Generalized analytical displacement model for wind turbine towers under aerodynamic loading

The goal of this work is two-fold: 1) to determine the angular deflection and displacement of the NREL 5 MW reference wind turbine tower under different atmospheric thermal stratifications, and under overlapping wind turbine wake effects using a comprehensive numerical analysis; 2) to develop and verify a generalized analytical model allowing to efficiently estimate wind turbine tower displacements under a variety of flow conditions. Large-eddy simulations are used to generate atmospheric flows similar to those of a characteristic diurnal cycle. One hour periods are selected and inputted into an aero-elastic simulation code which resolves the rotor-disk aerodynamic loading components, which are then used as inputs to a 3-D finite element model of the tower to compute the angular deflection and displacement. To improve efficiency in tower displacement predictions, a generalized analytical model is developed based on a simplified 2-D cantilever beam and 1-D momentum theory. Results are compared with those obtained from the numerical simulations. Results indicate that the tower deflection standard deviation increases with increasing atmospheric turbulence and wake superposition. Also, differentiated tower displacements are experienced under different atmospheric stratifications. Interestingly, lone standing wind turbines undergo larger tower deflections compared to those located within very large wind farms. The wind turbine rotor thrust and the aerodynamic thrust on the tower are found to have the greatest and least influence, respectively, on tower deflection. Displacement results from the finite element analysis are used to verify the accuracy of the new generalized analytical model showing a very good agreement. This new model has the advantage of estimating the tower deflection by just knowing the inflow velocity for any wind turbine, independent of the atmospheric stratification and wind farm arrangement.