electricity, using wind tur-

bines. At the end of 2008, worldwide nameplate capac-

ity of wind-powered generators was 121.2 GW. At that

time, wind power accounted for roughly 1.5% of world-

1 Copyright c 2010 by ASME

Proceedings of ASME Turbo Expo 2010: Power for Land, Sea and AirGT2010

June 14-18, 2010, Glasgow, UK

GT2010-

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Nomenclature

A Projected area of rotor (DH)

Cm Torque coefficient,T/(R2HU2)

Cms Static torque coefficient,Ts/(R2HU2)

CP Power coefficient,P/(1/2AU3)

d Blade chord(2r)

D Turbine diameter(2R)

H Blade height

N Rotational speed of rotor

P Output power(2NT/60)

R Tip radius of turbine

Rsh Turbine shaft radius

r Radius of semi-cylindrical blade

s Gap width

T Output torque

Ts Static torque

U Mean velocity in x-direction

Obstacle angle

Deflector angle

Speed ratio

Orientation angle

Density

Angular speed

wide electricity usage. This amount is growing rapidly,

having doubled between 2005 and 2008. Several countries

have achieved relatively high levels of wind power pen-

etration, such as 19% of stationary electricity production

in Denmark, 11% in Spain and Portugal, and 7% in Ger-

many and the Republic of Ireland. As of May 2009, eighty

countries around the world are using wind power on a com-

mercial basis [1]. Wind energy is perhaps the only power

Figure 1. Savonius rotor

generation technology that can deliver the necessary cuts in

CO2during the critical period up to 2020, when greenhousegases must begin to decline in order to avoid dangerous cli-

mate change. It has been estimated that the installed wind

capacity will produce 260 TWh and save 158 million tons

of CO2every year [2].

The storage and distribution of electrical power is still

a major problem, in particular when the generated quantity

is varying considerably with time and location, like is the

case for wind energy. A local electricity production, within

urban areas, would help solve this issue. The Savonius tur-

bine appears in principle to be particularly promising for

such conditions, since it is a slow-running machine with a

very compact design.

The Savonius Turbine

S.J. Savonius initially developed the vertical axis Savo-

nius rotor in the late 1920s. The concept of the Savonius

rotor is based on cutting a cylinder into two halves along

the central plane and then moving the two half cylinders

sideways along the cutting plane, so that the cross-section

resembles the letterS(Fig. 1, [3]).

The Savonius rotor, which is a slow-running vertical

axis wind machine (typically used for 1.0 or below, seeEq. 1) has unfortunately a poor efficiency when consider-

ing the standard design: theoretically,Cp 0.2 at best [4].Nevertheless, it presents many advantages for specific ap-

plications, in particular due to its simplicity, resulting ro-

bustness, compactness and low cost. If a higher efficiency

could be obtained, the Savonius rotor would become a very

interesting complementary source of electricity.




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Wind

R

AdvancingBlade

ReturningBlade

(0,0)

U

Figure 2. Schematic description and main parameters characterizing a

Savonius rotor

Performance of a Savonius Turbine

Using the notations of Fig. 2, the velocity coefficient is

defined as:

=R/U (1)

For a Savonius rotor of height H, a wind of incoming

velocity U, the mechanical power P and the mechanical

torque on the axis of a Savonius turbine can respectively be

written as follows:

Cp= P

RHU3 (2)

and

Cm= T

R2HU2 (3)

where Cpand Cmare respectively the power coefficient

and the torque coefficient. In the following sections, a ro-

tor is called aconventional Savonius rotorif semi-cylinder

blades are used without any flow guiding plates.

Purpose of the Present Work

The conventional, three-blade configuration of the ro-

tor has been extensively studied in the past [5]. The cor-

responding values ofCp and Cm have been determined nu-

merically and sometimes experimentally as a function of

the speed ratio . This has been used to validate exten-

sively our numerical procedure by comparison with pub-

lished, reference data [6].

These previous studies have demonstrated that Savo-

nius turbines show considerable drawbacks compared to

conventional turbines, in particular a low efficiency and

poor starting characteristics. Previous investigations of our

research group have shown that guiding and obstacle platesplaced appropriately in front of the turbine might increase

its efficiency [6,7]. Using a contoured shape might be even

more promising but would require considerably more free

parameters and will therefore be considered in a later step.

