Engineering wake models are essential tools in wind farm design and operation. Their computational efficiency enables rapid layout optimization, energy calculation, and turbine control setpoint design. As wind farms grow in scale and density, wake interactions between turbines limit overall energy capture and increase structural loading. Wind Farm Control strategies have become critical for mitigating these effects. While wake steering, the intentional yaw misalignment of upstream turbines, has consistently demonstrated power gains, new dynamic control strategies are emerging. Among these, the Helix approach has shown particular promise in accelerating wake recovery and improving downstream power production. While engineering models for wake steering are well established, dedicated models for the Helix approach remain unavailable. This study presents a novel steady-state engineering model for predicting the velocity deficit and added turbulence of wind turbines operating under Helix actuation. The proposed model extends double-Gaussian velocity deficit and bell-curve– shaped turbulence intensity formulations to account for Helix-specific effects of actuation amplitude and ambient turbulence. Calibration and validation against high-fidelity large-eddy simulations demonstrate strong agreement across a wide range of operating conditions. The model accurately reproduces wake recovery trends, variations in the velocity-deficit profile, turbulence distributions, and the resulting downstream power availability. Finally, a case study on a large offshore wind farm illustrates that, under typical offshore atmospheric conditions, Helix control and wake steering yield individual power gains of up to 2.5% and 6.1%, respectively, while their combined application achieves total power gains of up to 7.1%.

Fast response calculations in the frequency domain are valuable during the initial design of floating wind turbines, where many design variants must be evaluated. A direct frequency-domain treatment of aero-elastic rotor loads is typically infeasible due to the azimuthal time dependence of the system matrices. To overcome this limitation, we introduce a perturbation-based formulation inspired by Hill's method, which reformulates the response equations into separate orders involving constant system matrices derived via Fourier decomposition. This enables accurate and efficient response computation using the fast Fourier transform (FFT). For comparison, a Laplace-based perturbation method is also developed using the Laplace transform instead of the Fourier transform. To evaluate the novel fast response methods, we develop an azimuthally periodic and fully linearized model of a floating wind turbine. The response to various load cases is computed under different inflow and floater motion conditions. The proposed Fourier-based fast response method achieves high accuracy, with peak and standard deviation errors of 2 % and 3.5 %, respectively, while reducing computation time to 2.5 s for a 4096 s simulation-significantly faster than linear (45 s) and time-domain (90 s) models. Through detailed comparison, we find that one of our approaches, the so-called single perturbation method, offers an effective trade-off between accuracy and speed, making it suitable for design and optimization studies.

Accurate modeling of atmospheric turbulence is critical for the design and operation of next-generation large-scale wind turbines, particularly those exceeding 15 MW rated capacity and spanning well above the atmospheric surface layer (typically 10 − 20% of the atmospheric boundary layer (ABL)). In this study, Large Eddy Simulations (LES) were performed to investigate turbulence characteristics at high altitudes, up to 300 m above ground level — a region increasingly relevant for large turbine rotors. Turbulence coherence was analyzed and compared with field measurements to assess the fidelity of numerical predictions. Coherence estimates from LES were validated against lidar-based measurements obtained under stable, neutral, and unstable atmospheric conditions. Results show good agreement in the coherence decay rates and cross-spectral characteristics, with notable discrepancies only at very low frequencies (on the order of several 10 ⁻⁴ Hz) and large spatial separations (on the order of several 10 ² m). Consequently, a LES-tuned empirical lateral coherence model is proposed, featuring distinct coherence decay rates for each atmospheric stability regime (stable, neutral, and unstable ABL), offering improved representation of turbulence structures across a range of operating conditions. These findings provide a valuable reference for refining turbulence models for improving load estimation methodologies for next-generation wind turbines operating at hub heights above 200 m.

