Semi-infinite laguerre functions for wind turbine wake modeling

Abstract

With an increased demand for renewable energy wind farms, their efficiency receives growing attention from both the industry and academics. Mitigating wake interaction effects in wind farms is one of the ways wind farms could increase their efficiency. Control techniques to increase wake reenergizing are currently under development, however, are being held back by a lack of available medium-fidelity wake modeling methods. To sufficiently support developments in the wind industry, the wake model should yield an axial wind profile that can be used for load calculations for the downstream wind turbine and assess its energy production. Moreover, for the model to be useful in the research effort the method must either show an increase in accuracy or a decrease in time-cost. Finally, the model is desired to include the effects of wake control techniques in later iterations outside the scope of this research. This thesis investigates medium-fidelity models for wind turbine wake control techniques, with an exploratory study into applying a semi-infinite spectral method with an adjusted Laguerre basis to wind turbine wake modeling. The wake model used in this research is an altered version of the Ainslie wake model. To model the wake model a spectral method with Laguerre functions for the basis is employed in the radial direction and a marching scheme with a piecewise linear basis for the basis in the downstream direction. The potential benefits of spectral methods are lower rank systems and spectral convergence. The adjusted Laguerre functions used for this research naturally fit the boundary conditions for the wake model. At the start of the domain, a Dirichlet boundary condition is applied with fitted Laguerre functions to the result of a blade element simulation. The results did not account for wake expansion and diffused the wake much sooner than physical. The implementation of the explicit formulation for the triple product integral hindered higher-order simulations, disabling research into simulations for domains much higher than 11 radial modes. The errors for the different conservated quantities are significantly higher than they should be. From the verification efforts, a relation can be observed between the number of radial modes in the domain with respect to the number of radial modes used for the inflow, which suggests that the model should use much higher numbers of radial modes than this implementation allowed. i