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Renewable Energy 34 (2009) 521–529

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Renewable Energy

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Performance tests on helical Savonius rotors

M.A. Kamoji a, S.B. Kedare a, S.V. Prabhu b,*

a Department of Energy Science and Engineering, Indian Institute of Technology, Bombayb Department of Mechanical Engineering, Indian Institute of Technology, Bombay

a r t i c l e i n f o

Article history:Received 27 January 2008Accepted 5 June 2008Available online 26 July 2008

Keywords:Helical Savonius rotorConventional Savonius rotorCoefficient of powerCoefficient of static torque

* Corresponding author. Tel.: þ91 22 2576751525723480.

E-mail addresses: svprabhu@me.iitb.ac.in, svprabh

0960-1481/$ – see front matter � 2008 Elsevier Ltd.doi:10.1016/j.renene.2008.06.002

a b s t r a c t

Conventional Savonius rotors have high coefficient of static torque at certain rotor angles and a negativecoefficient of static torque from 135� to 165� and from 315� to 345� in one cycle of 360�. In order todecrease this variation in static torque from 0� to 360�, a helical Savonius rotor with a twist of 90� isproposed. In this study, tests on helical Savonius rotors are conducted in an open jet wind tunnel.Coefficient of static torque, coefficient of torque and coefficient of power for each helical Savonius rotorare measured. The performance of helical rotor with shaft between the end plates and helical rotorwithout shaft between the end plates at different overlap ratios namely 0.0, 0.1 and 0.16 is compared.Helical Savonius rotor without shaft is also compared with the performance of the conventional Savoniusrotor. The results indicate that all the helical Savonius rotors have positive coefficient of static torque atall the rotor angles. The helical rotors with shaft have lower coefficient of power than the helical rotorswithout shaft. Helical rotor without shaft at an overlap ratio of 0.0 and an aspect ratio of 0.88 is found tohave almost the same coefficient of power when compared with the conventional Savonius rotor. Cor-relation for coefficient of torque and power is developed for helical Savonius rotor for a range of Reynoldsnumbers studied.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Savonius [1] rotor is ‘‘S-shaped’’ cross-section constructed bytwo semi-circular buckets. The concept of Savonius rotor is basedon the principle developed by Flettner. It is simple in structure, hasgood starting characteristics, operates at relatively low operatingspeeds, and has ability to accept wind from any direction. Itsaerodynamic efficiency is lower than that of other types of windturbines such as Darrieus and propeller rotors. Savonius rotor isconsidered to be a drag machine. This means that the main drivingforce is drag force of wind acting on its blade. However, at low angleof attacks, lift force also contributes to torque production [2].Hence, Savonius rotor is not a pure drag machine but a compoundmachine and hence can go beyond the limitation of Cp of a pri-marily drag type machine (Cpmax¼ 0.08 for plate type turbine,Manwell et al. [3]). Although conventional Savonius rotors have lowaerodynamic efficiency, they have a high starting torque or highcoefficient of static torque. Due to this they are used at starters forother types of wind turbines that have lower starting torques.Though the starting torque is high, it is not uniform at all the rotorangles. At certain rotor angles, conventional Savonius rotors cannot

; fax: þ91 22 25726875,

u@iitb.ac.in (S.V. Prabhu).

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start on their own as the coefficient of static torque is negative.Conventional Savonius rotor is having negative torque for the rotorangles in the range of 135–165� and from 315� to 345�. Literaturesuggests that two stage and three stage conventional Savoniusrotors could overcome this problem of negative torque [4,5].However, with the increase in the number of stages, the maximumcoefficient of power decreases as reported by Kamoji et al. [4] andHayashi et al. [5]. The use of three bladed single stage rotor, witheach blade at 120� also reduces the torque variation in a rotor cyclebut the coefficient of power decreases as reported by Shankar [6]and Sheldahl et al. [7]. Saha and JayaRajkumar [8] report thattwisted three bladed Savonius rotor with a twist angle of 15� hasa maximum coefficient of power of 0.14 (tip speed ratio of 0.65)compared to 0.11 for a three bladed conventional Savonius rotor.

