Numerical study on instability and interaction of wind turbine wakes

Abstract: The optimization of new generation of the wind farms is dependent on our understanding of wind turbine wake development, wake dynamics and the interaction of the wakes. The overall goal of the optimization is decreasing the fatigue loading and increasing the power production of the wind farms. To this end, numerical simulations of the wake of wind turbine are performed by means of applying fourth order finite volume code, EllipSys3D along with the actuator line method. The basic idea behind such actuator line method is representing the blades  by employing the body forces in the Navier--Stokes equations. The forces are then determined through a combination of Blade Element Momentum (BEM) method and tabulated airfoil data.In the first part of thesis, the dynamics of the tip vortices behind a single wind turbine is investigated. The generated wind turbine wake is perturbed using small amplitude disturbances. The amplification of the wave along the spiral triggers some modes leading to wake instability. The perturbed wake is then analyzed using modal decomposition in which  the dominant modes leading to the onset of instability can be identified. Two different cases are studied; symmetric configuration, in that the wake is excited by identical perturbation near each blade tip; and non-symmetric configuration, in which general perturbations are used. The corresponding result confirms that the instability is dispersive and the growth occurs only for specific frequencies in symmetric case. However in general non-symmetric case, all the modes have positive spatial growth rate. This can be explained through the fact that breaking the symmetry results in superposition of the unstable modes related to three-bladed, two-bladed and one-blade wind turbine wake.A rotor experiment has been recently carried out at NTNU wind tunnel using horizontal axis model scale rotors, for detailed investigation of the wake development. A single rotor configuration was first tested and then a setup of two rotors inline was investigated.  Previous numerical investigation of single wind turbine wake using actuator line method shows that the quality of the result depend on the input tabulated airfoil data. Due to absence of the reliable data, a series of experiments using 2-D airfoil were carried out at DTU wind tunnel to obtain the tabulated airfoil data for the Reynolds number corresponding to NTNU rotor operating conditions. The numerical simulations using actuator line method together with the new experimental airfoil data were then carried out for studying the  phenomenon of wake interaction between the two wind turbines.Different cases are simulated with various tip speed ratio of the downstream turbine specifically adjusted to match the NTNU experiments. The characteristics of the interacting wakes were extracted including the rotor performance and the averaged velocity and turbulence fields as well as the development of wake generated vortex structures. The obtained  results were in agreement of NTNU experimental data showing that  numerical computations are reliable tools for prediction of wind turbine aerodynamics.The third aim of the project is to perform a comparison between an analytical vortex model and the actuator line of an isolated horizontal axis wind turbine (simulated with the ACL approach) to assess whether the predictions by the vortex model can substitute more expensive CFD approaches. The model is based on the constant circulation along three blade (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: one with constant circulation along the blade, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind turbine conditions (Tjae reborg wind turbine). The vortex model matched the numerical simulation of the turbine withconstant blade circulation in terms of the near wake structure and the local forces along the blade. The simple vortex codeis therefore able to provide an estimation of the flow around the wind turbine similar to the actuator line code but with anegligible computational effort. The results from the Tjae reborg turbine case showed some discrepancies between the twoapproaches although the overall agreement is qualitatively good. This could be considered as a validation for the analytical method for more general conditions.