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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia

Investigation into the relationship of the overlap ratio and shift angle of double stage three bladed vertical axis wind turbine (VAWT) J. Kumbernuss n, J. Chen, H.X. Yang, L. Lu Renewable Energy Research Group (RERG), Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong

a r t i c l e i n f o

abstract

Article history: Received 2 June 2011 Received in revised form 6 March 2012 Accepted 18 March 2012 Available online 8 May 2012

This study presents the experimental test results of Savonius-type vertical axis wind turbines (VAWT) with different overlap ratios and shift angles. Each wind turbine was tested under four different wind speeds. The power coefﬁcients (CP) of vertical axis wind turbines are governed by several key factors, e.g. the number of blades, the shape of the blades, the overlap ratio (OL) and the phase shift angle. The overlap ratio and the phase shift angle (PSA) are the most decisive ones since the measured data shows that their power coefﬁcient drops or rises with them signiﬁcantly. Three turbines with the overlap ratios of 0, 0.16 and 0.32 were designed and constructed. The wind turbines were then adjusted to the phase shift angles (PSA) of 0, 15, 30, 45 and 60 degrees before testing them in an open wind tunnel under the air velocities of 4 m/s, 6 m/s, 8 m/s and 10 m/s. The results show that a higher overlap ratio has a higher impact on improving the starting characteristics of the Savonius wind turbine than any phase shift angle changes. This investigation shows that a speciﬁc phase shift angle in relation to a speciﬁc air velocity will increase the power coefﬁcient signiﬁcantly. Besides the increase of the power coefﬁcient seen at speciﬁc air velocities and phase shift angles, did the recorded data show an unexpected second performance peak which appeared at higher tip speed ratios. This is surprising since the Savonius turbine is considered as being a drag driven turbine, and suggests that the lift characteristics of Savonius turbines might be more signiﬁcant than commonly considered. & 2012 Published by Elsevier Ltd.

Keywords: Overlap ratio Shift angle Vertical axis wind turbine VAWT Savonius wind turbine Phase-shift angle

1. Introduction Wind energy utilization systems have been in use for thousands years. One of the oldest types of the vertical axis wind turbines (VAWT) is the Savonius type. This turbine has been studied from the beginning of the last century to present by many researchers. The engineer Savonius (1931) ﬁrst published research data in 1931. Although the Darrieus type Vertical Axis Wind is more efﬁcient than the Savonius-type, the Savonius type still has several advantages like having good starting torque, simple mechanism, lower rotation speed, and omni-directional characteristics. The Savonius type wind turbine is commonly considered as a drag driven type of wind turbine since it does not use airfoils as rotor blades in contrast to the propeller or the Darrieus type of wind turbines. The general theory of the Savonius turbine is simple. The wind exerts a force on a surface and this surface is then moved around an axis. To estimate the power coefﬁcient (Cps) Hau (2006) gave the below equations (Eqs. (1) and (2)), which are most commonly used, where Ur is the relative air velocity, Ut is the movement of turbine blade tip, CD is the drag coefﬁcient of the Savonius turbine

n

Corresponding author. Tel.: þ852 95826110. E-mail address: [email protected] (J. Kumbernuss).

0167-6105/$ - see front matter & 2012 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.jweia.2012.03.021

and Uw is the free airstream velocity U r ¼ U w U t

C ps ¼

ð1Þ

ðr=2ÞC D As ðU w U r Þ2 U r ðr=2ÞAs U w 3

ð2Þ

However, the above equation neglects the blade numbers, the gap ratio, the turbine blade curvature, etc. as it just uses the CD of the turbine. A more detailed analytical model to determine the performance of a Savonius turbine was developed by Chauvin and Benghrip Chauvin and Benghrib (1989) and Chauvin et al. (1983), which was based on experiments performed before 1989. Chauvin constructed a two bladed Savonius turbine with pressure sensors mounted on its rotor blades. The turbine was tested in air velocities of 10 m/s and 12 m/s at tip speed ratios (TSR) from l ¼0.2 to l ¼1. The following equations to estimate the instantaneous dynamic torque are proposed by Chauvin: Cx ¼

Cy ¼

Rhf

P ðDP Ai DP Bi Þcosðyi þ aÞgDyi ð1=2ÞrAs U u 2

Rhf

P ðDP Aj DP Bj Þcosðyj þ aÞgDyj ð1=2ÞrAs U u 2

ð3Þ

ð4Þ

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Nomenclature A AR As AT c CD CP CPS Cst Ct Cx Cy d D Est H n N OL PA

maximum frontal area of the Savonius turbine aspect ratio AR¼H/D turbine swept area As ¼ DH wind tunnel area (m2) cord length of blade (m) aerodynamic drag coefﬁcient of the Savonius turbine power coefﬁcient CP ¼P/((1/2)rAsDU3) power coefﬁcient of the Savonius turbine C PS ¼ ðr=2ÞC D As ðU w U r Þ2 U r =ðr=2ÞAs U u 3 static torque coefﬁcient Cst ¼Ts/(1/4)rAsDU2 torque coefﬁcient Ct ¼T(/1/4)rAsDU2 P instantaneous torque in x direction C x ¼ Rhf ðDP Ai 2 B DP i Þcosðyi þ aÞgDyi =ðð1=2ÞrAs U u Þ P instantaneous torque in y direction C y ¼ Rhf ðDP Aj DP Bj Þcosðyj þ aÞgDyj =ðð1=2ÞrAs U u 2 Þ bucket diameter (m) rotor diameter (m) standard deviation Est ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 2 2 ððv1 va Þ þ ðv2 va Þ þ þ ðvn va Þ =n1Þ rotor height (m) total number of measurement values number of blades overlap ratio OL¼S a/D þ ((1/2)S) pressure difference between the two sides of the rotor blades of blade 1

