experimental investigations on single stage, two stage and three stage conventional savonius rotor

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2008; 32:877–895Published online 30 January 2008 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/er.1399

Experimental investigations on single stage, two stage and three stageconventional Savonius rotor

M. A. Kamoji1, S. B. Kedare1 and S. V. Prabhu2,*,y,z

1Energy Systems Engineering, Mechanical Engineering Department, Indian Institute of Technology Bombay, Mumbai 400076, India2Mechanical Engineering Department, Indian Institute of Technology Bombay, Mumbai 400076, India

SUMMARY

The performance of single stage (rotor aspect ratio of 1.0), two stage Savonius rotor with rotor aspect ratios of 1.0 and2.0 (stage aspect ratios of 0.50 and 1.0) and three stage Savonius rotor with rotor aspect ratios of 1.0 and 3.0 (stageaspect ratios of 0.33 and 1.0) are studied at different Reynolds numbers and compared at the same Reynolds number.The results show that the coefficient of power and the coefficient of torque increase with the increase in the Reynoldsnumbers for all the rotors tested. The coefficient of static torque is independent of the Reynolds number for all therotors tested. The performance of two stage and three stage rotors remains the same even after increasing the stageaspect ratio and the rotor aspect ratio by a factor of two and three, respectively. For the same rotor aspect ratio of 1.0,by increasing the number of stages (stage aspect ratio decreases), the performance deteriorates in terms Cp and Ct.However, at the same stage aspect ratio of 1.0 and same Reynolds number, two and three stage rotors show the sameperformance in terms of coefficient of power and coefficient of torque. The variation in coefficient of static torque islower for a three stage rotor when compared with the variation of coefficient of static torque for two stage or singlestage rotor. Copyright # 2008 John Wiley & Sons, Ltd.

KEY WORDS: Savonius rotor; single stage; two stage; three stage; coefficient of power (Cp); coefficient of torque (Ct);coefficient of static torque (Cts); rotor aspect ratio; stage aspect ratio

1. INTRODUCTION

A vertical axis wind machine proposed by FinnishEngineer Savonius [1] is basically a drag typerotor. The basic configuration of this rotor is an ‘S’shape, and it consists of two semicircular bladeswith a small overlap between them. The simple

structure, an ability to accept wind from anydirection and good starting torque characteristicshave made the Savonius rotor popular forventilators and pumping applications but not forpower generation because of its low aerodynamicefficiency compared with propeller and Darrieuswind machines. They have also been used as start-up

*Correspondence to: S. V. Prabhu, Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai400 076, India.yE-mail: [email protected], [email protected] Professor.

Received 14 June 2007Revised 19 November 2007

Accepted 26 November 2007Copyright # 2008 John Wiley & Sons, Ltd.

device for Darrieus rotors and for small scale powergeneration. A comparison study on different classesof wind turbines by Menet et al. [2] shows that forequal frontal width and mechanical stresses, Savo-nius rotors are better for local low power production.

The conventional single stage Savonius rotorhas a large static torque variation with the rotorangle. The rotor also develops a negative statictorque at certain angular positions. The torquevariation and the negative torque have an adverseimpact on the use of Savonius rotor for differentapplications. Researchers have focused on improv-ing the starting torque characteristics of theconventional Savonius rotor by testing single stage(with three and four blades) rotor or two stage(two blades in each stage) and three stage (twoblades in each stage) rotors.

Closed jet wind tunnel tests on two-, three- andfour-bladed rotors (with shaft in between the endplates) by Alexander and Holownia [3] show acoefficient of power of 15% for a two-bladedrotor, followed by three- and four-bladed rotors

having 30 and 50% less efficiency compared withtwo-bladed rotors. The results are corrected fortunnel blockage based on the corrections devel-oped by Maskell [4]. The investigations bySheldahl et al. [5] in a closed jet wind tunnelshowed a Cpmax of 24 and 16% for a two- andthree-bladed rotor (without shaft in between theend plates), respectively, at Reynolds number of8:64� 105: The blockage corrections are based onequations suggested by Pope and Harper [6]. Thecoefficient of static torque is positive at all therotor angles with two peaks and two troughs for athree-bladed rotor. Sheldahl et al. [5] report thatdetermination of blockage correction is difficultwhen an unusual shape, such as the Savoniusrotor, is tested.

Further investigations by Ushiyama and Nagai[7] in an open jet wind tunnel show that the threebucket rotor is inferior to the two bucket rotoralthough variation of static torque with rotorangle is less pronounced. The performance of twostage rotor is superior to the single stage rotor. The

1 2 34 5 6 7

Figure 1. Schematic diagram of the open jet wind tunnel: 1, bell mouth inlet; 2, closed test section; 3, damper; 4, contrarotating axial flow fans; 5, settling chamber; 6, contraction cone; and 7, open jet.

3

5

6

4

7

1

2

Figure 2. Schematic diagram of the rotational set-up: 1, pulley; 2, nylon string; 3, weighing pan; 4, spring balance; 5,Savonius rotor; 6, shaft; and 7, structure.

M. A. KAMOJI, S. B. KEDARE AND S. V. PRABHU878

Copyright # 2008 John Wiley & Sons, Ltd. Int. J. Energy Res. 2008; 32:877–895

DOI: 10.1002/er

tests were conducted on rotors without shaft inbetween the end plates. Investigation on the singlestage and three stage rotors with and withoutguide vanes in an open jet wind tunnel is reportedby Hayashi et al. [8]. The static and dynamictorque variations in one revolution of this threestage rotor (stage aspect ratio of 0.40) are positiveand smoother in comparison with single stageSavonius rotor. The Cp and Ct of three stagerotors were much smaller than single stage rotors.

