Aerodynamic calculation of loads and dynamic behavior of wind ...

axis normal to the rotor plane and parallel to the direction of the wind movement. As
the air is passing through the rotating disk, in order to resist the consequent change to
its initial condition, it exerts an angular force to the rotor, in a direction opposite to
that of the rotation of the disk. This reaction counteracts the torque exerted by the
rotor to the air, keeping the rotational speed constant. The work done by the
aerodynamic torque on the generator is converted into electrical energy. On the other
hand, the above-mentioned reaction causes, as an aftereffect, the air particles to gain
angular momentum and thus to have both a tangential as well as an axial velocity
component. This results to an increase of the kinetic energy, compensated by an
abrupt drop of the static pressure, right behind the actuator disk, additional to that
described in the previous section. The change of the tangential velocity from zero to
its highest value, takes place entirely in inside the thickness of the disk. In order to
determine the amount of such a speed increase, another factor has to be introduced;
the “tangential induction factor”, symbolized by a’. With this parameter’s help, we
can follow the gradual increase of the tangential velocity: at the middle of the disk
thickness and at a radial distance r from the axis of rotation, the induced tangential
velocity is Ωra’, while, immediately downstream, it changes to 2Ωra’.
Figure 3.5: The trajectory of an air particle passing through the rotor disk
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