Helical Savonius rotors could provide positive coefficient ofstatic torque. Helix can be defined as a curve generated by a markermoving vertically at a constant velocity on a rotating cylinder (ata constant angular velocity). Fig. 1 shows a single helical rotorblade. The inner edge remains vertical whereas the outer edgeundergoes a twist of 90� (a quarter pitch turn). The blade retains itssemi-circular cross-section from the bottom (0�) to the top (90�).Combination of two such blades is called as a helical Savonius rotorin this study. In spite of its good promise on generating positivestatic torque coefficient, there is no information on helical Savoniusrotor in the open literature. Hence, the main objective of thepresent study is to experimentally investigate the effect of overlap

Nomenclature

A aspect ratioa overlap distance (m)B blockage ratioCp coefficient of powerCpmax maximum coefficient of powerCt coefficient of torqueCts coefficient of static torqueCtsmax maximum coefficient of static torqueCtsmin minimum coefficient of static torqueD rotor diameter (m)Do end plate diameter (m)G overlap ratioH rotor height (m)Hw height of wind tunnel exit (m)

M mass (gms.)R blade radius (m)Re Reynolds numberrrope radius of the shaft (mm)rshaft diameter of the string (mm)S spring balance reading (g)T torque (N-m)Ts static torque (N-m)TSR tip speed ratioU free stream wind velocity (ms�1)

Greek symbolsr density of airm absolute viscosity of air (Pa s)u angular velocity of rotor (rad s�1)

M.A. Kamoji et al. / Renewable Energy 34 (2009) 521–529522

ratio (0.0, 0.1 and 0.16), aspect ratio (0.88, 0.93 and 1.17) and Rey-nolds number for a 90� twist, shaft-less helical rotor at Reynoldsnumbers of 120,000 and 150,000 on coefficient of power,coefficient of torque and coefficient of static torque. Effect of thepresence of shaft for a 90� twist helical rotor is covered. Theseexperimental results are compared with the conventional Savoniusrotor.

2. Experimental set-up and procedure

Uniform main flow is produced by an open jet-type wind tunneldriven by a two 7.4 kW contra rotating fans. Air exits from a squarecontraction nozzle with a wind tunnel outlet of 400 mm� 400 mm.Rotors to be tested are placed at a distance of 750 mm downstreamof the wind tunnel nozzle exit such that the centre of the stationaryor rotating rotor is in line with the centre of the wind tunnel exit.The measured velocity distribution at the rotor position is uniformwithin �1% in the central area of 250 mm� 250 mm. The maxi-mum size of all the helical rotor models tested in this study iswithin 250 mm� 250 mm.

Fig. 1. A schematic of a single helical rotor blade.

Fig. 2 shows the schematic of the experimental set-up forconducting tests on helical Savonius rotors. Experimental set-upconsists of a structure housing the helical Savonius rotor fabricatedusing studs and mild steel plates. The mild steel plates are held inplace by means of washers and nuts. Two bearings (UC 204, NTNmake) bolted to the mild steel plates support the helical Savoniusrotor. The usage of studs, nuts and bolts facilitated easyreplacement of rotors of different diameters and positioning ofrotor centre at the centre of the wind tunnel. The wind velocity isdetermined by a pitot tube connected to a micro manometer(Furness Controls make FC012). A brake drum dynamometer isused for loading the helical Savonius rotor. The weighing pan,pulley and spring balance (Salter make) are connected by a fishingnylon string of 1 mm diameter.

Friction is an important parameter that affects the measurementof torque of the rotating helical Savonius rotor. Friction in thebearings and the 1 mm nylon wire string wound on the rotor shaft

5

6

4

7

1

2

3

1. Pulley 2. Nylon string

3. Weighing pan 4. Spring balance

5. Helical Savonius rotor 6. Shaft

7. Structure

Fig. 2. Schematic diagram of the set-up.

Table 1Uncertainties of various parameters

Parameter Uncertainty (%)

Tip speed ratio 2.5Coefficient of static torque 4.5Coefficient of power 4.8

Table 2Details of overlap ratio, aspect ratio and rotor diameter of helical Savonius rotorscovered in this study

Rotor number Overlap ratio (a/D) Aspect ratio (H/D) Rotor diameter ‘D’ (mm)

1 With shaft 1.0 2242 0.00 0.88 2303 0.00 0.93 2304 0.00 1.2 2115 0.10 1.0 2156 0.16 1.0 215

M.A. Kamoji et al. / Renewable Energy 34 (2009) 521–529 523

must be minimized. The seals are removed from the bearings andbearings are washed in petrol to remove the grease beforemounting resulting in the reduction of friction. Wind velocity isadjusted corresponding to a given Reynolds number and the rotoris allowed to rotate from no load speed. Rotational speed of therotor is recorded by a non-contact type tachometer. Each bearing issprayed with W-D 40 (a commercially available spray) lubricantbefore each reading [9]. The rotor is loaded gradually to recordspring balance reading, weights and rotational speed of the rotor.

