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A simple analytical vortex model is presented and used to study an idealized wind turbine rotor in uniform and sheared inflow, respectively. Our model predicts that 1D momentum theory should be applied locally when modelling a non-uniformly loaded rotor in a sheared inflow. Hence the maximum local power coefficient (expressed with respect to the local, upstream velocity) of an ideal rotor is not affected by the presence of shear. We study the interaction between the wake vorticity generated by the rotor and the wind shear vorticity and find that their mutual interaction results in no net generation of axial vorticity: the wake effects and the shear effects exactly cancel each other out. This means that there are no resulting cross-shear-induced velocities and therefore also no cross-shear deflection of the wake in this model.

In the present work, a computationally efficient engineering model for the aerodynamic load calculation of non-planar wind turbine rotors is proposed. The method is based on the vortex cylinder model, and can be used in two ways: either as a correction to the currently widely used blade element momentum (BEM) method, or used as the main model, replacing the BEM method in the engineering modelling complex. The proposed method needs the same order of computational effort as the ordinary BEM method, which makes it ideal for time-domain aero-servo-elastic simulations. The results from the proposed method are compared with results from two higher-fidelity aerodynamic models: a lifting-line method and a Navier-Stokes solver. For planar rotors, the aerodynamic loads are identical to the current BEM model when the drag force is excluded during the calculation of the induced velocities. For non-planar rotors, the influence of the blade out-of-plane shape, measured by the difference of the load between the non-planar rotor and the planar rotor, is in very good agreement with higher-fidelity models. Meanwhile, the existing BEM methods, even with a correction of radial induction included, show relatively large deviations from the higher-fidelity method results.

This paper presents an analysis and optimization of Airborne Wind Energy Systems (AWESs), designed to maximize the Annual Energy Production (AEP) and, in the second part, the economic profit. A gradient-based optimization algorithm is used to perform the preliminary design of the main AWES sub-systems. A global sensitivity analysis is carried out to study how the design process, represented by the optimization problem, is influenced by aleatory and epistemic uncertainties. In particular, Ground-Gen and Fly-Gen AWESs are studied with a unified model to allow for a quantitative comparison. In the first part of the work, an ideal hybrid AWES design with ground and on-board power generation is considered. With this approach, the common characteristics of Ground-Gen and Fly-Gen AWES designs that maximize AEP are found. In the second part, Ground-Gen and Fly-Gen AWES optimal economic designs are analyzed individually. It is found that a fully developed AWES has strong potential to be highly competitive in the energy market, by providing cheap renewable energy. Fly-Gen AWESs are found to be slightly more profitable than Ground-Gen if the airborne unit is not replaced often. The main physical and economical characteristics of optimal designs are highlighted.

One promising design solution for increasing the efficiency of modern horizontal axis wind turbines is the installation of curved tip extensions. However, introducing such complex geometries may move traditional aerodynamic models based on Blade Element Momentum (BEM) theory out of their range of applicability. This motivated the present work, where a swept tip shape is investigated by means of both experimental and numerical tests. The latter group accounted for a wide variety of aerodynamic models, allowing to highlight the capabilities and limitations of each of them in a relative manner. The considered swept tip shape is the result of a design optimization, focusing on locally maximizing power performance within load constraints. For the experimental tests, the tip model is instrumented with spanwise bands of pressure sensors and is tested in the Poul la Cour wind tunnel at the Technical University of Denmark (DTU). The methods used for the numerical tests consisted of a blade element model, a near-wake model, lifting-line free-wake models, and a fully resolved Navier- Stokes solver. The comparison of the numerical and the experimental tests results is performed for a given range of angles of attack and wind speeds, which is representative of the expected conditions in operation. Results show that the blade element model cannot predict the measured normal force coefficients, but the other methods are generally in good agreement with the measurements in attached flow. Flow visualization and pressure distribution compare well with Computational Fluid Dynamics (CFD) simulations. The agreement in the clean case is better than in the tripped case, indicating an aggressive tripping of the flow in the measurements. Some uncertainties regarding the effect of the boundary layer at the inboard tunnel wall and the post stall behavior remain.

This paper presents analytic equations modelling the main physics and cost of a generic Airborne Wind Energy System flying crosswind. The power equation of a system that can handle ground and on-board generation is presented, under the assumption of steady-state flight. A structural and a take-off model are used to derive the key equations for the flying mass estimation of a hard-wing kite. A modification of the power equation is carried out to show how to include gravitation forces in the power estimation. Finally, an economic model is introduced. The model presented in this paper is intended to describe the key behavior of the system based on basic principles. It is suitable to be coupled with system design tools.

