The actuator-line method is used together with the incompressible Navier–Stokes equations to investigate the flow development behind wind turbines. Initial investigations focus on providing a thorough validation of the implementation in the spectral-element flow solver Nek5000 against existing numerical and experimental datasets. It is shown that the current implementation gives an accurate representation of the flow field for different turbine geometries, inflow conditions, yaw misalignment, and when considering multiple turbines. This enables an in-depth study of the wake physics in these configurations.

The yawed wind-turbine wake development is shown to depend on the tip-speed ratio, both in terms of the wake deficit and the generation of the counter-rotating vortices known to occur in yawed turbine wakes. For lower tip-speed ratios the wake deficit exhibited significant asymmetries with respect to the horizontal plane due to the advancing/retreating effect. At high tip-speed ratios this effect became negligible compared to the skewed wake effect, which affects the symmetry with respect to the vertical plane. These inhomogeneities in the averaged wake development also affect the tip-vortex breakdown, leading to different locations of the tip-vortex breakdown along the wake azimuth due to the significant azimuthal variations of the tip-vortex strength and convection velocity. An analysis of the interaction of a yawed wind-turbine wake with a sheared inflow exposed a dependency of the wake deflection and recovery on the yaw orientation, which then resulted in significant differences in the combined power output of a two-turbine setup. More detailed studies of the tip-vortex breakdown in sheared flows using single-frequency perturbations revealed that a sheared inflow changes the spatial growth rate of the tip vortices along the vertical axis, due to the varying tip-vortex convection velocity. However, by applying a scaling based on local vortex parameters, the growth rates collapse to the canonical case of an infinite row of point vortices. Finally, an idealized scenario of two in-line turbines with a steady tip-vortex development is investigated. By applying a range of controlled perturbations, modes were excited, which exhibited in-phase or out-of-phase displacement between the vortex system of the upstream and the downstream turbine for certain frequencies.

Den så kallade actuator line-metoden används tillsammans med inkompressibla Navier–Stokes ekvationer för att undersöka strömningens utveckling bakom vindturbiner. Inledande studier syftar till att utförligt validera implementationen i spektralelementkoden Nek5000 mot befintliga numeriska och experimentella datamängder. Det visas att den nuvarande implementationen ger en noggrann representation av strömningsfältet för alla undersökta turbingeometrier. Vidare fångas utvecklingen hos vaken väl för en rad olika inflödesvillkor, förturbingirning, och under interaktion mellan flera turbiner.

Vakutvecklingen för en girad turbin visas bero signifikant på kvoten mellan vingspetsens och friströmmens hastighet, både när det gäller hastighetsunderskottet i vaken och bildningen av de motroterande vakvirvlarna. För låga hastighetskvoter mellan vingspetsen och friströmmen uppvisar vakens hastighetsunderskott en betydande asymmetri med avseende på horisontalplanet genom en så kallad avancerande/retirerande effekt. För höga hastighetskvoter blir denna effekt däremot försumbar i jämförelse med vakens skevhet som påverkar symmetrin med avseende på vertikalplanet. Dessa inhomogeniteter i den medelvärdesbildade vakutvecklingen påverkar också det turbulenta nedbrottet hos vingspetsvirvlarna, vilket inträffar vid olika positioner i vinkelled på grund av signifikanta vinkelvariationer hos virvelstyrkan och konvektionshastigheten. En analys of interaktionen mellan en girad turbinvak och en inkommande skjuvströmning avslöjar ett beroende hos vakens förskjutning och återhämtning på girningens riktning, vilket resulterar i betydande skillnader i den sammantagna effekten hos två turbiner. Mer detaljerade studier av spetsvirvlarnas nedbrott i skjuvströmningar med enfrekvensstörningar visar att ett skjuvat inflöde förändrar den spatiella tillväxtgraden längs den vertikala axeln på grund av varierande konvektionshastighet hos spetsvirvlarna.Tillväxtgraderna sammanfaller dock med motsvarande värde för det klassiska fallet med två oändliga virvelrader, om de skalas med lokala virvelparametrar. Slutligen studeras en stationär virvelutveckling för ett idealiserat fall bestående av två turbiner i linje med varandra. Genom att applicera en rad kontrollerade störningar, exciteras moder som beroende på frekvens uppvisar förskjutningar i eller ur fas med virvelsystemen från turbinen uppströms och nedströms.

Vortices are present in nature and in many flows of industrial importance. The stability of configurations of vortices can have real-world consequences, because vortices play a crucial role in accelerated mixing. In particular, vortices are present in the wake of wind turbines and other rotors. Their blades create a system of multiple helical tip and hub vortices in the wake. The stability of the tip vortices greatly influences the wake recovery behind a turbine and, consequently, can affect the power production and fatigue of a downstream wind turbine in clustered wind farms. Also, concentrated vortices can cause vortex-structure interaction which increases vibration and noise. In this work, the stability of vortices is studied by analytical models and Navier-Stokes simulations. The vorticity generated in these simulations was studied in order to develop improvements to the numerical methods used to simulate blades and wings.

Numerical simulations of a moving rotor, representing a floating offshore wind turbine, showed that the wake is dominated by the stability modes predicted by the linear stability theory. Also, the observation that the stability of helical vortices has properties that can be related to the stability of a two-dimensional row of vortices, also noted previously in other works, motivated the development of a new formulation to study the stability of two-dimensional potential flows, based on the bicomplex algebra. Models based on vortex filaments and the Biot-Savart law were developed to study the stability of the system of multiple helical vortices created by turbine blades. The results indicate that the linear stability of the tip vortices is independent of the linear stability of the hub vortices (and vice-versa). For more complex configurations, such as two in-line turbines or blades that create multiple vortices near the tip, the numerical simulations and analytical studies indicate a more complex scenario, with multiple vortices interacting.

The Navier-Stokes simulations employ the actuator line method (ALM), which is a method used to model blades that allows coarser grids, reducing computational costs. In this method, the blades are represented by body forces that are calculated from the local flow velocity and airfoil data. However, until recently, the actuator line method misrepresented the forces near the tip of the blades. The recently developed vortex-based smearing correction resolved some of these limitations. In this work, the understanding of the vorticity generated by actuator lines is used to develop more accurate corrections for the velocity induced by a smeared vortex segment and for the magnitude of the vorticity generated in the simulations. Also, a non-iterative procedure for the smearing correction is proposed based on the lifting line method. These modifications improve the agreement of the ALM with a non-linear lifting line method. For the first time, configurations typical of airplane aerodynamics are simulated with the ALM, such as a wing with winglets and a combination of horizontal and vertical tails. The accuracy of these results may motivate other communities to adopt the ALM for a diverse set of applications, beyond rotor aerodynamics.