Tower design and analysis - Wind Power Generation and Wind Turbine Design - page 541

Table 1: GRFs for SDOF lumped mass model.

G DISP-NI 2.275

G DISP-CF 2.291

G B 1.019

G R,1 0.792

G BM-NI 2.429

Table 2: GRFs for coupled model with blade-tower interaction.

Ω (rad/s) G DISP-NI G DISP-CF G B G R,1 G R,2 G BM-NI

0.000 2.507 2.356 1.032 0.850 0.268 2.633

0.785 2.509 2.370 1.044 0.837 0.266 2.599

1.570 2.503 2.392 1.070 0.833 0.257 2.506

3.140 2.381 2.327 1.059 0.753 0.170 2.225

A series of numerical examples are presented from [43] to investigate the
magnitude of GRFs obtained for the model which allows for blade-tower interac-
tion, and these are compared with GRF values obtained from an equivalent SDOF
model which ignores blade-tower interaction by lumping the mass of the blades in
with that of the nacelle. A tower (steel) of height 50 m with rotor (GFR epoxy)
diameter of 60 m is considered with the details available in [43]. Four different
rotational frequencies of the rotor blades were considered. As rotational frequency
of the blades increases, the fundamental frequency of the blades also increases,
and this leads to increase in the natural frequencies of the coupled systems.
Tables 1 and 2 show the GRFs obtained for the lumped mass equivalent SDOF
and two DOF tower-blade interaction models for a mean wind velocity of 20 m/s
at the top of the tower. A time of 600 s was used to obtain the GRFs, as used in
Eurocode 1 (CEN 2004) [45]. Included in these tables are the displacement GRFs
obtained by numerical integration and in closed form, G DISP-NI and G DISP-CF ,
respectively, and the base bending moment GRF obtained using numerical integra-
tion, G BM-NI . It may be noted that the second mode affects the background and the
resonant components and changes the response obtained from the classical gust
factor approach.
It is evident from Tables 1 and 2 that the choice of modelling strategy, i.e.
lumped mass SDOF or two DOF blade/tower interaction, has a bearing on the
magnitudes of both the displacement and base bending moment GRFs obtained.
When the blades are stationary ( = 0 rad/s) in the two DOF case, the values of

G DISP-NI and G BM-NI obtained differ from the SDOF model values of G DISP-NI and
G BM-NI by over 10 and 8%, respectively. These differences remain nearly constant
until the case of

Ω

= 3.14 rad/s where they are equal to 5 and 8%, respectively.
The values of G DISP-NI and G DISP-CF showed a close match in most cases, though
it was observed that when the two modes were closest together (

Ω

Ω = 0 rad/s),