In this work, a computationally efficient engineering model for the aerodynamics of swept wind turbine blades is proposed for the extended blade element momentum (BEM) formulation. The model is modified based on a coupled near- and far-wake model, in which the near-wake is assumed to be the first quarter revolution of the non-expanding helical wake of the own blade. For the special case of in-plane trailed vorticity, the original empirical equations determining the steady-state value of the near-wake induction are replaced by the analytical results, which are in the form of incomplete elliptic integrals. For the general condition of helical trailed vorticities, the steady-state near-wake induction is approximated based on the results of the special conditions and a correction factor. The factor is calculated using empirical equations with influence coefficient tensors, to minimize the computational efforts. These influence coefficient tensors are pre-calculated and are fitted to the results from the numerical integration of the Biot-Savart law. With the indicial function approach, it is not necessary to explicitly save the information of the vorticities that were trailed in the previous time steps. This engineering approach is a combination of analytical results and numerical approximations, with low and constant computational effort for each time step. The proposed model is practically applicable to time-marching aero-servo-elastic simulations. The results of the swept blades with uniform inflow perpendicular to the rotor calculated from the proposed model are compared with the results from a BEM code, a lifting-line solver as well as a Navier-Stokes solver. The significantly improved agreement with the higher-fidelity models compared to the BEM method highlights the performance of the proposed method.

In the present work, a consistent method for calculating the lift and drag forces from the 2-D airfoil data for the dihedral or coned horizontal-axis wind turbines when using generalized lifting-line methods is described. The generalized lifting-line methods include, for example, lifting-line (LL), actuator line (AL), blade element momentum (BEM) and blade element vortex cylinder (BEVC) methods. A consistent interpretation of classic unsteady 2-D thin airfoil theory results for use in a generally moving frame of reference within a linearly varying onset velocity field reveals that it is necessary to use not only the relative flow magnitude and direction at one point along the chord line (for instance three-quarter-chord), but also the gradient of the flow direction in the chordwise direction (or, equivalently, the flow direction at the quarter-chord) to correctly determine the magnitude and direction of the resulting 2-D aerodynamic forces and moment. However, this aspect is generally overlooked and most implementations in generalized lifting-line methods use only the flow information at one calculation point per section for simplicity. This simplification will not change the performance prediction of planar rotors, but will cause an error when applied to non-planar rotors. The present work proposes a generalized method to correct the error introduced by this simplified single-point calculation method. In this work this effect is investigated using the special case, where the wind turbine blade has only dihedral and no sweep, operating at steady-state conditions with uniform inflow applied perpendicular to the rotor plane. We investigate the impact of the effect by comparing the predictions of the steady-state performance of non-planar rotors from the consistent approach with the simplified one-point approach of the LL method. The results are verified using blade geometry resolving Reynolds-averaged Navier-Stokes (RANS) simulations. The numerical investigations confirmed that the correction derived from thin airfoil theory is needed for the calculations to correctly determine the magnitude and direction of the sectional aerodynamic forces for non-planar rotors. The aerodynamic loads of upwind and downwind coned blades that are calculated using the LL method, the BEM method, the BEVC method and the AL method are compared for the simplified and the full method. Results using the full method, including different specific implementation schemes, are shown to agree significantly better with fully-resolved RANS than the often used simplified one-point approaches.

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.

The present work compares non-planar rotors designed using the blade element momentum (BEM) method and a vortex cylinder model. In a previous work, it is shown that blade element theory coupled with the superposition of the vortex cylinder model (BEVC) is able to model the loads of non-planar rotors. The result predicted by the BEVC model is in significantly improved agreement with higher-fidelity models than the loads as predicted using the BEM method. In this work, the BEM method and the BEVC method are integrated into a gradient-based optimization framework for aerodynamic planform optimization, in which the analytical gradients are obtained using the algorithmic differentiation (AD) method. In the present study, the rotor is assumed to be stiff for all cases such that the pure aerodynamic effects are highlighted. Loads of the optimized non-planar rotors with different geometries under different constraints designed from both methods are calculated using the BEM method, the BEVC method and also the higher-fidelity lifting-line (LL) method. Within the constraints of the present work it was found that the advantage of the BEVC method is not significant when comparing the integrated aerodynamic loads: the non-planar rotor designed using the BEM method gives similar total thrust and power as the rotor designed using the BEVC method when the designs are evaluated with the higher-fidelity LL method. However, the results confirmed that the distributed aerodynamic loads of the non-planar rotors predicted by the BEVC method are in improved agreement with the LL method compared to the BEM method.

