Vertical Axis Wind Turbine

For vertical-axis wind turbines, the blade element/moment (BEM) method is implemented as a double-multiple streamtube (DMS) calculation. The conservation of momentum and local aerodynamic coefficients on the airfoils are considered on the upwind and downwind parts of the rotor.

The conservation of momentum is used to find the induced velocity at the swept surface. For a DMS momentum balance, each swept surface element on the upwind side is associated with its mirror element across the (\(Y_r,Z_r\)) plane. The flow which leaves the upwind element is assumed to impinge on the downstream element. That means that the incoming flow at the downstream element (\(V_m\)) is taken to be

where \(V_0\) is the undisturbed incoming flow at the upwind element, and \(V_i\) is the induced velocity at the upwind element.

Double multiple streamtube:
image::DoubleMultipleStreamTube.png[image]

In practice, ghost elements are introduced in order to calculate the appropriate force at each surface element. In this way, the force associated with each surface element is updated smoothly, and the dynamic stall forces are updated for the real blade elements.

Momentum balance calculations for horizontal axis wind turbines include a correction for the fact that the lift on a blade of finite span goes to zero at the tips. This correction is known as the Prandtl correction. In the present implementation, the user can choose between allowing the code to compute the Prandtl factor (recommended for H-type rotors) or inputing a Prandtl factor (recommended 1.0 for Darrieus rotors).

Dynamic inflow acts as a time lag in the induced velocity computed by the described DMS-BEM method. In the implemented aerodynamic model, the Stig Øye dynamic inflow model is applied. This is the same model as implemented for horizontal axis wind turbines in SIMO.

Airfoil forces are computed by first looking up coefficients from an input table, as a function of Reynolds number \(Re\) and the instantaneous angle-of-attack \(\alpha\), and then correcting the coefficients for dynamic stall. Interpolating coefficients from the input table is the most computationally-intensive part of the DMS-BEM calculation.

The basic features of dynamic stall can be understood in terms of a time-delay on the motion of the separation point with respect to the instantaneous angle-of-attack. As a vertical-axis wind turbine rotates, the blade retreats from the wind over part of the cycle. When the windspeed is high, the angle-of-attack shifts rapidly from a large negative value to a large positive value, over a timescale that is comparable to the time lag in the dynamic stall equation; therefore dynamic stall is relevant. However, the dynamic stall equations are not well-defined when the angle of attack and separation point position parameter are of opposite sign. Special logic is included to handle this situation.

The rotor body and the support body may be connected by use of

Note that the applied electrical torque is handled by MOMENT COUPLING. Thus, no constant moment should be specified for the coupling. Any specified torsional stiffness will be set to zero during dynamic analysis.

The blade input is given for one blade, which is assumed to initially be in the body +x direction. Additional blades are equally distributed around the body +z axis.

Vertical axis wind turbine geometrical input (side views of one blade):
image::VerticalAxisWindTurbineGeometrical.png[image]

The implemented generator torque control system includes start-up logic as well as operational logic. A P-I controller for the generator torque is applied to achieve the desired rotor speed.

During the start-up period, the reference rotor speed is based on the rotor speed and the current time. The integral control parameter starts with a large value and is relaxed to the operational value after the start-up period.

After the start-up period, the reference rotor speed is based on the low-pass filtered wind speed.