Numerical study on instability and interaction of wind turbine wakes

Sammanfattning: Numerical simulations of the Navier-Stokes equations are conducted to achieve a better understanding of the behavior of wakes generated by the wind turbines. The simulations are performed by combining the in-house developed code EllipSys3D with the actuator line technique.In step one of the project, a numerical study is carried out focusing on the instability onset of the trailing tip vortices shed from a 3-bladed wind turbine. To determine the critical frequency, the wake is perturbed using low-amplitude excitations located near the tip spirals. Two basic flow cases are studied; symmetric and asymmetric setups. In the symmetric setup a 120 degree flow symmetry condition is dictated due to the confining the polar computational grid to 120 degree or introducing identical excitations. In the asymmetric setup, uncorrelated excitations are imposed near the tip of the blades. Both setups are analyzed using proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). By analysing the dominant modes, it was found that in the symmetric setup the amplification of specific waves (traveling structures) traveling along the tip vortex spirals is responsible for triggering the instability leading to wake breakdown, while by breaking the symmetry almost all the modes are involved in the tip vortex destabilization. The presence of unstable modes in the wake is related to the mutual inductance (vortex pairing) instability where there is an out-of-phase displacement of successive helix turns. Furthermore, using the non-dimensional growth rate, it is found that the mutual inductance instability has a universal growth rate equal to Π/2. Using this relationship, and the assumption that breakdown to turbulence occurs once a vortex has experienced sufficient growth, an analytical relationship is provided for determining the length of the stable wake. This expression shows that the stable wake length is inversely proportional to thrust, tip speed ratio and the logarithmic of the turbulence intensity.In second study, large eddy simulations of the Navier-Stokes equations are also performed to investigate the wake interaction. Previous actuator line simulations on the single model wind turbine show that the accuracy of the results is directly related to the quality of the input airfoil characteristics. Therefore, a series of experiments on a 2D wing are conducted to obtain high quality airfoil characteristics for the NREL S826 at low Reynolds numbers. The new measured data are used to compute the rotor performance. The results show that the power performance as well as the wake development behind the rotor are well-captured. There are, however, some difficulties in prediction of the thrust coefficients. The continuation of this work considers the wake interaction investigations of two turbines inline (full-wake interaction) and two turbines with spanwise offset (half wake interaction). It is demonstrated that the numerical computations are able to predict the rotor performances as well as the flow field around the model rotors, and it can be a suitable tool for investigation of the wind turbine wakes.In the last study, an evaluation of the performance and near-wake structure of an analytical vortex model is presented. The vortex model is based on the constant circulation along the blades (Joukowsky rotor) and it is able to determine the geometry of the tip vortex filament in the rotor wake, allowing the free wake expansion and changing the local tip vortex pitch. Two different wind turbines have been simulated: a wind turbine with constant circulation along the blade and the other setup with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind turbine conditions. The vortex model is compared with the actuator line approach and the presented comparisons show that the vortex method is able to approximate the single rotor performance and qualitatively describe the flow field around the wind turbine but with a negligible computational effort. This suggests that the vortex model can be a substitute of more computationally-demanding methods like actuator line technique to study the near-wake behavior.