Journal of Wind Engineering and Industrial Aerodynamics, 21 (1985) 223-231 223 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

ON THE AERODYNAMIC DESIGN OF THE SAVONIUS WINDMILL ROTOR

0.O. MOJOLA

Department of Mechanical Engineering, University of lfe, lie-Ire (Nigeria)

(Received June 19, 1984; accepted in revised form April 9, 1985)

S u m m a r y

2"his paper examines the performance characteristics of the Savonins windmill rotor under field conditions. Test data were collected on the speed, torque and power of the rotor at a large number of wind speeds for each of seven values of the rotor overlap ratio. The performance data of the Savonius rotor are also fully discussed and design criteria established.

N o t a t i o n

A Cp d D P R $

s/d (s/d)c U P

kc

swept area of rotor power coefficient (P/1/W U3A ) bucket diameter rotor diameter power rotor radius bucket overlap overlap ratio overlap ratio giving maximum Cp wind speed air density tip speed ratio (~2R/U) tip speed ratio corresponding to maximum Cp angular velocity of rotor

1. I n t r o d u c t i o n

After more than half a century since its invention by Savonius [1], the Savonius windmill rotor (Fig. 1) is at last beginning to attract significant at tent ion, not just because of its great simplicity but also because of its relatively good starting characteristics.

A large amount of performance data has been gathered [2--36] by a good number of researchers for an interesting variety of rotor geometry,

0167-6105/85/$03.30 © 1985 Elsevier Science Publishers B.V.

224

but there is still no generally accepted value of overlap ratio to be used in designing an "op t imum" rotor geometry. Part of the problem stems from non-standardisation of measurement and testing techniques employed by different workers and, perhaps, more importantly, the inevitability of blockage effects which bedevil most performance data collected from model tests in wind tunnels. One area of difficulty, particularly from the view- point of the designer, is the lack of information and guidance on the extent to which rotor performance data gathered from wind tunnels (with charac- teristically steady irrotational flows) can be extrapolated to field conditions which, of course, are neither statistically steady nor irrotational; and it is to this problem area that the efforts described in the present paper are directed.

S

Fig. 1. The Savonius windmill rotor.

2. Scope of the present work

The present investigation of rotor performance has been carried out entirely in the natural wind with a view to establishing under field con- ditions

(i) an optimum design value of overlap ratio for the rotor and (ii) some measure of the role of the tip speed ratio in the aerodynamic

design of the rotor.

3. Test facilities

3.1. The field testing station This was an open space with a fairly level ground, located behind the

University's greenhouses but far enough from the latter for the sheltering effect of the buildings to be minimised. The field testing station was the same station as that used for the field testing programme reported earlier by Mojola and Onasanya [37].

225

The wind speed characteristics at different time scales (ranging from 1-min averages to seasonal/annual distributions) at the testing site are il- lustrated in Fig. 4, which shows on the same scale the "f luctuat ions" of wind speed about their respective means. I t will be observed from the figure that the maximum fluctuation in the annual distribution of wind speed at the site is- only about one-half of the maximum fluctuation in the month ly distribution, and the latter maximum is, in turn, only about one- half of tha t for 30 min of wind speed data taken at 1-min intervals. It should also be observed that, in spite of the relatively large fluctuations associated with 1-min integrations of wind speed, there were brief moments (three of such are identified in Fig. 4a) during which the wind could be regarded as having "cons tan t" speed.

3.2. Test models For comprehensive testing at the field station, a rotor was used having a

bucket diameter of 580 mm and height of 887 mm. It was constructed from an oil drum by removing the circular top and bot tom and carefully splitting the drum into two equal half-cylinders, which were secured by small nuts and bolts to two circular end plates (1 m diameter galvanised sheets) which in turn were reinforced by four radial steel bars, such that the overlap distance between the drum halves could be easily varied. To minimise the tare (friction) torque, the output shaft (made of 25.4 mm diameter mild steel) was supported in two ball bearings of very low friction and the whole rotor assembly was mounted on a short (1.71 m high) tower which was employed in an earlier work [37] on rotor performance in the presence of wind shear. This short tower had been chosen again not only to permit direct comparison between the results of the present investigation and those earlier reported [37] , but also to facilitate the varying of the rotor overlap ratio.