They conclude that this inferiority of three stagerotors could be removed by enlarging the stageaspect ratio from 0.40 to 1.0 for three stage rotors.The studies were undertaken for rotors havingshaft between the end plates.

Tests on twisted blades in a three-bladed rotorwith a twist angle of 158 in an open jet wind tunnelare reported by Saha and Rajkumar [9] to havehigher Cp compared with three-bladed single stageSavonius rotor (with shaft in between the end

Table I. Details of the rotor diameter, rotor height, stage height, stage aspect ratio and rotor aspect ratio of conventionalSavonius rotors covered in this study.

No. of stagesDiameter ofrotor ðDÞ

Height of rotorðHÞ

Height of (stage)blade ðhÞ

Stage aspectratio ðh=DÞ

Rotor aspectratio ðH=DÞ

Single stage Savonius 208 208 208 1.0 1.0

Two stage Savonius 226 226 113 0.5 1.0131 262 131 1.0 2.0

Three stage Savonius 225 225 75 0.33 1.096.6 289.9 96.6 1.0 3.0

Figure 3. Schematic diagram of conventional Savonius rotor (rotor aspect ratio, H=D ¼ 1:0): (a) single stage (stageaspect ratio, h=D ¼ 1:0); (b) two stage (stage aspect ratio, h=D ¼ 0:5); and (c) three stage (stage aspect ratio,

h=D ¼ 0:33). 1, shaft; 2, flange; 3, Savonius blade; 4, end plate; and 5, intermediate plate.

EXPERIMENTAL INVESTIGATIONS ON CONVENTIONAL SAVONIUS ROTOR 879


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plates). The variation of coefficient of static torqueis similar for both the rotors at various rotorangles. A guide box tunnel attached to open jetwind tunnel is used by Irabu and Roy [10] toimprove and adjust the power output of Savoniusrotors. Tests on two- and three-bladed rotorswithout guide blade showed a Cpmax of 22.5 and16.4%, respectively. The Ctmax is attained at aphase angle of 50 and 2308 for a two-bladed rotorand at 105; 225 and 3458 for a three-bladed rotor.

A design study to produce local electricity wasproposed by Menet [11], which uses a two stageSavonius rotor with shaft in between the endplates. The rotor is designed for a wind velocity of10 m s�1 and uses a rewound conventional caralternator. This design confirms the high efficiency

and low technicality of the Savonius rotor for thelocal production of electricity. Murai et al. [12]have applied particle tracking velocimetry toestimate the pressure field around a static androtational Savonius rotor. The analysis shows thatthe lift force helps the turbine blades to rotate evenwhen the drag force is insufficient.

Savonius rotors are used for water pumpingapplications because of their high starting torques.The rotors are coupled to reciprocating orcentrifugal pumps. The rotor must overcome thehigher torque (load and friction torque) forstarting than running. Once, the system stopsdue to fluctuations in the wind speed, it will restartonly at a wind speed strong enough to overcomethis high starting torque. This reduces the avail-ability of rotor at low wind speeds. Low andintermittent wind velocities are prevalent in majorparts of the developing countries. This requires arotor with high and uniform coefficient of statictorque at all the rotor angles. Thus, two stage andthree stage rotors at different aspect ratios aretested and compared with the performance ofsingle stage rotors.

There is no literature on two stage and threestage Savonius rotors without shaft in between theend plates in an open jet wind tunnel. In this study,single, two and three stage Savonius rotors aretested in an open jet wind tunnel. The effect ofblockage on the performance of single stageSavonius rotor is studied before studying theperformance of two and three stage rotors. Intwo stages, one single stage rotor is placed overanother single stage with a 908 phase shift. In threestages, the three single stage rotors are placed oneabove the other with a phase shift of 608 to one

Figure 4. Schematic diagram of conventional Savoniusrotor (stage aspect ratio, h=D ¼ 1:0): (a) single stage(rotor aspect ratio, H=D ¼ 1:0); (b) two stage (rotoraspect ratio, H=D ¼ 2:0); and (c) three stage (rotor

aspect ratio, H=D ¼ 3:0).

Table II. Uncertainties in various basic parameters,coefficient of static torque and coefficient of power.

Parameter Uncertainty (%)

Density 3.3Velocity 3.4Diameter and height 0.5Torque 1.8Tip speed ratio 3.9Coefficient of static torque 6.2Coefficient of power 7.2



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another. Stacking of single stage rotors one abovethe other with a phase shift is expected tosmoothen the coefficient of static torque variationsand produce a positive coefficient of static torqueat all the rotor angles in a cycle of 3608: The effectof rotor aspect ratio and stage aspect ratio isstudied for two stage and three stage rotors interms of coefficient of power, coefficient of torqueand coefficient of static torque. The effect ofReynolds number on the performance of all therotors is studied by testing the rotors at differentReynolds numbers. The two number of two stagerotors and two number of three stage rotors arecompared at the same Reynolds numbers to studythe effect of stage aspect ratio on the performance ofthe rotors. Finally, single, two and three stages arecompared at the same Reynolds numbers to studythe effect of stage aspect ratio and rotor aspect ratio(ratio of rotor height to rotor diameter).

