Gyroscopic Effects of Horizontal Axis Wind Turbines Using Stochastic Aeroelasticity via Spinning Finite Elements

Horizontal axis wind turbine (HAWTs) structures, throughout the years, have presumed to be of relatively simple construction, but wind-induced aerodynamic vibrations, wind-field conditions, and power requirements tend to lead to the need for increasingly complicated designs. One phenomenon that requires special attention is the gyroscopic or Coriolis effect. In general, blades design codes are written to optimize for lightness and slenderness, but also to withstand excitations at high frequency. As a result, gyroscopic motion derives as a nonlinear dynamic condition in the out-of-plane direction that is difficult to characterize by means of the well-known vibrational theory that has been established for their design and analysis. The present study develops and presents a probabilistic analysis of the precession — gyroscopic — effects of a wind turbine model developed for tapered-swept cross-sections of n_t degree with nonlinear variations of mass and geometry along the body of the blade. A dynamic orthogonal decoupling method is utilized to successfully perform the aeroelastic analysis by decoupling the damped-gyroscopic equations of motion, as a result of the addition of Rayleigh damping — symmetric proportional mass and stiffness — within the linear system in study. Results are valid for yaw-free rotor configurations by means of unknown and random (though bounded) yaw rates. Simultaneously, those results can easily be expanded for yaw-controlled mechanisms. The yaw-free assumption presents a higher risk of potential reliability expectations, given the stochastic impairment of the gyroscopic nature that is present for out-of-plane axis motions, requiring special attention at higher frequencies. This impairment becomes particularly troublesome for blade profiles with tapered-swept cross-section variations. This uncertainty can be minimized by incorporating a mathematical framework capable of characterizing properly the yaw action such that gyroscopic effects can be fully interpreted and diagnosed. In summary, the main goal is to decipher the complexity of gyroscopic patterns of flexible rotor blades with complex shape configurations, but also to provide substantial elements to successfully approach yaw-mechanics of tapered-swept rotor blades.