Building on top of our previous results, the blade shape will

be simultaneously modified in the present work. The opti-

mization process thus relies on free design variables that

describe the position and angles of the plates, the blade

shape (skeleton line) as well as the gap width s (Fig. 3).

At the end, fifteen free parameters are thus considered (X1,

Y1, X2, Y2, Xd1, Yd1, Xd2,Yd2, XP1, YP1, XP2, YP2, XP3,YP3ands). The objective function considers only one output of

the simulation, that should be maximized: the output power

coefficient Cp.

Optimization Methodology

Optimization is a body of mathematical results and nu-

merical methods for finding and identifying the best can-

didate from a collection of alternatives, without having to

explicitly enumerate and evaluate all possible alternatives.

Optimization is a key engineering task, since the functionof any engineer is to design new, better, more efficient, and

less expensive systems as well as to devise plans and proce-

dures for an improved operation of existing systems. Nev-

ertheless, such a real optimization relying on suitable al-

gorithmic procedures is still a relatively new approach, in

particular when considering turbomachines [8,9].

The central goal when designing an improved Savo-

nius turbine is to achieve high efficiency, i.e., high power

output. Furthermore, it must be kept in mind that turboma-

chines often operate outside the nominal (or design) condi-

tions. Therefore, after optimizing the configuration for themaximum output power coefficient, known to occur for a

speed ratio 0.7, the full range of speed ratios will beconsidered.

In our group, a considerable experience is available

concerning the mathematical optimization relying on eval-

uations based on Computational Fluid Dynamics (CFD)

[10]. We therefore employ our own optimization library,

OPAL (for OPtimization ALgorithms), containing many




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Wind

X >R1

X >R2

RObstacle Y1

M

AdvancingBlade

ReturningBlade

Y2

x

y

(0,0)

Deflector

Xd1

Xd2

Y

d1

Yd

2

(a)

P4

P (X ,Y )1 P1 P1

P5

r

rVariable points

P (X ,Y )2 P2 P2

P (X ,Y )3 P3 P3

X

Y

(P0)Fixed points

Bladecenter

Turbine shaft

S

(b)

Figure 3. Schematic description of the free optimization parameters

characterizing a three-blade Savonius rotor : a) plate parameters

(X1,Y1,X2,Y2,Xd1,Yd1,Xd2 andYd2); b)XP1,YP1,XP2,YP2,XP3and YP3 used to modify the blade shape; additionally, the gap width s.

different optimization techniques. Different CFD solvers

(in-house codes, ANSYS-Fluent, ANSYS-CFX) have been

coupled in the past with this optimizer. It has already

been employed successfully to improve a variety of ap-

plications like heat exchangers [11], burners [12] or tur-

bomachines [6, 7, 13, 14]. These studies have in particu-

lar demonstrated the efficiency of evolutionary algorithms

(EA) for CFD-based optimization. Using EA, a very ro-

bust procedure can be obtained and local extremal values

do not falsify the results [15, 16]. Therefore, the present

study relies again on EA with a population size of 20 in

the first generation and a total number of generations of

23. The optimization process stops automatically after this

twenty-third generation, since the observed progress in the

objective function falls below the user-prescribed thresh-

old. When computing a new generation from the previous

one, a survival probability of 50%, an averaging probabil-

ity of 33.3% and a crossover probability of 16.7% (total100%) are implemented. In the additional mutation step,

CFD coupling with OPAL (optimizer)

GambitJournal file

GambitJournal file

FluentJournal file

FluentJournal file

Geometry

+

Mesh

Geometry

+

Mesh

Gambit 2.4

CFD

Simulation

+Post-processing

CFD

Simulation

+Post-processing

Fluent 6.3

Output file(objective value)

Output file(objective value)

Evolutionary

Algorithms

Evolutionary

Algorithms

OPAL

Input file(parameter values)

Input file(parameter values)

New configuration

C program on Linux for automatizationC program on Linux for automatization

Figure 4. Schematic description of optimizer (OPAL) and CFD code cou-

pling.

a mutation probability of 100% with decreasing mutation

amplitude is considered. All further details can be foundelsewhere [6], where the same procedure has been applied

to a simpler configuration.

