A COMPUTATIONAL FRAMEWORK FOR THE …palramu/Papers/Students/2012...ii THESIS CERTIFICATE This is to certify that the thesis titled ―A Computational Framework for the Design and

i

A COMPUTATIONAL FRAMEWORK FOR

THE DESIGN AND ANALYSIS OF

SAVONIUS WIND TURBINE

A report

submitted by

Sailesh Kolachana

(ED07B015)

in partial fulfillment of the requirements

for the award of the degree of

Bachelor of Technology (Engineering Design)

and

Master of Technology (Engineering Design)

Under the guidance of

Dr. Palaniappan Ramu

Department of Engineering Design

Indian Institute of Technology Madras

Chennai – 600036

June 2012

i

ABSTRACT

Vertical Axis Wind Turbines (VAWT) are ideal options for small scale generation of electricity

from wind. Savonius, one of the widely developed and used VAWTs are suitable for rooftops

and self sustaining light posts. Most research in designing a Savonius turbine is focused on the

experimental side. Power calculated using brake dynamometers provide a reasonable guess of

the performance, but it cannot capture all the aerodynamic characteristics on the blade. Also,

results from an experimental study are limited to the design that is being tested. When a

particular input is changed, the change in the output is not readily available unless sensitivity

information is available. An attractive alternative is a computer model in the place of the

experimental model. Computer models provide the user with the privilege to change inputs and

see the outcome instantly as against fabricating a prototype as in experimental studies. However,

computer models are only approximations of the experiments and are limited in modeling the

actual physics. In the case of vertical axis wind turbines like the Savonius, one needs to model it

in a transient multiple reference frame approach which requires the rotational velocity as an

input. There are no explicit equations that relate the angular velocity of the turbine to the input

wind velocity. In this work, we have obtained these relationships through the experimental

results available in the literature. This work aims at developing a transient computational model

following certain standards that are important to transient turbomachinery simulations, with

inputs from industry experts. The performance metrics obtained from the computational model is

compared to existing experimental results available and corroborated. The computational model

that is developed allows for estimating performance metrics for a new design. This framework

allows for propagating uncertainties in variables like wind speed and enable one for a robust or

reliable design.

ii

THESIS CERTIFICATE

This is to certify that the thesis titled ―A Computational Framework for the Design and Analysis

of Savonius Wind Turbine‖, submitted by Sailesh Kolachana to the Indian Institute of

Technology, Madras, for the award of the degree of Bachelor of Technology and Master of

Technology in Engineering Design, is a bonafide record of the research work done by him under

my supervision. The contents of this thesis, in full or in parts, have not been submitted to any

other Institute or University for the award of any degree or diploma.

Dr. Palaniappan Ramu

Project Guide

Department of Engineering Design

IIT Madras, Chennai – 600036

Place: Chennai

Date: 22nd

June 2012

iii

ACKNOWLEDGEMENT

The first person I should be thanking is Dr.Palaniappan Ramu for giving me this opportunity and

for pushing me to do this kind of work. I would not have accomplished whatever I did without

his guidance and motivation. His regular inputs helped me structure my project step by step.

I would like to extend my gratitude to Dr.Saravana Kumar and Dr.Ramanathan for helping me

with the workspace and facilities at the department..

I express my heartful thanks to Mr. Satya Narayana, an industry expert in CFD simulations with

wind turbines, who guided me with difficulties through the simulations.

I would also like to thank the authors mentioned in the reference page, who provided me with

base data on which I could build my project.

I owe my parents and family for their constant support and encouragement, without whom I

would probably never have stepped into an institute like IIT Madras in the first place.

Sailesh Kolachana

June 2012

iv

TABLE OF CONTENTS

ABSTRACT ..................................................................................................................................... i

NOMENCLATURE ..................................................................................................................... vii

LIST OF FIGURES ...................................................................................................................... vii

LIST OF TABLES ......................................................................................................................... ix

CHAPTER 1: WIND ENERGY AND WIND TURBINES ............................................................1

1.1 Wind Energy- Use and Advantages ...............................................................................1

1.2 Energy in the Wind ........................................................................................................1

1.3 Wind Turbines ...............................................................................................................2

1.4 Wind Turbine Classification ...............................................................................................3

1.5 Horizontal Axis Wind Turbines..........................................................................................3

1.5.1 HAWT advantages ...................................................................................................4

1.5.2 HAWT disadvantages ...............................................................................................4

1.6 Vertical Axis Wind Turbines ..............................................................................................4

1.6.1 VAWT advantages ...................................................................................................4

1.6.2 VAWT disadvantages ...............................................................................................5

1.7 Types of Vertical Axis Wind Turbines ..............................................................................5

1.7.1 Darrieus ....................................................................................................................5

1.7.2 Savonius ...................................................................................................................6

1.8 Thesis Outline .....................................................................................................................7

CHAPTER 2 : THE SAVONIUS VAWT .......................................................................................8

2.1 Savonius- Advantages and Disadvantages .........................................................................8

2.2 Savonius- Applications .......................................................................................................9

2.3 Savonius- Aerodynamics ....................................................................................................9

2.4 Savonius – Performance and Efficiency ...........................................................................11

2.5 Motivation of the Project ..................................................................................................12

v

2.6 Project Objective ..............................................................................................................12

CHAPTER 3: LITERATURE SURVEY......................................................................................13

CHAPTER 4: THE COMPUTATIONAL MODEL ......................................................................16

4.1 Introduction- CFD analysis...............................................................................................16

4.2 Features of the CFD analysis ............................................................................................16

4.3 CFD analysis – Steps ........................................................................................................16

4.3.1 2D- Geometry .........................................................................................................17

4.3.2 2D Mesh .................................................................................................................18

4.3.3 Mesh Extrusion: ......................................................................................................19

4.3.4 Analysis type and timestep details: ........................................................................20

4.3.5 Boundary conditions: ..............................................................................................20

4.3.6 Solver conditions: ...................................................................................................21

CHAPTER 5: RESULTS AND DISCUSSIONS ..........................................................................22

5.1 Comparison- Aerodynamic vs Experimental Values .......................................................23

5.2 Observation on Tip Speed Ratios .....................................................................................23

5.3 Torque Characteristics ......................................................................................................24

5.4 Stress Characteristics ........................................................................................................27

5.5 Variation in Size ...............................................................................................................27

5.5.1 Effect of diameter on the aerodynamic output at 10 m/s:.......................................28

5.5.2 Effect of height on the aerodynamic output at 10 m/s: ..........................................28

5.5.3 Effect of aspect ratio on the aerodynamic output at 10 m/s: ..................................28

5.6 Variation in Overlap Ratio................................................................................................28

5.7 Variation in Blades ...........................................................................................................29

CHAPTER 6: SUMMARY............................................................................................................31

APPENDIX ....................................................................................................................................32

7.1 Variation in Sizes ..............................................................................................................32

7.1.1 Experiments on Rotor 1 ..........................................................................................32

vi



7.2 Variation in Overlap Ratio................................................................................................39

7.2.1 Overlap Ratio – 18 % .............................................................................................39

7.2.2 Overlap Ratio – 20 % .............................................................................................40

7.2.3 Overlap Ratio – 22 % .............................................................................................40

7.2.4 Overlap Ratio – 25 % .............................................................................................41

7.2.5 Overlap Ratio – 30 % .............................................................................................41

7.2.6 Overlap Ratio – 40 % .............................................................................................42

7.3 Variation in the number of blades ....................................................................................42

7.3.1 Rotor 1 with three blades at 6 m/s windspeed ........................................................42

7.3.2 Rotor 1 with three blades at 7.2 m/s windspeed .....................................................43



7.3.5 Rotor 1 with three blades at 10 m/s windspeed ......................................................45

REFERENCES ..............................................................................................................................46

vii

NOMENCLATURE

Symbol Explanation

A Projected Rotor Area

D Diameter of Rotor

d Diameter of blade

h Height of rotor

o Overlap

𝑣 Windspeed (m/s)

