Yaw misalignment is currently being treated as one of the most promising methods for optimizing the power of wind farms. Therefore, detailed knowledge of the impact of yaw on the wake development is necessary for a range of operating conditions. This study numerically investigates the wake development behind a single yawed wind turbine operating at different tip-speed ratios and yaw angles using the actuator-line method in the spectral-element code Nek5000. It is shown that depending on the tip-speed ratio, the blade loading varies along the azimuth, resulting in a wake that is asymmetric in both the horizontal and vertical directions. Large tip-speed ratios as well as large yaw angles are shown to decrease the vertical asymmetry of the yaw-induced counter-rotating vortex pair. Both parameters have the effect that they increase the spanwise force induced by yaw relative to the wake rotation. However, while the strength of the counter-rotating vortex pair in the far wake increases with yaw angle, it is shown to decrease with the tip-speed ratio. The vertical shift in the wake center is found to be highly dependent on the yaw angle and the tip-speed ratio. These detailed insights into the yawed wake are important when optimizing potential downstream turbines. 

Sheared velocity profiles pervade all wind-turbine applications, thus making it important to understand their effect on the wake. In this study, a single wind turbine is modeled using the actuator-line method in the incompressible Navier–Stokes equations. The tip vortices are perturbed harmonically, and the growth rate of the response is evaluated under uniform inflow and a linear velocity profile. Whereas previous investigations of this kind were conducted in the rotating frame of reference, this study evaluates the excitation response in the fixed frame of reference, thus necessitating a frequency transformation. It is shown that increasing the shear decreases the spatial growth rate in the upper half of the wake while increasing it in the lower half. When scaled with the local tip vortex parameters, the growth rate along the entire azimuth collapses to a single value for the investigated wavenumbers. We conclude that even though the tip-vortex breakdown is asymmetric in sheared flow, the scaled growth rates follow the behavior of axisymmetric helical vortices. An excitation amplitude reduction by an order of magnitude extends the linear growth region of the wake by one radius for uniform inflow. In the sheared setup, the linear growth region is extended further in the top half than in the bottom half because of the progressive distortion of the helical tip vortices. An existing model to determine the stable wake length was shown to be in close agreement with the observed numerical results when adjusted for shear.

The hydrodynamic stability of a vortex system behind two in-line wind turbines operating at low tip-speed ratios is investigated using the actuator-line method in conjunction with the spectral-element flow solver Nek5000. To this end, a simplified setup with two identical wind turbine geometries rotating at the same tip-speed ratio is simulated and compared with a single turbine wake. Using the rotating frame of reference, a steady solution is obtained, which serves as a base state to study the growth mechanisms of induced perturbations to the system. It is shown that, already in the steady state, the tip vortices of the two turbines interact with each other, exhibiting the so-called overtaking phenomenon. Hereby, the tip vortices of the upstream turbine overtake those of the downstream turbine repeatedly. By applying targeted harmonic excitations at the upstream turbine's blade tips a variety of modes are excited and grow with downstream distance. Dynamic mode decomposition of this perturbed flow field showed that the unstable out-of-phase mode is dominant, both with and without the presence of the second turbine. The perturbations of the upstream turbine's helical vortex system led to the destabilization of the tip vortices shed by the downstream turbine. Two distinct mechanisms were observed: for certain frequencies the downstream turbine's vortices oscillate in phase with the vortex system of the upstream turbine while for other frequencies a clear out-of-phase behaviour is observed. Further, short-wave instabilities were shown to grow in the numerical simulations, similar to existing experimental studies [1].

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.

This article summarizes the results of the "Blind test 5" workshop, which was held in Visby, Sweden, in May 2017. This study compares the numerical predictions of the wake flow behind a model wind turbine operated in yaw to experimental wind tunnel results. Prior to the workshop, research groups were invited to predict the turbine performance and wake flow properties using computational fluid dynamics (CFD) methods. For this purpose, the power, thrust, and yaw moments for a 30 degrees yawed model turbine, as well as the wake's mean and turbulent streamwise and vertical flow components, were measured in the wind tunnel at the Norwegian University of Science and Technology (NTNU). In order to increase the complexity, a non-yawed downstream turbine was added in a second test case, while a third test case challenged the modelers with a new rotor and turbine geometry. Four participants submitted predictions using different flow solvers, three of which were based on large eddy simulations (LES) while another one used an improved delayed detached eddy simulation (IDDES) model. The performance of a single yawed turbine was fairly well predicted by all simulations, both in the first and third test cases. The scatter in the downstream turbine performance predictions in the second test case, however, was found to be significantly larger. The complex asymmetric shape of the mean streamwise and vertical velocities was generally well predicted by all the simulations for all test cases. The largest improvement with respect to previous blind tests is the good prediction of the levels of TKE in the wake, even for the complex case of yaw misalignment. These very promising results confirm the mature development stage of LES/DES simulations for wind turbine wake modeling, while competitive advantages might be obtained by faster computational methods.

Previous attempts to describe the structure of wind turbine wakes and their mutual interaction were mostly limited to large-eddy and Reynolds-averaged Navier-Stokes simulations using finite volume solvers. We employ the higher-order spectral element code Nek5000 to study the influence of numerical aspects on the prediction of the wind turbine wake structure and the wake interaction between two turbines. The spectral element method enables an accurate representation of the vortical structures, with much lower numerical dissipation than the more commonly used finite volume codes. The blades are modeled as body forces using the actuator line method (ACL) in the incompressible Navier-Stokes equations. Both tower and nacelle are represented with appropriate body forces. An inflow boundary condition is used which emulates the homogeneous isotropic turbulence of wind tunnel flows. We validate the implementation with results from experimental campaigns undertaken at the Norwegian University of Science and Technology, investigate parametric influences and compare computational aspects with the existing finite volume codes. The results show good agreement between the experiments and the numerical simulations.

Previous attempts to describe the structure of wind turbine wakes and their mutual interaction were mostly limited to large-eddy and Reynolds-averaged Navier-Stokes simulations using finite-volume solvers. We employ the higher-order spectral-element code Nek5000 to study the influence of numerical aspects on the prediction of the wind turbine wake structure and the wake interaction between two turbines. The spectral-element method enables an accurate representation of the vortical structures, with lower numerical dissipation than the more commonly used finite-volume codes. The wind-turbine blades are modeled as body forces using the actuator-line method (ACL) in the incompressible Navier-Stokes equations. Both tower and nacelle are represented with appropriate body forces. An inflow boundary condition is used which emulates homogeneous isotropic turbulence of wind-tunnel flows. We validate the implementation with results from experimental campaigns undertaken at the Norwegian University of Science and Technology (NTNU Blind Tests), investigate parametric influences and compare computational aspects with existing numerical simulations. In general the results show good agreement between the experiments and the numerical simulations both for a single-turbine setup as well as a two-turbine setup where the turbines are offset in the spanwise direction. A shift in the wake center caused by the tower wake is detected similar to experiments. The additional velocity deficit caused by the tower agrees well with the experimental data. The wake is captured well by Nek5000 in comparison with experiments both for the single wind turbine and in the two-turbine setup. The blade loading however shows large discrepancies for the high-turbulence, two-turbine case. While the experiments predicted higher thrust for the downstream turbine than for the upstream turbine, the opposite case was observed in Nek5000.