Aerodynamic Outputs

The outputs of the aerodynamic performance and loading calculations in Bladed are explained. To understand the outputs, the definitions of the rotor axial/tangential direction are defined in the figures below. Note that “axial” indicates in direction of vector \(n\) normal to the rotor plane and tangential indicates in the direction of tangent vector \(t\). Further note that the radial vector \(r\) assumes an un-coned rotor. These do not change with respect to blade pitch angle.

Table 1 lists all the aerodynamic outputs with descriptions and the output coordinate system used. The relevant coordinate systems include the blade coordinate system shown in Figure 1 and the aerofoil coordinate system shown in Figure 2.

Figure 1: Geometry of rotor including rotor coordinate system \((x_R, y_R, z_R)\) and blade coordinate system defined using the vectors \(r\), \(n\) and \(t\). The vectors \(r\), \(n\) and \(t\) do not change with respect to blade pitch angle.

Figure 2: Aerofoil section with velocities and aerodynamic loads. The blade is pointing out of the paper and moves towards the right, while the flow is coming from below. Applies to the clockwise upwind turbine case.

Table 1: Aerodynamic outputs in Bladed

Variable name	Explanation	Coordinate system
Axial induction factor	Velocity induced by rotor in axial direction normalised by the free stream flow speed	Blade Figure 1 |
Tangential induction factor	Velocity induced by rotor in tangential direction normalised by rotational speed times local radius	Blade Figure 1
Axial induced velocity	Velocity induced by rotor in axial (normal) direction	Blade Figure 1
Tangential induced velocity	Velocity induced by rotor in tangential direction	Blade Figure 1
Tip/hub loss factor	Magnitude of tip/hub loss factor	Not applicable
Inflow angle	Angle between effective flow speed velocity vector and tangential direction of rotor plane (\(\phi\) in the figure)	Aerofoil Figure 2
Angle of attack	Angle between effective flow speed vector and local chord line (\(\alpha\) in the figure) expressed at the quarter chord point	Aerofoil Figure 2
Angle of attack rate of change	Time derivative of angle of attack expressed at the quarter chord point	Aerofoil Figure 2
Reynolds number	Reynolds number computed at the blade section	Not applicable
Lift coefficient	Dynamic lift coefficient including the dynamic stall effects (if being activated) – defined at the quarter chord point	Not applicable
Drag coefficient	Dynamic drag coefficient including the dynamic stall effects (if being activated) – defined at the quarter chord point	Not applicable
Pitching moment coefficient 1	Dynamic pitching moment coefficient including the dynamic stall effects (if being activated) – defined at the quarter chord point	Not applicable
Incident axial wind speed	Axial component of the incident wind velocity vector	Blade Figure 1
Incident tangential wind speed	Tangential component of the incident wind velocity vector	Blade Figure 1
Relative normal to chord wind speed	Normal to chord component perpendicular to the chord line of the relative wind velocity vector including effect of induction	Aerofoil Figure 2
Relative chordwise wind speed	Chordwise component of the relative wind velocity vector including effect of induction	Aerofoil Figure 2
Relative wind speed	Relative wind speed including effect of induction	Aerofoil Figure 2
Axial aerodynamic force	Axial component of aerodynamic load per unit length	Blade Figure 1
Tangential aerodynamic force	Tangential component of aerodynamic load per unit length	Blade Figure 1
Aerodynamic twisting moment	Aerodynamic moment about the elastic axis per unit length. Orientation of moment axis is in direction of unit vector “r“	Blade Figure 1
Chordwise Aerodynamic force	Aerodynamic force in direction of the chord line	Aerofoil Figure 2
Normal to chord aerodynamic force	Aerodynamic force perpendicular to the chord line	Aerofoil Figure 2

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1. Bladed will convert the pitching moment coefficient \(C_m\) such that it is defined at the quarter chord point regardless of how it was defined in the input. The output of pitching coefficient will not correspond to the original aerofoil chordwise origin for forces and moments defined by the user in the aerodynamic polar input panel \(C_m^{XA}\). Bladed applies the following transformation to convert the input \(C_m^{XA}\) to \(C_m\) used for computation:

   \[ \begin{equation} C_m = C_m^{XA} + C_l (0.25 – Xa) \cos \alpha + C_d (0.25 – Xa) \sin \alpha \end{equation} \]

   with \(C_l\), \(C_d\), \(XA\) and \(\alpha\) specifying the lift coefficient, drag coefficient, the aerofoil chordwise origin for forces and moments and the angle of attack, respectively.↩