A set of tests are carried to calculate the static torque of the rotorat a given rotor angle using the brake drum measuring system. Thestatic torque of the rotor is measured at every 15� of the rotor angle.At a given wind velocity, the rotor is loaded to prevent it fromrotation at a given rotor angle. The values of load and spring balancereading are recorded to calculate the static torque at a given rotorangle.

3. Data reduction

Reynolds number based on the rotor diameter is given by

Re ¼ rUDm

(1)

where, Re is Reynolds number , r is the density of air, U is the freestream velocity, D is the rotor diameter and m is the absolute vis-cosity of air.

Tip speed ratio is given by

TSR ¼ uD2U

(2)

where u is the angular velocity of the rotor.Torque calculated from the measured load and spring balance

load is given by

T ¼ðM � SÞ

�rshaft þ rrope

�g

1000(3)

where, M is the load, S is spring balance load, rshaft is the radius ofthe shaft, rrope is the radius of the nylon string.

Fig. 3. Helical Savonius rotors (a) with provision for shaft between the end plates

Coefficient of torque (Ct), coefficient of static torque (Cts) andcoefficient of power (Cp) are given by

Ct ¼ 4TrU2D2H

(4)

Cts ¼ 4TsrU2D2H

(5)

Cp ¼ TSR � Ct (6)

Blockage ratio (B) is given by

B ¼ HDHwW

(7)

where, Hw is the height of the wind tunnel exit and W is the widthof the wind tunnel exit.

The maximum blockage ratio is within 39% for all the helicalrotor models studied. The effect of blockage ratio is negligible onCp, Ct and Cts for rotors in an open jet wind tunnel as reported byKamoji et al. [4]. Uncertainties in various basic parameters,coefficient of static torque and coefficient of power are presented inTable 1. The uncertainties in the coefficient of static torque andcoefficient of power at the maximum coefficient of power arearound 4.5% and 4.8%, respectively. Uncertainty calculations arecarried out based on Moffat [10].

4. Rotors covered in this study

The helical Savonius rotors (with and without shaft in betweenthe end plates) with a twist of 90� are fabricated in a rapid proto-typing machine. Fig. 3(a) shows a helical Savonius rotor with shaftin between the end plates. Two helical Savonius rotor blades eachwith a twist of 90� are assembled at an appropriate overlap ratio to

; (b) and (c) two views of helical rotor without shaft between the end plates.

a

2

2

R

D

1

1

Do

H

1 End plates, 2 Rotor blades,R = Radius of the rotor blade, D = Diameter of rotor,a = Overlap distance, H = Height of the rotor,Do = Diameter of the end plate

Fig. 4. Two bladed single stage conventional Savonius rotor with an overlap (withoutshaft in between the end plates).

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Tip speed ratio

0.00

0.04

0.08

0.12

0.16

0.20

Coe

ffic

ient

of

pow

er

With central shaft; Overlap ratio = 0.0; Aspect ratio = 1.0

Without shaft; Overlap ratio = 0.0; Aspect ratio = 0.88Without shaft; Overlap ratio = 0.1; Aspect ratio = 0.96

Without shaft; Overlap ratio = 0.16; Aspect ratio = 1.0

Helical 90 deg.;Re = 120000

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Tip speed ratio

0.000.040.080.120.160.200.240.280.32

Coe

ffic

ient

of

torq

ue

Helical 90 deg.;Re = 120000

0 45 90 135 180 225 270 315 360

Rotor angle (degree)

0.00

0.08

0.16

0.24

0.32

0.40

Coe

ffic

ient

of

stat

ic t

orqu

e

Helical 90 deg.;Re = 120000

Fig. 5. Variation of coefficient of power, coefficient of torque and coefficient of statictorque for helical Savonius rotor with 90� twist at a Reynolds number of 120,000.

M.A. Kamoji et al. / Renewable Energy 34 (2009) 521–529524

obtain a helical rotor without shaft. Fig. 3(b) shows a helicalSavonius rotor for a given overlap ratio in which no shaft existsbetween the two end plates. Table 2 shows the configurations ofthe helical Savonius rotors with shaft (rotor 1) and without shaft(rotor 2, 3, 4, 5 and 6) covered in this study.