This paper describes a benchmark of four airfoils in the Poul la Cour Tunnel (PLCT). The wind tunnel, the corrections used and the method of making adapters for the airfoils are also described. Very good agreement was in general observed between the measurements in PLCT and in other high quality wind tunnels. Some deviations were seen, but they were mainly attributed to the differences in separation on the airfoil. Apart from the benchmarking, this paper also highlights the challenges in testing airfoils in general such as obtaining 2D flow on thick airfoils that inherently shows separated flow and how to make adapters for airfoils tested in other wind tunnels.

In this paper, we present the design and computational model of a representative multi-megawatt airborne wind energy (AWE) system, together with a simulation framework that accounts for the flight dynamics of the fixed-wing aircraft and the sagging of the tether, combining this with flight control and optimisation strategies to derive the power curve of the system. The computational model is based on a point mass approximation of the aircraft, a discretisation of the tether by five elastic segments and a rotational degree of freedom of the winch. The aircraft has a wing surface area of 150 m2 and is operated in pumping cycles, alternating between crosswind flight manoeuvres during reel out of the tether, and rapid decent towards the ground station during reel in. To maximise the net cycle power, we keep the design parameters of the aircraft constant, while tuning the operational and controller parameters for different wind speeds and given contraints. We find that the presented design can generate a net cycle power of up to 3.8 megawatts., Journal of Physics: Conference Series, 1618 (3), ISSN:1742-6588, ISSN:1742-6596

A row of wind turbine rotors with a mutual spacing of three diameters is simulated using both Reynolds averaged Navier-Stokes (RANS) simulations and a simple inviscid vortex model. The angle between the incoming wind and the line connecting the turbines is varied between 45 and 90 degrees. The simulations show that the power production of the turbines deviate significantly compared with a corresponding isolated turbine even though there is no direct wake-turbine interaction at the considered wind directions. Nevertheless, both models indicate marked alterations in the upstream flow, which directly link to the turbines' power adjustments. Thus, turbines which are placed laterally relative to the prevailing wind (as seen at various test sites) have, at least numerically, a mutual effect on each other. Therefore, they might not necessarily produce the same power as a stand-alone turbine. Copyright © 2016 John Wiley & Sons, Ltd.

A vortex particle representation of turbulent fields is devised in order to address the following questions: Does a wind turbine affect the statistics of the incoming turbulence? Should this imply a change in the way turbulence boxes are used in wind turbine aero-elastic simulations? Is it acceptable to neglect the influence of the wake and the wind turbine on the turbulent inflow? Is there evidence to justify the extra cost of a method capable of including these effects correctly? To this end, a unified vorticity representation of the flow is used: the wind turbine model is represented by a bound vorticity lifting line while the turbine wake vorticity and the turbulence vorticity are projected onto vortex particles. In the present work the rotor blades are stiff leaving aero-elastic interactions for future work. Inflow turbulence is generated with the model of Mann and converted to vortex particles that are inserted at the inlet of the computational domain. First the quality of the reconstructed turbulent flow field is evaluated and then the wind turbine is added in the simulations. The lack of a driving-force to sustain turbulence is found to give a progressive decay of turbulence away from the insertion point. The presence of the wind turbine and its wake is found to have insignificant effect on upstream turbulence. Finally, the mean velocity profiles in the wake are found to be in good agreement with both lidar measurements and CFD simulations.

The aim of this work is to propose engineering models to include the external forces acting on the tether into the power estimation of an Airborne Wind Energy System flying crosswind. The influence of aerodynamic drag, centrifugal force and gravitational force on power production is investigated. These three types of external loading acting on the tether are lumped with the kite and the tether is considered straight. In this way, a set of equations describing the tether shape and its influence on the power production is reduced to just one power equation. The formulation with straight tether and lumped quantities is suitable for preliminary designs and analyses and points out how the tether influence the system. On top of the results concerning the tether modelling, a new analytical model which includes the centrifugal forces into the power estimation for circular paths is presented.

