Development and analysis of vertical-axis wind turbines - Wind Power Generation and Wind Turbine Design - page 295

Figure 12 shows how the angle of attack on a blade varies throughout its travel
about the rotor axis. The range of angle of attack is seen to decrease with increas-
ing tip speed ratio. The non-dimensional torque per unit blade span generated at
each azimuth angle, b , is shown in Fig. 13. This is a complex characteristic par-
ticularly at low tip speed ratios, l . The complexity of the torque profi le arises in
part from the fact that NACA0012 blades will stall under steady-state fl ow condi-
tions for any angle of attack, , greater than approximately 14°. On the other hand,

for the higher tip speed ratios of 4.0 and 6.0, the blade does not stall and there is a
positive torque produced for the vast majority of azimuth angles. However, at a tip
speed ratio of 2.0 the blades pass in or out of stall at four azimuth angles (

a

75°,
45°, 134° and 251°) and the blade is stalled for a very signifi cant fraction of the
total travel, which in turn results in limited overall torque generated and hence
only a modest coeffi cient of performance, C p . Although stalling of the blades in
this way reduces C p and causes signifi cant fatigue loads, it does mean that an electri-
cal generator connected to the rotor will benefi t from passive overspeed protection at
high wind speeds.
For the particular example chosen here with a mean blade Reynolds number of
Re m = 1.0

−

10 6 the maximum coeffi cient of performance is C p ,max × ≈ 0.43 at an

optimal tip speed ratio of l 4 as shown in Fig. 14. The performance of a VAWT

rotor is strongly dependent on the blade Reynolds number as illustrated in Fig. 14
which serves to show that as the physical scale of a turbine is reduced so the
maximum coeffi cient of performance decreases and the same is true of the range
of tip speed ratios over which the turbine performs effectively. It could be said that
VAWTs are particularly susceptible to reduction of C p at low Reynolds numbers,
since a lower Reynolds number limits the maximum lift coeffi cient that can be
achieved with increasing angle of attack prior to stall. Thus, the effect of Reynolds
number on the performance of small turbines may be more important for VAWTs
as compared to HAWTs. It can also be seen that the thickness of the aerofoil has
some infl uence on the C p versus l characteristic of the turbine (the NACA0012
aerofoil having a maximum thickness of 12% of the blade chord as opposed to
18% for the NACA0018).
The performance estimates from the double-multiple-streamtube methodol-
ogy presented here do not account for a number of effects that may signifi cantly
reduce the output from a VAWT in practice. Parasitic drag loss is one of the key
parameters that should be modelled by the designer of a VAWT. The loss of net
power output due to the presence of components such as the radial arms on
which the blades of a straight-bladed VAWT are mounted may be signifi cant.
Modelling such losses using a momentum model is relatively straightforward as
the drag coeffi cients for beams and streamlined spars are well known [47]. These
losses become increasingly important as the physical scale of the turbine is
reduced. In addition, care should be taken in the interpretation of results from
multiple-streamtube momentum models, particularly at high tip speed ratios,
where large induction factors may be calculated which in turn lead to unrealistic
wake velocity results.

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