All the helical Savonius blades are made from ABS plasticmaterial (class of thermoplastic based on acrylonitrile–butadiene–styrene copolymer). The blades are of 3 mm thickness. The rotorsare covered at the top and bottom by an acrylic plate of 10 mmthickness. The diameter of the top and bottom circular end plates is1.1 times the rotor diameter. Stainless steel flanges housing the twoend shafts are bolted to the two acrylic sheets as shown in Fig. 3(b).

Performance of helical Savonius rotor is compared with that ofconventional Savonius rotor. Fig. 4 shows a two bladed conven-tional Savonius rotor (without shaft in between the end plates)with an overlap ratio (ratio of overlap distance (a) to diameter ofthe blade (D)) of 0.15. Overlap ratio of 0.15 is an optimum valuefrom the standpoint of coefficient of power as reported in the lit-erature for conventional Savonius rotor [7,11,12]. The diameter ofthe top and bottom circular end plates is 1.1 times the rotordiameter. There is no central shaft in between the top and bottomplates.

5. Results and discussions

Helical Savonius rotors are tested for Reynolds numbers of120,000 and 150,000. Tests are conducted for determining

coefficient of power, coefficient of torque and coefficient of statictorque. Coefficient of static torque is obtained for rotor anglesranging from 0� to 360� in steps of 15�. Helical rotors without shaftare tested for different overlap ratios of 0.0, 0.1 and 0.16. Perfor-mance of helical rotors without shaft is compared with that ofa helical rotor having a shaft. Helical rotor with an overlap ratio ofzero resulted in maximum coefficient of power compared to rotorswith overlap ratio of 0.1 and 0.16. Helical Savonius rotors with zerooverlap ratios are tested for three aspect ratios namely 0.88, 0.93and 1.17. Helical rotor with an aspect ratio of 0.88 has highercoefficient of power compared to rotors with an aspect ratios of0.93 and 1.17. Helical rotor with an overlap ratio of zero and anaspect ratio of 0.88 is tested for different Reynolds numbersand compared with the performance of conventional Savoniusrotors [13].

5.1. Effect of overlap ratio

Figs. 5 and 6 show coefficient of power, coefficient of torque andcoefficient of static torque for a rotor with shaft and rotor withoutshaft (overlap ratios of 0.0, 0.1 and 0.16) at Reynolds numbers of120,000 and 150,000, respectively. It may be observed that thecoefficient of power increases with the increase in the tip speedratio up to a maximum value. Coefficient of power decreases withthe further increase in the tip speed ratio. Helical Savonius rotor

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tip speed ratio

0.00

0.04

0.08

0.12

0.16

0.20

Coe

ffic

ient

of

pow

er

With central shaft; Overlap ratio = 0.0

Without shaft; Overlap ratio = 0.0Without shaft; Overlap ratio = 0.1

Without shaft; Overlap ratio = 0.16

Helical 90 deg.;Re = 150000

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tip speed ratio

0.00

0.04

0.08

0.12

0.16

0.20

0.24

0.28

0.32

Coe

ffic

ient

of

torq

ue Helical 90 deg.;Re = 150000

0 45 90 135 180 225 270 315 360

Rotor angle (degree)

0.00

0.08

0.16

0.24

0.32

0.40

Coe

ffic

ient

of

stat

ic t

orqu

e

Helical 90 deg.;Re = 150000

Fig. 6. Variation of coefficient of power, coefficient of torque and coefficient of statictorque for helical Savonius rotor at a Reynolds number of 150,000.

M.A. Kamoji et al. / Renewable Energy 34 (2009) 521–529 525

with a shaft has the lowest coefficient of power (0.092) among allthe rotors covered in this study. Helical Savonius rotor withoutshaft for an overlap ratio of zero results in maximum coefficientpower among the three overlap ratios studied.