A fully automatic optimization finally takes place, us-

ing OPAL (decision-maker for the configurations to inves-

tigate), the commercial tool Gambit for geometry and grid

generation (including quality check) and the industrial CFD

code ANSYS-Fluent to compute the flow field around the

Savonius turbine. As a result of the CFD computation the

output power coefficient is determined, and is stored in a re-

sult file. The procedure is automated using journal scripts

(to restart Gambit, Fluent) and a master program written

in C, calling all codes in the right sequence as shown in

Fig. 4. By checking the values stored in the result file,

OPAL is able to decide how to modify the input parameters

before starting a new iteration. The fully coupled optimiza-

tion procedure is a complex task, which has been described

in detail in previous publications [1012].

Numerical Flow Simulations

From the literature it is known that an accurate CFD

simulation of the flow around a Savonius turbine is a chal-lenging task, mainly due to its highly time-dependent na-

ture and to the fact that flow separation plays an important

role for the efficiency of the system. It is therefore neces-

sary to check the full numerical procedure with great care.

Afterwards, the resulting methodology must be validated.

All flow simulations presented in this work rely on

the industrial software ANSYS-Fluent 6.3. The unsteady

Reynolds-Averaged Navier-Stokes equations are solved




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using the SIMPLE (Semi-Implicit Method for Pressure-

linked Equations) algorithm for pressure-velocity coupling.

The flow variables and all turbulent quantities are dis-

cretized in a finite volume formulation using a second-

order upwind scheme. For the present configuration, two-dimensional simulations are sufficient (no geometry change

in the third direction when excluding boundary effects), so

that very fine grids can be employed.

The unsteady flow is solved by using the Sliding Mesh

Model (SMM). Three complete revolutions are always

computed, using a constant time-step; the first one is used

to initiate the correct flow solution, while the flow proper-

ties (in particular the power coefficient Cp and the torque

coefficient Cm) are obtained by averaging the results during

the last two revolutions. On a standard PC, one evaluation

(i.e., three revolutions for one specific configuration) takesabout 280 minutes of computing time.

A grid-independence study has been first carried out

for one geometrical configuration. Several different two-

dimensional, unstructured grids of increasing density and

quality, composed of 3400 up to 116000 cells, have been

tested for the standard Savonius turbine with a specified ob-

stacle plate. All grids employing more than 71 000 cells

lead to a relative variation of the output quantity below

1.8% [6]. Since the cost of a CFD evaluation obviouslyincreases rapidly with the number of grid cells, the interme-

diate grid range between 75000 and 95000 cells has beenretained for all further results shown in the present paper.

The grid is refined in the vicinity of the turbine and of the

solid surfaces, capturing all relevant flow features (Fig. 5).

The minimum size of the computational domain has been

checked in a separate project [17]. It has been found that a

domain size equal to 27 times the rotor radius is needed to

get a result independent from any influence of the bound-

ary conditions. This is in agreement with previous studies,

mostly recommending 10 times the rotor radius on each

side of the turbine.

CFD Validation

After an acceptable grid and domain size have been

identified, the full numerical procedure and in particular the

employed turbulence model have been validated by com-

parison with published experimental results for a classical

three-blade Savonius turbine [5]. The influence of the tur-

bulence model is shown in Fig. 6. These results demon-

Figure 5. Zoom on the two-dimensional, unstructured grid in the vicinity

of the turbine

strate the excellent agreement obtained between CFD and

experiments for the target function,Cp, when using the re-

alizable k turbulence model. A similar tendency has

been observed for other studies involving cambered blades

[13, 14], proving the interest of the realizablek model

for fast CFD simulations. The fact that the Reynolds Stress

Model does not lead to an improvement compared to stan-

dard two-equation models is probably a result of its higher

sensitivity toward inflow turbulent boundary conditions,

which are usually not measured in the experiments.The near-wall treatment relies on standard wall func-

tions. The y+-values found near all walls in the employed

grid are around 60 and fall therefore within the recom-

mended range for best-practice CFD (30< y+


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0.2 0.4 0.6 0.8 1 1.2

Speed ratio()