From the pressure difference between the two blade surfaces, the instantaneous dynamic torque from both turbine blades can be calculated, and then averaged. It succeeds in relating the two blades and their force to each other, which gives a better performance estimate. However, for using this analytical model, the pressure differences of both blades at each rotation position have to be known. However, the development of its analytical solutions proves to be a very difﬁcult task, and the above equations can only deliver a rough estimate of the power coefﬁcient (Cp) if some of the properties of the turbine are known. Recently, with the advancement of numerical simulation software, some of the ﬂow phenomena can be visualized and explained. Menet and Bourabaa (2004) uses software packages as an investigation tool to estimate the ﬂow ﬁelds and performance of new turbine conﬁgurations. However, those numerical models are also not able to predict the performance of the Savonius turbines precisely as what Fujisawa (1996) has stated that ‘‘an analytical model provides only rough information on the performance and ﬂow’’, which is still valid, and makes experimental measurement necessary. As mentioned above, the Savonius turbine is commonly considered to be a drag driven turbine, but this investigation shows that the turbine clearly has lift characteristics, which might have been under estimated. It is a mix of lift and drag as recent research (Modi and Fernando, 1989; Jones et al., 1979) showed, which drives the wind turbine. Chauvin and Benghrib (1989) state that the lift coefﬁcient has a negative contribution to the total power coefﬁcient (CP) at low values of the tip speed ratio (TSR), which becomes more signiﬁcant at high values of the TSR. Therefore, if the lift characteristics of this turbine could be improved, a performance improvement could be expected. Changing the rotor blade design is one possible way for improving the turbine’s energy performance. Yasuyuki et al. (2003) investigated twisted (helical) rotor blades and reported an improved starting

PB

pressure difference between the two sides of the rotor blades of blade 2 R radius of rotation of blade Re Reynolds number Re¼ rUuD/ma and Re¼UD/n S rotor overlap (m) T torque (Nm) Ts static torque (Nm) U corrected air velocity U ¼UU(1þA) [m/s] or after Alexander j ¼ U 2 =U 2u ¼ 1=1mðAF =AT Þ Ur relative air velocity Ut movement of turbine blade tip UU (uncorrected) air velocity (m/s) Uw free airstream velocity V kinematic viscosity (m2/s) v1, v2 and vn measured values va the mean of the measured values Greek symbols blockage ratio b ¼As/AT wind tunnel blockage rate A¼As/4AW position of blade in degrees bucket rotation angle (deg.) TSR (tip speed ratio) l ¼ oD/2U rotor solidity s ¼Nc/R density of air (kg/m3) rotor angular speed (rad/s)

b

E y f l

s r o

torque as well as an increase in power coefﬁcient. Further investigations were made by Prabhu et al. (2009). He found that the performance would increase if the shaft was removed. Besides different shapes of blades, the ‘‘overlap ratio’’ (OL) of the rotor blades is another key factor for improving the performance. Blackwell et al. (1978) investigated this issue in 1978 and concluded that an overlap ratio (s/d) of 0.1–0.15 is likely to generate optimal performance, which is also conﬁrmed by this paper. For this report 3 single and 3 double stage vertical axis wind turbines were investigated. A total of 20 turbine conﬁgurations were tested. The focus of this study is on the effect of the overlap ratio and the phase shift angle (PSA) on the power coefﬁcient (Cps) of the Savonius type vertical-axis wind turbines.

2. Data processing The following equations were used to process the experimental data. The tip speed ratio l was calculated by using the following equation:

l¼

oD 2U u

ð5Þ

where o is the angular speed of the rotor. The static torque Cst was calculated as follows: C st ¼

Ts ð1=4ÞrAs DU u 2

ð6Þ

where the static torque TS is measured and AS is the turbine swept area calculated as As ¼ DH

ð7Þ

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The torque coefﬁcient Ct can be represented by the following equation: Ct ¼

T

ð8Þ

ð1=4ÞrAs DU u 2

3. Measurement uncertainty The percentage of the measurement uncertainty is shown in Table 1, which was derived by the standard deviation. After the ‘vmean’ was calculated, the standard deviation was derived. Here Est is the standard deviation shown in Eq. (9). ‘v1’, ‘v2’ and ‘vn’ are the measured values. The total number of measurement values is ‘n’ vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ !ﬃ u u ðv1 vmean Þ2 þ ðv2 vmean Þ2 þ þðvn vmean Þ2 t Est ¼ ð9Þ n1

Fig. 2. Photo of the ﬁnished VAWT.

Some measurements produced unforeseen results (the second and third performance peaks in Figs. 21, 29, 30, 32–34), and were repeated several times over a couple of days, to minimize measurement error.

4. Turbine layout and experiments The Savonius type wind turbine consists of three semicircular buckets with a small overlap (S) between two of them as shown in Fig. 1. All the tested wind turbines are made with the same material, nearly the same weight and structure. Their dimensions are shown in Table A1. They differ only in their blade forms, phase shift angles and overlap ratios (OL) as shown in Figs. 1 and 6–8.

Table 1 Uncertainty percentages. Parameter

Uncertainty (%)

Tunnel air velocity Wind tunnel correction ratio, j Power coefﬁcient Measured torque Measured turbine RPM l Tip speed ratio (TSR)

1.8 3.01 8.24 3.4 3.2 3.61

Fig. 3. The VAWT with 151 phase shift.

However, the swept areas of all the double-stage turbines are exactly the same. CNC milling process was employed to achieve a very high manufacturing precision. The turbine blades have different radii depending on the overlap ratio as shown in Figs. 6–8 and Table A1. Since each wind turbine consists of several parts, each wind turbine could be arranged into several turbine layouts. The overlap ratio could be changed from 0 to 0.16 and 0.32 as shown in Figs. 6–8, and the phase shift angle could be adjusted from 0 degree to 15, 30, 45 and 60 degree as shown in Figs. 2 and 3. The abbreviations of the turbine names are shown in Table A1.