2. EXPERIMENTAL SET-UP

A schematic diagram of the open jet wind tunnel isshown in Figure 1. Uniform main flow is producedby an open-jet-type wind tunnel driven by a two 10H.P. contra rotating fans. Air exits from a squarecontraction nozzle with a wind tunnel outlet cross-sectional area of 400 mm� 400 mm: Experimentalset-up for housing and conducting experiments onrotating rotor is shown in Figure 2. The set-up isplaced at a distance of 750mm downstream of thewind tunnel nozzle exit such that the centre of therotating rotor is in line with the centre of the windtunnel exit. The measured velocity distribution atthe rotor position is uniform within �1% in thecentral area of 250 mm� 250 mm:

Experimental set-up for conducting rotationalexperiments consists of a structure housing theSavonius rotor fabricated using studs and mildsteel plates. The mild steel plates are held in placeby means of washers and nuts. Two bearings (UC204, NTN make) bolted to the mild steel platessupport the Savonius rotor. The usage of studs,nuts and bolts facilitated easy replacement ofrotors of different diameters and positioning ofrotor centre at the centre of the wind tunnel.

TableIII.

Detailsofnumber

ofstages,blockage,

stageaspectratio,rotoraspectratioandtheircomparisonatagiven

Reynoldsnumber.

Comparisonofperform

ance

atRe¼

100000

No.of

stages

Blockage

ratioð%Þ

Stageaspect

ratio

Cpmax

Ct

TSR

Rotoraspect

ratio

Comparisonat

Reynoldsnumber

Single

20

1.0

15.4

19.7

0.78

1.0

100000and120000

80000

28

1.0

15.4

19.5

0.79

1.0

35

1.0

16.1

20.7

0.78

1.0

Two

32

0.5

14.5

17.5

0.83

1.0

100000and120000

22

1.0

13.7

18.9

0.72

2.0

Three

31

0.33

13.1

18.8

0.70

1.0

81500

17

1.0

13.2

17.1

0.77

3.0



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The wind speed is determined by a pitot tubeconnected to a micromanometer (Furness Controlsmake FC012, calibrated accuracy of �0:01mm ofwater column). A brake drum dynamometer is usedfor loading the Savonius rotor. The weighing pan,pulley and spring balance (digital scale, accuracy of2.5 g) are connected by a fishing nylon string of1mm diameter.

Seven different rotors are covered in this study.Table I shows the diameter of the rotor, height ofthe rotor, height of the stage, stage aspect ratioðh=DÞ and rotor aspect ratio ðH=DÞ for theconventional Savonius rotors covered in thisstudy. Figure 3 shows the schematic of singlestage, two stage and three stage Savonius rotorshaving the same rotor aspect ratio of 1.0 and stageaspect ratios of 1:0; 0:55; and 0.33, respectively.Figure 4 shows the schematic of single stage, twostage and three stage Savonius rotors having thesame stage aspect ratio of 1.0 and rotor aspectratios of 1.0, 2.0 and 3.0, respectively. The rotors

are covered at the top and bottom with circularacrylic end plates of 10mm thickness. Thediameter of top, bottom and intermediate circularend plates is 1.1 times the rotor diameter. There isno central shaft in between the top and bottomcircular end plates. The vertical edges of the bladeafter fabrication are filed such that the edge isrounded.

Three single stage rotors have stage and rotoraspect ratios of 1.0 and are made of semicircularmild steel pipes of 1mm thickness with blockageratios of 20; 28 and 35%. One of the two stagerotors has a stage aspect ratio of 0.5 and a rotoraspect ratio of 1.0. The second two stage rotor hasa stage aspect ratio of 1.0 and a rotor aspect ratioof 2.0. The two stage and three stage rotorscovered in this study are made up of semi-circularaluminium pipes of 2mm thickness. One of thethree stage rotors has a stage aspect ratio of 0.33and a rotor aspect ratio of 1.0. The second threestage rotor has a stage aspect ratio of 1.0 and a

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Tip speed ratio

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Coe

ffic

ient

of p

ower

0.00

0.10

0.20

0.30

0.40

0.50

0.60

Coe

ffic

ient

of

t orq

ue

Re = 77600 (U = 6m/s)

Re = 103500 (U = 8m/s)

Re = 129500 (U = 10m/s)

Re = 155000 (U = 12m/s)

Single stage Savonius; B = 28%

0 45 90 135 180 225 270 315 360Rotor angle (degree)

-0.30

-0.15

0.00

0.15

0.30

0.45

0.60

0.75

Coe

ffic

ient

of

stat

ic t

orqu

e

Re = 77600 ( U = 6 m/s )

Re = 103500 ( U = 8 m/s )

Single stage Savonius ; B = 28 %

Re = 129500 ( U = 10 m/s )

Re = 155000 ( U = 12 m/s )

(a)

(b)

Figure 5. Performance of single stage conventional Savonius rotor: (a) variation of coefficient of power and torque withtip speed ratio and (b) variation of coefficient of static torque with rotor angle.



DOI: 10.1002/er

rotor aspect ratio of 3.0. All the seven rotors havethe same overlap ratio of 0.15. Overlap ratio of0.15 is an optimum value from the standpoint ofpower performance as reported by Fujisawa [13].

