title: Low mach number CFD for wind turbine analysis
Creators: name: Carrion, Marina
Publisher: name: University of Liverpool Repository
Year: 2015

description: To maximise the amount of energy extracted from wind turbines, the rotor diameter has increased, reaching values of 160m in some cases. Large scale wind turbines are working at high Reynolds numbers and a wide range of flow conditions, with virtually incompressible flow present at the root and mildly compressible near the blade tips, where the Mach numbers can reach locally 0.48 for the largest wind turbines employed to date. In traditional aerodynamics, most CFD methods were designed to cope with high Mach number flows and consequently solve the compressible Navier-Stokes equations. This is the case of the Helicopter Multi-Block (HMB2) CFD method from Liverpool University. The present PhD thesis aims to provide an all-Mach-number capability to the HMB2 method, by implementing modified Roe schemes to account for low-Mach flows. For 2D cases, the modified Roe schemes showed great improvement in the convergence and the quality of the solution, when compared with the Original Roe and Osher schemes, and the Low-Mach Roe scheme showed the best performance. With the low-Mach capability included in the compressible solver, both MEXICO and NREL Annex XX experiments were simulated. A detailed analysis of the velocity field behind the MEXICO rotor was performed, where the low-Mach scheme (LM-Roe) showed less sensitivity on the grid size than the Osher scheme. Accurate prediction of wind turbine wake breakdown is also important for the performance analysis of the turbines and their optimal positioning within tightly-spaced wind farms. Using a fine mesh able to preserve the vortices up to 8R downstream the MEXICO rotor plane, the instabilities on the wake leading to vortex pairing were captured. FFTs of the axial velocity component enabled to identify the main harmonics in the wake. In the stable region, the wake was a perfect spiral and the main frequency was the bladepassing one. An approximate exponential growth was then observed and in the region where instabilities were present, higher frequencies dominated, leading an oscillatory pattern. Simple wake models were also investigated and a combination between a kinematic model to account for the wake initial expansion and a field model to account for the far wake decay was proposed, showing good agreement with the CFD solution. With the correct set of constants, it was proved that this simple model can be used to approximate the behaviour of wind turbine wakes with minimal computational cost. Another consequence of the increased size of wind turbines is that their stiffness lowers and aeroelasticity therefore plays an important role, since the blades can suffer great deformations. To account for the blade deformations, a tightly coupled CFD-CSD method was employed to analyse the MEXICO and NREL Annex XX wind turbines. For the latter, the tower and nacelle were considered as stiff bodies and the blades were allowed to deform. As a result of the aeroelastic calculations, the blades showed deformation in bending (towards the tower). The maximum deflections were present after the blades had passed in front of the tower, and maximum amplitudes of 0.59%R, at 20m/s were observed.