5. The wind tunnel

Fig. 1. Cross section of the tested VAWT.

The open wind tunnel used for the experiments is shown in Fig. 9 which consists of a contraction section, developed air ﬂow section, test section and diffuser section. The test section has a square cross-section of about 1 m by 1 m. The air velocity inside the wind tunnel was measured by a hotwire air velocity meter. The wind turbine inside the wind tunnel and the experiment setting are shown in Figs. 4 and 5.

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Fig. 4. The VAWT in a wind tunnel.

Fig. 6. VAWT with 0 rotor overlap ratio.

Fig. 5. Diagram of the experimental setup.

tunnel ranges from 0.32% to 0.47% at different frequencies. The Reynolds numbers of the wind turbines indicate (Table 2) that the ﬂow in the wind tunnel is turbulent. 5.1. Air velocity correction

A variable frequency controller drives the fan of the tunnel and regulates the air velocity in the range of 0–30 m/s. Fig. 10 shows the air velocity distribution of the main ﬂow ﬁeld measured horizontally through the test section at ﬁve different frequencies. The ﬂow ﬁeld inside the wind tunnel is uniform in the region from 0.12 m to 0.88 m. The turbulence intensity of the wind

The blockage ratio b was calculated by relating the maximum frontal area of the turbine AF to the cross section area of the wind tunnel AT (Eqs. (10) and (11)). Blockage ratio b ¼

AF AT

ð10Þ

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Wind tunnel blockage rate A ¼

AF 4AW

ð11Þ

In 1965, Pope and Harper (1966) and Maskell (1965) developed the basic equation to correct the air velocity inside the wind tunnel. In 1978, Alexander and Holownia (1978) changed Maskell’s method and applied it to Savonius rotors, i.e. (Eq. (12)).

j¼

U2 U 2u

¼

1 1mðAF =AT Þ

ð12Þ

where U is the corrected wind velocity, UU is the undisturbed wind velocity, AT is the cross sectional area perpendicular to the direction of the air stream in the wind tunnel. m is found by interpolation through the datum in Fig. 11, which was determined by the wind tunnel itself. Alexander and Holownia (1978) have shown that this method will produce reliable results up to a blockage rate, b ¼0.334. The corrected air velocities for measured

61

air velocity of 4 m/s, 6 m/s, 8 m/s and 10 m/s are shown in Table 2. 5.2. Reynolds number The Reynolds numbers were calculated based on the following equation: Re ¼

rU u D ma

ð13Þ

where Uu is the undisturbed air velocity, r is the density of air, ma is the air viscosity and D is the diameter of the rotor. In order to compare the tested turbines in this report with other wind turbines from other researchers, the Reynolds numbers are shown in Table 2. A direct comparison of the single and double stage turbines seems not possible considering the air velocity correction values of the single and double stage turbines. To avoid confusion about the air velocities for different wind turbine conﬁgurations the Reynolds number and the air velocity of the wind tunnel are listed together; e.g. 4 m/s at Re 6.64 104.

Fig. 7. VAWT with 0.16 rotor overlap ratio.

Fig. 10. The air ﬂow ﬁeld in the wind tunnel.

Table 2 Reynolds numbers of double and single stage wind turbines. Air Reynolds number Adjusted air velocity (double stage velocity turbines) (double stage turbines) (m/s) 4 6 8 10

7.31 104 1.1 105 1.46 105 1.83 105

Fig. 8. VAWT with 0.32 rotor overlap ratio.

Fig. 9. The wind tunnel for the VAWT tests.

4.88 7.33 9.77 12.21

Reynolds number Adjusted air velocity (single (single stage stage turbines) turbines) (m/s)

6.64 104 0.99 105 1.33 105 1.66 105

4.44 6.66 8.87 11.09

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3.5

SQUARE PLATE SAVONIUS ROTOR

3

m

2.5 2 1.5 1

0

0.05

0.1

0.2

0.15

0.25

0.3

0.35

AF /AT Fig. 11. m values for ﬂat plate and VAWT rotor versus AF/AT.

Fig. 12. Diagram of the static torque measurement setting.

Static torque at a phase shift angle of 0 degree (DS0PSA0OL)

Static Torque [Nm]

0.2 0.15 0.1 0.05 0 -0.05

0

20

40

60

-0.1

80

100

120

140

Degree DS0PSA0OL at 4m/s Re 66389 Static torque DS0PSA0OL at 8m/s Re 146154.5 Static torque

DS0PSA0OL at 6m/s Re 99598.3 Static torque DS0PSA0OL at 10m/s Re 165997.3 Static torque

Fig. 13. Static torque measurement results of the wind turbine DS0PSA0OL.

6. Experimental methodology A schematic diagram of the experimental setting is shown in Figs. 4 and 5. The tested turbine was placed inside the test section

of the wind tunnel, which was connected by a shaft to the digital torque meter, rotation meter, adjustable break and DC motor. The turbine was ﬁxed at the desired angle for the static torque measurements as shown in Fig. 12 before the tunnel was

J. Kumbernuss et al. / J. Wind Eng. Ind. Aerodyn. 107–108 (2012) 57–75

63

switched on. After a steady state air velocity was reached, the data was recorded. For the dynamic torque measurements, a DC motor was used to drive the turbine up to its maximum rotation speed, which was found when the torque meter read 0 Nm torque. Each turbine was measured at 10 different rotation speeds.

The results at 8 m/s (Re 1.46 105) and 10 m/s (Re 1.83 105) reach their lowest values at 85–90 degree, whereas the results at 4 m/s and 6 m/s have their lowest values at 95–100 degree. After the results at 4 m/s and 6 m/s reached their lowest marks, they follow the trend of the curves at 8 m/s (Re 1.46 105) and 10 m/s (Re 1.83 105) with an offset of 5 degree.