During wind turbine installation or idling, the blades often operate at large angles of attack, where vortex-induced vibration (VIV) can occur. This study experimentally investigates the aerodynamic characteristics of a plunging NACA0021 airfoil at a fixed angle of attack of 90∘ and amplitude of one chord length, focusing on vortex dynamics, lock-in effect, and unsteady force generation. Phase-locked particle image velocimetry (PIV) was conducted at two reduced frequencies of 0.19 and 0.38. At the lower reduced frequency, asymmetric vortex shedding prevents synchronization between shedding and plunge motion frequencies, whereas at the higher reduced frequency, lock-in occurs with periodic shedding of separated leading- and trailing-edge vortices. Compared with previously studied surging motion under identical conditions, plunging requires a higher frequency to achieve lock-in and produces weaker wakes that break down more quickly downstream. Additionally, the aerodynamic load is extracted from the PIV flow field. For the plunging motion, the aerodynamic loads are dominated by pressure forces, with a maximum streamwise coefficient of approximately four times the static value at 90∘ angle of attack. This contrasts with the surging motion, where higher force variations are observed, and both pressure and mean momentum convection play comparable roles in the overall force. These results indicate that lock-in behavior depends strongly on both motion frequency and kinematics, where the effective angle of attack variation and the resulting vortex dynamics also determine whether synchronization can occur.

The upscaling of wind turbines has extended rotor-swept areas into the atmospheric boundary layer, several hundred meters above the surface layer. Traditional wind field models have relied on neutral surface-layer characteristics. Recent research emphasizes incorporating atmospheric stability and dynamics at higher altitudes, as larger turbines experience greater load variations due to eddies comparable in size to the rotor, causing non-uniform inflow. This study evaluates a measurement-validated coherence model for aeroelastic analysis of a 5 MW and a 22 MW turbine. The model characterizes atmospheric stability using tuned coefficients and is applied alongside stability-dependent spectral wind field models. Six seeds of 30 minute simulations were conducted for each wind turbine model ranging from near cut-in to near cut-out wind speed, in intervals of 1 m/s, using on one hand, the proposed coherence model with stability-dependent spectra and on the other hand, the IEC Kaimal coherence model. Aeroelastic results reveal distinct turbine responses to atmospheric stability. The trends of higher tower fore–aft bending moments in unstable conditions and lower moments in stable conditions, together with increased blade-root flapwise moments at above-rated wind speeds under stable, high-shear conditions, are captured. Wavelet analysis confirms that larger turbines face greater load variations because eddies are smaller than the rotor, whereas smaller turbines experience more uniform frequency-time correlations with hub-height velocity. Simulations with flexible and rigid blades and towers indicate that flexibility effects are secondary to eddy size and coherence. Overall, it is demonstrated that simple stability-dependent empirical coherence and spectral models can effectively replicate the commonly observed impact of atmospheric stability on wind turbine loads.

Yaw engineering models are commonly used as add-ons to the industrial blade element momentum (BEM) framework to improve load and power predictions by accounting for the skewed wake effect. However, existing yaw engineering models show noticeable limitations in accurately predicting the induced velocity distribution across the blade span. In this study, we employ a genetic symbolic regression （SR） approach to develop a new set of yaw engineering models for both the normal and tangential induced velocities of a static yawed wind turbine. The model regression is performed using simulation data from Reynolds-averaged Navier–Stokes (RANS) simulations with an actuator line model (ALM) of the NREL 5-MW wind turbine, covering a range of yaw angles ((Formula presented.)) and thrust coefficients ((Formula presented.)) over which the skewed wake effect is dominant. The regressed models are selected based on an optimal trade-off between accuracy and complexity, with complexity constrained to remain comparable with Branlard's yaw engineering model. The selected models are subsequently verified using three unseen cases that span different operating conditions and wind turbine models. Verification is performed through a series of evaluations, including generalization performance tests, implementation within the BEM framework to assess their aerodynamic performances, and quantitative errors and loading analyses. The results demonstrate that the proposed models improve both the amplitude accuracy and azimuthal phase of induced velocities compared with the existing models of Coleman and Branlard, enabling it to accurately capture the phase of the peak aerodynamic forces across each annulus and to predict the nonrestoring yaw moment occurring in the inboard region of the turbine, which other models fail to reproduce.

