358
10 Wind Turbines
speed, these blade parts cyclically enter in stall. The velocity triangles in Fig. 10.6
demonstrate that, at maximum lift ( α ≈ 12.5°), the ratio of the blade speed on the
equator to the local wind speed is about 4.5. With the deceleration of the wind
at the turbine, the speed ratio based on the free wind speed is about 3. VAWTs
thus typically run much slower than HAWTs. Power limitation with wind speeds
exceeding the rated value cannot be realised adequately with a VAWT. There is
a spontaneous mechanism of progressive stall with the troposkin shape, but it is
impossible to limit the power to an approximate constant value as with a stallcontrolled HAWT. A straight-blade VAWT cannot be limited in power by simple
means. Machines with adjustable blade slope have been proposed, enabling decrease of the through-flow area, but these are mechanically vulnerable. Due to the
lower power coefficient and the intrinsic difficulty of power limitation, VAWT
types are only applied for small power.
10.3 Wind Turbine Performance Analysis
10.3.1 Momentum Analysis (Single Streamtube Analysis)
The simplest flow model represents the rotor of a horizontal-axis wind turbine as a
disc with uniform distribution of flow parameters just upstream and just downstream
of the rotor. This is called an actuator disc. A streamtube though the rotor is
considered with flow parameters which only change in the direction perpendicular
to the disc, so that the flow is rendered one-dimensionally. Swirl behind the turbine
and losses in the flow are neglected. Figure 10.8 sketches the flow through the
turbine.
Far upstream of the turbine, wind velocity is v 0 . and pressure is p 0 . The flow is
retarded by the disc, so that the velocity v 1 just upstream of the rotor is lower than v 0
and consequently pressure p 1 is higher than p 0 . Just downstream of the turbine, velocity v 2 equals velocity v 1 (continuity), but pressure p 2 is lower than p 1 . Thus, the
Fig. 10.8 One-dimensional
streamtube through a
horizontal-axis wind turbine
10 Wind Turbines
speed, these blade parts cyclically enter in stall. The velocity triangles in Fig. 10.6
demonstrate that, at maximum lift ( α ≈ 12.5°), the ratio of the blade speed on the
equator to the local wind speed is about 4.5. With the deceleration of the wind
at the turbine, the speed ratio based on the free wind speed is about 3. VAWTs
thus typically run much slower than HAWTs. Power limitation with wind speeds
exceeding the rated value cannot be realised adequately with a VAWT. There is
a spontaneous mechanism of progressive stall with the troposkin shape, but it is
impossible to limit the power to an approximate constant value as with a stallcontrolled HAWT. A straight-blade VAWT cannot be limited in power by simple
means. Machines with adjustable blade slope have been proposed, enabling decrease of the through-flow area, but these are mechanically vulnerable. Due to the
lower power coefficient and the intrinsic difficulty of power limitation, VAWT
types are only applied for small power.
10.3 Wind Turbine Performance Analysis
10.3.1 Momentum Analysis (Single Streamtube Analysis)
The simplest flow model represents the rotor of a horizontal-axis wind turbine as a
disc with uniform distribution of flow parameters just upstream and just downstream
of the rotor. This is called an actuator disc. A streamtube though the rotor is
considered with flow parameters which only change in the direction perpendicular
to the disc, so that the flow is rendered one-dimensionally. Swirl behind the turbine
and losses in the flow are neglected. Figure 10.8 sketches the flow through the
turbine.
Far upstream of the turbine, wind velocity is v 0 . and pressure is p 0 . The flow is
retarded by the disc, so that the velocity v 1 just upstream of the rotor is lower than v 0
and consequently pressure p 1 is higher than p 0 . Just downstream of the turbine, velocity v 2 equals velocity v 1 (continuity), but pressure p 2 is lower than p 1 . Thus, the
Fig. 10.8 One-dimensional
streamtube through a
horizontal-axis wind turbine