Vortex generators (VGs) have been widely applied to wind turbines thanks to their potential to increase aerodynamic performance. Due to the complex inflow perceived by a rotor and the proneness to flow separation, VGs on wind turbines usually experience highly unsteady flow. While there are models that exist to simulate the steady effects of VGs, we lack a fast and efficient tool to model the unsteady performance of airfoils equipped with VGs. This paper adopts an unsteady double-wake panel model with viscous–inviscid interaction developed to simulate a vertical axis turbine in dynamic stall, adding the capability of predicting the dynamic aerodynamic performance of VG-equipped airfoils. The results of a series of steady and unsteady cases of an airfoil with different VG configurations in various pitch motions in free and forced transition are verified against experimental data. Results show that the double wake model offers results with sufficient accuracy compared with experimental data to claim the model's validity in a preliminary evaluation of an airfoil's capability to prevent stall with VGs. A few limitations, including the accuracy in prediction the transition location, separation, and reattachment, have been identified for future development.

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Modern slender wind turbine blades use thick inboard airfoils and thicker trailing edges prone to flow separation. The increasing size of these flexible blades amplifies the importance of considering unsteady aerodynamics during the design phase. Environmental conditions result in Leading Edge Erosion (LER), further complicating the sectional unsteady aerodynamic behaviour. Although vortex generators are a well-studied method for passive separation control under steady conditions, their influence on unsteady aerodynamics for clean and rough blade sections is an area that requires further exploration. While some numerical studies exist, reliable experimental data is lacking in the literature. This work presents experimental results on the dynamic stall behaviour of a DU97W300 airfoil, a typical thick root section. The investigation covers both clean and rough conditions, both with and without VGs, to create an understanding of how VGs impact dynamic stall. Moreover, various VG array configurations are used to study the parametric dependence of dynamic stall phenomena on the VG array parameters.

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Using Large Eddy Simulation (LES) with Actuator Line Model (ALM), this work investigates the system of two surging wind turbine rotors operating under realistic turbulent inflow conditions (TI = 5.3%). The two rotors are placed in tandem with a spacing of 5D and the surging motions are harmonic. A widely used torque controlling strategy, MPPT (Maximum Power Point Tracking), is implemented to ensure a maximium power extraction under all conditions. The rotor performances as well as the field data are surveyed to examine the effectiveness and impacts of the controller. It is found that the power performances of the surging rotors are benefited by the controller with a small margin (∼1%) when the surging motions are moderate. The results also show that the controller reacts much slower than the considered surging frequency, making the power performances of the rotors worse than the quasi-steady predictions (targeted values) and complicating the system dynamics. In general, the implementation of the controller has minor impacts on the wake characteristics; however, the strengths of Surging Induced Periodic Coherent Structures (SIPCS) are found to be enhanced.

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The topic of vortex-induced vibrations on a wind turbine blade has recently gained much attention due to its growing size and flexibility. To address this concern, a wind tunnel test was conducted to study the forced plunging and surging motion of a NACA0021 airfoil at 90° angle of attack. Results indicate that vortex lock-in occurred for a motion amplitude of one chord length even for a small frequency ratio (between motion frequency and static Strouhal frequency) of 0.39. Analysis of the drag coefficient, derived from the phase-averaged Particle Image Velocimetry (PIV) data, shows that a plunging airfoil experiences higher average loading than a surging airfoil, which is deemed to be more harmful considering the higher loading in the crossflow-direction due to the variation of effective angle of attack.

