Gaussian entrainment model for wind turbine wakes.

This master’s thesis introduces an innovative analytical wake model that extends the entrainment model developed by Luzzatto-Fegiz [1]. This enhanced model aims to achieve improved accuracy in predicting wake behavior within real-world scenarios by incorporating a Gaussian-distributed wake velocity, both in axial and radial direction. Solely for comparative purposes, the already established Jensen model and Frandsen model are also utilized, both in their original form and in their Gaussian-distributed variations. To assess the effectiveness of these models, they are implemented in Matlab and graphically as well as analytically compared using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) analysis. Their predictions are analyzed against Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) data. The thesis initiates with a short explanation of wake theory, regarding both near wake and far wake. It gives an overview of existing wake models, highlighting their principles, strengths, and limitations. The first group of models includes three classic wake models that consider a top-hat distributed wake velocity, while the second group considers the wake velocity to be Gaussian-distributed. It is important to emphasize that the second group of models includes the Gaussian-distributed Jensen and Frandsen models that were designed by Liang et Fang [4] and presented in 2014. Subsequently, the Gaussian-distributed wake entrainment model is introduced as a novel approach and an improvement over the conventional entrainment model, following their lead and incorporating an enhanced representation of entrainment dynamics. Both the Gaussian-distributed model and the basic entrainment model consider mass conservation as well as momentum conservation, ensuring a comprehensive portrayal of wake dynamics for improved accuracy. To evaluate the performance of the Gaussian-distributed wake entrainment model, a comprehensive dataset containing LES and RANS data on observed wake entrainment phenomena is employed for comparative analysis in axial direction as well as radial direction. By contrasting the model predictions against this dataset, the research aims to gauge their accuracy in capturing intricate wake behavior. This analysis involves not only visual comparisons but also the application of analytical methods such as an evaluation of MAPE in axial direction and RMSE in radial direction, providing a comprehensive assessment of each model's performance. The study’s findings offer valuable insights into the strengths and limitations of each model, shedding light on the advancements brought by the Gaussian-distributed wake entrainment model. The outcomes may contribute to the field of wake modeling in wind turbine applications. By identifying the most accurate and reliable model for predicting wakes in various flow scenarios, this thesis has implications for engineering structure design and optimization, particularly within wind energy and fluid dynamics contexts. Moreover, the project's limitations will be discussed, and potential avenues for future research will be explored in order to enhance the applicability and robustness of the developed models.