Some effects of compressibility on small horizontal-axis wind turbines

~ Pergamon

Renewable Energy, Vol. 10, No. 1, pp. 1l q 7 , 1997 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved P I I : S 0 9 6 0 - 1 4 8 1 (96)00024-9 096~1481/97 $15.00 + 0.00

S O M E E F F E C T S OF C O M P R E S S I B I L I T Y O N SMALL HORIZONTAL-AXIS WIND TURBINES D. H. WOOD Department of Mechanical Engineering, University of Newcastle, Callaghan, NSW, 2308, Australia (Received 22 February 1996 ; accepted 29 March 1996)

Abstract--Many small wind turbines operate at high tip speed ratio and this gives rise to situations where compressibility may influence performance. The most important example is runaway, the operating point for an unloaded turbine where the rotational speed of the blades is maximised. Because compressibility significantly increases drag through the action of "shock-stall", it may provide an inherent mechanism for overspeed protection. This possibility is tested computationally for a turbine with a high optimum tip speed ratio, having an aerofoil section (NACA 0012) whose behaviour in compressible flow is well known. Calculations of turbine performance for differing windspeeds, and hence Mach numbers, show that compressibility effects occur too slowly to prevent overspeeding. However, it is suggested that aerofoils could be designed to maximise the onset of shock stall. Copyright © 1996 Elsevier Science Ltd.

1. INTRODUCTION Many small wind turbines operate at a high tip speed ratio, )~, primarily to improve the efficiency of electricity generation. For example, the prototype 5 kW machine described by Clausen et al. [1], which was based on that of Anderson et al. [2], has an optimum 2, 2opt, of 10, and the commercial 600 W - 3 kW range of turbines produced by World Power Technologies Inc operate most efficiently in the range 10 ~< 2 ~< 12 [3]. Since the rated wind speed for small turbines is around 10 m s-1, these values of 2 give a tip Mach number, Mtip, of about 0.3, which is generally considered as the upper limit for "incompressible" flow. Compressibility effects, therefore, may arise when either optimum performance is maintained as the wind speed, U0, is increased above the rated speed or if there is a loss of load at close to rated speed and 2 increases as the turbine moves towards runaway. If )~opt is about 10, then the runaway 2, 2 .... will usually be in the region of 15 20, where compressibility could be very significant. Because compressibility ultimately degrades rotor performance, it may provide an inherent mechanism for overspeed protection. This attractive possibility is the main motivation for the analysis described in this paper. The analysis uses blade element theory (BET) and assumes that compressibility effects, being due primarily to the rotation of the blades, are confined to the flow over the blades. 11

12

D.H. WOOD

Therefore, the usual simple, one-dimensional, incompressible wake model will be used, along with appropriate treatment of the high thrust region. A fundamental assumption of BET is that the individual blade elements have the same lift and drag coefficients, C~ and Cd, respectively, as aerofoils of the same section at the same angle of attack, ~. Specifically, it is necessary to categorise the variations of C~ and Ca with M and analyze their influence on rotor performance. Changes in aerofoil behaviour due to Mach number are discussed in most aerodynamics tests e.g. McCormick [4], and only a brief review will be given here. As M increases, the flow over the upper surface will eventually contain a supersonic region which must be terminated by a shock wave. If the shock wave is sufficiently strong, then the boundary layer will detach causing "shock stall". The value of M at which this occurs (for any cQ is called the "drag-divergence" Mach number, Mda. As the name suggests, there is a concomitant significant increase in the drag, but the lift is often not immediately affected. In marked contrast to stall in incompressible flow, drag divergence can occur at small values of c~, which, parenthetically, its one of the major problems in aerofoil design for commercial transport aircraft. Figure 1 shows Cd for the well-known N A C A 0012 aerofoil as a function of M and :~, taken from the data of Harris [5], which were assessed by McCroskey [6] as

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0.040

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,

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0.010

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r 10

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o~(degrees) 0.025 ,

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[

if

jl

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/

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0.010

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o~(degrees) Fig. 1. Drag coefficient dependence on angle of attack (c0 and Mach number (M) from [5]. (a) All data for Reynolds number = 3 x 10 6. Value of Mindicated in figure. (b) Low drag region on expanded scale. Symbols as in Fig. 1(a). Arrows indicate first appearance of shock wave. (In the interests of clarity, not all Mach numbers have arrows.)