𝜔 Angular Velocity

Density of air

𝜆 Tip speed ratio

T Torque of rotor

P Power

Cd Drag coefficient

Cp Power coefficient

Re Reynolds number

OR Overlap Ratio

viii

LIST OF FIGURES

Figure 1: Wind Turbine Classification ........................................................................................... 3

Figure 2: Darrieus VAWT [11]...................................................................................................... 6

Figure 3: The Savonius VAWT [12] .............................................................................................. 8

Figure 4 : Top View of the Savonius [13] .................................................................................... 10

Figure 5 : Relative Performance of various VAWT's [1] ............................................................. 11

Figure 6 : 2D geometry view in ICEM CFD ................................................................................ 17

Figure 7: 2D mesh view ............................................................................................................... 18

Figure 8: 2D extrusion view with boundaries ............................................................................... 19

Figure 9: Variation of power coefficient with velocity for a two bladed Savonius system.......... 23

Figure 10 : A typical graph of power coefficient versus tip speed ratio obtained by experiments

[3] .................................................................................................................................................. 24

Figure 11 : A typical torque graph of a 2 blade Savonius ............................................................ 25

Figure 12 : A graph showing sum of the torques of the blades .................................................... 25

Figure 13 :A pressure contour with the rotor horizontal axis at 0 degrees to the windspeed ....... 25

Figure 14: A pressure contour with the rotor horizontal axis at 30 degrees to the windspeed ..... 26

Figure 15: A pressure contour with the rotor horizontal axis at 60 degrees to the windspeed ..... 26

Figure 16 : A typical stress contour on the surface of the blades ................................................. 27

Figure 17 : Increase of the power coefficient with the diameter .................................................. 28

Figure 18 Variation of the power coefficient with the aspect ratio .............................................. 28

Figure 19 : Variation of power coefficient with overlap ratio ...................................................... 29

Figure 20 : Comparison of the 2 blade and 3 blade performance of Rotor 1 with windspeeds ... 30

Figure 21 : Comparison of the torque characteristics exhibited with an increase in blades ......... 30

Figure 22 : Torque of Rotor 1 at 6 m/s windspeed ....................................................................... 32

Figure 23 : Torque of Rotor 1 at 7.2 m/s windspeed .................................................................... 33



Figure 26 : Torque of Rotor 1 at 10 m/s windspeed .................................................................... 35

Figure 27 : Torque of Rotor 2 at 10 m/s windspeed ..................................................................... 36

Figure 28 : Torque of Rotor 3 at 4.82 m/s windspeed .................................................................. 36

ix

Figure 29: Torque of Rotor 3 at 6.57 m/s windspeed ................................................................... 37


Figure 31 : Torque of Rotor 3 at 7.77 m/s windspeed .................................................................. 38


Figure 33 : Torque of Rotor 1 at 18 % overlap ............................................................................. 40






Figure 39 : Three bladed Rotor 1 at 6 m/s windspeed .................................................................. 43

Figure 40 : Three bladed Rotor 1 at 7.2 m/s windspeed ............................................................... 43



Figure 43 : Three bladed Rotor 1 at 10 m/s windspeed ................................................................ 45

LIST OF TABLES

Table 1 : Applications of the Savonius Wind Turbine ................................................................... 9

Table 2: Description of the various sized rotors ........................................................................... 22

Table 3 : List of the experiments conducted over number of blades, overlap, wind velocities and

sizes ............................................................................................................................................... 22

Table 4 : Aspect Ratio details of different rotors .......................................................................... 27

Table 5 : Torque comparison with two and three blades .............................................................. 29

Table 6: Properties of Rotor 1 at 6 m/s ......................................................................................... 32

Table 7 : Properties of Rotor 1 at 7.2 m/s ..................................................................................... 33

Table 8: Properties of Rotor 1 at 8.3 m/s ...................................................................................... 33

Table 9: Properties of Rotor 1 at 9.4 m/s ...................................................................................... 34

Table 10: Properties of Rotor 1 at 10 m/s ..................................................................................... 35

Table 11: Properties of Rotor 2 at 10 m/s ..................................................................................... 35

x

Table 12: Properties of Rotor 3 at 4.82 m/s .................................................................................. 36

Table 13 : Properties of Rotor 3 at 6.57 m/s ................................................................................ 37

Table 14 : Properties of Rotor 3 at 7.28 m/s ................................................................................. 37



Table 17 : Conditions of the overlap ratio test .............................................................................. 39

Table 18 : Properties for an overlap ratio of 18 % ........................................................................ 39

Table 19: Properties of an overlap ratio of 20 % .......................................................................... 40

Table 20 : Properties of an overlap ratio of 22 % ......................................................................... 40




Table 24 : Properties of three bladed Rotor 1 at 6 m/s ................................................................ 42

Table 25 : Properties of three bladed Rotor 1 at 7.2 m/s ............................................................. 43

Table 26: : Properties of three bladed Rotor 1 at 8.3 m/s ........................................................... 44

Table 27 : Properties of three bladed Rotor 1 at 9.4 m/s ............................................................. 44

Table 28 : Properties of three bladed Rotor 1 at 10 m/s ............................................................. 45

1

CHAPTER 1: WIND ENERGY AND WIND TURBINES

1.1 Wind Energy- Use and Advantages

Wind energy has been used since the earliest civilization to grind grain, pump water from deep

wells and power sailboats. From as early as the thirteenth century, horizontal-axis windmills

were an integral part of the rural economy and only fell into disuse with the advent of cheap

fossil-fuelled engines. The 21st century has seen a rise in the demand for renewable sources of

energy owing to the shortage and cost of non-renewable resources like fossil fuels.

The advantages of wind energy are as follows:

• The wind blows day and night, which allows windmills/wind turbines to produce

electricity throughout the day.

• Energy output from a wind turbine will vary as the wind varies, although the most rapid

variations will to some extent be compensated for by the inertia of the wind turbine rotor

thus obtaining a continuous output in many cases.

• Wind energy is a domestic, renewable source of energy that generates no pollution and

has little environmental impact. Up to 95 percent of land used for wind farms can also be

used for other profitable activities including ranching, farming and forestry.

• The decreasing cost of wind power and the growing interest in renewable energy sources

should ensure that wind power will become a viable energy source worldwide.

1.2 Energy in the Wind

The energy that can be extracted from the wind is directly proportional to the cube of the wind

speed. Thus, an understanding of the characteristics of the wind (velocity, direction, variation) is

critical to all aspects of wind energy generation, from the identification of suitable sites to

predictions of the economic viability of wind farm projects, to the design of wind turbines

themselves, all is dependent on characteristics of wind. The most striking characteristic of the

wind is its random nature. The wind is highly variable, both geographically and temporally.

Moreover this variability exists over a very wide range of scales, both in space and time. This is

important because extractable energy from wind varies with the cube of wind velocity. Generally

more wind is witnessed on the tops of hills and mountains than in low level areas. Even more

2

locally, wind velocities are altered by obstacles such as trees or buildings. For any location there

is variation of wind pattern, wind speed may vary from year to year, also wind distribution will

change from decade to decade. These long-term variations are not well understood, and thus

make it difficult to make predictions of the economic viability of wind-farm projects. Wind

distribution is more predictable over shorter time spans like a year, but on shorter time frame like

few days the wind energy is difficult to predict. On the whole, it is important that we understand,

the wind carries some energy with it, out of which some part is harnessed by the wind turbine.

The kinetic energy of air mass moving at a velocity can be expressed mathematically as is Eq 1.

𝐸 =1

2𝑚𝑣2 (1)

𝑃 =𝑑𝐸

𝑑𝑡 (2)

The rate of change of kinetic energy of the air flowing at a certain velocity 𝑣 through a certain

volume is the power possessed by the moving wind. This is the amount of wind energy passing

through cross-section per unit time.

At a certain given velocity 𝑣,

𝑃 =1

2

𝑑𝑚

𝑑𝑡𝑣2 (3)

We understand that the rate of change of mass of the air flowing can be determined in Eq 4 as

𝑑𝑚

𝑑𝑡= 𝜌𝐴𝑣 (4)

As we substitute Eq 4 in Eq 3, we get

𝑃𝑜𝑤𝑒𝑟 =1

2𝜌𝐴𝑣3

(5)

This is the theoretical energy possessed by the wind flowing at a certain velocity 𝑣.

