Wind turbine simulations using spectral elements

Sammanfattning: Understanding the flow around wind turbines is a highly relevant research question due to the increased interest in harvesting energy from renewable sources. This thesis approaches the topic by means of numerical simulations using the actuator line method and the incompressible Navier–Stokes equations in the spectral element code Nek5000. The aim is to gain enhanced understanding of the wind turbine wake structure and wind turbine wake interaction. A verification study of the method and implementation is performed against the finite volume solver EllipSys3D using two types of turbines, an idealized constant circulation turbine and the Tjæreborg turbine. It is shown that Nek5000 requires significantly lower resolution to accurately compute the wake development, however, at the cost of a smaller time step.The constant circulation turbine is investigated further with the goal of establishing guidelines for the use of the actuator line method in spectral element codes, where the mesh is inherently non-equidistant and currently used guidelines of force distribution based on Gaussian kernels are difficult to apply. It is shown that Nek5000 requires a larger kernel width in the fixed frame of reference to remove numerical instabilities. Further, the impact of different Gaussian widths on the wake development is investigated in the rotating frame of reference, showing that the convection velocity and the breakdown of the spiral tip and root vortices are dependent on the Gaussian width. In the second part, the flow around single and multiple wind-turbine setups at different operating conditions is investigated and compared with experimental results. The focus is placed on comparing the power and thrust coefficients and the wake development based on the time-averaged streamwise velocity and turbulent stresses. Further the influence of the tower model is investigated both upstream and downstream of the turbine. The results show that the wake is captured accurately in most cases. The loading exhibits a significant dependence on the Reynolds number at which the airfoil data is extracted. When the helical tip vortices are stable the turbulent stresses at the tip vortices are underestimated in the numerical simulations. This is due to the finite resolution and the projection of the actuator line forces in the numerical domain using a prescribed Gaussian width, which leads to lower induced velocities in the helical vortices.