7. Measured results

7.1.1. The effect of the Reynolds number and air velocity An interesting fact shown in Fig. 13 is that Cst does not change a lot when the air velocity or Reynolds number is changed. The same ﬁnding was also reported by Prabhu et al. (2009) and Blackwell et al. (1978). Based on that, it was decided that the air velocity of 8 m/s (Re 1.46 105) was sufﬁcient for all further static torque tests.

Since the turbines measured are three bucket turbines, one rotation of the rotor is divided into three phases and each phase has 120 degree. The static torque was therefore measured from 0 degree to 120 degree as shown in Fig. 12. 7.1. The static torque measurements The static torque coefﬁcient (Cst) of the double stage turbine DS0PSA0OL is shown in Fig. 13. Four different air velocities were tested. The coefﬁcients for air velocity of 8 m/s (Re 1.46 105) and 10 m/s (1.83 105) are very close. The curves at 4 m/s (Re 7.31 104) and 6 m/s (Re 1.1 105) are following the trends of the curves at 8 m/s and 10 m/s until the 90 degree mark.

7.1.2. Effect of the phase shift Angle (PSA) Fig. 14 shows that the average Cst of the turbines with an overlap ratio of 0 increases in accordance with its phase shift angle. The turbine (DS60PSA0OL) with 60 degree phase shift angle shows the best Cst average, which is not surprising since this arrangement of the upper and lower turbine is counter cyclic.

Fig. 14. Static torque measurement results for 5 wind turbines at 8 m/s air velocity.

Fig. 15. Static torque measurement results for 3 wind turbines at 8 m/s air velocity.

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7.1.3. Effect of the overlap ratio (OL) Fig. 16 presents the starting torque characteristics of the wind turbines DS0PSA0OL, DS0PSA0.16OL and DS0PSA0.32OL. The turbine with 0 overlap ratio shows a negative Cst for the PSA between 85 and 95 degrees, whereas the 0.16 and 0.32 overlap ratio

turbines only show positive torque. The average Cst increases with larger overlap ratio (OL). The same applies to the single stage turbines shown in Fig. 15. A sharp increase between 95 and 110 degrees is noted. Similar sharp increases of the Cst were also found by other researchers

Fig. 16. Static torque measurement results of 3 wind turbines at 8 m/s air velocity.

Fig. 17. Static torque measurement results for 3 wind turbines at 8 m/s air velocity.

Fig. 18. Static torque measurements of 3 wind turbines at 8 m/s air velocity.

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(Jones et al., 1979). Besides, Figs. 16–18 demonstrate that the peak Cst moves according to the phase shift angle.

7.2. Dynamic torque and power coefﬁcient test results The dynamic torque measurements under 4 m/s air velocity proved to be unreliable and were not used for the dynamic torque analysis.

65

7.2.1. The single stage turbines Figs. 19, 20 and 22 show the power coefﬁcient (CP) curves of the turbines SS0OL, SS0.16OL and SS0.32OL at 6 m/s air velocity (Re 0.99 105). For different tip speed ratios (TSR) of the turbines at 6 m/s air velocity as shown in Fig. 21 and Table 3, all of the turbines give their CP max between l ¼0.633 (turbine SS0.16OL at Re 0.99 105) and l ¼0.621 (turbine SS0OL at Re 0.99 105). The same appears for the measurements of 10 m/s air velocity (Fig. 22), where the CP max occurs between l ¼ 0.566 (turbine

Fig. 19. Power coefﬁcients of 3 wind turbines at air velocity of 6 m/s.

Fig. 20. Power coefﬁcients of the turbines SS0OL, SS0.16OL and SS0.32OL at air velocity of 8 m/s.

Fig. 21. Torque coefﬁcients of 3 wind turbines at air velocity of 8 m/s.

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SS0.16OL at Re 1.33 105) and l ¼0.521 (turbine SS0OL at Re 1.33 105). The performance of the turbines SS0OL and SS0.32OL is similar. Their tip speed ratios (TSR) are very close but the generated dynamic torque of the SS0OL is higher than that of the turbine SS0.32OL as shown in Fig. 21, i.e. the CP max for the SS0OL is higher by 14%. Overall, the turbine SS0.16OL is superior to the turbines with the overlap ratios of 0 (turbine SS0OL Re 0.99 105) and 0.32 (turbine SS0.32OL Re 0.99 105) by about 25% shown in Fig. 19 and Table 3. The same appears at the air velocity of 8 m/s (Re 1.33 105) in Fig. 20 and Table 3 where the CP max of the turbine SS0.16OL for Re 1.33 105 is higher by about 40%. Table 3 The maximum power coefﬁcient at different air velocities with the highest CP values in bold. 6 m/s air velocity (Re 99,598.3) TSR l Overlap ratio 0 0.621 Overlap ratio 0.16 0.633 Overlap ratio 0.32 0.623

CP

8 m/s air velocity (Re 13,2794)

max

10 m/s air velocity (Re 16,5997.3)

max

TSR l

CP

max

TSR l

CP

0.125 0.189 0.109

0.481 0.571 0.624

0.114 0.178 0.093

0.521 0.566 0.534

0.147 0.155 0.122

max

The CP of the SS0.16 remarkably displays a second CP peak under 8 and 10 m/s air velocity. This phenomenon is visible in Figs. 19–22 and seems to become more prominent with higher air velocities. 7.2.2. The double stage wind turbines The measured results of the double stage turbines are shown in Figs. 25–36. Each chart shows the power coefﬁcient curve (CP) of the phase shifts 0, 15, 30, 45 and 60. 7.2.3. The 0 overlap ratio (OL) double stage turbines Fig. 23 seems to follow the example of the SS0OL curve (Fig. 19). Out of the turbines tested at 6 m/s, the turbine DS0PSA0OL at Re 1.1 105 (Fig. 23) produces the highest CP max of 0.136 at l ¼0.53. The CP max of all turbines measured in 6 m/s air velocity differs greatly in tip speed ratio as well as dynamic torque (Table 4). When increasing the air velocity, the CP curves change. At 8 m/s air velocity, the performance peaks (CP max) are between 0.127 and 0.139 at tip speed ratios of l ¼0.51–0.53 (Table 4). Besides, the turbines DS30PSA0OL, DS45PSA0OL and DS60PSA0OL show a slight CP increase to a second peak around CP 0.9 and 0.96 at l ¼0.89 as shown in Figs. 24 and 25.