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As the demand for renewable energy increases, wind turbine rotors will become larger with slender blades. Vortex Generators (VGs) are used for passive flow control to avoid flow separation and reduce unsteady loading on the thick root section of slender blades due to their simplicity, inexpensiveness, and the ability to retrofit them to blades. Aerodynamic load calculations for VGs involve long experimental campaigns or resource intensive CFD calculations. Due to their inherent time-intensive nature aeroelastic optimisation and design tools prefer to use simplified but accurate analysis tools for aerodynamic load calculations of clean airfoils. One such class of tools are viscous-inviscid interaction solvers that use Integral Boundary Layer (IBL) methods for viscous calculations in the boundary layer coupled with an inviscid solver for the rest of the domain. The most popular example of this tool is XFOIL. An engineering model for VGs in IBL methods has previously been developed and implemented in XFOIL. In this research, the model parameters are tuned for implementation in another tool RFOIL based on XFOIL. RFOIL has been developed for accurate and robust analysis of wind turbine airfoils with improvements for thick airfoils and rotational corrections. The aerodynamic performance predicted the VG model in both XFOIL and RFOIL is then validated with an extensive database of airfoil data consisting of airfoils between 21% to 60% thickness, as well as Reynolds numbers between 1 million to 14 million, equipped with and without VGs. Finally, the computation time for the VG model is compared with that for a clean airfoil analysis in the same viscous-inviscid interaction solvers RFOIL and XFOIL. The investigation provides an overview of the usability of the engineering model in airfoil design methodologies in the wind turbine industry.

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Traditional methods for determining the load of an object in unsteady cases, such as Control-volume Momentum Integration (CMI) and Noca methods, encounter challenges related to near-body acceleration and pressure estimation. This prompts the need for innovative techniques to overcome these limitations. This study introduces a novel vorticity-based approach to expand classical load determination methods. The numerical results of an unsteady actuator disc (AD) CFD simulation are used to verify and quantify the uncertainty of the three methods. In the AD model, the load is prescribed and used as a source term. The velocity and pressure fields are solved from the Navier-Stokes equations using the open-source CFD package OpenFOAM, which offers a robust validation framework. Systematic examination of the robustness and accuracy of the three methods across various load and motion unsteady scenarios reveals that the proposed vorticity-based method excels in steady-state scenarios, exhibiting the highest level of robustness and accuracy. In contrast, the traditional CMI method proves more robust and accurate in pure motion cases. In scenarios involving static and moving AD with load variations, the new vorticity-based method demonstrates superior robustness and accuracy, mainly when moderate vorticity dynamics. Conversely, in cases with increased vorticity dynamics in the wake, the accuracy of the vorticity-based method decreases, with the CMI method showing superiority.

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With the growing trend towards larger wind turbine rotor diameters, the impact of wind shear on rotor performance and loads becomes increasingly significant. Atmospheric stability strongly influences wind shear, leading to higher wind shear under stable atmospheric conditions. In this study, the aeroelastic performance of the IEA 22 MW rotor is assessed under inflow conditions generated by different methods. Inflow conditions were generated using turbulence models specified in the IEC Standards and also by Large Eddy simulations. Standalone OpenFAST simulations were conducted with the respective inflow conditions. It was found that at rated and above-rated wind speeds, the time-averaged wind turbine design loads were higher in stable atmospheric conditions, in comparison to the IEC NTM inflow conditions, while the opposite held for below-rated wind speeds. Specifically, the time-averaged root flapwise bending moment and rotor thrust were found to be higher by up to 7% in stable atmospheres. However, maximum design and fatigue loads were considerably higher in the IEC NTM case due to elevated turbulence levels. Compared to the IEC NTM case, the damage equivalent root flapwise bending moment was found to be 30% to 70% lower in the different scenarios.

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The impact of surge motion on aerodynamic unsteadiness in modern floating offshore wind turbines (FOWT) is a well-recognized phenomenon. When coupled with advanced controllers integrated into these turbines, it can lead to fluctuations in power output. This paper introduces a state-space model that incorporates dynamic inflow effects resulting from surge motion and a PID pitch controller. Additionally, an observation equation is formulated to predict the system power output. Through time series validations, the proposed state-space model demonstrates its ability to accurately capture power responses influenced by surge motions. The developed model serves as a valuable tool for the comprehensive analysis of FOWT, allowing for the exploration of the intricate interplay between unsteady aerodynamics, advanced control mechanisms, and power output.

