Vertical Axis Wind Turbine - General Aerodynamics

General Aerodynamics

The forces and the velocities acting in a Darrieus turbine are depicted in figure 1. The resultant velocity vector, is the vectorial sum of the undisturbed upstream air velocity, and the velocity vector of the advancing blade, .

Thus, the oncoming fluid velocity varies, the maximum is found for and the minimum is found for, where is the azimuthal or orbital blade position. The angle of attack, is the angle between the oncoming air speed, W, and the blade's chord. The resultant airflow creates a varying, positive angle of attack to the blade in the upstream zone of the machine, switching sign in the downstream zone of the machine.

From geometrical considerations, the resultant airspeed flow and the angle of attack are calculated as follows:

where is the tip speed ratio parameter.

The resultant aerodynamic force is decomposed either in lift (F_L) - drag (D) components or normal (N) - tangential (T) components. The forces are considered acting at 1/4 chord from the leading edge (by convention), the pitching moment is determined to resolve the aerodynamic forces. The aeronautical terms lift and drag are, strictly speaking, forces across and along the approaching net relative airflow respectively. The tangential force is acting along the blade's velocity and, thus, pulling the blade around, and the normal force is acting radially, and, thus, is acting against the bearings. The lift and the drag force are useful when dealing with the aerodynamic behaviour around each blade, i.e. dynamic stall, boundary layer, etc.; while when dealing with global performance, fatigue loads, etc., it is more convenient to have a normal-tangential frame. The lift and the drag coefficients are usually normalised by the dynamic pressure of the relative airflow, while the normal and the tangential coefficients are usually normalised by the dynamic pressure of undisturbed upstream fluid velocity.

A = Surface Area

The amount of power, P, that can be absorbed by a wind turbine.

Where is the power coefficient, is the density of the air, is the swept area of the turbine, and is the wind speed.