1.3 Wind Turbines

Wind Turbines are wind energy converters that harness the kinetic energy contained in air

masses. Most modern wind energy converters are equipped with rotors to extract wind power,

and consist of one or several rotor blades. The extracted wind power generates rotation and is

thereby converted into mechanical power at the rotor shaft. Mechanical power is taken up at the

3

shaft in the form of a moment at a certain rotation and is transferred to a machine (such as a

generator). Thus there are entire wind power stations that consist of several wind turbines each

having a wind energy converter (rotor), a mechanical gear and a generator.

Every wind turbine design works with a certain efficiency. As time evolved, wind turbines of

various designs came into picture. The variation of the design is mostly inherent in the geometry

of the blade of the rotor, the aerodynamic properties of which are crucial in determining the

efficiency of the blade. A broad classification of wind turbines exists this way, which is

discussed below in Figure 1.

Figure 1: Wind Turbine Classification

1.4 Wind Turbine Classification

Wind Turbines have various classifications among them, the main classifications being

horizontal and vertical axis wind turbines.

1.5 Horizontal Axis Wind Turbines

Horizontal-axis wind turbines (HAWT) get their name from the fact that their axis of rotation is

horizontal. They have the main rotor shaft and electrical generator at the top of a tower, and are

pointed into the wind. The variability of wind distribution and speed brings up the requirement of

Wind Turbines

Horizontal axis

1 blade

2 blade

3blade

(or more)

Vertical axis

Darrieus

2 blade

3blade

H Rotor

Savonius

2 blade

3 blade

4

a gear system connected to the rotor and the generator. The gear system enables a constant speed

of rotation to the generator thus enabling constant frequency generation. Turbine blades are made

stiff in order to prevent the blades from being pushed into the tower by high winds. Downwind

machines have also been built, as they no longer require a yaw mechanism to keep them facing

the wind, and also because in high winds the blades can turn out of the wind thereby increasing

drag and coming to a stop. Most of the HAWT's are upwind as downwind systems cause regular

turbulence which may lead to fatigue.

1.5.1 HAWT advantages

• Higher efficiency , better performance

• Variable blade pitch, which gives the turbine blades the optimum angle of attack.

• As wind energy increases with height, the tall tower in the HAWT gives access to higher

wind speed.

• More commercially viable.

1.5.2 HAWT disadvantages

• Due to inherent large structures, construction costs are very high and so are transportation

costs.

• Wind turbine operation often leads to production of noise.

• In case of downwind HAWTs’ the regular turbulence produced leads to structural failure.

HAWTs require an additional yaw control mechanism to turn the blades toward the wind.

1.6 Vertical Axis Wind Turbines

Vertical-axis wind turbines (or VAWTs) have the main rotor shaft arranged vertically as the

plane of rotation is vertical. Blades are also vertical in this arrangement. The biggest advantage

of VAWTs is they don’t require a yaw control mechanism to be pointed into the wind. Thus

these are useful in sites where wind direction is random or there is presence of large obstacles

like trees, houses etc. Also VAWTs’ don’t require a tower structure and can be placed nearby a

ground enabling access to electrical components. Some drawbacks are the low efficiency of wind

production and the fact that large drag is created for rotating the blades in a vertical axis.

1.6.1 VAWT advantages

• A massive tower structure is not required, as VAWTs’ are mounted closer to the ground

5

• They don’t require yaw mechanisms.

• These are located closer to the ground and hence easier to maintain.

• These have lower startup speeds than their horizontal counterparts.

• These have a lower noise signature.

• Are more efficient in gusty winds – already facing the gust.

• Can be installed in more locations - on roofs, along highways, in parking lots.

• Do not kill birds and wild - life - slow moving and highly visible.

• Can be significantly less expensive to build – are inherently simpler .

1.6.2 VAWT disadvantages

• VAWTs’ have lower efficiency as compared to HAWT’s

• Even though VAWTs’ are located closer to the ground, the equipment now resides at the

bottom of the turbines structure thus making it inaccessible.

• Because of their low height they cannot capture the wind energy stored in higher

altitudes.

1.7 Types of Vertical Axis Wind Turbines

1.7.1 Darrieus

Invented by F.M. Darrieus in the 1930s, Darrieus turbines shown in Figure 2, are lift-based

turbines designed to function on the aerodynamic principle of airplanes .The rotor blades are

designed as an airfoil in cross section, so the wind travels a longer distance on one side (convex)

than the other side (concave). As a result, the wind speed is relatively higher on the convex side.

If Bernoulli’s equation is applied, it can be shown that the differential in wind speed over the

airfoil creates a differential pressure, which is used to pull the rotor blade around as the wind

passes through the turbine. The Darrieus VAWT is primarily a lift-based machine, which is a

feature that makes it compete in performance with the conventional HAWTs.

Figure 2shows a typical Darrieus wind turbine characterized by its C-shaped rotor. It is normally

built with two or three rotor blades. It has a low starting torque, but high rotational speed,

making it suitable for coupling with an electrical synchronous generator. For a given rotor size,

weight and cost, its power output is higher than any drag-based VAWT .But the Darrieus VAWT

suffers disadvantage by not self-starting. For this purpose, there exists one more design called the

6

Savonius, which has an easy starting capability. Experimental studies of Savonius – Darrieus

wind turbines have been conducted. The result of the combined designs shows an improvement

in power generation efficiency.

Figure 2: Darrieus VAWT [11]

1.7.2 Savonius

Savonius wind turbines are drag based VAWTs that operate on the theory and principle of a

paddle propelling a boat through water. It was invented by a Finnish engineer, S.J. Savonius. If

no slip exists between the paddle and water, the maximum speed attained will be the same as the

tangential speed of the paddle.

Similarly, in a drag based VAWT, the speed at the tip of the blade can seldom exceed the speed

of the wind. In other words, the drag can also be described as the pressure force or the thrust on

the blades created by the wind as it passes through it.

Various types of drag based VAWTs have been developed in the past which use plates, cups,

buckets, oil drums, etc. as the drag device. The Savonius rotor is an S - shaped cross section rotor

which is predominantly drag based, but also uses a certain amount of aerodynamic lift. Drag

based VAWTs have relatively higher starting torque and less rotational speed than their lift based

counterparts.

Furthermore, their power output to weight ratio is also less .Because of the low speed, these are

generally considered unsuitable for producing electricity, although it is possible by selecting

proper gear trains. Drag based windmills are useful for other applications such as grinding grain,

7

pumping water and a small output of electricity. A major advantage of drag based VAWTs lies

in their self– starting capacity, unlike the Darrieus lift–based vertical axis wind turbines.

1.8 Thesis Outline

Chapter 2 helps us understand the Savonius vertical axis wind turbine, its aerodynamics

properties and how its performance is measured.

Chapter 3 explains the existing literature survey that was referred to.

Chapter 4 describes the computational model, the boundary and solver conditions that was built

using ANSYS modules ICEM CFD and CFX.

Chapter 5 describes the set of computational experiments that was carried out spanning the

geometrical parameters and the results of each.

Chapter 6 analyses the data obtained from the experiments in Chapter 5, and deduces necessary

inferences.

Chapter 7 presents future scope of work and conclusion.

8

CHAPTER 2 : THE SAVONIUS VAWT

Savonius turbines are one of the simplest turbines. Aerodynamically, they are drag-type devices,

consisting of two or three scoops. Because of the curvature, the scoops experience less drag

when moving against the wind than when moving with the wind. The differential drag causes the

Savonius turbine to spin. Because they are drag-type devices, Savonius turbines extract much

less of the wind's power than other similarly-sized lift-type turbines. Much of the swept area of a

Savonius rotor is near the ground, making the overall energy extraction less effective due to

lower wind speed at lower heights.

Figure 3: The Savonius VAWT [12]

2.1 Savonius- Advantages and Disadvantages

The Savonius turbine is of simple geometry and its construction is cheap. It starts rotating at

lower wind speeds as compared to its counterpart wind turbines, having a high starting torque. It

produces low noise and can make use of the wind flowing in any horizontal direction to its

rotation. However, in spite of these advantages, this wind turbine faces one main disadvantage of

having low efficiency.

