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Turbine data: Blade profile |
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Turbine data: Blade profile |
The geometric and structural properties of a blade are represented by the blade profile data. These profiles are defined at a number of discrete arc lengths along the blade length and are completely independent of the way the length is divided into sections and segments. There is a large number of properties to be defined in this way, so they are split into separate tables of geometry, inertia and structure data, with the arc lengths at which the profiles are defined being specified in the geometry table.
The figures below shows the relationships between the frames of reference for each of the tables. The $z$-axis direction is the same for all these frames and is perpendicular to the plane of the profile: we refer to this as the blade $z$-axis direction at that arc length.
You should give data for a complete range of arc lengths, covering the full length of the blade and at a resolution sufficiently fine to capture the variation of these properties along the length. The OrcaFlex calculation requires the values of these properties for each segment: these are obtained at the mid-segment arc length by linear interpolation, on arc length, of the profile data.
| Figure: | Blade profile frames of reference for clockwise rotation sense |
Most conventional turbines have a clockwise rotation sense and the above figure applies. If the turbine has an anticlockwise rotation sense, then the blade profile date is interpreted as shown in the below figure.
| Figure: | Blade profile frames of reference for anticlockwise rotation sense |
Blade profile data centres (e.g. shear centre, aerodynamic centre, neutral axis) are specified relative and with respect to the geometry frame. The geometry frame is located at the leading edge. Its $x$-axis points towards the suction side of the blade. Its $y$-axis points from the leading edge to the trailing edge. As such, if the turbine has anticlockwise rotation sense it forms a left-handed coordinate system, contrary to the usual OrcaFlex convention. The geometry frame is also used in the aerodynamic calculation to determine the angle of attack.
The blade profile geometry data are required by OrcaFlex in all cases. They characterise the physical extent of the profile and, together with the section wing type, parameterise the aerodynamic calculation.
The cumulative twist of the geometry frame relative to the blade root (i.e. excluding any blade pitch).
For a conventional turbine, with clockwise rotation sense, positive twist rotates the geometry frame anticlockwise, looking from root to tip, about the blade $z$-axis. For a turbine with anticlockwise rotation sense, positive twist rotates the geometry frame clockwise, looking from root to tip, about the blade $z$-axis.
| Note: | For a turbine with clockwise rotation sense, the sign convention for aerodynamic twist, for which a positive value defines an anticlockwise rotation about the blade $z$-axis, looking from root to tip, is contrary to the usual OrcaFlex convention. |
The chord length of the profile, as shown in the figure above. This value is used as a reference scale for other geometric data.
The maximum thickness of the profile, as a percentage of the chord.
The offset of the aerodynamic centre from the leading edge of the aerofoil. This is the point at which the relative velocity is calculated and at which the resulting wing lift force, drag force and pitching moment are applied. The $x$ and $y$ components are given, with respect to the geometry frame, as a percentage of the chord.
The linear mass density of the blade.
The radius of gyration about the blade $z$-axis through the centre of mass, as a percentage of the chord.
The ratio of the profile's radii of gyration about the inertia frame $y$ and $x$ axis directions. If the material density is constant over the cross section, then this ratio can be calculated \begin{equation} \sqrt \frac{I\urm{A,y}}{I\urm{A,x}} = \sqrt \frac{ \int \! \int x^2 \,\ud\! x \ud\! y }{ \int \! \int y^2 \,\ud\! x \ud\! y } \end{equation} If the material density varies over the cross section, then it should be included in the integrals \begin{equation} \sqrt \frac{ \int \! \int \rho(x,y) x^2 \,\ud\! x \ud\! y }{ \int \! \int \rho(x,y) y^2 \,\ud\! x \ud\! y } \end{equation} If ~ is given, then it is approximated as the ratio of thickness to chord length.
The offset of the centre of mass relative to the leading edge of the aerofoil. This is the point at which the weight and inertia act. The $x$ and $y$ components are given, with respect to the geometry frame, as a percentage of the chord.
The cumulative twist of the inertia frame relative to the blade root. The inertia frame defines the directions of the principal axes of the inertia tensor.If it is '~', the inertia twist is assumed to be equal to the aerodynamic twist.
For a conventional turbine, with clockwise rotation sense, positive twist rotates the inertia frame anticlockwise, looking from root to tip, about the blade $z$-axis. For a turbine with anticlockwise rotation sense, positive twist rotates the inertia frame clockwise, looking from root to tip, about the blade $z$-axis.
| Note: | For a turbine with clockwise rotation sense, the sign convention for inertia twist, for which a positive value defines an anticlockwise rotation about the blade $z$-axis, looking from root to tip, is contrary to the usual OrcaFlex convention. |
The bend stiffness of the blade, relating bend moment to curvature. The components of EI are defined with respect to the structural frame. Only used if the blade has free degrees of freedom.
The axial stiffness of the blade, i.e. the constant that relates tension to strain. Only used if the blade has free degrees of freedom.
The torsional stiffness of the blade, i.e. the constant that relates torque to twist per unit length. Only used if the blade has free degrees of freedom.
Pre-bend is provided for modelling blades which are not straight in their unstressed state. To specify the pre-bend, you give the local curvature components, in radians per unit length. For a conventional turbine, with clockwise rotation sense, this is with respect to a frame equivalent to the structural frame but excluding any structural twist. For a rotor with anticlockwise rotation sense, the curvature is with respect to the same frame, but the $x$-component is applied using an anticlockwise rotation. For example, for a blade without pitch at the root, to pre-bend out of the rotor plane and away from the tower, irrespective of any blade twist, one would specify a negative value for the curvature about the $y$-axis. To pre-bend the blade, such that the tip moves in the nominal direction of rotation, one would specify a positive value for the curvature about the $x$-axis. This applies irrespective of rotation sense.
| Note: | When pre-bend is used, curvature results are reported relative to the pre-bent curvature. |
The offset of the neutral axis from the leading edge of the aerofoil. The $x$ and $y$ components are given, with respect to the geometry frame, as a percentage of the chord.
The offset of the shear centre from the leading edge of the aerofoil. The $x$ and $y$ components are given, with respect to the geometry frame, as a percentage of the chord. It is the axis the structural frames are placed along, i.e. this axis passes through the segments and nodes of the finite element model. If it is '~', the shear centre component is assumed to be equal to the corresponding neutral axis component, i.e. if both components are '~', the shear centre is located on the neutral axis. If the shear centre is offset from the neutral axis, then a coupling is introduced that allows axial strain to induce bending moment, and allows curvature to induce tension.
The cumulative twist of the structural frame relative to the blade root. The stiffness data are defined with respect to the structural frame. If it is '~', the structural twist is assumed to be equal to the aerodynamic twist.
For a conventional turbine, with clockwise rotation sense, positive twist rotates the structural frame anticlockwise, looking from root to tip, about the blade $z$-axis. For a turbine with anticlockwise rotation sense, positive twist rotates the structural frame clockwise, looking from root to tip, about the blade $z$-axis.
| Note: | For a turbine with clockwise rotation sense, the sign convention for structural twist, for which a positive value defines an anticlockwise rotation about the blade $z$-axis, looking from root to tip, is contrary to the usual OrcaFlex convention. |