Fig. 22. Power coefﬁcients of 3 wind turbines at air velocity of 10 m/s.

Fig. 23. Power coefﬁcients of the turbines DS0PSA0OL, DS15PSA0OL, DS30PSA0OL, DS45PSA0OL, and DS60PSA0OL at air velocity of 6 m/s.

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Table 4 Maximum performance of the turbines with overlap ratio 0 with the highest CP Overlap ratio 0 at 6 m/s air velocity

Phase Phase Phase Phase Phase

shift shift shift shift shift

0 15 30 45 60

TSR l

CP

0.528792 0.503938 0.513864 0.626788 0.524909

0.136022 0.109069 0.088818 0.123191 0.133451

max

max

67

values in bold.

Overlap ratio 0 8 m/s air velocity TSR l

CP

0.529797 0.527472 0.510052 0.527615 0.532156

0.125147 0.13325 0.138051 0.139364 0.127501

max

Overlap ratio 0 10 m/s air velocity TSR l

CP

0.522251 0.548467 0.603679 0.50815 0.56625

0.122096 0.132187 0.115997 0.106794 0.123781

max

Fig. 24. Power coefﬁcients of the turbines DS0PSA0OL, DS15PSA0OL, DS30PSA0OL, DS45PSA0OL, and DS60PSA0OL at air velocity of 8 m/s.

Fig. 25. Torque coefﬁcients of the turbines DS0PSA0OL, DS15PSA0OL, DS30PSA0OL, DS45PSA0OL, and DS60PSA0OL at air velocity of 8 m/s.

For comparison, the single stage turbine SS0OL (at Re 1.33 105) (Fig. 21) seems not to display any increase of CP after the ﬁrst peak although it has a different Reynolds number.

7.2.3.1. The effect of the phase shift angle (PSA). The effect of the phase shift angle becomes visible when the CP max in Table 4 is compared. At the air velocity of 6 m/s, the turbines with PSA of 0, 15, 30, and 60 show their CP max at the same TSR (about 0.503– 0.528), but the turbine with the PSA of 45 degrees shows a higher TSR (of about 0.626) at its CP max.

The PSA affects the performance of the turbines as shown by the turbine DS30PSA0OL at 6 m/s air velocity, which reaches its CP max of 0.089 at TSR of l ¼0.513 and as shown in Fig. 26 its torque generation is much lower than other turbines. If its CP max is compared to the CP max of the highest performing turbine, the difference is 35% in power output. The test results of the turbine DS30PSA0OL demonstrate how the CP max of a turbine depends on the turbine conﬁguration and air velocity. At air velocity of 6 m/s the turbine DS30PSA0OL shows the worst performance (CP max) but under the air velocity of 8 m/s it performs second best.

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Fig. 26. Power coefﬁcients of the turbines DS0PSA0OL, DS15PSA0OL, DS30PSA0OL, DS45PSA0OL, and DS60PSA0OL at air velocity of 10 m/s.

Fig. 27. Power coefﬁcients of the turbines DS0PSA0.16OL, DS15PSA0.16OL, DS30PSA0.16OL, DS45PSA0.16OL and DS60PSA0.16OL at air velocity of 6 m/s.

Fig. 28. Torque coefﬁcients of the turbines DS0PSA0.16OL, DS15PSA0.16OL, DS30PSA0.16OL, DS45PSA0.16OL and DS60PSA0.16OL at air velocity of 6 m/s.

Overall, the performance curves of this test series are quite close to the results before and after their CP max, which is because the dynamic torque generation and the TSR are not very different among the turbines.

7.2.4. The 0.16 gap ratio As shown in Figs. 19–21, a second CP peak occurs for the single stage turbine SS0.16OL (Figs. 21–24). This phenomenon is also visible in some of the performance graphs of the

J. Kumbernuss et al. / J. Wind Eng. Ind. Aerodyn. 107–108 (2012) 57–75

double stage turbines (Figs. 27–30) with the same overlap ratio. The turbines DS30PSA0.16OL, DS45PSA0.16OL and DS60PSA0. 16OL (at Re 1.09 105) in Fig. 27 under the air velocity of 6 m/s display an increase of CP after their ﬁrst peak, which is also visible in the torque coefﬁcient chart shown in Fig. 28. A similar increase of CP is also displayed by the turbines DS0PSA0.16OL and DS15PSA0.16OL (at Re 1.46 105) under the air velocity of 8 m/s. Their CP rises after their ﬁrst CP max at l ¼1.0–1.2 (Fig. 29). The same event takes place under the air velocity of 10 m/s in Fig. 30. 7.2.4.1. The effect of the phase shift angle (PSA). In Table 5 the CP max values and the tip speed ratios of this test series is shown. The 6 m/s air velocity test series is interesting because the CP max values of all the

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turbines range from 0.19 to 0.199, but their tip speed ratios are different due to their different PSA. The TSR of the turbines DS0PSA0.16OL and DS15PSA0.16OL (at Re 1.09 105) is around l ¼0.63, but the TSR of the turbines DS30PSA0.16OL, DS45PSA0.16OL and DS60PSA0.16OL (at Re 1.09 105) are at a higher value of about l ¼0.67. This means that the turbines with 0 and 15 degrees of the PSA turn slower at a higher torque and the rotation speed of the turbines with the PSA of 30, 45 and 60 is higher but at a lower torque. At the air velocity of 8 m/s the TSR of all the turbines is quite close (between 0.565 and 0.589), but the CP max of each turbine differs greatly. One example is the turbine DS0PSA0.16OL (at Re 1.46 105), which shows the second lowest CP max of 0.179 but has the highest TSR (l ¼0.589). Overall, the turbine which shows the highest CP max does not necessarily have the highest TSR.

