Case APX rotor blade validation

In this subsection the measured non-rotating eigenfrequencies of an APX-45 wind turbine rotor blade are compared with those from the superelement approximation. The APX-45 rotor blades are designed by the Institute for Wind Energy of Delft University of Technology, The Netherlands [242], and manufactured by Aerpac Special Products B.V., Hengelo, The Netherlands [241]. The rotor blades are designed for both (full-span) pitch-controlled and (active) stall regulated 3-bladed wind turbines. The blade has a length of 21.75 m, and consists of two main parts: a 3.75 m long non-aerodynamic part where the cylindrical contour is transformed into an aerodynamic shaped root aerofoil, and an 18 m long aerodynamic part. The blade is mainly made of glass fibre reinforced epoxy (GRE). The interested reader is referred to Appendix A.2 for more detailed specifications.

We will use the blade definition file (i.e. FAROB1 output file Table.flx), which is used to manufacture the blade, as a starting point. This file contains - among other things - the blade mass, and the flexural rigidity in the two principal bending directions at a number of locations beginning at the blade tip and ending with the blade root. Undefined locations are interpolated in a subsequent step after converting the file to a MATLAB MAT-file. The flexural rigidity in both flap and lead-lag direction as function of the local radius is shown in Fig 4.6. Both plots show a non-smooth increase in flexural rigidity from blade tip to blade root. The flexural rigidity in flap direction shows a local maximum at the radial position with the

1 FAROB is the structural blade modeling module of the design code FOCUS.

maximum chord length (see Table A.1 on page 221) followed by a local minimum.

Aerpac Apx

Figure 4.6: Upper figure: flexural rigidity in lead-lag direction EIii, and lower figure: flexural rigidity in flap direction EIfi of an APX-45 rotor blade as function of local radius r, with o: values defined in FAROB output file Table.flx, and solid line: linear interpolated values.

Figure 4.6: Upper figure: flexural rigidity in lead-lag direction EIii, and lower figure: flexural rigidity in flap direction EIfi of an APX-45 rotor blade as function of local radius r, with o: values defined in FAROB output file Table.flx, and solid line: linear interpolated values.

The torsional spring constants for the superelement can be derived directly from the data in the MAT-file using the automated structural modeling procedure outlined in Section 3.4. Obviously, the resulting model accuracy depends strongly on the quality of the input data. Like the Euler-Bernouilli beam, the APX-45 rotor blade will be subdivided into an increasing number of superelements as illustrated in Fig. 4.7.

The non-rotating rotor blade eigenfrequencies obtained from the full-scale modal test performed by the Stevin Laboratory of Delft University of Technology [156] are used to evaluate the superelement approximation by comparing the relative frequency error

Superelement eigenfrequency

Measured eigenfrequency

The relative errors for the first two flap and lead-lag eigenfrequencies of the superelement approximation are plotted in Fig. 4.8. From this figure it is clear that the errors do not converge to zero with an increasing number of superelements. Numerical values are listed in the first column of Table 4.4. The reason for this bias might be one of the following:

• The model is used outside its range of validity and thereby violating the assumptions made in deriving the torsional spring constants;

Lead-lag

Flap

Lead-lag

Flap

APX-45 rotor blade

Two superelement approximation

Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

Get My Free Ebook


Post a comment