Friction is an important parameter that affectsthe measurement of torque of the rotatingSavonius rotor. Friction in the bearings and the1mm nylon wire string wound on the rotor shaft

must be minimized. The seals are removed fromthe bearings, and bearings are washed in petrol toremove the grease before mounting to reduce thefriction. Wind velocity is adjusted correspondingto a given Reynolds number and the rotor isallowed to rotate from no load speed. Rotationalspeed of the rotor is recorded by a non-contacttype tachometer. Each bearing is sprayed with

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60Tip speed ratio

0.00

0.05

0.10

0.15

0.20

Coe

ffic

ient

ofpo

wer

B = 20 %

B = 28 %

B = 35 %

Single Stage ; Re = 120000

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60Tip speed ratio

0.00

0.10

0.20

0.30

0.40

Coe

ffic

ient

ofto

rque

B = 20 %

B = 28 %

B = 35 %



-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

Coe

ffic

ient

of

stat

ic t

orqu

e

B = 20 %

B = 28 %

B = 35 %


Figure 6. Effect of blockage ratio on coefficient of power, coefficient of torque and coefficient of static torque for singlestage Savonius rotor at a Reynolds number of 120 000.



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W-D 40 (a commercially available spray)lubricant before each reading as suggested byMoutsoglou and Weng [14]. The rotor is loadedgradually to record spring balance reading,weights and rotational speed of the rotor.

A set of experiments is carried out to calculatethe static torque of the rotor at a given rotor

angle. The static torque of the rotor is observedat every 158 of the rotor angle. At a given windvelocity, the rotor is loaded to prevent itfrom rotation at a given rotor angle. The valuesof load and spring balance reading are recordedto calculate the static torque at a given rotorangle.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.05

0.10

0.15

0.20

0.25

Coe

ffic

ient

of p

ower

Re = 84500 ( U = 6 m/s )

Re = 112500 ( U = 8 m/s )

Two stage Savonius ; Stage aspect ratio = 0.5 Rotor aspect ratio = 1.0

Re = 140500 ( U = 10 m/s )

Re = 168500 ( U = 12 m/s )

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.10

0.20

0.30

0.40

0.50

Coe

ffic

ient

of

torq

ue

Re = 84500 ( U = 6 m/s )

Re = 112500 ( U = 8 m/s )

Two stage Savonius ; Stage aspect ratio = 0.5 ; Rotor aspect ratio = 1.0

Re = 140500 ( U = 10 m/s )

Re = 168500 ( U = 12 m/s )


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coe

ffic

ient

of

stat

ic t

orqu

e

Re = 84500 ( U = 6 m/s )

Re = 112500 ( U = 8 m/s )

Two stage Savonius ; Stage aspect ratio = 0.5 ; Rotor aspect ratio = 1.0

Re = 140500 ( U = 10 m/s )

Figure 7. Effect of Reynolds number on the coefficient of power, coefficient of torque and coefficient of static torquefor two stage Savonius rotor.



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3. DATA REDUCTION

The Savonius rotors are tested at differentReynolds numbers. The wind velocity for a givenReynolds number is determined from the follow-ing equation:

Re ¼rUD

mð1Þ

where U is the free stream velocity, Re isReynolds number, m is the absolute viscosity ofair, r is the density of air and D is the rotordiameter.

The tip speed ratio (TSR), torque ðTÞ; statictorque (Ts), coefficient of torque (Ct), coefficientof static torque (Cts) and coefficient ofpower (Cp) are calculated using the following

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.05

0.10

0.15

0.20

0.25

Coe

ffic

ient

ofpo

wer

Re = 48900 ( U = 6 m/s )

Re = 65000 ( U = 8 m/s )

Two stage Savonius ; Stage aspect ratio = 1.0Rotor aspect ratio = 2.0

Re = 81500 ( U = 10 m/s )

Re = 97800 ( U = 12 m/s )

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tip speed ratio

0.00

0.10

0.20

0.30

0.40

0.50

Coe

ffic

ient

ofto

rque

Re = 48900 ( U = 6 m/s )

Re = 65000 ( U = 8 m/s )

Two stage Savonius ; Stage aspect ratio = 1.0 ;Rotor aspect ratio = 2.0

Re = 81500 ( U = 10 m/s )

Re = 97800 ( U = 12 m/s )


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coe

ffic

ient

ofst

atic

torq

ue

Re = 65000 ( U = 6 m/s )

Re = 81500 ( U = 8 m/s )

Two stage Savonius ; Stage aspect ratio = 1.0 ;Rotor aspect ratio = 2.0

Re = 97800 ( U = 10 m/s )

Figure 8. Effect of Reynolds number on the coefficient of power, coefficient of torque and coefficient of static torquefor two stage Savonius rotor.



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equations:

TSR ¼oD2U

ð2Þ

where o is the angular velocity.

T ¼ Ts ¼ðM � SÞ � ðrsh þ drÞ � 9:81

1000ð3Þ

where M is the load, S is the spring balanceload, rs is the radius of the shaft, dr is the

diameter of the string.

Ct ¼4T

rU2D2Hð4Þ

Cts ¼4Ts

rU2D2Hð5Þ

where H is the height of the Savonius rotor.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.05

0.10

0.15

0.20

0.25

Coe

ffic

ient

ofpo

wer

Stage aspect ratio = 0.5 ; Rotor aspect ratio = 1.0


Two stage Savonius ; Re = 120000

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.10

0.20

0.30

0.40

Coe

ffic

ient

ofto

rque





0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coe

ffic

ient

ofst

atic

tor

que




Figure 9. Effect of stage aspect ratio on the coefficient of power, coefficient of torque and coefficient of static torquefor two stage Savonius rotor at a Reynolds number of 120 000.



