Environmental Engineering Reference
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models. Other bibliographic sources of information on analysis methods include
those of Abramovich [5] and Islam et al. [40]. An extremely useful and relatively
simple momentum model uses the actuator disc/blade element momentum theory
(or strip theory) in a similar manner to the momentum model used for analysis of
HAWTs. This type of analysis is outlined below and can be implemented relatively
easily by anyone with a basic knowledge of fl uid mechanics.
3.1 Double-multiple-streamtube analysis
The performance of a VAWT may be estimated using a momentum analysis at one
of a number of levels of complexity [24]. The simplest approach is where a single
streamtube is considered in which the interaction between the air fl ow and rotor
is treated as a single actuator disc located on the axis of the rotor, perpendicular
to the incident air fl ow. However, it is preferable to use a multiple-streamtube
analysis since the resultant air velocities and forces acting on the blades are strong
functions of the blade azimuth angle, b (Fig. 7). Strickland was one of the pioneers
of this approach [41]. However, to more accurately represent the fl ow through
the rotor, a VAWT may be represented as an “actuator cylinder”, whereby the
cylinder surface is swept by the length of the rotating blades as shown sche-
matically in Fig. 10. Air in the freestream interacts fi rst with the upstream half of
the cylinder and then the downstream half. A number of authors have described
this double-multiple-streamtube methodology including Paraschivoiu [42-44] and
Madsen [45]. Sharpe [23] in particular presented a very clear exposition of this
method and his approach is summarised in the following section.
Using a methodology analogous to the actuator disc/momentum analysis for a
HAWT one can defi ne two velocity induction factors, a u and a d , which defi ne the
deceleration of the local air velocity relative to the freestream velocity, U , on
the upstream and downstream faces of the cylinder, respectively. A number of
Rotor (actuator cylinder)
U w
U d
U a
U u
U
p
p d
+
p d
p
p u
+
p u
p
Figure 10: Plan view of a double-multiple-streamtube analysis of the fl ow through
a VAWT rotor, after Sharpe [23].
 
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