Table 3 shows the values of maximum coefficient of power andthe corresponding tip speed ratio at Reynolds numbers of 120,000and 150,000 for various helical Savonius rotors tested in this study.It may be seen that the tip speed ratio at which the maximumcoefficient of power is observed decreases with the increase in theoverlap ratio for helical Savonius rotors without shaft. Maximumcoefficient of power for a helical Savonius rotor without shaft isaround 0.175 for a zero overlap ratio at a tip speed ratio of around0.9 and at a Reynolds number of 150,000. Tip speed ratio at which

Table 3Maximum coefficient of power and the corresponding tip speed ratio for helicalSavonius rotor with and without shaft (overlap ratio¼ 0, 0.1 and 0.16)

Overlap ratio Re¼ 120,000 Re¼ 150,000

Cpmax TSR Cpmax TSR

0.0 (Rotor with shaft) 0.092 0.9 0.095 1.00.0 (Rotor without shaft) 0.165 0.8 0.175 0.90.1 (Rotor without shaft) 0.117 0.7 0.128 0.80.16 (Rotor without shaft) 0.11 0.8 0.116 0.8

maximum coefficient of power is experienced appears to be sen-sitive to Reynolds number.

Table 4 shows the maximum and minimum coefficients of statictorque and the corresponding rotor angle. Helical Savonius rotorswith and without shaft (overlap ratio¼ 0, 0.1 and 0.16) havepositive coefficient of static torque for all the rotor angles. Thepercentage variation between the maximum and minimumcoefficients of static torque is lowest for a helical Savonius rotorwith an overlap ratio of 0.1 compared to overlap ratios of 0.0 and0.16. It is observed that, for helical Savonius rotors with shaft andwithout shaft (overlap ratio¼ 0.0), there is no sharp increase in thestatic torque coefficient between rotor angles of 60–120� and from240� to 300�. This sharp increase in the static torque coefficient isobserved for rotors with overlap ratios of 0.1 and 0.16. This increasecould be due to the overlap between the blades.

5.2. Effect of aspect ratio

Fig. 7 shows the effect of aspect ratio on the coefficient of power,coefficient of torque and coefficient of static torque for a helicalSavonius rotor with a 90� twist at a Reynolds number of 120,000.Performance of helical Savonius rotor with an aspect ratio of 0.88 ismarginally higher (Cpmax¼ 0.165 at a TSR¼ 0.7) compared to thehelical rotor with a rotor aspect ratio of 0.93 (Cpmax¼ 0.16 ata TSR¼ 0.74). Coefficient of static torque varies from 0.27 to 0.0038for a rotor with an aspect ratio of 0.88 and from 0.17 to 0.04 fora rotor with an aspect ratio of 1.17. Coefficient of static torque variesfrom 0.08 to 0.33 for a helical Savonius rotor with an aspect ratio of0.93.

5.3. Effect of Reynolds number

Helical Savonius rotor with an overlap ratio of 0.0 is tested atdifferent Reynolds numbers corresponding to wind velocities of4 m/s, 6 m/s, 8 m/s, 10 m/s, 12 m/s and 14 m/s. Fig. 8 shows thevariation of coefficient of power, coefficient of torque andcoefficient of static torque for a helical rotor with an aspect ratio of0.88 and overlap ratio of 0.0 at different Reynolds numbers. Table 5gives the maximum coefficient of power and the corresponding tipspeed ratio at different Reynolds numbers. Maximum coefficient ofpower increases with the increase in the Reynolds number. Shel-dahl et al. [7] report that for conventional Savonius rotor (at a givenrotor diameter) the delayed separation around the blades at higherwind velocities may be responsible for the increase in the maxi-mum coefficient of power with the increase in the Reynoldsnumber. This increase in the Cpmax with increase in Re was alsoreported by Shankar [6] and Sheldahl et al. [7] for conventionalSavonius rotors. Tip speed ratio at which maximum coefficient ofpower occurs increases with the increase in the Reynolds numberfrom 57,700 to 202,000. At a Reynolds number of 202,000, maxi-mum coefficient of power of 0.2 occurs at a tip speed ratio of 0.71.Maximum coefficient of power occurs at a tip speed ratio in therange of 0.65–0.71. Coefficient of static torque is almostindependent of the Reynolds numbers in the range studied. This isalso reported by Kamoji et al. [4] and Hayashi et al. [5] for con-ventional single, two and three stage conventional Savonius rotors.