0

0.05

0.1

0.15

0.2

PowerCoefficie

nt(Cp)

Exp. (K. Irabu & J. Roy, 2007)

Realizable k-model

SST model

Standard k- model

RSM model

Figure 6. Validation of computational model: power coefficient com-

pared to experimental results for a three-blade Savonius turbine [5]

ence in Cp between this value and the one obtained after

only three revolutions equals 0.024. This is an estimationof the uncertainty associated with the considered optimiza-

tion process. As shown later in Fig. 8, this inherent uncer-

tainty is very small compared to the range ofCp explored

during the optimization and is thus deemed acceptable. It

amounts to only 6% of the pressure coefficient associated

with the optimal design. The influence of the number of

revolutions on the estimation ofCpby CFD has been inves-

tigated systematically in a separate project [17], confirming

the present findings. Only three revolutions have been thus

computed for each design in order to reduce the needed

computational time.

Results and Discussions

Optimization of all turbine parameters

The mathematical optimization procedure described

previously (Evolutionary Algorithms relying on automated

evaluations through CFD) can now be employed to find the

optimal position of both guiding plates, the gap width and

the blade shape. This is done first for a constant speedratio = 0.7, considering a fixed incident wind velocityU=10 m/s. This value of is retained since it is knownfrom the literature that it corresponds to the zone of peak

power coefficient of the conventional Savonius turbine. As

explained previously, fifteen degrees of freedom are left

simultaneously for the optimization (Fig. 3). Regarding

the blade shape, the points P4 and P5 are considered to

be fixed; only P1, P2, P3 are changing position. Knowing

0 15 30 45 60 75

Time

0

0.4

0.8

1.2

Powercoefficient

(Cp)

0 20 40 60 80 100

No. of revolutions

=0.7

Instantaneous power coeff.

Average Power Coeff.

Employed number of revolutions

Figure 7. Influence of the number of revolutions on the instantaneous

and on the average power coefficient Cp computed by CFD for the opti-

mum design shown later.

all 5 points, the full profile is reconstructed using standard

splines (Nonuniform rational B-splines, NURBS). The or-

der of a NURBS curve defines the number of nearby con-

trol points that influence any given point on the curve. The

curve is represented mathematically by a polynomial of de-

gree one less than the order of the curve. This means that

the spline order is 5 in our case and the degree of the poly-

nomial is 4. The objective function contains one single out-

put of the simulation, that should be maximized as far as

possible: the power coefficientCp. The parameter spaceconsidered in the optimization has been defined as docu-

mented in Table 1. These domains are selected to prevent

any domain overlap along theY-direction, to keep realistic

blade shapes and to cover a wide region for positioning the

guiding plates. The reference point of the parameter space

for the blade skeleton line is point P0, which is the center of

the original, semi-cylindrical shape with radius ras shown

in Fig. 3. The reference point for the remaining space pa-

rameters (guiding plates and gap width) is the global cen-

ter of turbine rotation. During the calculations, a circular

turbine shaft is included with a radius Rsh computed fromRsh/R=0.03.

The results presented in Fig. 8 indicate that the con-

sidered objective is indeed considerably influenced by the

fifteen free parameters. As a whole, 240 different geomet-

rical settings have been evaluated by CFD, requesting 47

days of total computing time on a standard PC. Note that

the user-waiting time could be considerably reduced by car-

rying out the requested CFD on a more powerful computer




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Table 1. Acceptable range for the input parameters (parameter space)

Parameter Minimum allowed Maximum allowed

Blade shape

XP1/r 0.53 1.2

YP1/r 0.24 0.24

XP2/r 0.24 1.1

YP2/r 0.94 0.24

XP3/r 0.24 1.1

YP3/r 0.24 0.94

Guiding plates

X1d/R 1.2 0.0Yd1/R 1.1 1.65

X2d/R 1.88 0.0

Yd2/R 1.76 2.6

X1/R 1.88 1.1

Y1/R 0.7 0.0

X2/R 1.88 1.1

Y2/R 1.88 0.7

Gapwidth

s/R 0.03 0.18

or in parallel on a PC cluster [10]. Such a parallel proce-

dure, already implemented in OPAL, has not been used in

the present case but could reduce the needed time by orders

of magnitude, as demonstrated in other studies. Relying

on parallel computers and possibly carrying out each CFD

evaluation again in parallel [10] is clearly necessary when

considering three-dimensional problems. Fortunately, itis quite straightforward to implement, so that researchers

having access to parallel clusters can solve corresponding

problems within an acceptable lapse of time.