Small horizontal-axis wind turbines

13

being of high quality. The second part of the figure highlights the low-drag region with the arrows indicating the c~ at which a shock wave first appeared. This point was judged from the pressure coefficients plotted in [5] ; a shock wave is easily determined from the large and rapid increase it causes in surface pressure. It can be seen that drag divergence is associated with shock wave f o r m a t i o n on the upper surface o f the aerofoil and Mdd depends on ~. Part of the complexity of M a c h n u m b e r variations is that the lift is also increased, at least initially. F r o m [6], the slope of the linear portion of the lift curve can be approximated as

dG/do:=O.llO/fl,

for

M40.6,

=O.llO/fl+O.667(M--0.6) 2, for = 2.31--2.625M,

for

0.6~
0.8 ~< M ~ 0.88,

(1)

where fl = x/1 - M 2 is the P r a n d t l - G l a u e r t compressibility correction factor, see eq. (1) of [6], and c~ is m e a s u r e d in degrees. The third equation in (1) shows that the additional lift as M increases ceases a b r u p t l y at M = 0.8, and the lift then goes quickly to zero at M = 0.88. This M a c h n u m b e r is just above the zero-lift, and largest, M a a - - M c C r o s k e y [6] puts it between 0.76 and 0.78 for the N A C A 0012. C o m b i n i n g the variations in lift, from eq. (1), and drag, as explained in the next Section, gives the results in Fig. 2 for the m a x i m u m LID ; the ratio decreases with M as does the angle at which it occurs. Both these results have implications for the p e r f o r m a n c e o f wind turbines. The remainder of this p a p e r describes the inclusion of these large changes in aerofoil properties within a suitably modified B E T analysis to estimate the resulting changes to turbine performance. The g e o m e t r y o f the blade is described in the next Section along with the parameterisation of the drag data in Fig. 2 for use with BET. The results are given in the subsequent Section which is followed by one containing the discussion. Finally, the conclusions are given in Section 4. 2. T H E T E S T B L A D E

There are few reliable data on M a c h n u m b e r effects on aerofoils, so that data such as those in Fig. 1 are not c o m m o n . F o r this reason it was decided to use these data which

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Fig. 2. Dependence on Mach number of maximum lift-to-drag ratio, (L/D) and angle at which it occurs, C%ax.Solid squares show average values from [6] with the error bars indicating scatter in the data. Solid line from eqs (1) and (2). X, ct,,,,x. ....

14

D.H. WOOD

were obtained at a chord Reynolds number (Re) of 3 × 10 6. It is, of course, impossible to change M without changing Re, but the former changes are much more significant and the data of [5] do not cover a wide range of Reynolds number; the latter were, therefore, ignored. Furthermore, large values of 2 are associated with small ~ so that eq. (1) can be used for CI. The upper limit on the validity ofeq. (1) was determined from the data of [5] as a function of M ; this gave the maximum 6', which was assumed to apply for any greater than the upper limit. This limit was always greater than ~.... shown in Fig. 2. The categorisation of the M-dependence of Cd was based on the analysis of McCroskey [6]. His Fig. 9, which includes data from a large number of experiments, shows no significant increase in the zero-lift Ca for M < Mdd. Figure l(b) is not exactly consistent with this result as the higher Mach number drags seem to increase above the results for M = 0.35, rather than M = 0.30. Therefore it was assumed that M = 0.35 defined the incompressible distribution. The departure from this is given by ACd(M,~) = C d ( M , ~ ) - Cd(M = 0.35, ~). ACd is plotted in Fig. 3 as a function ofA~ = ~--~M where aM was chosen to maximise the collapse. The solid line shows AC d = 0,

for

Ac~ ~< - 2 . 2 5 '~

= 0.01089+9.509x 10 3Ao~+2.l15x 10-3(mo0 2 otherwise. For both ranges of

(2)

A7,

C~M= 30.55-- 80.54M+ 113.8M 2 --72.318M 3.

(3)

(The results are not shown.) The use ofeqs (2) and (3) made the inclusion of compressibility effects very straightforward. Figure 4 shows the chord and twist distribution of each of the two blades of the low solidity turbine with a high Zopt = 9. The design was based on that of Anderson et al. [2], with a slight adjustment to the twist to accommodate the change from the N A C A 4412 used in [2] to the symmetrical N A C A 0012 profile. The calculations used standard BET with Glauert's empirical correction to the wake equations at high thrust and Prandtl's tip

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0.030

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0.010

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Aa (degrees) Fig. 3. Dependence of ACd on Ac~from data of [5]. Solid line shows eq. (2).

Small horizontal-axis wind turbines 25

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15

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0.15 m.

~

10

0.10

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.

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0.05

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r/rup Fig. 4. Twist (0v) and chord (c) distribution of test blade for investigating Mach number effects.

loss correction. The program structure and layout is similar to that described by Anderson

[7]. 3. RESULTS AND DISCUSSION

Calculations were performed for U0 = 0, 10, 20, and 30 m s - ~; note that variations in Uo were assumed not to alter the Reynolds number, so that Uo = 0 is the incompressible case. In terms o f the conventional power and thrust coefficients, Cp and C,, respectively, the effects o f changing Uo are shown in Fig. 5. At U0 = 10 m s-J, there are no important 0.5

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Fig. 5. Performance of test blade as wind speed changes. [ ] , Uo = 0 ; + , Uo = ] 0 m s - L ; ~ , Uo = 20 m s 1 ; X , Uo = 30 m s 1. (a) Power coefficient. (b) Thrust coefficient.