5.4. Comparison of helical Savonius rotor with the conventionalSavonius rotor

Figs. 9 and 10 show the comparison of coefficient of power,coefficient of torque, coefficient of static torque of helical Savoniusrotor (overlap ratio of 0.0 and 0.1) and conventional Savonius rotor(overlap ratio of 0.15) at Reynolds numbers of 120,000 and 150,000,respectively. Open jet wind tunnel test on conventional Savoniusrotor is reported to have a maximum coefficient of power [12] at an

Table 4Maximum and minimum coefficients of static torque and the corresponding rotor angle for helical Savonius rotor with and without shaft

Overlap ratio Re¼ 120,000 Re¼ 150,000

Ctsmax Location of Ctsmax Ctsmin Location of Ctsmin Ctsmax Location of Ctsmax Ctsmin Location of Ctsmin

Rotor with shaft 0.28 165� and 345� 0.06 60� and 240� 0.29 165�and 345 0.06 60� and 240�

0.0 (rotor without shaft) 0.33 0� and 180� 0.08 90� and 270 0.32 165� and 345� 0.09 75� and 255�

0.1 (rotor without shaft) 0.31 0� and 180� 0.15 60� and 240� 0.32 165� and 345� 0.15 60� and 240�

0.16 (rotor without shaft) 0.32 165� and 345� 0.13 45� , 105� , 225� and 285� 0.33 165� and 245� 0.14 45� , 105� , 225� and 285�

M.A. Kamoji et al. / Renewable Energy 34 (2009) 521–529526

overlap ratio of 0.15. Table 6 shows the comparison of maximumcoefficient of power and the corresponding tip speed ratio for he-lical Savonius rotor (overlap ratio 0.0 and 0.10) and the conven-tional Savonius rotor (overlap ratio¼ 0.15). The maximumcoefficient of power of helical Savonius rotor (overlap ratio¼ 0.0) iscomparable with that of conventional Savonius rotor. The tip speedratio for maximum power coefficient is lower for helical Savoniusrotor than that of the conventional Savonius rotor.

Helical Savonius rotor with an overlap ratio of 0.1 is havinglower coefficient of power than the conventional Savonius rotor.

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

of

pow

er

Aspect ratio = 0.88

Aspect ratio = 0.93

Aspect ratio = 1.17

Helical 90 deg.;Overlap ratio = 0.0;Re = 120000

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

0.25

0.30

Coe

ffic

ient

of

torq

ue

Helical 90 deg.;Overlap ratio = 0.0;Re = 120000

180 2250 45 90 135 270 315 360

Rotor angle (deg.)

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

Helical 90 deg.;Overlap ratio = 0.0;Re = 120000

Fig. 7. Variation of coefficient of power, coefficient of torque and coefficient of statictorque for helical rotor with aspect ratios of 0.88, 0.93 and 1.17 at a Reynolds number of120,000.

This makes the helical Savonius rotor to operate at lower revolu-tions per minute at a given wind speed. Lower rotational speedsresult in less vibration related problems for large helical Savoniusrotors.

Table 7 shows the maximum and minimum coefficients ofstatic torque and the corresponding rotor angles for helical Savo-nius rotor (overlap ratio¼ 0.0 and 0.1) and conventional Savoniusrotor.

The conventional Savonius rotor is having negative coefficient ofstatic torque suggesting that it would not operate at these angles. Itis desirable to have the minimum variation in the maximum andminimum coefficients of static torque. The minimum coefficient ofstatic torque must be more than the combined torques of tarefriction torque and the external load torque. Helical Savonius rotorwith an overlap ratio of 0.1 is having minimum variation in the

1.00.0 0.2 0.4 0.6 0.8 1.2 1.4

Tip speed ratio

0.00

0.04

0.08

0.12

0.16

0.20

Coe

ffic

ient

of

pow

er

Re = 57702 (4m/s)

Re = 86554 (6m/s)Re = 115405 (8m/s)

Helical 90 deg;Aspect ratio = 0.88;Overlap ratio = 0.0

Re = 144256 (10m/s)

Re = 173107 (12m/s)

Re = 201958 (14m/s)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Tip speed ratio

0.000.040.080.120.160.200.240.280.320.36

Coe

ffic

ient

of

torq

ue Helical 90 deg.;Aspect ratio = 0.88;Overlap ratio = 0.0

0 45 90 135 180 225 270 315 360

Rotor angle (degree)

-0.08

0.00

0.08

0.16

0.24

0.32

0.40

Coe

ffic

ient

of

stat

ic t

orqu

e

Helical 90 deg.;Aspect ratio = 0.88;Overlap ratio = 0.0

Fig. 8. Variation of coefficient of power, coefficient of torque and coefficient of statictorque for helical Savonius rotor at different Reynolds numbers (wind velocities).