The present study investigates the differences in the predicted lift for a wind tunnel model from either surface pressures or side wall pressures. The investigated model is the NACA63-418 tested in the Poul la Cour tunnel. The measurements are compared with previous conducted wind tunnel campaigns for a Reynolds number of 3E6. The 3D CFD model of the wind tunnel will be used for investigating details of the flow mechanisms, and to validate assumptions and findings from the experimental data. The CFD simulations show that when the flow is attached the lift based on the side wall pressures results in almost the same lift as calculated from the surface pressures. Around the maximum lift and in the stalled region the flow is not anymore 2D. For the NACA63-418 airfoil the lift based on the side wall pressures are generally highest. The CFD simulations confirm that the method used to predict the lift from the limited side wall pressure strips in the wind tunnel is applicable.

The present paper introduces a new, physically consistent definition of effective induction that should be used in engineering models for power kite performance that use aerodynamic coefficients for the wing. It is argued that in such cases it is physically inconsistent to use disc-based induction models – like momentum models – and thus a new, physically consistent induction model using vortex theory methodology is derived. Simulation results using the new induction model are compared to the previously often used momentum method and Actuator Line (AL) CFD simulations. The comparison shows that the new vortex based model is in much better agreement with the AL results than the momentum method. The new model is as computationally light as the momentum induction method.

We analyze the new Danish Poul la Cour Tunnel (PLCT) facility using 2D and 3D Computation Fluid Dynamics simulations, with the aim to address the need for wind tunnel corrections. The assessment of tunnel corrections is based on 2D free simulations representing undisturbed airfoil flow, 2D tunnel configurations and a full 3D tunnel setup using laminar/turbulent Improved Delayed Dettached Eddy Simulations. By comparing lift, drag and pressure distributions and detailled flow patterns, the influence of the 2D and 3D tunnel is evaluated. In the present study a NACA 633-418 airfoil is investigated in the tunnel.

Passive load alleviation on wind turbine blades can be achieved through geometric bend-twist coupling, for example by sweeping the blade backwards. In order to obtain the correct load distribution of a curved blade with in-plane sweep and/or out-of-plane dihedral, the influence of the blade shape on the aerodynamics must be modelled correctly. This includes the influence of the curved bound vortex, and it is especially important when designing a wind turbine blade with aeroelastic tailoring. In this paper, the background for modelling the curved bound vortex influence will be described in detail and a modified method is proposed. The proposed method of bound vorticity modelling is compared for curved and straight translating wings as well as wind turbine blades with results from a panel code and a Navier-Stokes solver. From this comparison, the advantages of the current modification with respect to the other lifting-line implementations are shown. The method proposed in the present work is general and applicable to any lifting-line like model.

Joukowski introduced in 1912 a helical vortex model to represent the vorticity of a rotor and its wake. For an infinite number of blades but finite tip-speed ratio, the model consists of a vortex cylinder of longitudinal and tangential vorticity, a root vortex and a bound vortex disk. A superposition of cylinders is used in this paper to model rotors of radially varying circulation. The relations required to form a consistent system of cylinders are derived. The model contains a term which is not accounted for in the standard blade element momentum (BEM) algorithm. This term is identified as the contribution from the pressure drop due to the wake rotation. The BEM algorithm can be corrected to account for this effect. Unlike previous work on the topic, the contribution is derived for a radially varying circulation. A high-thrust correction is also presented to extend the model. The optimal power coefficient obtained with this model for the constant circulation rotor is assessed and compared with that of existing solutions. Results from prescribed thrust distributions are compared with that of actuator disk simulations. Steady simulations are performed to compare with the BEM algorithm. The model is also applied to compute the velocity field in the entire domain and perform unsteady simulations. Results for an unsteady simulation corresponding to a pitch change of the rotor is used to compare the model with measurements and a BEM code with a dynamic inflow model. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper an extension of the spectrum of applicability of rotors with active aerodynamic devices is presented. Besides the classical purpose of load alleviation, a secondary objective is established: power capture optimization. As a first step, wind speed regions that contribute little to fatigue damage have been identified. For these regions the turbine energy output can be increased by deflecting the trailing edge (TE) flap as a function of local, instantaneous speed ratios. For this purpose, sizing of TE flap configuration for maximum power generation is established using blade element momentum theory. The investigation then focuses on operation in non-uniform wind field conditions. Firstly, the deterministic fluctuation in local tip speed ratio due to wind shear was evaluated. The second effect is associated with delays in adapting the rotor speed to time varying inflow. The increase of power generation due to wind shear has been demonstrated with an increase of energy yield of 1%. Finally a control logic based on inflow wind speeds has been devised.