9

2.2 Savonius- Applications

Savonius turbines are used whenever cost or reliability is much more important than efficiency.

Table 1 : Applications of the Savonius Wind Turbine

Anemometers Most anemometers are Savonius turbines,

because efficiency is completely irrelevant for

that application.

Deep Water Buoys Much larger Savonius turbines have been used

to generate electric power on deep-water

buoys, which need small amounts of power

and get very little maintenance

Flettner Ventilators The most ubiquitous application of the

Savonius wind turbine is the Flettner

Ventilator which is commonly seen on the

roofs of vans and buses and is used as a

cooling device. The ventilator was developed

by the German aircraft engineer Anton Flettner

in the 1920s. It uses the Savonius wind turbine

to drive an extractor fan. The vents are still

manufactured in the UK by Flettner Ventilator

Limited.

Other applications The upcoming needs of small scale electricity

production are coming handy in urban sites. So

we see their use in self sustaining street lights

and rooftops

2.3 Savonius- Aerodynamics

From an aerodynamic point of view, the different VAWT, have a number of aspects in common

that distinguish them from the HAWT. Most of the rotation of the Savonius turbine is caused due

to drag forces. The turbine consists of two blades (or more blades), the advancing blade and the

retreating blade in the case of a two-bladed Savonius. The blades of a Savonius rotate on a

10

Figure 4 : Top View of the Savonius [13]

horizontal plane whose axis is at right angle to the wind direction. The aerodynamic angle of

attack of the blades varies constantly during the rotation. So during rotation, one blade moves on

the downwind side and the other on the upwind side. The torque extraction from the blade that

moves on the downwind side is less compared to the energy extracted by the upwind blades. This

describes the characteristic of the torque. Hence, power generation is less in the downwind sector

of rotation.

The torque caused by drag forces is generally lesser than that produced by lift forces.

In one revolution, a single rotor blade generates a mean positive torque but there are also short

sections with negative torque.

Various approaches, with a variety of weightings of the parameters involved have been published

in the literature. Menet et al [1] specify values of 0.15-0.2 to be the maximum value of power

coefficient Cp for the single stage Savonius type wind turbine.

The following Figure 4 [13] shows us a characteristic of the flow and the basic terminology of

the blades. The equations result in saying that the Cp can be expressed as a function of the drag

coefficients and the tip speed ratio.

As the Savonius torque is generated by the difference of drag forces as in Eq 6 we can say,

11

𝐹𝑑 = 𝐹𝑑𝑟 − 𝐹𝑑𝑎 (6)

𝐹𝑑 =

1

2𝜌𝐴𝐶𝑑𝑟 𝑉𝑠𝑖𝑛𝜃 − 𝜔𝑅 2 −

1

2𝜌𝐴𝐶𝑑𝑎 𝑉𝑠𝑖𝑛𝜃 + 𝜔𝑅 2 (7)

𝑇 = 𝐹𝑑𝑅𝑑𝜃

𝜋

0

(8)

𝐶𝑝 = 𝑇𝜔/(

1

2𝜌𝐴𝑣3)

(9)

𝐶𝑝 = 𝜆/3𝜋[𝐶𝑑𝑟 6𝜆2 − 3𝜆 𝜋 − 1 + 4 − 𝐶𝑑𝑎 6𝜆2 + 3𝜆 𝜋 − 1 + 4 ] (10)

Figure 5 : Relative Performance of various VAWT's [1]

Eq 10 explains that, for obtaining Cp as a function as expressed in the above, a knowledge of the

drag coefficient of each of the blades is necessary. However the drag coefficient (Cd) is not a

value that we can define with respect to time. Hence this cannot be taken further unless the drag

coefficients are known with respect to time.

2.4 Savonius – Performance and Efficiency

The performance of the Savonius wind turbine is determined by the coefficient of performance

(Cp). It is theoretically defined as the ratio of the aerodynamic power generated by the wind

turbine to the power possessed by the wind incoming on the the surface of the rotor.

12

However, Cp is indicated as a function of the tip speed ratio(𝜆), as the performance of wind

turbines reaches an optimum for a certain tip speed ratio.

𝜆 = 𝜔𝑅/𝑣 (11)

2.5 Motivation of the Project

Most research on the Savonius has been on the experimental side. The results from an

experimental setup are limited to the design being tested.

An attractive alternative is a computer model in the place of the experimental model.

Computer models provide the user with the privilege to change inputs and see the

outcome instantly.

2.6 Project Objective

To develop a computational model that can capture the physics demonstrated by

experimental Savonius models available in the literature.

Identify design variables, make perturbations and observe changes.

This thesis answers the following questions.

Given a range of wind speeds, how do you decide upon your overall size?

Does there exist an optimal overlap for the blades?

Does performance increase when the number of blades are increased?

What are the stresses exerted by the winds on the blade surfaces?

13

CHAPTER 3: LITERATURE SURVEY

J L Menet[1] presented a study wherein he suggested the performance of one particular design of

the Savonius rotor. It was a small Savonius rotor (i.e. of low power) for local production of

electricity. They designed, developed and ultimately built a prototype of such a rotor, which was

a complete electromechanical system. An optimised configuration was chosen for the geometry

of the prototype. The building data were calculated on the basis of the nominal wind velocity V =

10 m/s. He indicates that studies done on the prototype have confirmed the high efficiency and

the low technicality of the Savonius rotors for local production of electricity. It means that for

urban usage, Savonius rotors are of low performance, but looking at it over a longer period of

time, they make use of the lesser and multi directional wind speeds and proves more effective.

They present a decision matrix for opting the material for the rotor, the choice of geometry, shaft

and generator details etc. They consider nominal parameters and present a certain relationship of

the power coefficient with angular velocity. This was interpolated to a relationship between wind

velocity and angular velocity. However the interpolations are done neglecting the electrical and

mechanical losses.

UK Saha et al. [2] conducted wind tunnel tests on 14 prototypes of Savonius rotor models, all of

the same overall dimension. The variation of the prototypes came in the number of blades, the

number of stages and their respective combinations. Both semicircular and twisted blades have

been used in either case. A family of rotor systems was manufactured with identical stage aspect

ratio keeping identical the projected area of each rotor. The overlap ratio, being another

important geometrical parameter has been suggested to be around 20% to 30% for the models.

Experiments were carried out to optimize the different parameters like number of stages, number

of blades (two and three) and geometry of the blade (semicircular and twisted). Further attempt

was made to investigate the performance of two-stage rotor system by inserting valves on the

concave side of blade. Velocities of wind speeds were considered between the range of 6 m/s and

11 m/s. Spanning 84 experiments on all these parameters, the 2 stage 2 blade Savonius model

was considered to be showing the highest value of power coefficient. Among a comparison

between the semicircular and the twisted ones, the twisted model was found to be more efficient

than the semicircular one.

14

Sargolzaei et al. [9] simulated Savonius wind turbine using a concept called artificial neural

networks (ANNs) to estimate power ratio and torque. They experimentally investigated seven

prototype Savonius wind turbine and compared their overlap ratios with their predicted ANNs

results. Their predicted results were in good agreement with their experimental results that

existed in the literature. They found that the increase of wind speed causes torque

increase.However; this necessarily need not increase the power coefficient. For all their models

they found maximum torque was at 60⁰ and minimum torque was at 120⁰.

Burcin Deda Altan et al. [8] introduced a new curtain arrangement to improve the performance

of Savonius wind rotors. The curtain arrangement was placed in front of the rotor preventing the

negative torque opposite the rotor rotation. The geometrical parameters of the curtain

arrangement were optimized to generate an optimum performance. The rotor with different

curtain arrangements was tested out of a wind tunnel, and its performance was compared with

that of the conventional rotor. The maximum power coefficient of the Savonius wind rotor is

increased to about 38.5% with the optimum curtain arrangement. The experimental results

showed that the performance of Savonius wind rotors could be improved with a suitable curtain

arrangement.