Table 5Variation of coefficient of power with tip speed ratio for a helical Savonius rotor withan overlap ratio of 0.0

Reynoldsnumber

Corresponding windvelocities (m/s)

Cpmax TSR at whichmaximum Cp occurs

57,700 4 0.11 0.7086,600 6 0.15 0.72115,500 8 0.16 0.65144,000 10 0.17 0.66173,000 12 0.19 0.72202,000 14 0.20 0.71

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tip speed ratio

0.00

0.04

0.08

0.12

0.16

0.20

Coe

ffic

ient

of

pow

er

Helical 90 deg.; Aspect ratio = 0.88; Overlap ratio = 0.0

Helical 90 deg.; Aspect ratio = 0.96; Overlap ratio = 0.10Conventional Savonius; Aspect ratio = 1.0; Overlap ratio = 0.15

Re = 150000;Without shaft

M.A. Kamoji et al. / Renewable Energy 34 (2009) 521–529 527

coefficient static torque and the minimum torque coefficient ishigher among the rotors studied.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.61.4

Tip speed ratio

0.000.040.080.120.160.200.240.280.32

Coe

ffic

ient

of

torq

ue

Re = 150000Without shaft

5.5. Correlations for performance of helical Savonius rotors

Helical Savonius rotor with an aspect ratio of 0.88 and overlapratio of 0.0 is found to have maximum coefficient of power amongthe helical Savonius rotors tested in this study. Variation of co-efficient of torque for a single stage Savonius rotor at differentReynolds numbers (86,600, 100,000, 115,400, 120,000, 144,300,173,100 and 202,000) is shown in Fig. 11. These curves almostmerge into a single curve for Ct/Re0.3 as shown in Fig. 12.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Tip speed ratio

0.00

0.04

0.08

0.12

0.16

0.20

Coe

ffic

ient

of

pow

er

Helical 90 deg.; Aspect ratio = 0.88; Overlap ratio = 0.0

Helical 90 deg.; Aspect ratio = 0.96; Overlap ratio = 0.10Conventional Savonius; Aspect ratio = 1.0; Overlap ratio = 0.15

Re = 120000;Without shaft

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tip speed ratio

0.000.040.080.120.160.200.240.280.32

Coe

ffic

ient

of

torq

ue

Re = 120000Without shaft

0 45 90 135 180 225 270 315 360

Rotor angle (degree)

-0.16

-0.08

0.00

0.08

0.16

0.24

0.32

0.40

Coe

ffic

ient

of

stat

ic t

orqu

e

Re = 120000;Without shaft

Fig. 9. Variation of coefficient of power, coefficient of torque and coefficient of statictorque for helical Savonius rotors and conventional Savonius rotors at Reynoldsnumber of 120,000.

0 45 90 135 180 225 270 315 360

Rotor angle (degree)

-0.16

-0.08

0.00

0.08

0.16

0.24

0.32

0.40

Coe

ffic

ient

of

stat

ic t

orqu

e

Re = 150000;Without shaft

Fig. 10. Variation of coefficient of power, coefficient of torque and coefficient of statictorque for helical Savonius rotors and conventional Savonius rotors at Reynoldsnumber of 150,000.

Correlation equations are linear and are fitted upto tip speed ratiosof 0.6. The parameter Ct/Re0.3 computed using the correlationcompares with the experimental results within �6%. Following isthe correlation for helical Savonius rotor with an aspect ratio of 0.88and overlap ratio of 0.0 for Reynolds number ranging from 86,600to 202,000.

Ct

Re0:3¼ �0:0128� TSR þ 0:0162 (8)

Using the correlation equation for helical Savonius rotor, per-formance curves for coefficient of power and coefficient of torqueare shown in Figs. 13 and 14. Coefficient of power and coefficient oftorque computed from the developed correlations compare withthe experimental results within �5%.