The optimal configuration (highest point in the right

column in Fig. 8, all corresponding parameters being con-

nected by a thick gray line) can now readily be identified for

= 0.7. The corresponding geometry is shown in Fig. 9.The optimum parameter values are listed in Table 2.

0.53-0.24 0.24 -0.940.24 0.24 -1.2 1.1 -1.88 1.76 -1.88 -0.7-1.88 -1.880.030.024

1.2 0.24 1.1 -0.24 1.1 0.94 0 1.65 0 2.6 -1.1 0 -1.1 -0.7 0.18 0.38

X /rp1 X /rp2 X /rp3Y /rp1 Y /rp2 Y /rp3

X /Rd1 X /Rd2 X /R1 X /R2Y /Rd1 Y /Rd2 Y /R1 X /R2

s/RCP

Blade shape Guiding plates positionsGap width

0.156

Three-bladeSavonius turbinewithout guiding

plates

0.363

Optimumconfiguration

Optimumconfiguration

0.024 Absoluteuncertainty

Figure8. Input parameters of the optimization and power coefficient rep-

resented using parallel coordinates. The parametersof the optimal config-

uration are connected with a thick gray line. The power coefficient of the

conventional three-blade turbine (semi-cylindrical shape) is also shown

with a black circle.

AdvancingBlade

Deflector

Obstacle

Wind

U

Returning blade

Figure 9. Optimum configuration obtained with the optimization proce-dure.

One instantaneous picture of the velocity field is shown

as an example in Fig. 10, demonstrating that the employed

grid captures all important flow features in the vicinity of

the rotor and guiding box. This is of course a dynamic

process, difficult to illustrate in a static figure.

At=0.7 the optimal point found by the optimizationprocedure corresponds to an absolute increase of the power




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Table 2. Optimal configuration

Part Parameter Value Angle

Blade shape XP1/r 0.6077 -

YP1/r -0.1338

XP2/r 0.2735

YP2/r -0.7136

XP3/r 0.7065

YP3/r 0.5901

Guiding plates Xd1/R -0.3089 =81.13

Yd1/R 1.436

Xd2/R -0.4591Yd2/R 2.388

X1/R -1.3638 =77.58

Y1/R -0.1075

X2/R -1.691

Y2/R -1.5935

Gap width s/R 0.0988 -

coefficient by 0.207 compared with the conventional three-blade Savonius turbine (semi-cylindrical blade shape). As

a whole, this means a relative increase of the performance

(measured by the power output coefficient) by 57% for the

optimum design.

Off-design performance

It is now important to check how this gain would

change as a function of, since such a turbine must be

able to work also for off-design conditions. Therefore, the

performance of the optimal configuration has been finallycomputed for the full range of useful-values, as shown in

Fig. 11. This figure demonstrates that the improvement of

both torque coefficient and power output coefficient is ob-

served throughout for all values of, compared to the con-

ventional three-blade Savonius turbine. The relative per-

formance increase compared to the standard Savonius con-

figuration is always higher than 50% in the usual operating

range(0.6 1), demonstrating again the interest of the

Figure 10. Instantaneous velocity vectors magnitude (m/s) around the

optimum configuration (zoom) at the design point (=0.7).

optimized configuration.

Self-starting capability

For decentralized, low-cost wind-energy applications

as considered here, it is essential to obtain a self-starting

system. To investigate this issue, the static torque exerted

on a turbine at a fixed angle has been computed by CFD

as a function of this angle. Figure 12 shows the obtained

static torque coefficient Cmsobtained for the optimal design

compared to the classical three-blade turbine. The experi-

mental results of [5] for a conventional three-blade turbineare also shown for comparison in Fig. 12. Due to peri-

odicity, the results are only plotted for between 0 and

120. Compared to the classical turbine, these computa-

tions demonstrate that the modifications have a consider-

able and positive effect on the static torque coefficient, ex-

cept in a small range (90 100). There, the statictorque coefficient is less than the classical one, but remains

strictly positive. Averaging over all angle positions, Cms is

increased by 0.091 for the optimum design.

