Tower Design and Manufacture - Small Wind Turbines: Analysis, Design, and Application - page 214

Fig. 10.5 Geometry and
parameters of a straight
octagonal tower for
h = 18 m, U = 50 m/s, and
turbine parameters as in
Table 10.2

1300

1200

1100

ω n (Hz)

2

1

diameter (m)

deflection (m)

12 0 20 40 60 80 100

d/t

Table 10.3 Comparison of predicted tower behaviour to finite element results

Parameter Present value Value from FEA

CF max stress 0.584 0.557

CF max buckling 0.632

Linear buckling factor 2.68

Turbine deflection (m) 0.81 0.73

Tower natural frequency—method A (Hz) 1.07 1.51

Tower and turbine natural frequency—method A (Hz) 0.765 0.842

Tower natural frequency Eq. 10.20 (Hz) 1.48 1.51

Tower and turbine natural frequency—method B (Hz) 1.185 0.842

fitness c ðÞ¼ a m min m ðÞ

CF c ðÞ
max C ðÞ þ 1 a m a CF

Þ n 1 c ðÞ

max n ðÞ ð 10 : 25 Þ
For the initial calculations, n 1 was excluded by setting a m ? a CF = 1. Note that
the maximum CF in Eq. 10.25 was 0.60 for all runs, whereas the minimum mass
and maximum natural frequency (when used) were determined from each gener-
ation in the same manner as for the blade optimisation in Chap. 7 . Table 10.4
shows the important parameter and input values for the optimisation; the same CF
was used for buckling and stress.
Table 10.5 shows that the most critical parameter is the minimum diameter
which has a large effect on the optimal mass as well as the distribution of maxi-
mum CF, Fig. 10.6 , largely because reducing d min increases the maximum CF in
the top section. In all cases, the maximum CF reached the limit of 0.60, and the
minimum diameter of the optimal tower converged to d min . This is not surprising
given that the top of the tower will contribute significantly to the bending moment
at the base, and the magnitude of the moment is determined by the diameter.
In practice, d min is often set by the design of the tower flange and the yaw
mechanism which must withstand the gyroscopic moments of Load Case B from
Chap. 9 , and must allow central clearance for slip rings or the power and other
cables to and from the turbine.

m t c ðÞ þ a CF

ð