Table 6Comparison of maximum coefficients of power of helical Savonius rotor (overlapratios 0.0 and 0.1) with conventional Savonius rotor (overlap ratio¼ 0.15)

Reynolds number Helical Savonius;overlap ratio¼ 0.0;aspect ratio¼ 0.88

Helical Savonius;overlap ratio¼ 0.1;aspect ratio¼ 0.96

ConventionalSavonius; overlapratio¼ 0.15; aspectratio¼ 1.0

Cpmax TSR Cpmax TSR Cpmax TSR

Re¼ 120000 0.17 0.70 0.12 0.70 0.17 0.78Re¼ 150000 0.17 0.65 0.13 0.77 0.18 0.76

Table 7Maximum and minimum coefficients of static torque and the corresponding rotor angle for helical Savonius rotor (overlap ratio 0.0 and 0.1) and conventional Savonius rotor(overlap ratio 0.15)

Overlap ratio Re¼ 120,000 Re¼ 150,000

Ctsmax Location of Ctsmax Ctsmin Location of Ctsmin Ctsmax Location of Ctsmax Ctsmin Location of Ctsmin

0.0 (Helical rotor without shaft) 0.33 0� and 180� 0.08 90� and 270� 0.32 165� and 345� 0.09 75� and 255�

0.1 (Helical rotor without shaft) 0.31 0� and 180� 0.15 60� and 240� 0.32 165� and 345� 0.15 60� and 240�

0.15 (Conventional Savonius) 0.36 45� and 225� �0.09 150� and 330� 0.37 45� and 225� �0.05 165� and 345�

1.00.6 0.7 0.8 0.9 1.1 1.2 1.3

Tip speed ratio

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Coe

ffic

ient

of

torq

ue

Coefficient of torque at different Reynolds number

Helical Savonius rotor;Aspect ratio = 0.88;Overlap ratio = 0.0

Fig. 11. Variation of Ct with TSR at different Reynolds numbers from 86,600 to 202,000for helical Savonius rotor.

0.6 0.8 1.0 1.2 1.4

Tip speed ratio

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009Helical Savonius rotor;Aspect ratio = 0.88;Overlap ratio = 0.0

+ 6%

- 6%

Present experimental results

Correlation; = -0.0128 x TSR + 0.0162CtRe0.3

Ct

Re0.

3

Fig. 12. Correlation curve for helical Savonius rotor for different Reynolds numbersfrom 86,600 to 202,000.

0.00

0.03

0.06

0.09

0.12

0.15

0.18

0.21

Coe

ffic

ient

of

pow

er

Helical Savonius rotor

Aspect ratio = 0.88;Overlap ratio = 0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Tip speed ratio

Experimental results; Re = 202000

Correlation results; Re = 202000

Fig. 13. Comparison of coefficient of power for experimental and correlation results forhelical Savonious rotor at Reynolds numbers of 202,000.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Tip speed ratio

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Coe

ffic

ient

of

torq

ue

Helical Savonius rotor

Experimental results; Re = 202000

Correlation results; Re = 202000

Aspect ratio = 0.88;Overlap ratio = 0.0

Fig. 14. Comparison of coefficient of torque for experimental and correlation resultsfor helical Savonious rotor at Reynolds numbers of 144,300, 173,100 and 202,000.

M.A. Kamoji et al. / Renewable Energy 34 (2009) 521–529528

6. Conclusions

Helical Savonius rotors having a twist of 90� are tested in anopen jet wind tunnel for overlap ratios of 0.0, 0.1 and 0.16. Tests arecarried out to study the influence of overlap ratio, aspect ratio andReynolds numbers on the performance of helical Savonius rotors.These results are compared with the results of the conventionalSavonius rotor available in the literature. The conclusions that maybe drawn from this study are as follows.

1. Helical Savonius rotor with shaft has the lowest coefficient ofpower of 0.09 at a TSR of 0.9.

2. Helical Savonius rotor without shaft for an overlap ratio of zerohas maximum coefficient of power of around 0.174 at a Rey-nolds number of 150,000 compared with the overlap ratios of0.1 and 0.16.

3. Helical Savonius rotor with a lower aspect ratio of 0.88 showsa higher performance than rotors with an aspect ratio of 0.93and 1.17.

4. Coefficient of power of helical Savonius rotor without shaftwith an overlap ratio of 0.0 is almost same as that of conven-tional Savonius rotor.

5. Helical Savonius rotor is sensitive to the Reynolds number.Increase in the Reynolds number increases the maximumcoefficient of power of the rotor.

6. The static torque coefficients at all the rotor angles for all helicalSavonius rotors tested in this study are positive. However, forconventional Savonius rotor, there are several rotor angles atwhich static torque coefficient is negative.

7. Correlation equation for a helical Savonius rotor with aspectratio of 0.88 and overlap ratio of zero is developed for Reynoldsnumbers ranging from 86,600 to 202,000.

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