Structural Dynamic Behavior of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 629

2. In this way, the accelerations associated with each flap coordinate function can be
evaluated numerically be substituting the current values for the flap velocities and
displacements into the force side of the equation.

3. The blade tip displacements are computed by solving the second-order differential
equation relating acceleration, velocity, and displacement. The solution is performed
via the modified Euler predictor-corrector method, which uses the current blade tip
accelerations and the previous values of the displacements and velocities.

4. The blade loads are computed only at the completion of a trim solution.

5. The solution during time-dependent prescribed yawing motions is run at the completion
of the trim solution. Loads are computed at the completion of each revolution during
the yawing solution. Yawing motion is prescribed according to the simple equation

f( t ) = f 0 + f a sin(w f t ) (11-41)

6. A set of nine blade motion and blade load parameters is computed for each specified
spanwise location on the blade axis (typically 11 stations) at each azimuthal position
of the blade during a revolution (typically 36 azimuths). These parameters are the

-- flap displacement, v ;
-- flapwise slope, v ¢;
-- flap velocity, dv/dt ;
-- edgewise shear load, S h ;
-- flapwise shear load, S z ;
-- spanwise tension load, T ;
-- flapwise moment load, M h ;
-- edgewise moment load, M z ;
-- pitching moment load, M x .

Sample Blade Load Analysis

The turbine modeled in this example is the Grumman prototype HAWT (see Table 3-1),
which has a three-bladed, rigid-hub rotor 10.1-m in diameter that runs downwind of a shell
tower [Adler et al. 1980]. The lift and drag models are simplifications of the airfoil data
presented by Sweeney and Nixon [1978]. Other input data are as follows:

U H = 9.1 m/s m = 0.143

t 0 = 0.25 t p = 0

y 0 = 15 deg f 0 = 10 deg

W = 7.54 rad/s c = 0.46 m

b 0 = 3.5 deg q t = 0 deg

The natural frequency of the blade's first ( i.e. lowest frequency) flapwise bending mode is
approximately 3.95 Hz, or about 3.3 times the rotor rotational frequency.
Flap bending moments in the operating turbine were measured at a spanwise station 1.8
m from the rotor axis (20 percent of span) and averaged over 20 revolutions. The test data
were azimuth-averaged in this manner to remove random wind effects that are not modeled in
this analysis. After averaging, the mean value of the measured flap bending moment was