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This study presents a comprehensive numerical analysis of a full-scale horizontal-axis floating offshore wind turbine (FOWT) rotor subjected to harmonic surging motions under both laminar and turbulent inflow conditions. Utilizing high-fidelity computational fluid dynamics (CFD) simulations, namely, large eddy simulation (LES) with actuator line model (ALM), this research investigates the rotor performance, wake characteristics, and wake structures of a surging FOWT in detail. The study delves into the influence of varying inflow turbulence intensities, surging settings, and their interplay on the aerodynamic performance and the wake aerodynamics of a FOWT rotor. The results show that, through employing the phase-averaging technique, surge-induced periodic coherent structures (SIPeCS) can be identified in the wake of all the surging cases studied, irrespective of the inflow conditions and the surging settings. Additionally, the findings show that the faster wake recovery observed in the surging cases is not caused by enhancing the instability-induced turbulence level, a previously accepted hypothesis. Instead, the results indicate that it is due to the enhanced advection process resulting from the induction fields of SIPeCS that causes the wake to recover faster. The analysis of rotor performance shows that the time-averaged rotor performances are affected by the intricate aerodynamics arising from the surging motions. With certain surging settings, the time-averaged thrust and the time-averaged power of a surging rotor are found to be simultaneously lower and higher compared with those of a fixed rotor. Furthermore, the study underscores the importance of considering both the magnitude of surging and the rate of surging simultaneously to fully characterize the hysteresis load on a surging rotor.@en

Machine learning method has always been popular to solve wind turbine related problems at a data level. However, with the limitation of the availability of relevant data, transfer learning has gained increasing attention. In this study, traditional machine learning method of artificial neural networks (ANN), together with parameter-based transfer learning method has been used to estimate wind turbine load. First, ANN load model was built for DTU 10MW wind turbine as well as NREL 5MW wind turbine. Then, parameter-based transfer learning has been applied to the above-mentioned models to estimate load for a different turbine type or two mixed turbine types. Results indicate that ANN method provides good estimation on wind turbine fatigue load. For DTU 10MW ANN model, the trend of accuracy becomes steady as the number of input samples increases and 1500 samples is deemed as the optimal number of samples for training DTU 10MW. In addition, with transfer learning, it was succeeded in building NREL 5MW model with corresponding DTU 10MW pretrained model but failed in establishing mixed dataset model neither with DTU 10MW nor with NREL 5MW pretrained model. @en

Different Design Driving Load constraints (DDLs), are explored in this work to determine under which constraints and conditions a winglet can have an added value to the wind turbine blade design. Multi-objective Bayesian optimization is used to maximize the rotor's power production while minimizing the flapwise DDLs. Surrogate models, created using machine learning techniques such as Gaussian Processes and Bayesian Neural Networks, are used in combination with an acquisition function, to determine what designs should be evaluated by the lifting line model AWSM, with the goal to obtain designs that lie on the Pareto front of two or more objectives. The recent Bayesian Neural Networks as surrogate model were able to find the Pareto-front most effectively in this work. Furthermore, the results show that different DDL constraints led to different winglet designs, with noticeable differences between upwind and downwind winglet designs. Winglet designs were found to be able to increase power without increasing the thrust, root flapwise bending moment and flapwise bending moment at radial locations on the blade. A noticeable increase in power was found when introducing sweep to the winglet design.

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Floating offshore wind turbines may experience large surge motions, which can cause blade–vortex interaction if they are similar to or faster than the local wind speed. Previous research hypothesized that this blade–vortex interaction phenomenon represented a turbulent wake state or even a vortex ring state, rendering the actuator disc momentum theory and the blade element momentum theory invalid. This hypothesis is challenged, and we show that the actuator disc momentum theory is valid and accurate in predicting the induction at the actuator in surge, even for large and fast motions. To accomplish this, we develop a dynamic inflow model that simulates the vorticity–velocity system and the effect of motion. The model's predictions are compared to other authors' results, a semi-free-wake vortex ring model, other dynamic inflow models, and CFD simulations of an actuator disc in surge. The results show that surge motion and rotor–wake interaction do not result in a turbulent wake or vortex ring state and that the application of actuator disc momentum theory and blade element momentum theory is valid and accurate when applied correctly in an inertial reference frame. In all cases, the results show excellent agreement with the higher-fidelity simulations. The proposed dynamic inflow model includes a modified Glauert correction for highly loaded streamtubes and is accurate and simple enough to be easily implemented in most blade element momentum models.@en