Gupta et al. [10] compared a three-bucket Savonius wind turbine with a three-bucket Savonius–

Darrieus wind turbine. They found that the power coefficient of the combined turbine decreases

as the overlap ratio increases. The maximum power coefficient of 51% was found where there

was no overlap. They claimed that the combined rotor without overlap, which showed 51%

efficiency, was the highest efficiency of a Savonius wind turbine at any overlap condition under

these test conditions.

Md. Imtiaj Hassan et al. [7] present a Computational Fluid Dynamics (CFD) analysis of a

Twisted Savonius rotor. Simulations were performed in a CFD software Flow-3D, using

Reynolds Averaged Navier-Stokes Equations (RANSE) solver with structured rectangular mesh.

Expected performance of the twisted Savonius rotor has been determined, this includes starting

15

characteristics, static torque and rotational speed of the turbine. Simulation results show better

performance of twisted Savonius rotor as compared to the other conventional Savonius rotors.

M.A. Kamoji et al. [4], modified forms of the conventional Savonius rotors in an effort to

improve the coefficient of power and to obtain uniform coefficient of static torque. To achieve

these objectives, the rotors are being studied with and without central shaft between the end

plates. Tests in a closed jet wind tunnel on modified form of the conventional Savonius rotor

with the central shaft were to have a coefficient of power of 0.32. They studied the effect of

geometrical parameters on the performance of the rotors in terms of coefficient of static torque,

coefficient of torque and coefficient of power. The parameters studied are overlap ratio, blade arc

angle, aspect ratio and Reynolds number.

16

CHAPTER 4: THE COMPUTATIONAL MODEL

4.1 Introduction- CFD analysis

As a consequence of the rapid evolution of computational power within the last two decades,

the significance of numerical flow simulations in the design of hydraulic machinery has grown to

a considerable extent. At present CFD simulations can often replace elaborate experiments due to

the fact that even complex geometries and entire machines can be modeled. Separate numerical

investigations of single turbo-machinery components are common practice, yet these simulations

do not account for interactions between the components which have strong influence on the

operational behavior of the entire machine. Due to these interactions—e.g. between the

stationary guide vanes and the rotating runner, the so called rotor-stator interactions—the flow in

turbo-machines is unsteady and highly turbulent. The investigation of these phenomena requires

transient simulations and special numerical treatment with respect to the interface between the

components. The approach used in an extruded 2D computational fluid dynamics analysis of the

Savonius blades. The model used in analysis consists of a stream of air impinging on the blade

system.

4.2 Features of the CFD analysis

Multiple Frames of Reference: The CFD simulation requires the interfacing of a rotor domain

and a stator domain to effectively determine performance, as the rotor is in a rotating frame and

the incoming wind in a non rotating frame.

Transience: This features a transient simulation of the rotation over every single degree of

rotation.

4.3 CFD analysis – Steps

2D geometry

2D mesh

Mesh extrusion

Boundary conditions

Interfacing

Solution monitoring and control

17

Post processing results

4.3.1 2D- Geometry

The geometry is a combination of 3 domains- the blades, the inner fluid domain and the outer

fluid domain. The thickness of the blades needs to be defined, which is 3mm in our case. The

model was made with the dimensions as indicated by UK Saha [2] and ML Simmonds[3].

Figure 6 : 2D geometry view in ICEM CFD

The inner fluid domain is shaped as a circle and the outer fluid domain is shaped as a rectangle.

This is because the wind flow direction is rotary is the inner domain and linear of the outer

domain.

Inner domain constraints: The diameter of the inner fluid domain needs to be 10-20 % greater

than the diameter of the rotor. We have considered 10 % , which means the diameter of the inner

fluid domain is 1.1 time that of the rotor.

Outer domain constraints: The outer domain being rectangular must be 10D×5D (10D in the

wind direction). This gives 5D for upstream and 5D for downstream. However, the size was

18

bought down to 6D×4D (6D in the wind direction, shown in Figure 6) as it exhibited the same

result characteristics as to that of the 10D×5D dimension

Figure 7: 2D mesh view

4.3.2 2D Mesh

The mesh chosen for the 2D mesh geometry is a quad dominant geometry. The choice of a quad

mesh was as a quad mesh gives better control and also will reduce numerical error so to say that

the results obtained will mostly due to the flow behavior and not due to the numerical error as

compared to the triangular mesh.(shown in Figure 7)

19

Mesh for Inner domain: The flow patterns inside the inner domain exhibit variations, due to

which the mesh pattern needs to be uniform inside. The size of the mesh should necessarily be

lesser than the thickness of the blade. We have considered the mesh element size to be one third

the blade thickness.

Mesh for Outer domain: The mesh size for the outer domain goes increasing in value as we

move radially outwards. The outer fluid mesh must have a node-wise connection to the inner

fluid mesh.

Figure 8: 2D extrusion view with boundaries

4.3.3 Mesh Extrusion:

The simulation cannot just be carried out in a 2D fashion and the pre processing software CFX-

Pre requires a certain thickness of the fluid domain to be present to calculate the torque over the

blade surface. So the existing mesh is extruded by more than one layer(shown in Figure 8),

specifying a certain height for each layer. We have considered 2 layers each of height h/2.

20

4.3.4 Analysis type and timestep details:

The analysis is transient and it needs to be run in timesteps. So an ideal timestep in

turbomachinery applications is 0.5 to 2 degrees especially when the rpm is greater than 100. The

length of a timestep is inversely proportional to the rpm.

Length of each timestep =Number of degrees moved per timestep/(6×rpm) (12)

Total run time : 360× Number of degrees moved per timestep/(6×rpm) (13)

4.3.5 Boundary conditions:

The following are the boundary conditions that have been applied. The rotating and stationary

domains are specified.

Rotating Domain: The rotating domain has a certain angular velocity. The fluid is atmospheric

air with atmospheric pressure. The domain requires initialization conditions to be preset (the

wind velocity and the atmospheric pressure). The turbulence mode is set to the k-epsilon model.

It is a two equation model. That means it includes two extra transport equations to represent the

turbulent properties of the flow. This allows a two equation model to account for history effects

like convection and diffusion of turbulent energy.

Stationary Domain: The stationary domain has a free stream velocity. The domain is set to

stationary. Adding to that, the atmospheric pressure conditions are applied and the initialization

is done.

Inlet, Outlet: Inlet and Outlet are default boundary conditions in ANSYS CFX. Inlet requires

the speed of inlet air and the outlet requires the relative pressure, 0 Pa, at the initial conditions.

Blade surfaces: The blade surfaces are enabled a ―wall‖ condition. This condition enables the

calculation of properties such as force, torque on the surface.

Interfacing: Once the domains have been specified a default fluid-fluid interface is detected

between the rotating and stationary domain. Here the transient rotor stator is selected.

This model should be used any time it is important to account for transient interaction effects at a

sliding (frame change) interface. It predicts the true transient interaction of the flow between a

stator and rotor passage. It ultimately accounts for all interaction effects between components

21

that are in relative motion to each other. The interface position is updated each timestep, as the

relative position of the grids on each side of the interface changes.

The principle disadvantage of this method is that the computer resources required may be large,

in terms of simulation time, disk space and quantitative post processing of the data. The resource

requirement problem is exacerbated if unequal pitch between components occurs. In these

situations, spatial periodicity cannot formally be used to limit the analysis to a single blade

passage per component.

4.3.6 Solver conditions:

Convergence loops: The solver calculates parameters the torque(required parameter) for every

timestep. Each timestep is run for a certain number of loops for convergence. As per general

guidelines, this is set from 7 to 10 for the simulations.

Transient results (velocity contours, pressure contours) have to be defined with a certain

frequency of timesteps. This helps record the contour details of pressure, velocities and forces.

22

CHAPTER 5: RESULTS AND DISCUSSIONS

The power coefficient (Cp) is a crucial parameter that determines the performance of a Savonius.

Following is the parameters that have an effect on the power coefficient (Cp)

Number of blades

Overlap Ratio

Overall Size

Wind Velocity

To evaluate the effect that these parameters have, a set of experiments was conducted spanning

all the parameters. The inputs of these experiments have been taken from the literature.