3.3. Instrumentation and testing techniques Accurate estimates of the wind speed (and indeed the wind shear) at the

field testing station were obtained by means of an array of three high- precision cup,counter anemometers located with their cup centres at levels A, B and C shown in Fig. 2. The relative positions, in plan view, of the anemometers with respect to the rotor and with respect to themselves are indicated in Fig. 3. In so far as there are still no specific guidelines on rotor-- anemometer distances (in both the vertical and horizontal planes) in field testing work, and this is one area in which standardisation is badly needed, the distances chosen in Fig. 3 have been somewhat arbitrary. For further discussion of this matter reference may be made to Mojola and Onasanya [37] , but for the purpose of the present work it would suffice to state here that in order to compensate as much as possible for the effects of wind shear across the height of the rotor, the wind speed at the location of the rotor was calculated from

226

UB + (UA + UC)I2 U = (1)

2

where UA, UB and U c denote the wind speeds measured by anemometers A, B and C, respectively.

At each wind speed and for each of seven values of rotor overlap ratio, detailed measurements were made of the rotor speed, ou tpu t torque, and power. Both tachometry and the visual revolutions-timing technique were employed to measure the rotor speed, and the two methods gave quite good agreement. A specially designed Prony-brake dynamometer , after calibration against a standard but limited-range dynamometer , was used to measure the rotor torque. The power output of the rotor was then com- puted from the product of the torque and speed of the rotor.

z-R°f°r C

7mm - - B

- - A 80ram

/ / / / ~" / / / / / / / / / / / / / / / / / '

Rofor

6.8m Anemomefers

TTT+TCT Predominanf Wind Direcfion

Fig. 2. Set-up for field testing.

Fig. 3. Plan view of the relative posi t ions o f windmill ro to r and cup anemometers .

~ ~ . , , .~.~.~_~__.~ 0~_ Jan

6 12 18 2l, 30 1 I [ I

Fig. 4. Wind speed variations on dif ferent t ime scales at the testing station.

227

Because of the statistically unsteady nature of the wind, measurement of windmill performance under field conditions is most susceptible to a great deal of scatter and may even generate entirely spurious results unless the testing procedure is planned such that a vast number of repetitive readings are taken to ensure that smooth statistical averages are obtained. This was the approach adopted in the present work, and it proved to be quite tedious. There is clearly a need for a less tedious and more rational method of field testing.

4. Test results

In almost all previous investigations of the Savonius windmill rotor it has been the practice to confine performance testing to a rather narrow range of values of s/d, usually near s /d = O. However, in the present work we have chosen to consider a very wide (indeed, almost the widest possible) range of values of s/d, to ensure that the aerodynamic design of the Savonius rotor is properly guided by a comprehensive data base on performance.

Figure 5 shows the variation of the power coefficient, Cp, against the tip speed ratio, k, for seven values (namely, 1/8, 1/5, 1/4, 1/3, 1/2, 3/4 and 7/8) of the overlap ratio, s/d. It will be observed from the figure that the maximum value of Cp (0.267) was obtained at an overlap ratio of 1/4, which does not agree with the suggestion of several workers, based on irrotational flow data, that the maximum power coefficient of the Savonius rotor is attained when the overlap ratio lies between 0.10 and 0.15. This departure of the present test data from the irrotational flow behaviour should perhaps be regarded as a measure of the significance of the turbulence and vertical shear which characterise the natural wind.