DOI: 10.1002/er

Coefficient of power is given by

Cp ¼ TSR� Ct ð6Þ

Uncertainties in various basic parameters, coeffi-cient of static torque and coefficient of power are

presented in Table II. The uncertainties in thecoefficient of static torque and coefficient of powerat the maximum coefficient of power are around 6and 7%, respectively. Uncertainty calculations arecarried out based on Moffat [15].

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.05

0.10

0.15

0.20

Coe

ffic

ient

of

pow

er

Re = 84000 ( U = 6 m/s )

Re = 112000 ( U = 8 m/s )

Three stage Savonius ; Stage aspect ratio = 0.33 Rotor aspect ratio = 1.0

Re = 140000 ( U = 10 m/s )

Re = 168000 ( U = 12 m/s )

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.10

0.20

0.30

0.40

0.50

Coe

ffic

ient

ofto

rque

Re = 84000 ( U = 6 m/s )

Re = 112000 ( U = 8 m/s )

Three stage Savonius ; Stage aspect ratio = 0.33 ;Rotor aspect ratio = 1.0

Re = 140000 ( U = 10 m/s )

Re = 168000 ( U = 12 m/s )

0 45 90 135 180 225 270 315 360

Rotor angle (degree)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coe

ffic

ient

ofst

atic

tor

que

Re = 84000 ( U = 6 m/s )

Re = 112000 ( U = 8 m/s )

Three stage Savonius ; Stage aspect ratio = 0.33 ; Rotor aspect ratio = 1.0

Re = 140000 ( U = 10 m/s )

Figure 10. Effect of Reynolds number on the coefficient of power, coefficient of torque and coefficient of static torquefor three stage Savonius rotor at different wind velocities.



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4. RESULTS AND DISCUSSIONS

Experiments on single, two and three stageconventional Savonius rotors are carried out inan open jet wind tunnel. Table III gives the detailsof number of stages, blockage ratios, stage aspectratio and rotor aspect ratio of the Savonius rotors

tested. The rotors are tested at different Reynoldsnumbers to study the effect of Reynolds numberon the performance of the rotors. The rotorsare compared at Reynolds numbers as shown inTable III to study the effect of stage aspect ratio,rotor aspect ratio and the effect of staging.Performance studies of all rotors are made on

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.05

0.10

0.15

0.20

Coe

ffic

ient

of

pow

er

Re = 36000 ( U = 6 m/s )

Re = 48000 ( U = 8 m/s )

Three stage Savonius ; Stage aspect ratio = 1.0 Rotor aspect ratio = 3.0

Re = 60000 ( U = 10 m/s )

Re = 72000 ( U = 12 m/s )

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tip speed ratio

0.00

0.10

0.20

0.30

0.40

0.50

Coe

ffic

ient

of

torq

ue

Re = 36000 ( U = 6 m/s )

Re = 48000 ( U = 8 m/s )


Re = 60000 ( U = 10 m/s )

Re = 72000 ( U = 12 m/s )


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coe

ffic

ient

ofst

atic

torq

ue

Re = 48000 ( U = 6 m/s )

Re = 60000 ( U = 8 m/s )


Re = 72100 ( U = 10 m/s )

Figure 11. Effect of Reynolds number on the coefficient of power, coefficient of torque and coefficient of static torquefor three stage Savonius rotor.



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the basis of coefficient of power, coefficient oftorque with tip speed ratios and coefficient of statictorque with rotor angles. The static torquecoefficients are measured at every 158 rotor angle.

4.1. Performance of single stage Savonius rotors

Figure 5(a) shows the variation of coefficient ofpower and coefficient of torque with tip speed

ratios for single stage Savonius rotors with ablockage of 28% at different Reynolds numbers(the corresponding wind velocities are indicated inbrackets). The tip speed ratio at no load conditionvaries in the range from 1.24 to 1.45. With theaddition of load on the break drum, the tip speedratio decreases with the corresponding increase inthe Cp. The optimum range of value of tip speedratio for Cpmax lies between 0.7 and 0.9. With a

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tip speed ratio

0.00

0.05

0.10

0.15

0.20

Coe

ffic

ient

ofpo

wer



Three stage Savonius ; Re = 81500

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.10

0.20

0.30

0.40

0.50

Coe

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ient

ofto

rque





0.00

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0.35

0.40

Coe

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ofst

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torq

ue




Figure 12. Effect of stage aspect ratio on the coefficient of power, coefficient of torque and coefficient of static torquefor three stage Savonius rotor at Reynolds number of 81 500.



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0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.05

0.10

0.15

0.20

0.25

Coe

ffic

ien

tof

pow

er

Single stage Savonius ; Rotor aspect ratio = 1.0

Two stage Savonius ; Rotor aspect ratio = 2.0

Stage aspect ratio = 1.0Re = 80000

Three stage Savonius ; Rotor aspect ratio = 3.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Coe

ffic

ient

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rque

Single stage Savonius ; Rotor aspect ratio = 1.0

Two stage Savonius ; Rotor aspect ratio = 2.0


Three stage Savonius ; Rotor aspect ratio = 3.0


0.12

0.16

0.20

0.24

0.28

0.32

Coe

ffic

ient

ofst

atic

torq

ue(T

wo

and

thre

est

age

roto

rs)

Two stage ; Rotor aspect ratio = 2.0

Three stage ; Rotor aspect ratio = 3.0


-0.20

-0.10

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0.10

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0.30

0.40

Coe

ffic

ient

ofst

atic

torq

ue( S

ingl

est

age

rot o

r)

Single stage; Rotor aspect ratio = 1.0

Figure 13. Effect of rotor aspect ratio on the coefficient of power, coefficient of torque and coefficient of static torquefor single, two and three stage Savonius rotors with a stage aspect ratio of 1.0 at a Reynolds number of 80 000.