The accuracy of the Beddoes–Leishman and Risø dynamic stall models is evaluated against experiments on thick wind turbine airfoils with a relative thickness of 35% and trailing edge thicknesses of 10% and 2%, both with and without vortex generators. The dynamic lift, drag, and pitching moment coefficients simulation results are compared with the measurements, obtained in the TU Delft LTT wind tunnel at a Reynolds number of Re=1×10⁶ and dynamic reduced frequency of 0.064. The study revealed that while the aforementioned models successfully predicted the direction of the dynamic cycles, they inaccurately captured the dynamic stall behavior of thick flatback and non-flatback airfoils in all configurations, particularly in separated flows. There was no significant difference observed in the performance of the two models. The reasons for modeling failure are thoroughly examined from both fundamental and mathematical perspectives, and suggestions for improvements are provided. The findings raise concerns regarding the accuracy and reliability of the dynamic load assessment and aeroelasticity analysis for modern large wind turbines, using current dynamic stall models and underscore the necessity for enhancing the existing models.

When wind passes through the rotor of a wind turbine, the velocity is decreased while turbulence is increased. The region of decreased wind speed behind the rotor is known as the wind turbine wake and is bounded by a complex structure of helical vortices. This structure occurs to be more stable in low ambient turbulence and low tip speed ratio conditions, leading to a delayed recovery of the wake. The diminished wind speed in the wake leads to a decline in power output for downstream wind turbines, with this loss scaling proportionally to the cube of the velocity. This study uses field tests and simulations to evaluate enhanced wake recovery with segmented Gurney flaps on a 3.8-MW research wind turbine. Four Gurney flaps were attached at regions near the tip of each blade. This configuration is hypothesized to induce turbulence that destabilizes the vortex system, resulting in faster wake recovery. Field tests using a scanning LiDAR were conducted to quantify the wind turbine wake recovery between the baseline and the retrofitted configuration in various atmospheric conditions. The results show a consistent increase in wake recovery for the Gurney flap configuration, generally at all downstream distances. This was illustrated by a reduction of axial velocity deficits of roughly 10% at hub height, at five diameters downstream distance. The influence of retrofitting on turbine power and loads was limited. Summarizing, a very successful field test campaign was executed, which demonstrated the use of segmented Gurney flaps as a promising add-on to promote enhanced wind turbine wake recovery for improved overall wind farm performance.

This study experimentally investigates the performance of vortex generators (VGs) designed for steady stall control in preventing unsteady trailing-edge flow separation and dynamic stall during pitch oscillations occurring on inboard and midboard wind turbine blade sections. Surface pressure measurements are conducted in the TU Delft low-speed wind tunnel on a DU-97-W-300 airfoil undergoing pitch oscillations while equipped with VGs of various vane sizes and shapes. In steady conditions, vanes with heights smaller than the local boundary layer thickness optimally balance delaying stall following trailing-edge separation with achieving maximum lift-to-drag ratio among the tested triangular vane VGs. However, these same VGs with vane heights smaller than or equal to the steady local boundary layer thickness are insufficient to suppress the onset and upstream progression of a trailing-edge separation front in all pitching cycles. VGs whose vane height exceeds the local boundary layer thickness for a larger part of the pitch cycle prevent the onset and upstream progression of the trailing-edge separation front for a larger percentage of cycles. Contrary to past literature, rectangular vanes yield a higher steady aerodynamic efficiency than triangular vanes. Rectangular vanes also suppress trailing-edge flow separation in all pitching cycles at all tested reduced frequencies, indicating more effective boundary layer energization than triangular vanes, thus proving to be a better VG shape for steady and unsteady stall suppression on thick airfoils.