Practical realization

From the technical point of view many existing sys-

tems already rely on a tail vane for optimal alignment into

the wind direction. A similar technical solution would be

used for the Savonius turbine using guiding plates. In this

manner the orientation of the system can be simply, effi-

ciently and automatically controlled. As a whole, the op-

timized configuration is only slightly more complex, more

expensive and heavier than the original system. Therefore,




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0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Speed ratio ()

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

TorqueCoefficient

(Cm)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Speed ratio()

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

PowerCoefficient(Cp)

0

20

40

60

80

100

Relativeincease(%)

Conventional three bladeSavonius

Optimum design

% Relative increase

(a)

(b)

Figure 11. Performance of the optimized configuration (black squares)

compared to the conventional three-blade Savonius turbine (empty

squares): a) torque coefficient; b) power coefficient. The corresponding

relative increase compared to the standard configuration is shown with

black plus.

the improved power and torque coefficients should easily

compensate these drawbacks within a short time after in-

stallation.

It has been shown in Fig. 11 that the optimum design

leads to a broader operating range. It can be in particular

employed for higher speed ratios, making it attractive to

exploit wind energy at higher velocity. The present study

does not consider transient effects (wind gusts, storms), a

problem common to all wind turbines and mostly leading

to material limitations.

0 30 60 90 120

Rotation angle()

0

0.2

0.4

0.6

Statictorquecoefficient(Cms)

Our CFD results:Conventional design

Optimum design

Exp. K. Irabu & J. Roy (2007)(Conventional design)

Negative Torque (no self-starting capability)

Figure 12. Static torque coefficient Cms as a function of the fixed rotor

angle for the optimal design (filled squares) compared to the classicalthree-blade Savonius turbine (black plus). The experimental results of [5]

are also shown for comparison (empty squares).

Conclusions

The Savonius turbine is a promising concept for small-

scale wind-energy systems, but suffers from a poor effi-

ciency. Therefore, the major objective of the present study

is to identify an improved design, leading to higher values

of the power coefficient and of the static torque of the three-

blade Savonius turbine, thus obtaining a higher efficiency

and better self-starting capability. For this purpose, frontalplates guiding the wind toward the advancing blade are in-

troduced. Simultaneously, the installation of these guiding

plates improve the self-starting capability of the system.

After validating the numerical procedure against ex-

perimental measurements, accurate CFD simulations of the

unsteady flow around a conventional three-blade Savonius

turbine have been carried out. The realizablek turbu-

lence model can be employed for a quantitative analysis of

the performance, provided a sufficiently fine grid is used.

The blade shape, position and angles of the guiding

plates and gap width have then been optimized in a fully

automatic manner, in order to obtain the best possible per-

formance, as measured by the power coefficient Cp. The

optimization relies on evolutionary algorithms, while all

geometrical configurations are evaluated by CFD. This op-

timization procedure is able to identify considerably bet-

ter configurations than the conventional three-blade Savo-

nius turbine, leading in particular to a relative increase of

the power output coefficient by 57% at =0.7. A perfor-




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mance gain of at least 25% is found for the full operating

range of the conventional design. At the same time, the

operating range is extended up to=1.5. This positive ef-fect is also observed for the torque coefficient. The optimal

design still ensures self-starting capability for all rotatingangles. Therefore, this optimal configuration appears to be

very promising for wind energy generation, in particular in

urban areas.

A further optimization should consider a contoured

nozzle as guiding box in front of the turbine. It would also

be interesting to consider simultaneously the optimization

over the full operating range. In both cases, the computa-

tional costs will increase considerably.

ACKNOWLEDGMENTThe Ph.D. work of Mr. Mohamed is supported finan-

cially by a bursary of the Egyptian government.

REFERENCES

[1] http://en.wikipedia.org/wiki/Wind power. Last ac-

cessed November 2009.

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Optimization of three-bladed Savonius wind Turbine