Analytical Unsteady Aerodynamic Models for Horizontal Axis Wind Turbines
Abstract
This thesis describes the development of unsteady aerodynamic models of wind turbines within the framework of blade element momentum theory. The main purpose is to build analytical models, and test them against available wind tunnel and field test data. The unsteady wake is modeled using vortex methods. The analysis covers unsteady loading due to fast pitch change at constant wind speed, and varying wind speed at constant pitch. The analysis can be extended to more complex conditions.
The work starts by modeling dynamic inflow effects as an inertia force, with a new developed expression of the apparent mass and rotational inertia of the rotor vortices. Further assumptions lead to a Ricatti differential equation for the axial induction, which has an analytical solution. First, linear pitch changes are investigated, and the unsteady thrust and torque are calculated. The model is shown to be accurate in comparison to the available experiments. The model is then extended to low tip speed ratios in the form of an Abel differential equation, which appeared to be more accurate. However, comparison with measurements has shown that the assumptions leading to the Abel equation model are inconsistent. The unsteady load is characterized by a large overshoot for high pitch rate. To alleviate this an analytical solution of exponential pitch angle is developed.
%An analytical model is obtained for the exponential pitch case and validated against experiment.
Next, the unsteady load due to varying wind speed at constant pitch is modeled. The dynamic inflow model is extended to include the circulatory effect of the wake. A new unsteady model is developed from first principles. The wake is modeled as an initial vortex cylinder and vortex rings released onto the wake with each revolution of the blades. The circulatory effect is described by a new function. The model is simplified further by approximating the wake effect to get an analytical solution for the case of linearly varying wind speed. The unsteady lift is modeled and combined with the dynamic inflow model to obtain a fully unsteady model in state space form. The different models are validated with experiments, and the unsteady lift effect is found to have importance for short time period transients.
Description
Keywords
Energy, Engineering, Engineering--Mechanical
Citation
Hammam, M. (2016). Analytical Unsteady Aerodynamic Models for Horizontal Axis Wind Turbines (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24827