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0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tip speed ratio

0.00

0.05

0.10

0.15

0.20

Coe

ffic

ient

ofpo

wer

Single stage Savonius ; Stage aspect ratio = 1.0

Two stage Savonius ; Stage aspect ratio = 0.5

Rotor aspect ratio = 1.0Re = 80000

Three stage Savonius ; Stage aspect ratio = 0.33

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Tip speed ratio

0.00

0.05

0.10

0.15

0.20

0.25

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0.35

Coe

ffic

ient

ofto

rque

Single stage Savonius ; Stage aspect ratio = 1.0

Two stage Savonius ; Stage aspect ratio = 0.5


Three stage Savonius ; Stage aspect ratio = 0.33


0.14

0.16

0.18

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0.22

0.24

0.26

0.28

Coe

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wo

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rs)

Two stage ; Stage aspect ratio = 0.5

Three stage ; Stage aspect ratio = 0.33


-0.2

-0.1

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0.1

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0.3

0.4

Coe

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ue( S

ingl

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age

rot o

r)

Single stage; Stage aspect ratio = 1.0

Figure 14. Variation of coefficient of power, coefficient of torque and coefficient of static torque for single, two andthree stage Savonius rotors with a rotor aspect ratio of 1.0 at a Reynolds number of 80 000.



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further decrease in the tip speed ratio thecoefficient of power decreases to zero at a tipspeed ratio of zero. The coefficient of powerincreases with the increase in the Reynoldsnumbers (wind velocities). The no load, tip speedratio increases with the increase in the Reynoldsnumber (wind velocity). The delayed separationaround the blades at higher wind velocities causesan increase in the Cpmax with the increase in theReynolds number for a rotor with a givendiameter. The present results indicate a Cpmax of17.1% at a tip speed ratio of 0.78 for a rotor with ablockage ratio of 28% at a Re of 120 000(compared with Cpmax of 17.1% at TSR of 1.0[12] at Re of 120 000 and Cpmax of 13% at TSR of0.7 [8] at Re of 140 000).

Figure 5(a) shows the variation of coefficient oftorque with the tip speed ratio at differentReynolds numbers for rotor with a blockage of28%. The Ct increases with the decrease in the tipspeed ratio. The Ctmax is observed at a tip speedratio in the range of 0.5–0.1. The coefficient oftorque is higher for higher Reynolds number (windvelocities).

Figure 5(b) shows the static torque variations inone revolution of the single stage Savonius rotorfor different Reynolds numbers. It is seen thatReynolds numbers have little effect on thecoefficient of static torque. The single stage rotorexhibits a negative coefficient of static torque atrotor angles in the ranges of 150–165 and 330–3458: The maximum coefficient of static torque isobtained at rotor angles in the ranges of 30–40 and210–2208: The variation in the coefficient ofstatic torque is large for a single stage Savoniusrotor, with two maximum and two minimumvalues in one revolution. There is a steep risein the coefficient of static torque for rotor angles inthe ranges of 345–30 and 165–2108; suggestingthat at low angles of attack the lift contributesto the sharp increase in the coefficient of statictorque. The coefficient of static torque decreasesgradually from a rotor angle of 30 to 1658 and from210 to 3458:

Figure 6 shows the effect of blockage ratio onthe Cp, Ct and Cts for single stage Savonius rotorat a Reynolds number of 120 000 at blockageratios of 20, 28 and 35%. The effect of blockage is

negligible for Cp, Ct and Cts at the Reynoldsnumber of 120 000.

4.2. Performance of two stage Savonius rotors

Figures 7 and 8 show the variation of Cp, Ct andCts for two stage Savonius rotor for differentReynolds numbers at stage aspect ratios of 0.5 and1.0. The variations of coefficients of power andcoefficients of torque are similar to those of singlestage Savonius rotor. With two stages, four peaksin the coefficient of static torque are observed inone revolution of the rotor. The four peaks or thefour troughs correspond to the number of blades(four) on the two stage rotor. The two stage rotorshave peak coefficient of static torque at rotorangles of 45; 135; 225 and 3158 and a minimumcoefficient of static torque at rotor angles of 0; 90; 180 and 2708:

Figure 9 shows the effect of stage aspect ratio(0.5 and 1.0) for a two stage rotor on the Cp, Ctand Cts at a given Reynolds number of 120 000.The rotor with a stage aspect ratio of 0.5 is havingmarginally higher Cp compared with the rotorwith a stage aspect ratio of 1.0. The coefficients oftorque and static torque are almost similar forboth the rotors. The performance of the two stagerotors almost remains the same even after increas-ing the stage aspect ratio and rotor aspect ratio bya factor of two, suggesting that stage aspect ratiohas negligible effect on the performance of twostage Savonius rotor.

