Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 51

The mechanism described above accounts for the extraction of kinetic energy but in no way explains what happens to that energy: it may well be put to useful work, but some may be spilled back into the wind as turbulence and eventually be dissipated as heat.

Nevertheless, we can begin an analysis of the aerodynamic behaviour of wind turbines without any specific turbine design just by considering the energy extraction process. The general device that carries out this task is called an actuator disc; see Figure 3.2.

Upstream of the disc, the streamtube has a cross‐sectional area smaller than that of the disc and an area larger than the disc downstream. The expansion of the streamtube is because the mass flow rate must be the same everywhere. The mass of air that passes through a given cross‐section of the streamtube in a unit length of time is ρ AU, where ρ is the air density, A is the cross‐sectional area, and U is the flow velocity. The mass flow rate must be the same everywhere along the streamtube, and so

(3.1)

The symbol ∞ refers to conditions far upstream, D refers to conditions at the disc, and W refers to conditions in the far wake.

It is usual to consider that the actuator disc induces a velocity variation that must be superimposed on the free‐stream velocity. The streamwise component of this induced flow at the disc is given by −aU_∞, where a is called the axial flow induction factor, or the inflow factor. At the disc, therefore, the net streamwise velocity is

(3.2)

Figure 3.2 An energy extracting actuator disc and streamtube.