This study presents the experimental validation of regenerative wind farms (RGWFs), a novel wind farm concept designed to enhance overall wind farm performance. RGWFs employ multi-rotor systems with lifting devices (MRSLs), an innovative wind energy harvester engineered to stimulate strong vertical energy entrainment, thereby accelerating wake recovery. In the experiments, MRSLs are scaled for wind tunnel testing, with their rotors modeled using porous disks and their lifting devices represented by wings. The tested RGWFs comprise up to 3 × 3 MRSLs. Flow quantities within RGWFs and aerodynamic loads on MRSLs are measured using volumetric particle tracking velocimetry and strain gauges. Compared to conventional wind farms, flow analysis indicates that vertical energy entrainment is significantly enhanced in RGWFs, as evidenced by a more than 200 % increase in thrust on the second-row MRSLs and so on. These experimental results, which are in line with the previous numerical predictions, highlight the promising potential of RGWFs.

Large wind turbines face more intricate atmospheric conditions with turbulent coherent structures sized similarly to the rotor diameter, posing loading challenges. The present study assesses twelve distinct wind fields using the Large Eddy Simulations (LES) and International Electrotechnical Commission (IEC) Kaimal model scaled to their LES counterpart. The hub height wind speed in the different cases was set to 8.5 m/s (below-rated), 11.5 m/s (at-rated), and 14.5 m/s (above-rated). In a previous study, it was found that the unscaled IEC model-based wind field is conservative and scaled IEC model-based wind fields were found to yield different loads than upon use of LES-based wind fields in different atmospheric stability conditions. The present study aims to understand these differences. Utilizing Spectral Proper Orthogonal Decomposition (SPOD), the original wind fields were decomposed and reconstructed to study the influence of large and small coherent structures represented by their distinct frequencies. SPOD analysis was complemented by wind field spectral analysis considering atmospheric surface layer height, integral length scales, and co-coherence estimates. Integral length scales in the scaled IEC Kaimal model were found to be half of those in unstable atmosphere LES wind fields. The aero-elastic impact on the IEA 22 MW reference wind turbine with a 280 m rotor diameter was evaluated. The analysis reveals that large coherent structures, particularly low-frequency (≤0.06 Hz) ones, significantly impact wind turbine loads, contingent upon atmospheric stratification. Compared to the scaled IEC Kaimal model wind field, the maximum tower fore–aft bending moment and the maximum blade root flap-wise bending moment were found to be higher, for example, by 10% and 5% respectively in an unstable atmosphere during below-rated wind turbine operation. In the same scenario, standard deviation of the tower fore–aft bending moment was found to be higher by up to 50% while standard deviation of the blade root flap-wise bending moment was found to be lower by up to 25%. These findings underscore the critical importance of accurately modeling atmospheric turbulence and its coherent structures for more reliable design and operation of large wind turbines.

The airfoil DU91-W2-150 was investigated in the Low Speed Low Turbulence Tunnel at the Delft University of Technology to study unsteady aerodynamics. This experimental study tested the airfoil under a wide range of angles of attack (AoA) from 0° to 310° at three Reynolds numbers ((Formula presented.)) from (Formula presented.) to (Formula presented.). Pressure on the airfoil surface was measured and particle image velocimetry (PIV) measurements were conducted to capture the flow field in the wake. By examining the force coefficient and comparing the wake contours, it shows that an upwind concave surface provides a higher load compared to a convex surface upwind case, highlighting the critical role of surface shape in aerodynamics. When comparing separation at specific locations along the chord for all three (Formula presented.) values, it is observed that as (Formula presented.) increases, separation tends to occur at lower AoA, both for positive stall and negative stall. The examination of the aerodynamic force variation indicates that, during reverse flow, fluctuations are more pronounced compared to forward flow. This is owing to separation occurring at the aerodynamic leading edge (geometric trailing edge) in reverse flow. In terms of vortex shedding frequency, the study found a nearly constant normalized Strouhal number ((Formula presented.)) of 0.16 across various (Formula presented.) and AoA values in fully separated regions, indicating a consistent pattern under these conditions. However, a slight increase in (Formula presented.), between 0.16 and 0.20, was observed for AoA values exceeding 180°, possibly due to the convex curvature of the airfoil in the upwind direction. In conclusion, this research not only corroborates previous findings for small AoA values but also adds new data on the aerodynamic behavior of the DU91-W2-150 airfoil under large AoA values, offering various perspectives on the effects of surface curvature, (Formula presented.), and flow conditions on key aerodynamic parameters.