4.3. Performance of three stage Savonius rotors

Figures 10 and 11 show the effect of Reynoldsnumber on the Cp, Ct and Cts for three stageSavonius rotor at stage aspect ratios of 0.33 and1.0, respectively. The variations of coefficients ofpower and coefficients of torque are similar tothat of single stage Savonius rotor. The optimumtip speed ratio at the Cpmax increases with theincrease in the Reynolds number. With threestages, six peaks in the coefficient of statictorque are observed in one revolution of therotor. The six peaks or the six troughs corre-spond to the number of blades (six) on the threestage rotor. Figure 12 shows the effect of stage



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aspect ratio on the Cp, Ct and Cts for threestage Savonius rotor at a Reynolds number of81 500. The comparison shows that there is nodifference in the performance between the threestage rotors. There is no effect of stage aspectratio on the performance of three stage rotorswhen the rotors are compared at the sameReynolds number. The performance of threestage rotor remains the same even after increas-ing the stage aspect ratio and rotor aspect ratioby a factor of three.

4.4. Comparison of performances of single, two andthree stage Savonius rotors

Comparison of single, two and three stageSavonius rotors for Cp, Ct and Cts is made asfollows:

* same stage aspect ratio of 1.0 and at a Reynoldsnumber of 80 000;

* same rotor aspect ratio of 1.0 and at a Reynoldsnumber of 80 000.

4.4.1. Effect of rotor aspect ratio on the perfor-mances of single, two and three stage Savoniusrotors at the same stage aspect ratio of 1.0 and at anRe of 80 000. Figure 13 shows the effect of rotoraspect ratio on the performance of single, two andthree stage Savonius rotors with stage aspect ratioof 1.0 at a Reynolds number of 80 000. Thecoefficient of power of single stage rotor is higher(Cpmax ¼ 15:7% at tip speed ratio ¼ 0:6–0.7) whencompared with that of two stage (Cpmax ¼ 12:5%at tip speed ratio ¼ 0:6–0.8) rotor and three stage(Cpmax ¼ 12:2% at tip speed ratio of 0.6–0.7)rotor. The reported values for three stage rotorare Cpmax of 8.0% at a tip speed ratio of 0.68 at anRe of 140 000 with rotor aspect ratio of 1.25 [8].The range of tip speed ratio at which the maximumcoefficient power occurs is almost the same for allthe rotors. The coefficient of torque is higher forsingle stage rotor when compared with two andthree stage Savonius rotors. The coefficient ofstatic torque variation is large for a single stagerotor in a 3608 cycle or for one completerevolution of the rotor. Figure 13 also shows thecomparison between two and three stage rotors forstatic torque coefficient at a Reynolds number of

80 000 for stage aspect ratio of 1.0. The coefficientof static torque varies from a maximum of 0.26 toa minimum of 0.15 in a 3608 cycle for a two stageSavonius rotor. For three stage rotor the statictorque coefficient varies from 0.22 to 0.28 in a 3608cycle. The difference in the variation of coefficientof static torque between the two stage andthree stage is less when compared with the singlestage rotors.

4.4.2. Effect of stage aspect ratio on the perfor-mances of single, two and three stage Savoniusrotors at the same aspect ratio of 1.0 and at a Re of80 000. Figure 14 shows the effect of stage aspectratio on the performance of single, two and threestage Savonius rotors with rotor aspect ratio of 1.0at a Reynolds number of 80 000. The performancein terms of Cp and Ct decreases for rotors withsame rotor aspect ratio, but different stage aspectratios when compared at the same Reynoldsnumbers. By increasing the number of stages (i.e.stage aspect ratio decreases) for a rotor with agiven rotor aspect ratio of 1.0, the performancedeteriorates. The Cts varies from a maximum of0.26 to a minimum of 0.16 for two stage rotor,whereas for a three stage rotor it varies from amaximum of 0.25 to a minimum of 0.20 in a 3608cycle. The Cts variation decreases with the increasein the number of stages.

5. CONCLUSIONS

Tests on one stage, two stage and three stageSavonius rotors are conducted in an open jet windtunnel at different Reynolds numbers to study theeffect of stage aspect ratio, rotor aspect ratio andthe effect of number of stages. The followingconclusions may be drawn from the present study.

1. The coefficient of power, coefficient of torqueand no load tip speed ratio increase withincrease in the Reynolds number (wind velo-cities) for one, two and three stage Savoniusrotors.

2. The coefficient of static torque is almostindependent of the Reynolds number forsingle, two and three stage Savonius rotors.



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3. The effect of blockage on the Cp, Ct and Cts isnegligible at the range of Reynolds numbers of100 000 and 120 000 for a single stage Savoniusrotor.

4. Coefficient of static torque of two stagerotors remains the same even after increasingthe stage aspect ratio and rotor aspect ratioby a factor of two. In coefficient of statictorque variation with rotor angle for twostage rotors, four peaks and four troughs areobserved in one complete revolution of therotor which corresponds to the number ofblades (four).

5. Coefficient of static torque of three stagerotors remains the same even after increasingthe stage aspect ratio and rotor aspect ratioby a factor of three. In coefficient of statictorque variation with rotor angle forthree stage rotors, six peaks and six troughsare observed in one complete revolutionof the rotor which corresponds to number ofblades (six).

6. The variation in coefficient of static torque isminimum for a three stage Savonius rotor(Ctsmax ¼ 0:28; Ctsmin ¼ 0:20), followed by twostage Savonius rotor (Ctsmax ¼ 0:26;Ctsmin ¼ 0:15) and then by single stage Savo-nius rotor (Ctsmax ¼ 0:31; Ctsmin ¼ �0:17).

