Page 309 - Wind Energy Handbook

BLADE DYNAMIC RESPONSE 283

the time into short timesteps (which may be of fixed or variable length), as
described in Section 5.8.5. In this way, all the non-linearities and non-stationary
aspects of the system, such as those listed above, can be dealt with to any desired
level of accuracy. A useful comparative survey of such codes is given by Molenaar
and Dijkstra (1999).
Two principal approaches to the modelling of structural dynamics are embodied
in these software packages. Some use a full finite-element representation of the
structure, which is broken down into small elements. The equations of motion are
solved for each element, with boundary conditions matched at the interfaces
between elements. An example of such a code is Adams-WT (Hansen, 1998), which
consists of a general purpose finite-element code (Adams) interfaced to an aero-
dynamic module.
The other main approach is the modal analysis method as described in the
preceding section, in which simple finite-element methods are used to predict just
the first few modes of vibration of the structure as a whole, or of its main parts. The
equations of motion for these modes, which include periodic coefficients, are then
derived and solved with appropriate boundary conditions over each time step. This
gives a much smaller set of equations (although the equations themselves may be
more complex). The higher frequency modes of the system tend to contribute very
little to the system dynamics and loads, and so the modal method generally gives a
very good approximation to the performance of the structure. An example of a code
based on this approach is Bladed for Windows (Bossanyi, 2000), which allows the
most important rotor and tower modes to be calculated. These are then linked to
the remaining system dynamics (drive train, control systems, etc.), and to an
aerodynamics module similar to that of Adams-WT.
Both of these codes include a full three-dimensional, three-component model of
the turbulent wind field computed using the Veers method (Veers, 1988) as
described in Section 5.7.6. Bladed for Windows additionally has an offshore module,
allowing stochastic wave loading and current loading on the tower to be modelled
for an offshore turbine. As with the effect of aerodynamics, the effect of the
vibrational velocities of the structure on the hydrodynamic forces is significant. This
leads to considerable interactions between the wind and wave loading. Jamieson
et al. (2000) have demonstrated that if wind and wave loading are treated in
isolation from each other, an over-conservative design is likely to result.
The use of sophisticated calculation methods such as those described above are
rapidly becoming mandatory for the certification of wind turbines, particularly at
the larger sizes. A few illustrative examples of results obtained with Bladed for
Windows are described below.
Figure 5.33 shows a Bladed for Windows simulation of the in- and out-of-plane
bending moments at the root of one of the blades, during operation in steady,
sheared wind. The in-plane moment is almost a sinusoidal function of azimuth,
being dominated by the gravity loading due to the self-weight of the blade which,
relative to the blade, changes direction once per revolution. The mean is offset from
zero because of the mean positive aerodynamic torque developed by the blade.
There is a slight distortion of the sinusoid, partly because of the variation of
aerodynamic torque due to wind shear and the effect of tower shadow, and partly
because of the in-plane vibration of the blade.