Blade Section Mass
To accurately model the dynamic behavior of rotor blades, it is essential to define their mass and inertia distribution. This is primarily done in the Blades screen under the Mass and Stiffness tab by enabling the Mass checkbox. Additional options are available to model point masses and blade icing:
Additional Mass/InertiaIce on blades
It is also possible to define blade Imbalances and Vibration Dampers, which add to the total blade mass.
Blade Mass and Inertia Distribution
The following table provides an overview of the inputs required to define the blade sectional mass distribution at each blade station.
| Property | Description | Unit |
|---|---|---|
Mass/unit length |
Mass per unit length at each station along the blade. | \(\bunit{kg/m}\) |
Polar mass moment of inertia/unit length |
The inertial resistance to motion around the principal inertia z-axis. | \(\bunit{kg m}\) |
Radii of gyration ratio |
Ratio of radii of gyration in the principal inertia y- and x-axis directions. See Equation \(\eqref{eq:radiiofgyrationratio}\). | \(\bunit{-}\) |
Radii of Gyration Ratio
If the Radii of gyration ratio is not specified, it defaults to the relative profile thickness given by ratio of Thickness to Chord, but it can be defined explicitly by un-checking the Use default radii of gyration ratio checkbox.
It can be calculated with the following equation:
where
\(r_x\) is the radius of gyration in the principal inertia x-axis direction,
\(r_y\) is the radius of gyration in the principal inertia y-axis direction,
\(\mu\) is the Mass/unit length,
\(I_{x_{i}}\) is the is the mass moment of inertia in the principal inertia x-axis direction,
\(I_{y_{i}}\) is the is the mass moment of inertia in the principal inertia y-axis direction.
Point Masses
If additional point masses are required at specific locations along the blade, click the Additional Mass/Inertia tab and enter the point masses in the table.
Additional pitching inertia should also be specified on this screen.
Click the Add button to add each point mass, and then enter the data required by clicking on the appropriate entry.
Note that masses are automatically sorted by radial position.
To remove a mass, highlight it by clicking on its number, and click Delete.
For each point mass, the following data is required:
| Property | Description | Unit |
|---|---|---|
Mass |
The mass required. | \(\bunit{kg}\) |
Distance along blade |
Position of the mass along the blade, measured from the blade root. | \(\bunit{m}\) |
Chordwise position (x') |
Position of the mass perpendicular to the chord as a percentage of the chord. | \(\bunit{\%}\) |
Chordwise position (y') |
Chordwise position of the mass, measured backwards from the leading edge as a percentage of the chord. | \(\bunit{\%}\) |
The figure below demonstrates how the point masses are positioned relative to the leading edge of the blade.
Blade Icing
Bladed represents blade ice accretion by adding mass to the blade at the aerofoil leading edge. It is defined in the Blades screen under the Blade Information tab.
This additional mass will modify the blade mass totals and mass distribution properties such as Polar mass moment of inertia/unit length and the location of the Mass centre.
There are two available methods for the calculation of ice mass on the turbine blades.
- Germanischer Lloyd (GL, 2010)
- IEC 61400-1 edition 4 standard.
For both ice models, the radial distance from the rotor axis is assumed to be a nominal radius i.e. ignoring the effect of rotor cone, blade prebend and blade root mounting angle.
The GL 2010 rotor radius \(R\) is always half of the Nominal rotor diameter as shown in the Turbine and Rotor screen found in under the Rotor screen in the Bladed GUI.
Each blade station radial position \(r\) can be calculated using the blade root length added to the blade station Distance along blade root Z-axis at each blade station.
Note
The change in mass due to blade icing is not reflected in the Turbine Information screen accessed when clicking the Mass totals....
Instead, the mass distribution and blade mass with ice are provided in the verification file .$VE output when simulations are run.
Ice accretion can also modify the aerodynamic properties of aerofoils. No modification is applied to the aerofoil data that has been input into Bladed. If design standards require these modifications to be made then it is recommended that the user applies these corrections manually to the aerofoil input data.
GL 2010 Method
The methodology used for the GL 2010 approach is as follows. The mass distribution increases linearly from zero at the rotor axis to the value \(\mu_{e}\) at half the radius and then remains constant up the blade tip. The value \(\mu_{e}\) is calculated as follows:
where
\(R\) is the rotor radius in \(\bunit{m}\),
\(c_{\max}\) is the maximum chord in \(\bunit{m}\),
\(c_{\min}\) is tip chord in \(\bunit{m}\),
\(\rho\) is the ice density with default value \(700 \bunit{kg/m^3}\).
The chord length at the blade tip is an input in Bladed. The maximum chord value is computed using the values from the Blade Geometry information input by the user.
IEC Ed 4 Method
The methodology used for the IEC Ed 4 is to apply a mass distribution that increases linearly from zero at the rotor axis to the maximum value at the blade tip. The ice mass distribution is calculated using:
where
\(M(r)\) is the mass distribution on the leading edge of the rotor blade in \(\bunit{kg/m}\),
\(\rho\) is a constant parameter with default value of \(0.125 \bunit{kg/m^3}\),
\(C_{85}\) is the chord length at 85% rotor radius in \(\bunit{m}\),
\(r\) is the radial position measured from the rotor axis in \(\bunit{m}\).
The parameter \(C_{85}\) is calculated by Bladed based on the geometry information input by the user.
Last updated 13-12-2024