Aeroelastic Modelling of Wind Turbines
Figure 1: Comparison of Three Different Beam Structural Models – the Classical First-order Beam Model, the Second-order Beam Model and the Model Applying Sub-body Modelling
5.4 5.2
4.6 4.8 5.0
0 9,500 510 Time (s) 100 50 9,000 0 8,500 -50 8,000 0 510 Time (s) First order beam r/R = radial position/rotor radius.
Figure 2: Plan Form of the Pre-swept Blade (Left) and Image of the Rotor and its Wake Here Represented as Freely Moving Vortex Particles (Right)
Unsteady turbulent flow simulations, although possible nowadays by means of computational fluid dynamics (CFD),10
are seldom used in
aeroelastic analysis due to their high cost. So aeroelastic modelling at present relies on approximate models. To a large extent, the level at which we need to calculate the aerodynamic loads depends on the structural model. Since all wind turbine components are modelled as 1D beam structures, only the integrated sectional aerodynamic forces along the blade will be needed.
z(r) = ar-rOR-rOb
The radial distribution of the sweep along the blade is given by the above expression, where r denotes the radial position, r0 the radial position at which sweeping starts, R the rotor radius, a the sweep at the tip and b the parameter defining the shape of the sweep.
Table 1: Purely Aerodynamic Simulations – Effect of Pre-sweeping on the Power Production at 8 m/s Mean Wind Speed as Percentage of the Power Production of the Unswept Blade
a = 1 BEM -0.12 a = 3 -0.53 -0.86 -2.01
Free-wake +1.08 +1.68 +1.40 +1.06 -3.30 BEM = blade element momentum.
a = 4
b = 2 b = 4 b = 2 b = 4 b = 2 b = 4 -0.07
-3.23 -9.23
Because the blades are lifting bodies formed by aerofoil shaping similar to that of a wing, the origin of all the existing approximate aerodynamic models is based on classical aerodynamic theories. The simplest approach is to use aerofoil theory which provides sectional lift, drag and pitching moment as functions of the effective angle of attack and the effective (relative) flow velocity. Sectional aerodynamic properties are usually available for steady 2D flow conditions. Therefore, in order to use this information in aeroelastic simulations, three additional sub-models are needed: a flow solver that can provide the effective inflow conditions along the blade (i.e. angle of attack and relative velocity); a correction of the 2D polars so as to account for 3D effects; and a dynamic inflow model accounting for the unsteady character of the inflow, which in certain cases should also be capable of handling dynamic stall.
The most commonly used flow solver is based on the blade element momentum (BEM) theory,11
due to its low computational cost and its
with respect to the chord and the relative velocity will be in the range of 106–107; and practically incompressible, since even at the tip the local Mach number will remain lower than 0.3.
42
simple implementation. However, there are certain drawbacks. BEM is an approximate model that strongly relies on empirical corrections. BEM is based on strip theory, which means that there is no 3D coupling either between the sections along the blade or between the blades. Also the presence of the wake is accounted for by means of induction factors defined at the rotor plane. The expressions for the
MODERN ENERGY REVIEW – VOLUME 4 ISSUE 1 Second order beam Multi-body (10 bodies) 15 20 -100 0 510 Time (s) 15 20 15 20 5.0 4.5 4.0 3.5 0 510 Time (s) 15 20
Flapwise bending moment at blade root (KNm)
Flapwise displacement at blade tip (m)
Torsion moment at blade root (KNm)
Angle of attack at r/R = 0.75 (degrees)
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