Researchers Mohamed M. Hammam and David H. Wood, affiliated with the University of Auckland, have recently published a study in the Journal of Fluids and Structures that delves into the yaw response of tail fins for small wind turbines and wind vanes used for wind direction measurement. Their work provides analytical solutions for the yaw response, extending beyond the limitations of current linear models.
The study focuses on the minimal form of the general second-order equation for the yaw angle, γ, derived by Hammam and Wood in 2023. This equation includes a nonlinear damping term controlled by a small parameter that depends on the vortex flow coefficient, Kv, which is absent in all linear models. The researchers employed perturbation techniques to analyze this minimal equation.
Using the Krylov-Bogoliubov-Mitropolskii averaging method, they derived a truncated series solution that compares favorably with numerical solutions, except for minor deviations at large times. Another form of averaging, introduced by Beecham and Titchener in 1971, yielded a compact solution that identifies an equivalent linear system with equivalent frequency and damping ratio. The researchers obtained two limiting analytic solutions for small and large |γ0|, with the former used to identify model parameters from experimental data.
The approximate solutions revealed that a high Kv is crucial for the rapid decay of yaw amplitude for tail fins at high |γ0|. For wind vanes, high aspect ratios reduce nonlinearity to minimize yaw error. The study also found that linear response, independent of Kv, occurs whenever sin(πγ0) ≈ πγ0. Furthermore, the low-angle analytical solution allows for the exact identification of nonlinearity, which could extend the modeling of wind vanes to high γ.
This research provides valuable insights for the energy sector, particularly in the design and optimization of small wind turbines and wind direction measurement systems. By understanding and controlling the yaw response, engineers can improve the efficiency and accuracy of these devices, contributing to more effective wind energy harvesting and monitoring.
Source: Hammam, M. M., & Wood, D. H. (2023). Analytical Solutions of the Minimal Nonlinear Equation for the Yaw Response of Tail Fins and Wind Vanes. Journal of Fluids and Structures.
This article is based on research available at arXiv.