Mathematical Analysis and Modeling of Unequally Loaded Rotors of Wind Turbines
Creators: name: Saghlatoun, Saeedeh
Publisher: name: Schulich School of Engineering
Year: 2024
Subjects: subject: Unequally loaded rotors
subject: wind turbine
subject: Blade Element Momentum Theory
subject: UBEM
subject: Engineering--Mechanical
subject: Energy

description: The operation of wind turbines is subject to numerous natural and human-related factors that can cause inequality of aerodynamic loads on the rotor blades. Wind is a chaotic and stochastic phenomenon, posing challenges in accurately determining wind speed and its direction. Similar points over the blades of a rotating wind turbine may experience different wind speeds due to turbulent wind regimes, icing, wind shear, and other extreme meteorological phenomena. Moreover, human errors in the installation of blades with different pitch angles or manufacturing errors of the blades can further exacerbate the issue of unequal blade loading. Despite these common occurrences in the operation of commercial-scale wind turbines, most wind turbine analyses assume that the rotor blades are identical and rotate with equal aerodynamic loading. However, inequality of loads on wind turbines can have significant effects on the system's operation, reliability, and efficiency. To address this issue, a mathematical analysis has been developed to study the effects of inequality of loads on the rotor and the related consequences on the main operating parameters of wind turbines. One of the most widely used and well-known theories for designing wind turbines is Blade Element Momentum Theory (BEM). In the present research work, this theory has been extended to consider the steady-state unequal contributions to the induced velocities and other parameters that affect the operation of a horizontal-axis wind turbine. This extension has provided the model for the Unequal Blade Element Model (UBEM), which includes extra terms and imposes more complexity into the calculation. To examine the accuracy of the mathematical model, a wind turbine (MoWiTO-06) with different pitch angles was tested experimentally in ForWind's wind tunnel at the University of Oldenburg, Germany. The experimental data obtained from MoWiTO-06 is the only measurement that has been done on an unequally loaded rotor and the outcomes of simulation obtained from UBEM are the first computational investigation of such rotors. The results of computational and experimental investigations have demonstrated that inequality can lead to remarkable changes in torque, thrust, and extracted power. Also, it has been demonstrated that more experiments on different wind turbines operating under different forms on inequality are necessary to examine the UBEM model. Installing instruments on all blades of wind turbines would enable the monitoring of the unequal aerodynamic loads on the blades. Furthermore, the computational cost of UBEM has been assessed to determine whether it is possible to have a faster analysis since UBEM is not as fast as BEM. Different approaches have been examined and among them, replacing the conventional Prandtl tip loss factor instead of finite blade functions for high tip speed ratios enhanced the speed of simulation but affected its accuracy negatively. Prandtl tip loss factor saves 70% of the computational cost. Reducing the distance between trailing vortices and each blade element was considered as another potential solution. However, the simulations did not show a considerable reduction in computational cost. To speed up calculations, only the vortices located in the tip and hub regions were considered, but the results were not in agreement with the most accurate results. Therefore, according to what has been studied in the present research, there is no solution that can reduce the execution time of UBEM with acceptable accuracy for all tip speed ratios. Overall, the findings of this research work underscore the importance of considering the effects of inequality of loads on the operation of wind turbines. By providing a mathematical model to study the impact of unequal blade loading on the rotor, this research could help improve the reliability, efficiency, and overall performance of wind turbines. The results highlight the need for further investigation and refinement of computational models to accurately capture the effects of load inequality in wind turbine design and operation.