Fig. 29. Power coefﬁcients of the turbines DS0PSA0.16OL, DS15PSA0.16OL, DS30PSA0.16OL, DS45PSA0.16OL and DS60PSA0.16OL at air velocity of 8 m/s.

Fig. 30. Power coefﬁcients of the turbines DS0PSA0.16OL, DS15PSA0.16OL, DS30PSA0.16OL, DS45PSA0.16OL and DS60PSA0.16OL at air velocity of 10 m/s.

Table 5 Maximum performance of the turbines with the overlap ratio 0.16 with the highest CP Overlap ratio 0.16 at 6 m/s air velocity

Phase Phase Phase Phase Phase

shift shift shift shift shift

0 15 30 45 60

TSR l

CP

0.631095 0.635505 0.674979 0.676509 0.672073

0.194032 0.199079 0.197465 0.190639 0.194316

max

max

values in bold.

Overlap ratio 0.168 m/s air velocity TSR l

CP

0.589336 0.57754 0.572397 0.575874 0.565933

0.173885 0.17358 0.18309 0.195432 0.179597

max

Overlap ratio 0.1610 m/s air velocity TSR l

CP

0.578259 0.559864 0.596772 0.595614 0.606792

0.146456 0.17197 0.170686 0.162934 0.158561

max

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A remarkable result for this test series is that the PSA seems to be not so important at lower air velocities like 6 m/s (Table 5), as the CP max of the turbines did not change greatly although the TSR and the dynamic torque are different. Under higher air velocities like 8 m/s or 10 m/s (Figs. 29–30) the inﬂuence of the PSA on the dynamic torque generation becomes more signiﬁcant. The CP max can differ by 15%. 7.2.5. The 0.32 gap ratio The CP curves of the turbines with the 0.32 overlap ratio are shown in Figs. 31, 32 and 34. The performance chart at 6 m/s air velocity (Fig. 31) shows that the turbine DS60PSA0OL has its CP max at TSR l ¼0.77, which is surprising since the single-stage chart of the turbine (SS0.32OL) (Fig. 19) does not show such a high TSR as its CP max peak. 7.2.5.1. The effect of the phase shift angle (PSA). Fig. 32 shows an unusual performance curve of the turbines DS15PSA0.32OL, DS30PSA0.32OL, DS45PSA0.32OL and DS60PSA0.32OL (at Re 1.46 105) at 8 m/s air velocity. First the CP rises to its ﬁrst performance peak (CP max) of around 0.14, which lies at the expected tip speed ratio value of l ¼0.55 as most of the other CP max do (Tables 3–5 when wind speed is 8 m/s). After its ﬁrst peak, it decreases but then it rises at the tip speed ratio of l ¼ 0.82 to its second but higher CP peak of around 0.15. After that, the turbines DS30PSA0.32OL, DS45PSA0.32OL and DS60PSA0.32OL

seem to have a third peak at around l ¼1.1. This is interesting for two reasons:

Firstly, the ﬁrst CP max of all other turbines is higher than their second peak (if they display a second peak).

Secondly, the second peak appears to be at a lower tip speed ratio. Most of the measured turbines show their second peak at around l ¼0.9–1.1 (Figs. 22, 27, 28 and 30). The fact that neither the double stage 0 angle phase shift turbine (DS0PSA0.32OL) nor the single stage turbine (SS0.32OL) display such a unique curvature, leading to the assumption that its appearance is due to the phase shift. Table 6 shows that any phase shift angle larger than 0 will increase the performance of a turbine with 0.32 OL. The 45 degree one gives the best overall performance.

8. Discussions As seen before, the overlap ratio has a direct inﬂuence on the overall performance of the turbines, which is clear from Figs. 35–37, where different CP values can be easily found for different overlap ratios (0, 0.16 and 0.32). The highest performance is produced when the overlap ratio is 0.16, followed by the 0.32 overlap ratio. The worst performance was measured with the 0 overlap ratio.

Fig. 31. Power coefﬁcients of the turbines DS0PSA0.32OL, DS15PSA0.32OL, DS30PSA0.32OL, DS45PSA0.32OL and DS60PSA0.32OL at air velocity of 6 m/s.

Fig. 32. Power coefﬁcients of the turbines DS0PSA0.32OL, DS15PSA0.32OL, DS30PSA0.32OL, DS45PSA0.32OL and DS60PSA0.32OL at air velocity of 8 m/s.

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Fig. 33. Torque coefﬁcients of the turbines DS0PSA0.32OL, DS15PSA0.32OL, DS30PSA0.32OL, DS45PSA0.32OL and DS60PSA0.32OL at air velocity of 8 m/s.

Fig. 34. Power coefﬁcients of the turbines DS0PSA0.32OL, DS15PSA0.32OL, DS30PSA0.32OL, DS45PSA0.32OL and DS60PSA0.32OL at air velocity of 10 m/s.

