Reference Frames in Bladed

Reference frames are used in Bladed for describing both simulation inputs and outputs.

A reference frame comprises an origin \(O_f\) representing a point \((0,0,0)\) within that frame. A reference frame is also characterised by three orthogonal axes \((X_f,Y_f,Z_f)\) connected at the origin. Unless stated otherwise, all reference frames follow the right hand rule.

Sometimes it is convenient to use two axes in a reference frame to define a plane. For example the axes \(X_f\) and \(Y_f\) would define a plane normal to the \(Z_f\) axis.

Reference frame may also be shortened to frame. A reference frame can also be referred to as a coordinate system.

Global Frame

A single global reference frame is defined in Bladed. The global frame is an inertial frame and so fixed in space and time throughout all calculations. The global frame is used to define the turbine structure and environmental conditions such as wind and wave.

The global reference frame origin is denoted \(O_G\) and the orthogonal axes denoted \((X_G, Y_G, Z_G)\). The axis \(Z_G\) is positive upwards.

For onshore simulation the undisturbed ground corresponds to the plane spanned by \(X_G\) and \(Y_G\) defined by \(Z_G = 0\). For offshore the same plane corresponds to the mean sea level.

The global reference frame can be shortened to global frame. The global frame is sometimes referred to as the inertial frame.

Body-Fixed Frame

A wind turbine in Bladed is built from multiple components using a multibody structural dynamics approach. The $i$th component has an associated body-fixed frame denoted \((x_{b,i},y_{b,i},z_{b,i})\). A body-fixed frame can translate and rotate with respect to the global frame. These motions define the rigid body motions of a component. Figure 1 shows a series of components with body-fixed frames defined in the global frame. A mean wind direction is also defined in the global frame enabling the computation of wind loading on the wind turbine structure during simulation.

The turbine assembly model describes how the various turbine components interconnect to form the complete wind turbine structure.

Figure 1: Illustration of the global frame. A series of body-fixed frames of select turbine components are defined relative to the global frame. Environmental conditions are also defined relative to the global frame such as the mean wind direction and upflow angle represented here by the vector \(V\).

Distal Frame

A component may have one or more distal frames. A distal frame is defined relative to the component body-fixed frame. The distal frame determines the orientation of the body-fixed frame of subsequent (child) components connected in the turbine assembly. The properties of the component will determine the orientation of the distal frame. These properties include it's dimensions, whether the body deflects, and any rotational or sliding joints. Examples of how the distal frame depends on the component properties is illustrated in Figure 2. A summary of examples of physical components and their properties is provided below:

• A tower component simulated using a single fore-aft attachment mode. The tower has an undeflected height represented by the vector \(\bvector{u}\) between the tower body-fixed origin and distal frame origin. When the mode shape deflects the distal frame origin will translate by the strain \(e_1\) and the frame rotates by some angular strain \(e_2\).
• A turbine hub component that connects to multiple blades. This component has multiple distal frames. These may be offset from the body-fixed origin by rigid offsets \(\bvector{u_1}\) and \(\bvector{u_2}\). In this instance the rigid offset include both translational and rotational offsets as well.
• A turbine bearing component. A bearing may have a rigid offset \(\bvector{u}\) and also a single rotational degree of freedom.

Figure 2: A series of examples demonstrating how the distal frame will depend on the properties of a component: (a) tower component, (b) hub component and (c) a bearing.