With the increasing size of floating offshore wind turbines (FOWTs), stall-induced aeroelastic instability has become a critical issue. This study numerically investigates this instability for FOWTs at stand-still conditions using time and frequency domain approaches. A nonlinear aeroelastic model based on quasi-steady theory and a linearized version are used for time and frequency domain simulations, respectively. Hydrodynamic damping considers both radiation and viscous drag effects. The aeroelastic instability of a stand-still NREL OC3-Hywind 5MW FOWT is analyzed for various inflow yaw misalignment angles. Frequency domain simulation shows rotor edgewise and tower side-side modes exhibit stall-induced instability due to aerodynamic negative damping at specific yaw misalignment and azimuth angles. The platform's yaw mode also shows small negative damping, despite large hydrodynamic damping, while other platform modes remain dynamically stable. Safety margins of FOWTs are analyzed for multi-mode stability, and an active control strategy is proposed to prevent stall-induced instability in all unstable modes. Limit cycle oscillations in the rotor's in-out plane are observed from time domain simulation. Instability regions predicted by both analyses highly overlap, but frequency domain results are more conservative. Blade instability may cause high-frequency vibrations in platform movements with limited amplitudes and severe oscillations in tower structures.

Numerical simulations of wind farms consisting of innovative wind energy harvesting systems are conducted. The novel wind harvesting system is designed to generate strong lift (vertical force) with lifting devices. It is demonstrated that the trailing vortices generated by these lifting devices can substantially enhance wake recovery rates by altering the vertical entrainment process. Specifically, the wake recovery of the novel systems is based on vertical advection processes instead of turbulent mixing. Additionally, the novel wind energy harvesting systems are hypothesized to be feasible without requiring significant technological advancements, as they could be implemented as multi-rotor systems with lifting devices (MRSLs), where the lifting devices consist of large airfoil structures. Wind farms with these novel wind harvesting systems, namely MRSLs, are termed regenerative wind farms, inspired by the concept that the upstream MRSLs actively entrain energy for the downstream ones. With the concept of regenerative wind farming, much higher wind farm capacity factors are anticipated. Specifically, the simulation results indicate that wind farm efficiencies can be nearly doubled by replacing traditional wind turbines with MRSLs under the tested conditions, and this disruptive advancement can potentially lead to a profound reduction in the cost of future renewable energy.

Denser turbine spacing in wind farms leads to increased wake interactions, causing power losses when each turbine operates under its own greedy control scheme. To mitigate these effects, research is exploring strategies that consider the entire wind farm rather than singular turbines. The so-called helix approach has recently gotten significant attention from the research community. It aims to reduce wake losses through periodic individual pitch control. Wake steering on the other hand uses yaw actuation to laterally deflect the wake away from downstream turbines. In this paper, we adapt and validate a steady-state surrogate model to compute the time-averaged velocity field behind a wind turbine operating with the helix approach. The model is tuned using data from Large Eddy Simulations. We compare the helix model to wake steering and baseline operation in a wind farm case study, demonstrating that the helix approach offers promising benefits under specific wind conditions.

The aerodynamics of the multi-rotor system with lifting-devices (MRSL), an innovative concept of wind energy harvesting machine, is preliminary investigated using Large Eddy Simulation (LES) with actuator techniques. In the current setup, turbulent inflow conditions are considered, but inflow wind shear is excluded. Consistent with previous studies, the results demonstrate faster wake recovery of the MRSL compared to its conventional counterpart, namely the wind turbine system without the lifting-devices. Additionally, a set of high-fidelity simulations further reveals that the enhanced wake recovery is robust under both laminar and turbulent inflow conditions, remaining largely unaffected by variations in the ambient turbulence level. The present work provides proof-of-concept evidence that the effectiveness of MRSLs is not significantly hindered by ambient turbulence, motivating future research to evaluate their performance within a realistic atmospheric boundary layer.