Table 6 Maximum performance of the turbines with the overlap ratio 0.32 with the highest CP Overlap ratio 0.32 at 6 m/s air velocity

Phase Phase Phase Phase Phase

shift shift shift shift shift

0 15 30 45 60

TSR l

CP

0.645228 0.634144 0.631144 0.622956 0.777311

0.10857 0.147031 0.143427 0.150464 0.169944

max

max

in bold.

Overlap ratio 0.32 8 m/s air velocity TSR l

CP

0.546659 0.545671 0.826694 0.828231 0.820665

0.104601 0.141697 0.148523 0.157007 0.149854

The CP performance level is determined by the overlap ratio and within those CP performance levels, some phase shift angles perform better than others, which is visible in Table 7. Each turbine performs according to its phase shift angle, air velocity and overlap ratio differently. The feature of the second and third peak (Fig. 36) depends on the air velocity. In general, the CP curves at air velocities like 6 m/s do not show a second peak, but higher air velocities of 8 m/s and 10 m/s show this phenomenon. The fact that most of the second and third peaks are near or above the l ¼1 mark (Figs. 36 and 37), leads to the impression that the second and third peak phenomenon is created by the lift characteristics of the turbines. The phase shift rate has an effect on the curvature of the graph but not

max

Overlap ratio 0.32 10 m/s air velocity TSR l

CP

0.688234 0.554688 0.546782 0.551312 0.556424

0.099497 0.139607 0.129514 0.124674 0.124942

max

on the appearance of the second peak. This is supported by the fact that the single stage turbine displays a second peak as well (Figs. 16–18). However, there are exceptions. When studying Fig. 36, it seems that the phenomena of the third peak as well as the fact that the CP peak value is found at l ¼0.95 are related to the phase shift angle. The curves of the double stage turbine (DS0PSA0.32OL) with the 0 phase shift angle, as well as the single stage turbine (SS0.32OL) do not show such phenomena. The phenomenon of the third peak appears, as soon as there is a phase shift angle. The TSR range in which the CP peak value is found, seems to indicate that the phase shift is enhancing the lift characteristics of the turbine (Figs. 35 and 37). More work is needed to explain this phenomenon.

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Fig. 35. Power coefﬁcients of most of the double stage turbines at air velocity of 6 m/s. The dotted line depicts the turbines with 0.16 overlap rate, the continuous line denotes the 0.32 overlap rate and the dashed line shows the 0 overlap rate turbines.

Fig. 36. Power coefﬁcients of most of the double stage turbines at air velocity of 8 m/s. The dotted line depicts the turbines with 0.16 overlap rate, the continuous line denotes the 0.32 overlap rate and the dashed line shows the 0 overlap rate turbines.

Fig. 37. Power coefﬁcients of most of the double stage turbines at air velocity of 10 m/s. The dotted line depicts the turbines with 0.16 overlap rate, the continuous line denotes the 0.32 overlap rate and the dashed line shows the 0 overlap rate turbines.

J. Kumbernuss et al. / J. Wind Eng. Ind. Aerodyn. 107–108 (2012) 57–75

9. Conclusions A detailed experimental study of the performance of the Savonius-type vertical axis wind turbines was carried out in this paper. The overlap ratio is found to be of the highest importance. Considering the great CP declination from 0.16 to 0.32 and then 0 overlap ratios, it is noted that the overlap ratio should be carefully determined when designing a Savonius wind turbine since a too small and a too big overlap ratio can seriously decrease the performance of the turbine. The phase shift angle affects the performance of the turbine depending on the air velocity. We have seen that larger phase shift angles produce better performance of the turbines at lower air velocities and smaller ones will increase the performance at

73

higher air velocities. With the extensive knowledge of the performance of this type of wind turbine, the turbine design could be made according to the local wind condition. If higher wind speed is expected, one could choose a different PSA as shown in Table 7 because the CP for that wind speed is different. From this report the best phase shift angle can be determined for each wind turbine (Table 7). The best overall CP for all air velocities of the 0 OL turbines is 60 degree, and the same applies for the 0.32 OL turbines, but for the 0.16 OL turbines it is 30 degree. During this investigation a second performance peak was found in the torque measurements of the wind turbines. To explain this phenomenon, the investigation will continue in future.

Table 7 Summary chart of the CP max, the TSP and the CT the CP max of each turbine conﬁguration is shown in bold; the phase shift ratios which have the best overall performance are depicted in italics. Air velocity

Overlap ratio 0 6 m/s

8 m/s

PSA

TSR

CT

CP

0 15 30 45 60

0.529 0.504 0.514 0.627 0.525

0.257 0.216 0.173 0.197 0.254

0 15 30 45 60 0 15 30 45 60

10 m/s

TSR

CT

CP

0.136 0.109 0.089 0.123 0.133

0.530 0.527 0.510 0.528 0.532

0.236 0.253 0.271 0.264 0.240

Overlap ratio 0.16 0.631 0.307 0.636 0.313 0.675 0.293 0.677 0.282 0.672 0.289

0.194 0.199 0.197 0.191 0.194

0.589 0.578 0.572 0.576 0.566

Overlap ratio 0.32 0.645 0.168 0.634 0.232 0.631 0.227 0.623 0.242 0.777 0.219

0.109 0.147 0.143 0.150 0.170

0.547 0.546 0.827 0.828 0.821

max

TSR

CT

CP

0.125 0.133 0.138 0.139 0.128

0.522 0.548 0.604 0.508 0.566

0.234 0.241 0.192 0.210 0.219

0.122 0.132 0.116 0.107 0.124

0.295 0.301 0.320 0.339 0.317

0.174 0.174 0.183 0.195 0.180

0.578 0.560 0.597 0.596 0.607

0.253 0.307 0.286 0.274 0.261

0.146 0.172 0.171 0.163 0.159

0.191 0.260 0.180 0.190 0.183

0.105 0.142 0.149 0.157 0.150

0.688 0.555 0.547 0.551 0.556

0.145 0.252 0.237 0.226 0.225

0.099 0.140 0.130 0.125 0.125

max

max

Fig. 38. The red graph above shows the power coefﬁcient of DS15PSA0.16OL at 8 m/s (as shown in Fig. 26). The blue colored graph depicts a possible (assumed) performance of a drag driven turbine, and the green color shows a possible (assumed) performance of a lift driven turbine. The idea for future work is that the red color graph is in fact the result of both turbine performances. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

