Low-Computational-Cost Parabolic RANS Solver for Simulating and Optimizing Wind Turbine Columns

A computational fluid dynamics tool for prediction of wakes and their interactions within a wind turbine column is presented. A Reynolds-averaged Navier-Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary-layer approximations, in order to achieve a good trade-off between computational cost and accuracy, with the aim of application in optimization problems of wind farms. Boussinesq hypothesis and a length scale varying as a function of the streamwise location, calibrated from higher accuracy large eddy simulation (LES) dataset, are modeled through a mixing length model and a parabolic transport equation of the turbulent kinetic energy. The novelty of this work consists in modeling the mixing length to accurately predict time-averaged velocity field in the presence of wake interactions as well as varying incoming free-stream turbulence. The actuator disc model is implemented in the parabolic scheme for simulating turbine effects and estimating power production. The RANS simulations have a good agreement with the LES dataset in comparing the wake field, time-averaged turbulence statistics and power production, for cases designed to test effects of tip speed ratio, spacing between turbines and free-stream turbulence. Furthermore, the RANS solver is also assessed with good agreement with wind tunnel experiments of a turbine model. The tool is then leveraged in optimization problems considering different algorithms and objective functions. The proposed Parabolic RANS (P-RANS) solver is a great alternative for analytical and engineering wake models in obtaining more accurate predictions while requiring two orders of magnitude lesser computation than LES.