Quantification and reduction of uncertainty of model predictions of wind turbines and plants via high-fidelity simulations
With increasing energy demands renewable energy sources are continuing to receive attention and investment to become a larger source for electricity production. Today, wind generated power through wind turbines creates 4\% of the electricity in the United States. The wind energy share of the electricity market is expected to grow rapidly as the United States Department of Energy goal is to reach 20\% wind generated electricity by 2030. Computational models for wind plants can be used to predict wind plant performance and optimize the turbine placement and controls. However, uncertainties associated with such models, due to, among others, the computationally expedient simplifications need to be carefully assessed, quantified and reduced.
A numerical investigation of model wind turbines employing large-eddy simulation and the curvilinear immersed boundary method to resolve the geometrical details of the turbine is undertaken revealing that the unstable hub vortex interacts with the turbine tip shear layer. Using a spatio-temporal filtering technique, wake meandering, a large scale displacement of the wake, is reconstructed into three-dimensional helical meander profiles. Statistics of the amplitudes and wavelengths corresponding to the intensity and streamwise elongation of the periodic wake meandering indicate complex coherent structures. Similar simulations are performed using the computationally expedient wind turbine actuator surface models with and without a nacelle model to parameterize the turbine. All simulations are validated against substantial experimental measurements. The simulations with the nacelle model are able to accurately capture the geometry dependent near wake and the dynamics in the far wake. The simulations without the nacelle model predict a stable, columnar hub vortex which does not interact with the turbine tip shear layer. Moreover, the amplitude of the meandering profiles is shown to be larger in the immersed boundary method simulations and simulations with a nacelle model compared to the simulation without the nacelle model proving that the nacelle and unstable hub vortex augment the meandering intensity in wind turbines.
Due to the exceptional performance of the computationally efficient actuator surface with nacelle model, several turbine designs are simulated with diameters ranging from the laboratory scale (0.1 meters) to the utility scale (96 meters). Despite significant geometrical differences, a characteristic velocity based on the turbine thrust collapses the profile of both the wake turbulence kinetic energy and the amplitude of wake meandering based on the meandering profile for all turbine sizes. This result suggests that the turbulence levels and wake meandering intensity are explicitly linked. The wavelengths of wake meandering are properly scaled by the diameter of the turbine. In agreement with numerous measurements, the wake meandering and hub vortex Strouhal number based on the incoming hub height velocity and diameter is found to be approximately 0.3 and 0.7, respectively, for all turbines. Dynamic mode decomposition of the velocity field indicates that the modes related to these frequencies contain a majority of the energy in the meandering wake and confirms that an unstable hub vortex is a necessary requirement for simulating wind turbine wakes.