16

D.H. WOOD

compressibility effects even a.t the highest values of 2 and 2ru, remains at about 17. As U0 is increased to 20 m s-1, optimum performance is not degraded but "~runreduces to about 13 as Mt~p increases to 0.75 (Fig. 6). There are some interesting changes around 2 = 3, as compressibility first degrades aerofoil characteristics at high angles of attack. At U0 = 30 m s-l, both the m a x i m u m Up and ~'opt have decreased as has 2run ; to about 10. Figure 6 emphasises that performance is not just dependent on Mach number. Firstly, runaway occurs at very different values of M~p. Secondly, the results for U0 = 30 m s- 1 at 2 = 5 show a significant reduction in Cp whereas those for U0 = 10 m s 1 at 2 = 15 do not for a similar value of M,~p. The results of Fig. 5 indicate that shock stall could not be used for overspeed protection on the test blade mainly because 2run decreases less rapidly than M 1. Thus it seems that to use shock stall for overspeed protection would require an aerofoil of considerably lower Mad. Figure 5.4 of [4] indicates that the thinner the aerofoil section the higher the M~a for no lift. However as Cl increases, Mad decreases more rapidly for thin sections than for thick sections with the crossover point being around C~ = 0.3. This result is not encouraging, but it must be remembered that conventional aerodynamic design has been aimed at maximising Mad, whereas overspeed protection provides a unique requirement to minimise Mda. It could be very worthwhile to see whether a significant reduction could be achieved without seriously degrading the incompressible properties of the aerofoil. 4. CONCLUSIONS With sufficient data available on the Mach number dependence of lift and drag, it is straightforward to alter a blade element calculation to include the effects of compressibility on the performance of a horizontal-axis wind turbine. Attention was focused on small turbines, as they typically operate at higher tip speed ratios than large machines, and thereby are more likely to be affected by compressibility. Because compressibility ultimately degrades aerofoil performance, the main motivation for this study was to explore the use of shock stall--the shock-wave-induced separation of the blade's boundary layer as a passive means of overspeed protection. The calculations used a test blade incorporating the well-known N A C A 0012 aerofoil section, for which there are sufficient data on the variation of lift and drag which Mach number. As Mach number increases, the lift coefficient initially increases, while the drag coefficient, the

1.0

Mtip 0.6 0.4 0.2 0.0

5

10

15

Fig. 6. Variation of tip Mach number with wind speed and tip speed ratio. Symbols as in Fig. 5.

Small horizontal-axis wind turbines

17

m a x i m u m lift-to-drag ratio, and the angle at which it occurs, all decrease. Because these variations are greater than those with a Reynolds number, the latter were ignored. The incompressible optimum tip speed ratio was nine. Calculations were performed for a range of wind speed and hence Mach numbers. It was found that the windspeed had to be of the order of 30 m s 1 before there was a significant reduction in optimum performance. It was obvious from the results that shock stall could not be used for overspeed protection, but it was suggested that it may be possible to design an aerofoil for earlier onset of shock stall without seriously compromising its incompressible performance.

Acknowledgements--This work was supported by the Australian Research Council. REFERENCES

1. M. E. Bechley, P. D. Clausen, P. R. Ebert, A. Pemberton and D. H. Wood, Development and testing of a 5 kW wind turbine, Solar '95, Hobart, Tasmania (1995). 2. M. B. Anderson, D. J. Milborrow and J. N. Ross, Performance and wake measurements on a 3 m diameter horizontal-axis wind turbine, 4th Intl Symp. Wind Energy Systems, Stockholm (1982). 3. World Power Technologies Inc., Catalogue, Duluth, Minnesota, U.S.A. (1992). 4. B. W. McCormick, Aerodynamics, Aeronautics, and Floht Mechanics. John Wiley & Sons, New York, U.S.A. (1979). 5. C. D. Harris, Two-dimensional aerodynamic characteristics of the N A C A 0012 airfoil in the Langley 8-foot transonic pressure tunnel, N A S A Tech. Memo. 81927 (1981). 6. W. J. McCroskey, A critical assessment of wind tunnel results for the N A C A 0012 airfoil, N A S A Tech. Memo. 100019 (1987). 7. M. B. Anderson, An experimental and theoretical study of horizontal-axis wind turbines. Ph.D. Thesis, Cambridge University, Cambridge, U.K. (1981).