Navier-Stokes actuator disc models have become a mature methodology for investigating wind turbine rotor performance with numerous articles published annually making use of this approach. Despite their popularity, their ability to predict near wake expansion remains questionable. The objective of this paper is to analyse the predictive ability of actuator disc models and compare results with other popular types of codes. The methodology employs the use of an actuator disc Computational Fluid Dynamics approach to model an actuator disc and a real (finite bladed) turbine case. Results are validated with existing experimental data. In addition, results from an actuator line model with and without tip corrections and a 3D vortex panel method are presented to aid the discussion. Results show that all models give a poor wake expansion prediction particularly in the inboard to mid-board areas. A good prediction is found in the outboard regions. In addition, contrary to the well known positive effects of tip corrections on load prediction, this work shows that this does not bring any particular benefit on wake expansion prediction. The conclusions from this work help to guide the use of actuator disc models in more complex flow scenarios including floating offshore wind turbine analysis.

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The currently most used theory for rotor aerodynamics — Blade Element Momentum is based on the assumption of stationary wake conditions. However, an unsteady rotor loading results in an unsteady wake flow field. This work aims to study the impact of an unsteady actuator disc on the wake flow field using a free wake vortex ring model. The numerical results are compared to a wind tunnel measurement, where the wake flow of an actuator disc model undergoing transient load was obtained. The numerical results complement the experimental work while providing information such as the vorticity field and contributions from different vortex elements. The velocity at different locations is compared between the experimental and numerical results. The observed velocity peaks in the experimental results are also observed in the numerical results. A steeper ramp time results in a steeper velocity transient slope, and in turn in a larger amplitude of peak values. It is revealed that the rolling-up processes is the main cause for the velocity difference at various locations and in the three cases by decomposing velocity induced by different vortex element.

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Two new engineering models are presented for the aerodynamic induction of a wind turbine under dynamic thrust. The models are developed using the differential form of Duhamel integrals of indicial responses of actuator disc type vortex models. The time constants of the indicial functions are obtained by the indicial responses of a linear and a nonlinear actuator disc model. The new dynamic-inflow engineering models are verified against the results of a Computational Fluid Dynamics (CFD) model and compared against the dynamic-inflow engineering models of Pitt-Peters, Øye, and Energy Research Center of the Netherlands (ECN), for several load cases. Comparisons of all models show that two time constants are necessary to predict the dynamic induction. The amplitude and phase delay of the velocity distribution shows a strong radial dependency. Verifying the models against results from the CFD model shows that the model based on the linear actuator disc vortex model predicts a similar performance as the Øye model. The model based on the nonlinear actuator disc vortex model predicts the dynamic induction better than the other models concerning both phase delay and amplitude, especially at high load.

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Blade Element Momentum (BEM) is the most important aerodynamic analysis method for wind turbines. BEM is derived assuming stationary conditions, which limits its ability to model the unsteady aerodynamic effects. This becomes increasingly relevant for the flexible blades of current large-scale turbines, and the employment of passive and active aerodynamic control strategies, such as yaw, pitch control and smart rotor control. Currently, sub-models are included to consider the unsteady aerodynamic effects for wind turbine design. Previous research developed several dynamic-inflow engineering models to be integrated into BEM, to account for the unsteady flow acceleration. However, their applicability for unsteady load and the relative performance between the models are not fully known. The development of the dynamic wake of an actuator disc under unsteady load needs further understanding, to improve the engineering prediction of dynamic-inflow effect. This research aims to evaluate the accuracy of BEM with current dynamic-inflow engineering models; to further understand the dynamic wake flow-field of an actuator disc undergoing unsteady load; to improve current dynamic-inflow engineering models for wind turbine design using numerical and experimental approaches. A free wake vortex ring (FWVR) model is firstly developed. The accuracy of BEM with current dynamic-inflow engineering models of Pitt-Peters, Øye and ECN in predicting the induction of an actuator disc with unsteady load is verified using the developed FWVR model. The wake flow response of an actuator disc undergoing unsteady loads is studied experimentally by using a disc model with variable porosity. The unsteady load is generated by a ramp type variation of porosity of the disc, at several reduced times of the ramp motion. The wake development of an actuator disc undergoing the same unsteady load tested in the experiments is further studied using the FWVR model. The steady actuator-disc model is extended to unsteady load. Results from this linear actuator-disc model are compared with those from the FWVR model. Finally, a new engineering model is developed using the differential form of the Duhamel’s integrals of indicial response of the actuator-disc type vortex-models. The time constants of the indicial functions are obtained by the indicial responses of a linear and a nonlinear actuator-disc model, respectively. The work provides more insights into the wake development of an unsteady actuator disc. The experimental results create a database for validation of unsteady numerical models, in prediction of the dynamic induction in the near wake of an actuator disc or a rotor. The limitation of current dynamic-inflow engineering models are evaluated and discussed. The new engineering model, which is developed based on the indicial response of the nonlinear actuator-disc model, can better predict the dynamic-inflow effects, especially for the radial distribution of the dynamic-inflow effect. @en