Table 2: Description of the various sized rotors

Reference Description Rotor Dimension ( H×D)

Reference 1 ( dimensions and data adopted from UK Saha) 17 cm×19.8 cm

Reference 2 ( dimensions and data adopted from JL Menet ) 101.5 cm×44.5 cm

Reference 3( dimensions and data adopted from Simmonds) 177 cm×94.5 cm

Table 3 : List of the experiments conducted over number of blades, overlap, wind velocities and sizes

Rotor Number of Blades Range of wind

velocities tested

Number of

Experiments

Overlap Ratio

1 2-semicircular 6m/s – 10 m/s 5 0.2

2 2-semicircular 10 m/s 1 0.2

3 2-semicircular 4.8 m/s - 8.9 m/s 5 0.33

1 3-semicircular 6m/s-10 m/s 5 -

1 2-semicircular 10 m/s 7 0.18-0.4

For details in any particular experiment, refer Appendix. The results of experiments performed

over variables size, overlap, and the number of blades are given section-wise.

23

5.1 Comparison- Aerodynamic vs Experimental Values

Figure 9: Variation of power coefficient with velocity for a two bladed Savonius system

From the results, we can say that the computational results have similar trend to the experimental

results available in the literature. The values are off by a factor of 2 to 3.

5.2 Observation on Tip Speed Ratios

The power coefficient is a function of the tip speed ratio given certain geometry of a Savonius

rotor. For 95% of the experiments found in literature run over the rotor models over various sizes

and overlaps, the tip speed ratio for almost all practical cases stands between 0.6-0.9.

So, for 95% of the experimental cases that have been run,

0.6 < 𝜆 < 0.9 (14)

0.6𝑣

𝑅< 𝜆 <

0.9𝑣

𝑅 (15)

0.05

0.1

0.15

0.2

0.25

0.3

0.35

4 5 6 7 8 9 10 11

Co

effi

cien

t o

f P

erfo

rma

nce

Velocity (m/s)

Experiments by Simmonds et

al.(Rotor 3)

Computational Result- Rotor 3

Experiments by Saha et

al.(Rotor 1)

Computational Result- Rotor 1

24

Figure 10 : A typical graph of power coefficient versus tip speed ratio obtained by experiments [3]

As the transient CFD simulation requires the rotational speed of the rotor as an input, the above

approximation could be a good measure to predict the range of the rotational speed given the

geometry and the windspeeds as shown in Eq 14 and Eq 15.

5.3 Torque Characteristics

We see a pattern convergence after crossing 100 degrees of rotation. The initialization of the

Savonius has been done at 0 degrees. We see the first peak of the first blade at 210 degrees and

the first peak of the second blade at 390 degrees of rotation.

With a uniformity in cases, the Savonius rotor peaks the torque of its advancing blade at 30

degrees to the axis along which the wind speed is travelling. This pattern repeats itself over every

360 degrees of rotation.

25

Figure 11 : A typical torque graph of a 2 blade Savonius

Figure 12 : A graph showing sum of the torques of the blades

Figure 13 :A pressure contour with the rotor horizontal axis at 0 degrees to the windspeed

-4.00E-01

-2.00E-01

0.00E+00

2.00E-01

4.00E-01

14

5

89

13

3

17

7

22

1

26

5

30

9

35

33

97

44

1

48

5

52

9

57

3

61

7

66

1

70

5

74

9

79

3

83

7

88

1

92

5

96

9

10

13

10

57To

rqu

e

Degrees of Rotation

2 blade Savonius- Torque Characteristic

Torque_Blade1

Torque_Blade2

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

1

48

95

14

2

18

9

23

6

28

33

30

37

7

42

4

47

1

51

8

56

5

61

2

65

9

70

6

75

3

80

0

84

7

89

4

94

1

98

8

10

35

2 blade Savonius - Sum of Torque

Characteristic

Torque_Blade1 + Blade2

26

Figure 14: A pressure contour with the rotor horizontal axis at 30 degrees to the windspeed

Figure 15: A pressure contour with the rotor horizontal axis at 60 degrees to the windspeed

Here is a characteristic of the pressure contour at 30 degrees which shows a high pressure

difference on the advancing blade, hence causing it to turn. The pressure contours around the

blade show the characteristics wherein the advancing blade experiences positive torque due to a

pressure difference and the retreating blade experiences resistance. The pressure patterns when

the Savonius axis is at three different orientations are shown by Figures 13, 14 and15

27

5.4 Stress Characteristics

Figure 16 : A typical stress contour on the surface of the blades

The values are with respect to atmospheric pressure. The above case is for Rotor 3 at 8.85 m/s.

The maximum increase pressure on the surface is around 100 Pa.

5.5 Variation in Size

Three models of various geometries were taken under consideration.

Table 4 : Aspect Ratio details of different rotors

Rotor Diameter Height Aspect Ratio Velocity range of testing

1 19.8 cm 17.3 cm 0.873 6-10 m/s

2 44.5 cm 101.5 cm 1.13 10 m/s

3 94.5 cm 177.8 cm 1.88 4.8 – 8.8 m/s

Rotor 3, unlike Rotor 1 has been showing a constant aerodynamic power coefficient with respect

to the range of wind speeds between (4.8 – 8.8) m/s. We extend this graph to 10 m/s and

compare performance of the three rotors at 10 m/s.

28

5.5.1 Effect of diameter on the aerodynamic output at 10 m/s:

Figure 17 : Increase of the power coefficient with the diameter

5.5.2 Effect of height on the aerodynamic output at 10 m/s:

The increase of height of the rotor does not affect the aerodynamic performance as observed in

Eq 16 and Eq 17.

𝐶𝑝 ∝ 𝑇 ; 𝐶𝑝 ∝ 1/𝐴 (16)

𝑇 ∝ ℎ ; 𝐴 ∝ ℎ (17)

Hence the value of Cp remains unaltered.

5.5.3 Effect of aspect ratio on the aerodynamic output at 10 m/s:

Figure 18 Variation of the power coefficient with the aspect ratio

5.6 Variation in Overlap Ratio

A study of the performance has been observed at various overlap ratios has been observed from

10 to 40 % of overlap, and the performance has been recorded to find an optimum at 22 %

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0 10 20 30 40 50 60 70 80 90 100

Po

wer

Co

effi

cien

t

Diameter (cm)

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Po

wer

Co

effi

cien

t

Aspect Ratio

29

overlap. The simulations have been carried out in certain steps and the results are shown in

Figure 19.

Figure 19 : Variation of power coefficient with overlap ratio

5.7 Variation in Blades

Table 5 : Torque comparison with two and three blades

2 blade - torque 3 blade – torque

The torque values are largely positive We see an equally high contribution due to

negative torque, which brings down the overall

torque.

The overall torque is that of the sum over 2

blades

The overall torque is that of the sum over 3

blades.

For the Rotor 1 model that was compared with respect to 2 blades and 3 blades (according to

Figure 21), we find that the optimal performance for both cases is shown at around 8 m/s. But we

cannot assure the similar optimal performance pattern as the wind speed increases, as the

performance curve becomes flatter as the size increases.

In spite of the 3 blade obtaining torque as a sum of that from three different blades, the power

coefficient values of a 2 blade are greater than that of a 3 blade rotor. So we infer that owing to

large negative torque values (Figure 22), the overall efficiency of a blade in a 3 blade Savonius is

lesser than that of a 2 blade Savonius. Table 5 summarizes these differences.

