Aerofoils
In this article we cover all topics regarding the definition of aerofoil data for each individual aerofoil, how to group them into libraries and into interpolated aerofoil sets. For information on how to assign the different types of aerofoil data (singular aerofoil or interpolated aerofoil set) to a blade section please refer to the Blade's aerodynamics properties article.
Aerofoil Data
Aerofoil data is presented by means of lookup tables of lift, drag and pitching moment coefficients tabulated against angle of attack. One such lookup table is referred to here as an Aerofoil dataset. Such tables are usually obtained for particular aerofoil sections at particular Reynolds numbers, for example in wind tunnel tests or by the use of computational fluid dynamics. Figure 1 displays an illustration of the aerodynamic coordinate system on the aerofoil section and the associated polar data used for typical wind turbine calculations.
The Aerofoil properties:
ChordwiseOriginForForcesAndMoments: (Optional) The fraction of the chord from the leading edge to the position about which Cl, Cd, and Cm have been calculated. This is traditionally 0.25 (25%), but can be any location so long as it is consistent with the provided aerodynamic data, see \(\bar{x}_{origin}\) in Figure 1. This is used to correct the location of the supplied forces and moment applying it at the origin of the QuarterChordCoordinateSystem. When this property is not defined, it is assumed that the forces and moments are applied at the origin of the QuarterChordCoordinateSystem and no correction is done.AerodynamicPerformance: The relationship between the angle of attack, and the lift, drag and pitch moment coefficients.Angle: The angle of attack for which the Cl, Cd, and Cm apply.Cl: The non-dimensional coefficient of liftCd: The non-dimensional coefficient of dragCm: The non-dimensional coefficient of pitching
ReynoldsNumber: The Reynolds number at which the aerodynamic properties were obtained.ThicknessToChordRatio: The ratio between the thickness and the chord length of the measured aerofoil.
During simulation, Bladed uses linear interpolation to lookup the lift, drag and pitching moment coefficient based on angle of attack 1. Nearest neighbour values in cases where the angle of attack is exceeded. The user should supply data for angles of attack ranging from -180° up to 180° as the full range will be needed for most calculations. The forces and moments obtained by the lookup table interpolation are displaced to the QuarterChordCoordinateSystem as defined in the AerodynamicProperties of each blade section.
Aerofoil Library
In the JSON each aerofoil has a user defined name and needs to be set inside the AerofoilLibrary. The AerofoilLibrary is a unique parameter inside the JSON, a single JSON file can only contain a single aerofoil library.
An example of an AerofoilLibrary is provided, where ... represents extra angles of attack within the dataset:
"AerofoilLibrary": {
"aerofoil_name_1": {
"ChordwiseOriginForForcesAndMoments": 0.316,
"AerodynamicPerformance": [
{
"Angle": -3.14159265358979,
"Cl": 0.0,
"Cd": 0.0844,
"Cm": 0.0
},
...
{
"Angle": 0.0,
"Cl": 0.4135,
"Cd": 0.0838,
"Cm": -0.0983
},
...
{
"Angle": 3.14159265358979,
"Cl": 0.0,
"Cd": 0.0844,
"Cm": 0.0
}
],
"ReynoldsNumber": 10000000.0,
"ThicknessToChordRatio": 0.5
},
...
"aerofoil_name_n": {
...
}
A single Aerofoil dataset from the aerofoil library can be directly assigned to an AerodynamicSection AerodynamicSection in the AerodynamicProperties. However this will ignore the Aerodynamic data ThicknessToChordRatio and ReynoldsNumber. An alternative is to assigned an InterpolatedAerofoilLibrary instead, whereas those variables will be taken into consideration before and during the simulation by the use of linear interpolation between different Aerofoil data sets.
Interpolated Aerofoil Library
An InterpolatedAerofoilLibrary is a set of aerofoils from the AerofoilLibrary bundled into a set to interpolated along the ThicknessToChordRatio and ReynoldsNumber. The names of the aerofoil sets in the InterpolatedAerofoilLibrary are user defined, just like the single aerofoils inside the AerofoilLibrary. In the same way as individual aerofoils these set can be assigned to an AerodynamicSection in the AerodynamicProperties of each blade section.
The following JSON snippet shows an example where all the available aerofoils for a whole blade are bundled together as a lookup matrix, and an example where two aerofoils with different relative thickness are interpolated between themselves and in Reynolds:
"InterpolatedAerofoilLibrary": {
"interpolated_aerofoil_set_whole_blade":[
"Cylinder",
"aerofoil_36pc",
"aerofoil_21pc",
"aerofoil_18pc"
],
"interpolated_aerofoil_set_reynolds_example": [
"aerofoil_18pc_reynolds_9M",
"aerofoil_18pc_reynolds_6M",
"aerofoil_18pc_reynolds_3M",
"aerofoil_21pc_reynolds_9M",
"aerofoil_21pc_reynolds_6M",
"aerofoil_21pc_reynolds_3M",
]
}
Note
Interpolation over Reynolds number is only performed for aerofoils with the same ThicknessToChordRatio. The associated ReynoldsNumber can be different. This is because the interpolation does not support scattered data.
An example of a combination where interpolation over ThicknessToChordRatio and ReynoldsNumber is performed:
| Foil name | Thickness to chord ratio | Reynolds number |
|---|---|---|
| Foil 11 | 0.2 | 1e6 |
| Foil 12 | 0.2 | 8e6 |
| Foil 21 | 0.5 | 2e6 |
| Foil 22 | 0.5 | 5e6 |
An example of a combination where the interpolation is performed only on the ThicknessToChordRatio:
| Foil name | Thickness to chord ratio | Reynolds number |
|---|---|---|
| Foil 11 | 0.2 | 1e6 |
| Foil 12 | 0.25 | 8e6 |
| Foil 21 | 0.45 | 1e6 |
| Foil 22 | 0.5 | 8e6 |
-
The linear interpolation is done directly if a single aerofoil is assigned to a section. However when an Interpolated Aerofoil Library is assigned to the section the aerofoil data is linearly interpolated on
ThicknessToChordRatio, before starting the simulation, and then onReynoldsNumberduring the simulation to arrive to a single lookup table of aerodynamic data.↩