Turbulence measurements were not made in the present investigation but the level of vertical wind shear was found to be comparable to that earlier reported by Mojola and Onasanya [37]. It should also be observed from the figure that there is a general tendency for the peak of the Cp--k curves to drift towards the Cp-axis with increase in the value of s/d. Here, again, the behaviour of the field data contrasts sharply with that of wind-tunnel data which seem to suggest that Cp--~, curves for all values of s /d peak at about the same value of h. It was concluded from an earlier work [37] investi- gating the effects of shear on the performance of the Savonius rotor that even in the presence of shear the Cp--h curves for different values of s /d peaked at about the same value of ~. However, in the light of the more comprehensive data now available, it should be admitted here that that conclusion was rather sweeping as it was based on what we now adjudge to be insufficient data.

Figure 6 shows how Cpm~x and the tip speed ratio corresponding to Cpma~ vary with the rotor overlap ratio. It is interesting to observe that Cpm~x at s /d = 1/4 is about three times (the extrapolated) Cpm ~ at s/d = 0, and even more interesting to note that this result confirms one of the as-

228

sertions made by Savonius [1] over half a century ago. I t is also worthy of remark that a steep rise in Cpm = over the range 1/8<.s/d<.l/4 is accom- panied by a nearly steep fall over the range 1/4<.s/d<.l/2, and that beyond s/d = 3/4 the trend of the Cpm ~ curve strongly suggests that Cpm,x = 0 at

,, ~',,~

7/8 9< x,"Q-~" x ,o,o

0_-16

Ep _0.12

0.08 A:O~40 ° 0

0.04 A X

o.~, . ol.6 oi8 lio

[]

li2 y* Ii6 Fig. 5. Variation of power coefficient with tip speed ratio.

28 - 0 - C Pmctx

' L \ 0 A /~ , " o . ~.o

6 O.E

X c

0.08 - - - - - Q ~ \ o.~_

o.o# \ o.L S/d

o °i2 o.~, of 6 o# ~.o

Fig. 6. Variation of Cpmax and X c with rotor overlap ratio.

229

s/d = 1, which, in fact, should be the case because when s/d = 1 the Savonius rotor reduces to a circular cylinder. No satisfactory explanation can be offered here on the behaviour of the hc curve, particularly its intriguing similarity with the Cpm ~ curve.

In order to underscore the point made earlier that Cpm ~ is no t only a function of s/d but also of h, we have plotted in Fig. 7 the overlap ratio giving the highest values of Cp for given values of h. It will be seen from the figure that the range 1/4<.s/d<.l/3 gives the best rotor performance for 0.7<~h~<1.6 (which covers most of the useful working range of the Savonius rotor) while larger values of s/d (the extrapolation to s/d = 1 notwithstand- ing) appear to yield better results for 0~<~<0.7. The inescapable conclusion that follows from the foregoing, and this is really the crux of the argument in this paper, is that in order to optimise the performance of a Savonius rotor under field conditions, the rotor should be designed such that the overlap ratio of the blades is allowed to vary with the tip ratio in a manner similar to tha t suggested by Fig. 7. Plans are well underway by the author to field-test such a rotor [38] at the same time and in the same place against the conventional rotor with fixed geometry.

1.0

0.8

0.6

(s/d) c 0.4

0.2

0.2 I

\

k 0.4 0.6 0.8 1.0 1.2 1./~ 1.6

I ] I I I I I

Fig. 7. Variation of (s/d)c with tip speed ratio.

5. Conclusions

(i) Because of the difficulties inherent in field testing of windmills and the large discrepancies that may arise between the test data of different workers, there is a real need to adopt a unified method of field testing not only for the Savonius windmill but for windmills in general.

(ii) Under field conditions the power coefficient is maximum for an overlap ratio of about 0.25.

(iii) Because no single value of overlap ratio gives opt imum rotor perfor- mance for all values of h, the possibility should be explored of a Savonius rotor with variable overlap ratio.

230

Acknowledgement

The author acknowledges the contributions of Mr. C.F. Attang during the preliminary stage of this work.

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