Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 57

The exertion of a torque on the rotor disc by the air passing through it requires an equal and opposite torque to be imposed upon the air. The consequence of the reaction torque is to cause the air to rotate in a direction opposite to that of the rotor; the air gains angular momentum, and so in the wake of the rotor disc the air particles have a velocity component in a direction that is tangential to the rotation as well as an axial component; see Figure 3.4.

The acquisition of the tangential component of velocity by the air means an increase in its kinetic energy that is compensated for by a fall in the static pressure of the air in the wake in addition to that which is described in the previous section.

The flow entering the actuator disc has no rotational motion at all. The flow exiting the disc does have rotation, and that rotation remains constant as the fluid progresses down the wake. The transfer of rotational motion to the air takes place entirely across the thickness of the disc (see Figure 3.5). The change in tangential velocity is expressed in terms of a tangential flow induction factor a^′. Upstream of the disc the tangential velocity is zero. Immediately downstream of the disc the tangential velocity is 2rΩa^′. In the plane of the disc the tangential velocity is rΩa^′ (see also Figure 3.10 and the associated discussion). Because it is produced in reaction to the torque, the tangential velocity is opposed to the motion of the rotor.

Figure 3.4 The trajectory of an air particle passing through the rotor disc.

Figure 3.5 Tangential velocity grows across the disc thickness.

An abrupt acquisition of tangential velocity cannot occur in practice and must be gradual. Figure 3.5 shows, for example, a sector of a rotor with multiple blades. The flow accelerates in the tangential direction through the ‘actuator disc’ as it is turned between the blades by the lift forces generated by their angle of attack to the incident flow.