0.15

0.2

0.25

0.3

0 5 10 15 20 25 30 35 40 45

Po

wer

Co

effi

cien

t

Overlap Ratio (%)

Blade overlap

charateristics

30

Figure 20 : Comparison of the 2 blade and 3 blade performance of Rotor 1 with windspeeds

Figure 21 : Comparison of the torque characteristics exhibited with an increase in blades

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

5.5 6.5 7.5 8.5 9.5 10.5Co

effi

cien

t o

f P

erfo

rma

nce

Velocity (m/s)

2 blades versus 3 blades

Experiments by Saha et al.(2

blade)

Computational Output (2 blade)

Experiments by Saha et al.(3

blade)

Computational Output (3 blade)

-4.00E-01

-2.00E-01

0.00E+00

2.00E-01

4.00E-01

1

46

91

13

6

18

1

22

6

27

1

31

6

36

1

40

6

45

1

49

6

54

1

58

6

63

1

67

6

72

1

76

6

81

1

85

6

90

1

94

6

99

1

10

36To

rqu

e

Degrees of Rotation

Rotor 1 - 10 m/s

Torque_Blade1

Torque_Blade2

Torque_Blade3

-1.00E-01

0.00E+00

1.00E-01

2.00E-01

3.00E-01

1

20

39

58

77

96

11

5

13

4

15

3

17

2

19

1

21

0

22

9

24

8

26

7

28

6

30

5

32

4

34

3

36

2

38

1

40

0

To

rqu

e

Degrees of Rotation

Rotor 1 - 10 m/s

Torque_Blade1

Torque_Blade2

31

CHAPTER 6: SUMMARY

A computational model of a Savonius VAWT was developed in Ansys –CFX. The idea was to

develop a computational model that can capture the physics demonstrated by experimental

models available in the literature. Once such a computational model is available, it is easy to

make perturbations to input design variables and observe output changes. Based on simple

studies, following are our observations.

We understand from Figure 9 that a higher variance in wind speeds from the nominal

values of 8-10 m/s suggests for the implementation of larger sized rotors (with diameter

greater than 1m).

The optimal overlap for maximum performance at a certain wind speed is found to be

at 20-22 % given a nominal wind speed at 10 m/s. This corroborates the observation in

literature. (Figure 19)

The overall efficiency of a system does not increase in a Savonius when the number of

blades is increased from 2 to 3.(Figure 21)

The highest stress value over the experiments was observed at the highest windspeed

tested at the 30 degrees orientation.

The torque characteristics hit peak value when the axis of the rotor is inclined at 30

degrees to the axis of the incoming wind speed.(Figure 13,14,15). The peak torque

exhibits a similar trend with the average torque that determines the power coefficient,

which takes lesser time to compute.

32

APPENDIX

The results for experiments done on variations with size, the overlap and the number of blades

can be referred to under this section. The graphs show the torque characteristics that repeat

themselves over 360 degrees of rotation.

7.1 Variation in Sizes

7.1.1 Experiments on Rotor 1

7.1.1.1 Rotor 1 at 6 m/s windspeed

Table 6: Properties of Rotor 1 at 6 m/s

Blades 2-semicircular

Input Wind Velocity 6 m/s

Angular Velocity 390 rpm

Tip speed Ratio 0.676

Overlap Ratio 0.2

Coefficient of Performance 0.24

Figure 22 : Torque of Rotor 1 at 6 m/s windspeed

-5.00E-02

0.00E+00

5.00E-02

1.00E-01

1

22

43

64

85

10

6

12

7

14

8

16

9

19

0

21

1

23

2

25

3

27

4

29

5

31

6

33

7

35

8

37

9

40

0

42

1

44

2

46

3

To

rqu

e

Degrees of Rotation

Rotor 1 at 6 m/s

Torque_Blade1

Torque_Blade2

33

7.1.1.2 Rotor 1 at 7.2 m/s windspeed

Table 7 : Properties of Rotor 1 at 7.2 m/s


Input Wind Velocity 7.2 m/s



Overlap Ratio 0.2

Coefficient of Performance .259

Figure 23 : Torque of Rotor 1 at 7.2 m/s windspeed


Table 8: Properties of Rotor 1 at 8.3 m/s





Overlap Ratio 0.2


-1.00E-01

-5.00E-02

0.00E+00

5.00E-02

1.00E-01

1.50E-01

1

21

41

61

81

10

1

12

1

14

1

16

1

18

1

20

1

22

1

24

1

26

1

28

1

30

1

32

1

34

1

36

1

38

1

40

1

42

1

44

1

To

rqu

e

Degrees of Rotation

Rotor 1 - 7.2 m/s

Torque_Blade1

Torque_Blade2

34






Angular Velocity 600rpm


Overlap Ratio 0.2



-1.00E-01

-5.00E-02

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

1

19

37

55

73

91

10

9

12

7

14

5

16

3

18

1

19

9

21

7

23

5

25

3

27

1

28

9

30

7

32

5

34

3

36

1

37

9

39

7

41

5

To

rqu

e

Degrees of Rotation

Rotor 1 - 8.3 m/s

Torque_Blade1

Torque_Blade2

-1.00E-01

0.00E+00

1.00E-01

2.00E-01

1

20

39

58

77

96

11

5

13

4

15

3

17

2

19

1

21

0

22

9

24

8

26

7

28

6

30

5

32

4

34

3

36

2

38

1

40

0

41

9

43

8

To

rq

ue

Degrees of Rotation

Rotor 1 - 9.4 m/s

Torque_Blade1

Torque_Blade2

35







Overlap Ratio 0.2










Overlap Ratio 0.2


-1.00E-01

0.00E+00

1.00E-01

2.00E-01

3.00E-01

1

18

35

52

69

86

10

3

12

0

13

7

15

4

17

1

18

8

20

5

22

2

23

9

25

6

27

3

29

0

30

7

32

4

34

1

35

8

37

5

39

2

To

rqu

e

Degrees of Rotation

Rotor 1 - 10 m/s

Torque_Blade1

Torque_Blade2

36









Overlap Ratio 0.33



-4.00E+00

-2.00E+00

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1

20

39

58

77

96

11

5

13

4

15

3

17

2

19

1

21

0

22

9

24

8

26

7

28

6

30

5

32

4

34

3

36

2

38

1

40

0

41

9

43

8

To

rqu

e

Degrees of Rotation

Rotor 2 - 10 m/s

Torque_Blade1

Torque_Blade2

-5.00E+00

0.00E+00

5.00E+00

1.00E+01

1.50E+01

1

20

39

58

77

96

11

5

13

4

15

3

17

2

19

1

21

0

22

9

24

8

26

7

28

6

30

5

32

4

34

3

36

2

38

1

40

0

41

9

43

8

To

rqu

e

Degrees of Rotation

Rotor 3 - 4.82 m/s

Blade_Torque1

Blade_Torque2

37







Overlap Ratio 0.33


Figure 29: Torque of Rotor 3 at 6.57 m/s windspeed







Overlap Ratio 0.33


-1.00E+01

0.00E+00

1.00E+01

2.00E+01

1

19

37

55

73

91

10

9

12

7

14

5

16

3

18

1

19

9

21

7

23

5

25

3

27

1

28

9

30

7

32

5

34

3

36

1

37

9

39

7

41

5

43

3

To

rq

ue

Degrees of Rotation

Rotor 3 - 6.57 m/s

Blade_Torque1

Blade_Torque2

38








Overlap Ratio 0.33








-10

0

10

20

30

11

7

33

49

65

81

97

11

31

29

14

51

61

17

71

93

20

92

25

24

1

25

72

73

28

93

05

32

13

37

35

33

69

38

5

40

14

17

43

3

To

rqu

e

Degrees of Rotation

Rotor 3 - 7.28 m/s

Torque_Blade1

Torque_Blade2

-2.00E+01

-1.00E+01

0.00E+00

1.00E+01

2.00E+01

3.00E+01

1

19

37

55

73

91

10

9

12

7

14

5

16

3

18

1

19

9

21

7

23

5

25

3

27

1

28

9

30

7

32

5

34

3

36

1

37

9

39

7

41

5

43

3

To

rq

ue

Degrees of Rotation

Rotor 3 - 7.77 m/s

Blade_Torque1

Blade_Torque2

39


Overlap Ratio 0.33



7.2 Variation in Overlap Ratio

Conditions :

