Page 481 - Wind Energy Handbook

TOWER 455

fluctuations will be significantly smaller during operation at the lower rotational
speed, it would be advisable to select a somewhat lower tower natural frequency
than this to minimize overall fatigue damage.
Once a satisfactory tower design – in terms of strength and natural frequency–
has been evolved for a given turbine, it is a straightforward matter to scale up the
machine to larger rotor sizes, provided all the tower dimensions are scaled
similarly, the hub-height wind speed is unchanged, and the tip speed is maintained
constant. It can be shown that in these circumstances the tower natural frequency
varies inversely with rotor diameter, as does the rotational speed of the rotor, so
that the dynamic magnification factors are unchanged. Similarly, tower stresses due
to extreme wind loading are the same as before.
The situation is less straightforward if the tower height is to be varied for a
particular turbine. Assuming, as before, that the extreme hub-height wind speed
remains the same, and that the wind loading on the tower is negligible compared
with the wind loading on the rotor, then the tower base overturning moment is
simply proportional to hub height H. Constant stresses can be maintained at the
tower base by scaling all cross section dimensions up in proportion to the cube root
of the hub height. If the same scaling is maintained all the way up the tower, then
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p
p
3
3
the tower natural frequency will vary as I B =H ¼ H 4=3 =H ¼ 1=H 5=6 , neglect-
ing tower mass, where I B is the second moment of area of the tower base cross
section. Thus doubling the tower height would result in a 44 percent reduction in
natural frequency. Alternatively, if the tower base overturning moment were
assumed to vary as H 1:5 to allow for the effect of wind shear on hub-height wind
speed and the contribution of wind loading on the tower, then constant tower base
ffiffiffiffiffi
p
stresses could be maintained by scaling the cross section dimensions up by H.On
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p
this basis, tower natural frequency would vary as 1= H. The practical conse-
quences of ‘tuning’ the tower natural frequency are discussed with respect to
tubular towers in the next section.
7.9.3 Steel tubular towers
In the absence of buckling, a waisted conical shell, with a semi angle of 458 below
the critical zone for tip clearance, would be the most efficient structure for
transferring a horizontal rotor thrust acting in any direction to ground level.
However, apart from the practicalities of transport and erection, instability of thin-
walled shells in compression precludes such a design solution, and the steel tubular
towers in common use have a very modest taper. It can be noted in passing that the
manufacture of gently tapering towers has only been made possible by the develop-
ment of increasingly sophisticated rolling techniques, and that early tubular towers
were constructed from a series of cylindrical tubes of decreasing diameter with
short ‘adaptor’ sections welded between them.
A tapered tower is generally fabricated from a series of pairs of plates rolled into
half frusta and joined by two vertical welds. The height of each frustum so formed
is limited to 2 or 3 m by the capacity of the rolling equipment. Care has to be taken
in the execution of the horizontal welds to minimize local distortion, which
weakens the tower under compression loading.