Vertical axis wind turbine



Vertical-axis wind turbines (VAWT) are a type of wind turbine where the main rotor shaft runs vertically. Among the advantages of this arrangement are that generators and gearboxes can be placed close to the ground, and that VAWT do not need to be pointed into the wind. Major drawbacks for the early designs (savonius, darrieus, giromill and cycloturbine) included the pulsatory torque that can be produced during each revolution and the huge bending moments on the blades. Later designs like turby, quietrevolution and aerotecture solved the torque issue by using the helical twist of the blades, similar to Gorlov's water turbines.

Drag-type VAWT, such as the Savonius rotor, typically operate at lower tipspeed ratios than lift-based VAWT such as Darrieus rotors and cycloturbines.

General Aerodynamics
The forces and the velocities acting in a Darrieus turbine are depicted in figure 1. The resultant velocity vector, $$\vec{W}$$, is the vectorial sum of the undisturbed upstream air velocity, $$\vec{U}$$, and the velocity vector of the advancing blade, $$-\vec{\omega }\times\vec{R}$$.

$$\vec{W}=\vec{U}+\left( -\vec{\omega }\times\vec{R} \right)$$

Thus, the oncoming fluid velocity varies, the maximum is found for $$\theta =0{}^\circ $$ and the minimum is found for $$\theta =180{}^\circ $$, where $$\theta $$ is the azimuthal or orbital blade position. The angle of attack, $$\alpha $$, 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:

$$W=U\sqrt{1+2\lambda \cos \theta +\lambda ^{2}}$$

$$\alpha =\tan ^{-1}\left( \frac{\sin \theta }{\cos \theta +\lambda } \right)$$

where $$\lambda =\frac{\omega R}{U}$$ is the tip speed ratio parameter.

The resultant aerodynamic force is decomposed either in lift (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 normalized by the dynamic pressure of the relative airflow, while the normal and the tangential coefficients are usually normalized by the dynamic pressure of undisturbed upstream fluid velocity.

$$C_{L}=\frac{L}{{1}/{2}\;\rho SW^{2}}\text{    };\text{     }C_{D}=\frac{D}{{1}/{2}\;\rho SW^{2}}\text{      };\text{      }C_{T}=\frac{T}{{1}/{2}\;\rho SU^{2}}\text{      };\text{     }C_{N}=\frac{N}{{1}/{2}\;\rho SU^{2}}$$