The Blade Element Momentum model, which is based on the actuator disc theory, is still the model most used for the design of open rotors. Although derived from steady cases with a fully developed wake, this approach is also applied to unsteady cases, with additional engineering corrections. This work aims to study the impact of an unsteady loading on the wake of an actuator disc. The load and flow of an actuator disc are measured in the Open Jet Facility wind tunnel of Delft University of Technology, for steady and unsteady cases. The velocity and turbulence profiles are characterized in three regions: the inner wake region, the shear layer region and the region outside the wake. For unsteady load cases, the measured velocity field shows a hysteresis effect in relation to the loading, showing differences between the cases when loading is increased and loading is decreased. The flow field also shows a transient response to the step change in loading, with either an overshoot or undershoot of the velocity in relation to the steady-state velocity. In general, a smaller reduced ramp time results in a faster velocity transient, and in turn a larger amplitude of overshoot or undershoot. Time constants analysis shows that the flow reaches the new steady-state slower for load increase than for load decrease; the time constants outside the wake are generally larger than at other radial locations for a given downstream plane; the time constants of measured velocity in the wake show radial dependence.The data are relevant for the validation of numerical models for unsteady actuator discs and wind turbines, and are made available in an open source database (see Appendix).@en

The state of the art engineering dynamic in ow models of Pitt-Peters, ¬ye and ECN have been used to correct Blade Element Momentum theory for unsteady load prediction of a wind turbine for two decades. However, their accuracy is unknown. This paper is to benchmark the performance of these engineering models by experimental and numerical methods. The experimental load and ow measurements of an unsteady actuator disc were performed in the Open Jet Facility at Delft University of Technology. The unsteady load was generated by a ramp-type variation of porosity of the disc. A Reynolds Averaged Navier-Stokes (RANS) model, a Free Wake Vortex Ring (FWVR) model and a Vortex Tube Model (VTM) simulate the same transient load changes. The velocity
eld obtained from the experimental and numerical methods are compared with the engineering dynamic in ow models. Velocity comparison aft the disc between the experimental and numerical methods shows the numerical models of RANS and FWVR model are capable to predict the velocity transient behaviour during transient disc loading. Velocity comparison at the disc between the engineering models and the numerical methods further shows that the engineering models predict much faster velocity decay, which implies the need for more advanced or better tuned dynamic in ow models.
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Although the Blade Element Momentum method has been derived for the steady conditions, it is used for unsteady conditions by using corrections of engineering dynamic inflow models. Its applicability in these cases is not yet fully verified. In this paper, the validity of the assumptions of quasi-steady state and annuli independence of the blade element momentum theory for unsteady, radially varied, axi-symmetric load cases is investigated. Firstly, a free wake model that combines a vortex ring model with a semi-infinite cylindrical vortex tube was developed and applied to an actuator disc in three load cases: (i) steady uniform and radially varied, (ii) two types of unsteady uniform load and (iii) unsteady radially varied load. Results from the three cases were compared with Momentum Theory and also with two widely used engineering dynamic inflow models—the Pitt-Peters and the Øye for the unsteady load cases. For unsteady load, the free wake vortex ring model predicts different hysteresis loops of the velocity at the disc or local annuli, and different aerodynamic work from the engineering dynamic inflow models. Given that the free wake vortex ring model is more physically representative, the results indicate that the engineering dynamic inflow models should be improved for unsteady loaded rotor, especially for radially varied unsteady loads. @en