Table 17 : Conditions of the overlap ratio test





7.2.1 Overlap Ratio – 18 %

Table 18 : Properties for an overlap ratio of 18 %

Overlap Ratio 18 %


-2.00E+01

0.00E+00

2.00E+01

4.00E+01

1

18

35

52

69

86

10

3

12

0

13

7

15

4

17

1

18

8

20

5

22

2

23

9

25

6

27

3

29

0

30

7

32

4

34

1

35

8

37

5

39

2

40

9

To

rqu

e

Degrees of Rotation

Rotor 3 - 8.85 m/s

Blade_Torque1

Blade_Torque2

40

Figure 33 : Torque of Rotor 1 at 18 % overlap


Table 19: Properties of an overlap ratio of 20 %

Overlap Ratio 20 %




Table 20 : Properties of an overlap ratio of 22 %

Overlap Ratio 22 %


-1.00E-01

0.00E+00

1.00E-01

2.00E-01

3.00E-01

1

19

37

55

73

91

10

9

12

7

14

5

16

3

18

1

19

9

21

7

23

5

25

3

27

1

28

9

30

7

32

5

34

3

36

1

37

9

39

7

41

5

43

3

To

rqu

e

Degrees of Rotation

Overlap Ratio -18 %

Torque_Blade1

Torque_Blade2

-1.00E-01

0.00E+00

1.00E-01

2.00E-01

3.00E-01

1

18

35

52

69

86

10

3

12

0

13

7

15

4

17

1

18

8

20

5

22

2

23

9

25

6

27

3

29

0

30

7

32

4

34

1

35

8

37

5

39

2

To

rqu

e

Degrees of Rotation

Overlap Ratio - 20 %

Torque_Blade1

Torque_Blade2

41




Overlap Ratio 25 %





Overlap Ratio 30 %


-0.1

0

0.1

0.2

0.31

16

31

46

61

76

91

10

6

12

1

13

6

15

1

16

6

18

1

19

6

21

1

22

6

24

1

25

6

27

1

28

6

30

1

31

6

33

1

34

6

36

1

37

6

39

1

To

rqu

e

Degrees of Rotation


Torque_Blade1

Torque_Blade2

-0.1

0

0.1

0.2

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5

24

1

25

7

27

3

28

9

30

5

32

1

33

7

35

3

36

9

38

5

40

1

To

rqu

e

Degrees of Rotation


Torque_Blade1

Torque_Blade2

42




Overlap Ratio 40 %



7.3 Variation in the number of blades

7.3.1 Rotor 1 with three blades at 6 m/s windspeed

Table 24 : Properties of three bladed Rotor 1 at 6 m/s




-1.00E-01

0.00E+00

1.00E-01

2.00E-01

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5

24

1

25

7

27

3

28

9

30

5

32

1

33

7

35

3

36

9

38

5

To

rqu

e

Degrees of Rotation


Torque_Blade1

Torque_Blade2

-1.00E-01

-5.00E-02

0.00E+00

5.00E-02

1.00E-01

1.50E-01

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5

24

1

25

7

27

3

28

9

30

5

32

1

33

7

35

3

36

9

38

5

40

1

41

7


Torque_Blade1

Torque_Blade2

43

Tip speed Ratio 0.6

Overlap Ratio 0.2


Figure 39 : Three bladed Rotor 1 at 6 m/s windspeed

7.3.2 Rotor 1 with three blades at 7.2 m/s windspeed

Table 25 : Properties of three bladed Rotor 1 at 7.2 m/s





Overlap Ratio 0.2


Figure 40 : Three bladed Rotor 1 at 7.2 m/s windspeed

-2.00E-01

-1.00E-01

0.00E+00

1.00E-01

2.00E-01

1

48

95

14

2

18

9

23

6

28

3

33

0

37

7

42

4

47

1

51

8

56

5

61

2

65

9

70

6

75

3

80

0

84

7

89

4

94

1

98

8

10

35To

rq

ue

Degrees of Rotation

Rotor 1 - 6 m/s

Torque_Blade1

Torque_Blade2

Torque_Blade3

-4.00E-01

-2.00E-01

0.00E+00

2.00E-01

14

5

89

13

3

17

7

22

1

26

5

30

93

53

39

7

44

1

48

5

52

9

57

3

61

76

61

70

5

74

9

79

3

83

7

88

1

92

59

69

10

13

10

57

To

rqu

e

Degrees of Rotation

Rotor 1 - 7.2 m/s

Torque_Blade1

Torque_Blade2

Torque_Blade3

44


Table 26: : Properties of three bladed Rotor 1 at 8.3 m/s





Overlap Ratio 0.2




Table 27 : Properties of three bladed Rotor 1 at 9.4 m/s




Tip speed Ratio 0.6

Overlap Ratio 0.2


-4.00E-01

-2.00E-01

0.00E+00

2.00E-01

4.00E-01

1

46

91

13

6

18

1

22

6

27

1

31

6

36

1

40

6

45

1

49

6

54

1

58

6

63

1

67

6

72

1

76

6

81

1

85

6

90

1

94

6

99

1

10

36To

rqu

e

Degrees of Rotation

Rotor 1 - 8.3 m/s

Torque_Blade1

Torque_Blade2

Torque_Blade3

45


7.3.5 Rotor 1 with three blades at 10 m/s windspeed

Table 28 : Properties of three bladed Rotor 1 at 10 m/s






Figure 43 : Three bladed Rotor 1 at 10 m/s windspeed

-4.00E-01

-2.00E-01

0.00E+00

2.00E-01

4.00E-01

14

69

11

36

18

12

26

27

13

16

36

14

06

45

14

96

54

15

86

63

16

76

72

17

66

81

18

56

90

19

46

99

11

03

6To

rqu

e

Degrees of Rotation

Rotor 1- 9.4 m/s

Torque_Blade1

Torque_Blade2

Torque_Blade3

-4.00E-01

-2.00E-01

0.00E+00

2.00E-01

4.00E-01

1

46

91

13

6

18

1

22

6

27

1

31

6

36

1

40

6

45

1

49

6

54

1

58

6

63

1

67

6

72

1

76

6

81

1

85

6

90

1

94

6

99

1

10

36To

rqu

e

Degrees of Rotation

Rotor 1 - 10 m/s

Torque_Blade1

Torque_Blade2

Torque_Blade3

46

REFERENCES

[1] JL Menet(2004),A double step Savoniusrotor for the local generation of electricity: a design

study, Renewable Energy 29 (2004), Page(1843–1862)

[2] UK Saha , S Thota, D Maity(2008), Optimum design configuration of Savonius rotor through

wind tunnel experiments ; Journal of Wind Engineering and Industrial Aerodynamics 96

(2008),Page (1359– 1375)

[3]M.H.Simmonds and A. Bodek(1964) , Performance test of a Savonius Rotor, Microfiche

Reference Library, Technical Report T10, McGill University, January 1964.

[4]M.A.Kamoji, S.B.Kedare, S.V.Prabhu(2009), Experiments on a single stage modified

Savonius rotor , Page (1064-1073).

[5]Kawamura T., Hayashi T., Miyashita K.(2001) Application of the domain decomposition

method to the flow aroundthe Savonius rotor, 12th International Conference on Domain

Decomposition Methods, T Chan, T Kako, H.Kawarada and O Pironneau (Editors)

[6]Menet, J.L., Bourabaa, N. (2004). Proceeding Conference,Increase in the Savonius Rotor

Efficiency via a Parametric Investigation. London, UK

[7]Md. I. Hassan, T.Iqbal, N. Khan, M.Hinchey, V.Masek(2009),CFD analysis of a twisted

Savonius wind turbine Memorial University of Newfoundland, Canada.

[8]B.D.Altan ,M.Atilgan , Ozdamar. P (2008) An experimental study of the Savonius rotor

performance with curtaining by, Experimental Thermal and Fluid Science 32 (2008) , Page

(1673–1678)

[9]Sargolazei J(2007), Prediction of power ratio and torque in wind turbine Savonius rotors using

artificial neural networks , Proceedings of the WSEAS International Conference on Renewable

Energy Sources, Arcachon, France, October Page (14-16)

[10] Gupta, R., Biswas, A., Sharma, K. K. (2008). Comparative study of a three bucket savonius

rotor with a combined three bucket Savonius –three bladed Darrieus rotor. Renewable Energy,

33, Page (1974-1981)

[11] http://www.reuk.co.uk/Darrieus-Wind-Turbines.htm

[12] http://www.turbinesinfo.com/innovative-wind-turbines/

[13] http://www.search.com/reference/Savonius_wind_turbine

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