Analysis of the Jensen´s model, the Frandsen´s model and their Gaussian variations

This paper analyzes the Jensen´s model, the Frandsen´s model and their Gaussian variations. All of the models are simple methods to describe wakes of turbines. The Jensen´s model, which is based on conservation of mass, is widely used in the literature to optimize placement of turbines. Based on different simplifying assumptions, the Jensen´s model has many versions. The Frandsen´s model is a relatively new wake model, and is derived by conservation of momentum. By assuming Gaussian distributions instead of uniform ones, both models can derive their Gaussian variations, which are more consistent with real wakes. In this paper, all of the models are analyzed to better understand their similarities and discrepancies. A modified form of the Jensen´s model which considers the length of near wake regions is presented in this paper. The results are compared with the large-eddy simulation (LES) data.