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10. Future work When the value of l approaches 1, are the turbine blade tips rotating at the same speed as the passing air, which means that the drag inﬂuence on the torque approaches 0 and the lift force becomes the dominant force to produce the torque. Our presented research shows that a larger overlap rate of the turbine changes the lift characteristics of the turbine drastically. Considering this result, the conclusion could be drawn that we are actually looking at two curves uniﬁed by the plotted graph (a ﬁctional graph depicting this is shown in Fig. 38). The ﬁrst peak shows the performance of a drag driven turbine, with the CP peak value at l ¼ 0.55 and the performance declines after that. The second peak indicates a lift driven turbine with its CP peak value at l ¼1.15 and the performance declines after that. The performance peak of a lift driven VAWT (Darrieus type (Darrieus, 1931) for example) depends on several key factors, like the airfoil, the rotation speed, and the turbine solidity besides others. The solidity of a Darrieus (Darrieus, 1931) turbine is expressed in Eq. (14), where ‘‘s’’ is the solidity ‘‘N’’ the number of blades, ‘‘c’’ the chord length and ‘‘R’’ radius of the turbine (Paraschivoiu, 2002).

s¼

Nc R

ð14Þ

If applied to the Savonius turbine, the solidity is one. Paraschivoiu (2002) published an interesting comparison between Darrieus turbines with low solidity and Darrieus turbines with high solidity turbines, which was based on an earlier publication by (Strickland, 1975). In this comparison Paraschivoiu concludes that the optimal solidity of a lift driven (Darrieus) turbine is around s ¼0.3. If a lower solidity is chosen, the CP max may drop but the operational TSR range will be extended. If a higher solidity is chosen, the CP max will also drop but the operational TSR range will be shortened.

Although Strickland (1975) did not investigate very high solidities, it is possible that the trend will continue until the solidity is s ¼1. At this point, it is expected that the CP max and the TSP are considerably lower than that of s ¼0.3. Based on the above discussion, a new investigation into the transmission of a Savonius turbine layout into a Darrieus turbine layout at higher tips speed ratios (TSR) l ¼1–2 could provide interesting results. This would be instrumental for designing improved turbine structures, which then could possibly unify the strengths of the Savonius and the Darrieus types of vertical axis wind turbines. We will follow this direction to continue our effort.

Acknowledgments The work described in this paper was supported by a Grant from the Sun Hung Kai Properties Group based in Hong Kong (Project no. ZZ1T) and a Grant from the Inter-Faculty Research Grant of The Hong Kong Polytechnic University. Thanks also go to its Industrial Center and the staff members in its Precision Machining Department. The wind tunnel test was carried out in the Shandong Jianzhu University, China.

Appendix A Table A1.

Appendix B Table B1.

Table A1 The turbine dimensions.

Rotor diameter D (m) Rotor height (H) (double stage turbine) (m) Rotor height (H) (single stage turbine) (m) Overlap ratio (OL) The rotor overlap (S) (m) Bucket diameter (d) depending on the overlap ratio (OL) (mm) Adjusted phase shift angle (PSA) (Fig. 4) Rotor diameter (D) (m) Swept area of the double stage turbine As (m2) Swept area of the single stage turbine As (m2) Blockage rate (according to Eqs. (6) and (7) for double stage turbine) Blockage rate (according to Eqs. (6) and (7) for single stage turbine) Aspect ratio (according to Eqs. (6) and (7) for double stage turbine) Blockage rate (according to Eqs. (6) and (7) for single stage turbine)

Turbine design 1 (single or double stage)

Turbine design 2 (single or double stage)

Turbine design 3 (single or double stage)

0.25 0.54 0.27 0 0.012 (Fig. 7) 61.25 (Fig. 7) 0, 15, 30, 45 and 60 0.25 0.135 0.0675 0.135 0.0675 2.16 1.08

0.25 0.54 0.27 0.16 0.034 (Fig. 8) 66.75 (Fig. 8) 0, 15, 30, 45 and 60 0.25 0.135 0.0675 0.135 0.0675 2.16 1.08

0.25 0.54 0.27 0.32 0.06 (Fig. 9) 73.25 (Fig. 9) 0, 15, 30, 45 and 60 0.25 0.135 0.0675 0.135 0.0675 2.16 1.08

Table B1 Turbine abbreviations.

0 overlap ratio (OL) 0.16 overlap ratio (OL) 0.32 overlap ratio (OL)

Phase shift angle 0 (PSA) double stage turbine (DS)

Phase shift angle 15 (PSA) double stage turbine (DS)

Phase shift angle 30 (PSA) double stage turbine (DS)

Phase shift angle 45 (PSA) double stage turbine (DS)

Phase shift angle 60 (PSA) double stage turbine (DS)

Single stage turbine (SS)

DS0PSA0OL DS0PSA0.16OL DS0PSA0.32OL

DS15PSA0OL DS15PSA0.16OL DS15PSA0.32OL

DS30PSA0OL DS30PSA0.16OL DS30PSA0.32OL

DS45PSA0OL DS45PSA0.16OL DS45PSA0.32OL

DS60PSA0OL DS60PSA0.16OL DS60PSA0.32OL

SS0OL SS0.16OL SS0.32OL

J. Kumbernuss et al. / J. Wind Eng. Ind. Aerodyn. 107–108 (2012) 57–75

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