A vortex system consisting of a bound vortex disk, a root vortex and a vortex cylinder is presented and applied for skewed wake situations. Both the longitudinal and tangential components of vorticity of the cylinder are considered. A subset of this system leads to a model, which is commonly used in Blade Element Momentum method codes for yawed conditions. Here, all the components of the full vortex system are analyzed in view of extending Blade Element Momentum models. The main assumptions of the current study are a constant uniform circulation, an infinite number of blades, an un-expanding wake shape and a finite tip-speed ratio. The investigation remains within the context of inviscid potential flow theory. The model is derived for horizontal-axis rotors in general, but results are presented for wind-turbine applications. For each vortex element, the velocity components in all directions are computed analytically or semi-analytically for the entire domain. Simplified engineering models are provided to ease the evaluation of velocities in the rotor plane. The predominant velocity components are assessed. Copyright © 2015 John Wiley & Sons, Ltd.

In the present paper, single-wake dynamics have been studied both experimentally and numerically. The use of pulsed lidar measurements allows for validation of basic dynamic wake meandering modeling assumptions. Wake center tracking is used to estimate the wake advection velocity experimentally and to obtain an estimate of the wake expansion in a fixed frame of reference. A comparison shows good agreement between the measured average expansion and the Computational Fluid Dynamics (CFD) large eddy simulation–actuator line computations. Frandsen's expansion model seems to predict the wake expansion fairly well in the far wake but lacks accuracy in the outer region of the near wake. An empirical relationship, relating maximum wake induction and wake advection velocity, is derived and linked to the characteristics of a spherical vortex structure. Furthermore, a new empirical model for single-wake expansion is proposed based on an initial wake expansion in the pressure-driven flow regime and a spatial gradient computed from the large-scale lateral velocities, and thus inspired by the basic assumption behind the dynamic wake meandering model. Copyright © 2014 John Wiley & Sons, Ltd.

The study presents and compares aerodynamic simulations for an airfoil section with an adaptive trailing edge flap, which deflects following a smooth deformation shape. The simulations are carried out with three substantially different methods: a Reynolds-averaged Navier–Stokes solver, a viscous–inviscid interaction method and an engineering dynamic stall model suitable for implementation in aeroelastic codes based on blade element momentum theory. The aerodynamic integral forces and pitching moment coefficients are first determined in steady conditions, at angles of attack spanning from attached flow to separated conditions and accounting for the effects of flap deflection; the steady results from the Navier–Stokes solver and the viscous–inviscid interaction method are used as input data for the simpler dynamic stall model. The paper characterizes then the dynamics of the unsteady forces and moments generated by the airfoil undergoing harmonic pitching motions and harmonic flap deflections. The unsteady aerodynamic coefficients exhibit significant variations over the corresponding steady-state values. The dynamic characteristics of the unsteady response are predicted with an excellent agreement among the investigated methods at attached flow conditions, both for airfoil pitching and flap deflection. At high angles of attack, where flow separation is encountered, the methods still depict similar overall dynamics, but larger discrepancies are reported, especially for the simpler engineering method. Copyright © 2014 John Wiley & Sons, Ltd.

The present study investigated physical phenomena related to stall-induced vibrations potentially existing on wind turbine blades at standstill conditions. The study considered two-dimensional airfoil sections while it omitted three-dimensional effects. In the study, a new engineering-type computational model for the aeroelastic response of an elastically mounted airfoil was used to investigate the influence of temporal lag in the aerodynamic response on the aeroelastic stability in deep stall. The study indicated that even a relatively low lag significantly increases the damping of the model. A comparison between the results from a model with lag imposed on all force components with the results from a model with lag imposed exclusively on the lift showed only marginal difference between the damping in the two cases. A parameter study involving positions of the elastic hinge point and the center of gravity indicated that the stability is relatively independent of these parameters. Another parameter study involving spring constants showed that the stability of each mode is dependent only on the spring constant acting in the direction of the leading motion of the mode. An investigation of the influence of the added mass terms showed that only the pitch-rate and flapwise-acceleration terms have any influence on the stability. An investigation of three different profiles showed that the stability is heavily dependent on the aerodynamic characteristics of the profiles—mainly on the lift. It was also shown that only the edgewise mode is unstable in deep stall. Moreover, independent of the amount of temporal lag in the aerodynamic response of the model, the inflow-angle region in the vicinity of 180° remains unstable in the edgewise mode. Therefore, this inflow-angle region may create stability problems in real life. The other type of vibrations potentially present at standstill conditions is vortex-induced, being outside the scope of the present study. Copyright © 2014 John Wiley & Sons, Ltd.