7. For the same stage aspect ratio of 1.0,single stage Savonius rotors show betterperformance in terms of Cp and Ctwhen compared with two stage and three stageSavonius rotors at a Reynolds number of80 000. However, there is no difference in theperformance in terms of coefficient of powerand coefficient of torque between the two andthree stage rotors.

8. The variation of coefficient of static torquefor three stage rotor is low. The Cp andCt of three stage rotor are the same as twostage rotor at the same stage aspect ratio of 1.0.Hence, it is better to use three stage rotorinstead of two stage rotor for a same stageaspect ratio.

9. The performance deteriorates in terms of Cpand Ct by increasing the number of stageswhile keeping the rotor aspect ratio same, i.e.1.0.

10. Three stage rotors are preferable in areaswith intermittent very low wind velocitiesas these can self-start because of uniformcoefficient of static torque. Rotors withhigh rotor aspect ratio rotate at higherspeeds, reducing the requirement of highgear ratio, and are suitable for low powerproduction.

The suitability of three stage Savonius windrotors for water pumping application may beexplored in order to get an estimate of thedischarge over a period of time.

NOMENCLATURE

a ¼ overlap distance (mm)A ¼ aspect ratio ðH=DÞB ¼ blockage ratio ðHD=HwWÞCp ¼ coefficient of power ð2To=rU3DHÞCpmax ¼ maximum power coefficient ð2To=r

U3DHÞCt ¼ coefficient of torque ð4T=rU2D2HÞCts ¼ coefficient of static torque ð4Ts=rU2

D2HÞCtsmax ¼ maximum coefficient static torque

ð4Ts=rU2D2HÞdr ¼ diameter of the string (mm)D ¼ rotor diameter (mm)Do ¼ end plate diameter (mm)G ¼ overlap ratio a=2Rh ¼ stage height (mm)h=D ¼ stage aspect ratioH ¼ rotor height (mm)Hw ¼ height of wind tunnel exit (mm)H=D ¼ rotor aspect ratioM ¼ mass (g)rsh ¼ radius of the shaft (mm)R ¼ blade radius (mm)Re ¼ Reynolds number ðrUDm�1ÞS ¼ spring balance load (g)T ¼ torque for rotational rotor (Nm)TSR ¼ tip speed ratioTs ¼ static torque for stationary rotor

(Nm)U ¼ free stream wind velocity ðm s�1ÞW ¼ width of wind tunnel exit (mm)



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Greek letters

y ¼ rotor angle (rad)m ¼ absolute viscosity ðN sm�2Þr ¼ density of air ðkgm�3Þo ¼ angular velocity of rotor ðrad s�1Þ

Subscripts

max ¼ maximumo ¼ endr ¼ ropew ¼ wind tunnels ¼ staticsh ¼ shaft

REFERENCES

1. Savonius SJ. The S-rotor and its applications. MechanicalEngineering 1931; 53(5):333–338.

2. Menet J-L, Valdes L-C, Menart B. A comparativecalculation of the wind turbines capacities on the basis ofthe L–s criterion. Renewable Energy 2001; 22:491–506.

3. Alexander AJ, Holownia BP. Wind tunnel tests on aSavonius rotor. Journal of Industrial Aerodynamics 1978;3:343–351.

4. Maskell EC. A theory of the blockage effects on bluff bodiesand stalled wings in a closed wind tunnel. AeronauticalResearch Council Reports and Memoranda 3400, 1965.

5. Sheldahl RE, Blackwell BF, Feltz LV. Wind tunnelperformance data for two and three bucket Savoniusrotors. Journal of Energy 1978; 2(3):160–164.

6. Pope A, Harper JJ. Low Speed Wind Tunnel Testing. Wiley:New York, 1966.

7. Ushiyama I, Nagai H. Optimum design configurations andperformance of Savonius rotors. Wind Engineering 1988;1(12):59–75.

8. Hayashi T, Li Y, Hara Y. Wind tunnel tests on a differentphase three-stage Savonius rotor. JSME InternationalJournal, Series B 2005; 48(1):9–16.

9. Saha UK, Rajkumar MJ. On the performance analysis ofSavonius rotor with twisted blades. Renewable Energy2006; 31(11):1776–1788.

10. Irabu K, Roy JN. Characteristics of wind poweron Savonius rotor using a guide-box tunnel. Experi-mental Thermal and Fluid Science 2007; 32(2):580–586.

11. Menet J-L. Adouble-step Savonius rotor for local produc-tion of electricity: a design study. Renewable Energy 2004;29:1843–1862.

12. Murai Y, Nakada T, Suzuki T, Fujio Y. Particle trackingvelocimetry applied to estimate the pressure field around aSavonius turbine. Measurement Science and Technology2007; 18:2491–2503.

13. Fujisawa N. On the torque mechanism of Savonius rotors.Journal of Wind Engineering and Industrial Aerodynamic1992; 40:277–292.

14. Moutsoglou A, Weng Y. Performance tests of a Beneshwind turbine rotor and a Savonius rotor. Wind Engineering1995; 19(6):349–362.

15. Moffat RJ. Describing the uncertainties in experimentalresults. Experimental Thermal and Fluid Science 1988;1:3–17.



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experimental investigations on single stage, two stage and three stage conventional savonius rotor

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