Development and analysis of vertical-axis wind turbines - Wind Power Generation and Wind Turbine Design - page 298

angle of attack on a VAWT blade of the order of 3° for l = 3.5 and c / R = 0.2. Flow
curvature has the effect of increasing the normal force on the blades on the upstream
half of the actuator cylinder and decreasing this force on the downstream half [23].
The second important issue is what is commonly known as “dynamic stall”.
This complex transient phenomenon arises because of the rapidly changing angle
of attack on a VAWT blade. At low tip speed ratios a hysteresis effect arises
whereby stall occurs at higher angles of attack, a , than for steady-state fl ow (when

a is increasing). Subsequent reattachment of the fl ow is also delayed for decreas-

ing . A number of empirical and theoretical models have been developed by authors

such as Allet et al. [ 39 ], Oler et al. [48], Major and Paraschivoiu [49] and Liu et al .
[50]. These models may be incorporated into a double-multiple-streamtube analysis
to improve the modelling of the transient effects of stall and also into more complex
vortex models such as the Sandia codes [51] . More recently Ferreira et al. [ 52 ] have
reported on a detailed fl ow visualisation study of the dynamic stall phenomenon.

a

3.1.4 Application and limitations of the double-multiple-streamtube method
The double-multiple-streamtube analysis described above is relatively straight-
forward and can provide quantitative results that are useful for optimisation of
VAWT geometry in terms of fundamental parameters such as: operating tip speed
ratio, blade profi le, rotor solidity and aspect ratio. The model may also be used to
estimate the forces on the blades which can then form the input to structural analy-
sis and optimisation of the rotor. The accuracy of the double-multiple-streamtube
model is comparable to that of more complex analysis methods. Sharpe [23],
for example, showed that his prediction of C p,max for the Sandia 17-m diameter
Darrieus turbine was within a few percent of the experimental results reported by
Worstell [53]. Wilson [24] presents a comparison of the results from a number of
double-multiple-streamtube analyses with the experimental data of Worstell [53]
and very good agreement is seen for tip speed ratios, l > 3.
It should be noted that care must be taken in the application of the momentum
analysis methodology. In particular, it is possible for high induction factors to be
predicted for VAWTs operating at high tip speed ratios which may lead to unreal-
istic wake fl ows. Corrections for some other fl ow phenomena not dealt with above,
such as tip losses, can also be incorporated in the double-multiple-streamtube
methodology.

3.2 Other methods of VAWT analysis

Inviscid fl ow models have been used by many of the key researchers in the fi eld
of VAWT analysis in years past and this approach has been summarised in the key
overview article by Wilson [24]. While fi xed wake models are relatively straight-
forward to implement, free vortex simulations are extremely complex and costly in
terms of computer processing time. Nevertheless the free vortex model methodol-
ogy is accepted to be the most comprehensive and accurate method of modelling
VAWTs [51]. This methodology has also been recently applied to the analysis of
vertical-axis marine current turbine by Li and Calisal [54]. CFD codes have now