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Ebook Aerodynamics of wind turbines (2nd edition): Part 2

(BQ) Part 2 book "Aerodynamics of wind turbines hansen" has contents: Unsteady BEM model, introduction to loads and structures, dynamic structural model of a wind turbine, beam theory for the wind turbine blade, sources of loads on a wind turbine, wind simulation, fatigue, final remarks. | 3212 J&J Aerodynamic Turbines 15/11/07 1:43 PM Page 85 9 Unsteady BEM Model To estimate the annual energy production from a wind turbine at a given site with known wind distribution it is sufficient to apply a steady BEM method as described in Chapter 6 to compute the steady power curve. But due to the unsteadiness of the wind seen by the rotor caused by atmospheric turbulence, wind shear and the presence of the tower it is necessary to use an unsteady BEM method to compute realistically the aeroelastic behaviour of the wind turbine. To do this a complete structural model of the wind turbine is also required; this must be coupled with the unsteady BEM method since, among other things, the velocity of the vibrating blades and the tower change the apparent wind seen by the blades and thus also the aerodynamic loads. Since the wind changes in time and space it is important at any time to know the position relative to a fixed coordinate system of any section along a blade. The fixed or inertial coordinate system can be placed at the bottom of the tower. Depending on the complexity of the structural model a number of additional coordinate systems can be placed in the wind turbine. The following example illustrates a very simple model, with the wind turbine described by four coordinate systems as shown in Figure 9.1. First, an inertial system (coordinate system 1) is placed at the base of the tower. System 2 is non-rotating and placed in the nacelle, system 3 is fixed to the rotating shaft and system 4 is aligned with one of the blades. Note that due to the orientation of coordinate system 2, the tilt angle θtilt must be negative if the shaft is to be nose up as sketched in Figure 9.1. A vector in one coordinate system XA = (xA, yA, zA) can be expressed in another coordinate system XB = (xB, yB, zB) through a transformation matrix aAB: XB = aAB XA. (9.1) The columns in the transformation matrix aAB express the unit vectors of system A in system B. Further, the .