Turbines

Turbines are used to model horizontal axis wind turbines. The OrcaFlex turbine object comprises dedicated models for the generator, gearbox, hub and blades. Blade pitch and generator torque/motion control are supported through external functions. Blades can be represented as rigid objects, or allowed to be flexible to capture aeroelastic coupling effects. The blade structural model is analogous to that for lines.

Aerodynamic loading is calculated in OrcaFlex using a blade element momentum (BEM) method adapted from AeroDyn. Initially, we assume a quasi-steady BEM model, or equilibrium wake, in which the induction factors for each blade segment are recalculated every time step (or every iteration of the implicit solver), as a function of the instantaneous relative flow conditions. To capture the physics of dynamically varying flow conditions, the Øye dynamic inflow model can optionally be applied to the quasi-steady induction values and the González and Minnema Pierce models can be included to modify the steady aerofoil coefficients.

Axial and tangental induction (or axial alone) can be included in the BEM calculation; Prandtl tip loss and hub loss, and Pitt and Peters skewed wake correction, can all, independently, be enabled. The skewed-wake correction, if it is enabled, is decoupled from the induction factor calculation. The flow conditions can optionally account for the influence of a tower.

Defining a turbine

Figure: Turbine frames of reference

A turbine is a collection of component parts, and to define it we must set down their relative positions and orientations, their frames of reference. The turbine frame itself may be fixed or connected to a parent object, but cannot be free. Its position and attitude relative to its parent are explicitly specified. If the initial rotor angle is zero, the hub frame of reference is initially coincident with that of the turbine. Otherwise, the hub is initially rotated, about the turbine's $z$-axis, by the initial rotor angle. The hub and main rotor shaft rotate about the turbine's $z$-axis, with positive rotation defined to be clockwise about the positive turbine $z$-direction. Thus for a conventional turbine, operating without tilt or skew, the turbine $z$-axis would point in the same direction as the wind velocity.

When a child is connected to the turbine, the connection is either made to the hub frame or to a specific blade (more precisely, to the node structural frame at the specified arc length along the blade). So that child objects can distinguish between these connection points, they are represented by unique text strings in the user interface and API. Connections to the hub simply refer to the turbine name (in the same way as connections made to other objects); connections to specific blades refer to the name of the turbine appended with ' (blade #)', where # is the blade number.

Defining blades

Each blade has a fitting frame, the frame of reference which defines the position and orientation of its connection to the hub. The fitting frame, relative to the hub, is determined by the hub radius, pre-cone angle and blade count. The first blade's fitting frame, relative to the hub, is obtained as follows:

  1. initially, the two frames are coincident
  2. reorient the fitting frame so that the $x$ and $z$ axes are interchanged. This will reverse the direction of the $y$-axis
  3. translate the fitting frame origin by the hub radius in the fitting $z$-direction
  4. rotate the fitting frame through the pre-cone angle about the hub $y$-axis

This results in the $xz$-planes of the two frames coinciding and, for a conventional turbine, with clockwise rotation sense, the fitting $y$-axis pointing away from the direction of rotation (for a turbine with anticlockwise rotation sense, it points in the direction of rotation). The final position is illustrated in the figure above. The blade pitch angle then represents rotation of the blade root about the fitting $z$-axis.

A blade is divided into a number of sections. You define for each section its length, wing type, and the number of segments into which it should be further divided. (The structure of sections and segments follows that of lines). Each wing type has a table of aerodynamic coefficients, and these are applied to all sections using that wing type. The geometrical and structural properties of the blade are represented by the blade profile data, specified at a number of discrete arc lengths along the blade independently of the section data. These properties are determined, for an individual segment, by linear interpolation of this blade profile, evaluated at the mid-segment arc length.

The ends of a blade are referred to as end A and end B. End A is always at the blade root, i.e. where it meets the hub. End B is always at the blade tip.

All the blades of a given turbine have identical structure. You define the structure for a single blade, and OrcaFlex distributes them evenly around the hub according to the blade count.

Defining a tower

The turbine can, optionally, be associated with a tower, the presence of which modifies the wind field. This disturbed wind field represents the inflow in the turbine's aerodynamic calculation.

The tower is modelled as a profiled cylinder, which is free to change length but cannot undergo bending. The two ends of the tower are referred to as end A and end B. Each end can be fixed, or connected to another object, at a user specified position. In this way, each end follows the motion of its parent and the tower's centre line is simply the vector between them.

The tower associated with an OrcaFlex turbine has the sole purpose of influencing the wind field used in the turbine's aerodynamic calculation. Structural and aerodynamic properties of the tower itself are typically modelled by a line, in which case the ends of the turbine's tower are naturally connected to the respective ends of this line.

To calculate the tower's impact on the wind field, you must specify its: outer diameter; drag coefficient, in the case of the Bak tower influence model or either tower shadow model; and turbulence intensity, in the case of the Eames tower shadow model. This is done by specifying tower profiles, which relate these properties to the unstretched arc length along the tower. The arc length is the distance to a point on the tower's centre line measured from end A. These profiles are linearly interpolated, on arc length, to find the properties at any given point on the tower. In this way, the tower properties are a continuous function of tower arc length.