Standard blade element momentum (BEM) codes use Prandtl's tip-loss correction which relies on simplified vortex theory under the assumption of optimal operating condition and no wake expansion. The various tip-loss functions found in the literature are listed. A simple comparison between them shows important differences in Annual Energy Production which reveal a large uncertainty in current BEM-based computations. A new tip-loss correction for implementation in BEM codes has been developed using a lifting-line code to account for the effect of wake expansion, roll-up and distortion under many operating conditions. A database of tip-loss corrections is established for further use in BEM codes. This model is closer to the physics of the flow and hence, a better assessment of the performance of wind turbines by this method is expected.

The aeroelastic response of wind turbines is often simulated in the time domain by using indicial response techniques. Unsteady aerodynamics in attached flow are usually based on Jones's approximation of the flat plate indicial response, although the response for finite-thickness airfoils differs from the flat plate one. The indicial lift response of finite-thickness airfoils is simulated with a panel code, and an empirical relation is outlined connecting the airfoil indicial response to its geometric characteristics. The effects of different indicial approximations are evaluated on a 2D profile undergoing harmonic pitching motion in the attached flow region; the resulting lift forces are compared with computational fluid dynamics (CFD) simulations. The relevance for aeroelastic simulations of a wind turbine is also evaluated, and the effects are quantified in terms of variations of equivalent fatigue loads, ultimate loads, and stability limits. The agreement with CFD computations of a 2D profile in harmonic motion is improved by the indicial function accounting for the finite-thickness of the airfoil. Concerning the full wind turbine aeroelastic behavior, the differences between simulations on the basis of Jones's and finite-thickness indicial response functions are rather small; Jones's flat-plate approximation results in only slightly larger fatigue and ultimate loads, and lower stability limits. Copyright © 2012 John Wiley & Sons, Ltd.

Passive load alleviation can be achieved through geometric bend-twist coupling, for example, by sweeping the blade backwards. The influence of the blade sweep on the trailing vorticity and bound vorticity is not modelled in the current fast aeroelastic wind turbine codes suitable for certification. A near wake trailed vorticity model which was coupled with a blade element momentum theory based aerodynamic model has been modified to take into account the blade sweep. The extended model is compared with the original near wake model, a blade element momentum (BEM) model and full rotor computational fluid dynamics (CFD) results for the modified IEA 10MW reference wind turbines. The steady-state loadings calculated from the extended model are in better agreements with CFD compared to the original model and the BEM for four different swept blades. It is also shown that the influence of the blade sweep on normal loading is not correctly modelled by BEM and this error will be inherited to the near wake model results. Thus, further modification to BEM will likely improve the predicted normal loading for swept blades, even if no near wake model is used.

This work presents a method to determine flutter and divergence instability limits for a two-dimensional (2-D) airfoil section fitted with an actively controlled trailing edge flap. This flap consists of a deformable trailing edge, which deformation is governed by control algorithms based on measurements of either heave displacement, local angle of attack or aerodynamic pressure difference measured over the airfoil. The purpose of the controlled deformable flap is to reduce fluctuations in the aerodynamic forces on the airfoil, which, according to recent studies, have a significant potential for fatigue load alleviation. The structural model of the 2-D airfoil section contains three degrees of freedom: heave translation, pitch rotation and flap deflection. A potential flow model provides the aerodynamic forces and their distribution. The unsteady aerodynamics are described using an indicial function approximation. Stability of the full aeroservoelastic system is determined through eigenvalue analysis by state-space formulation of the indicial approximation. Validation is carried out against an implementation of the recursive method by Theodorsen and Garrick for flexure-torsion-aileron flutter. The implemented stability tool is then applied to an airfoil section representative of a wind turbine blade with active flap control. It is thereby observed that the airfoil stability limits are significantly modified by the presence of the flap, and they depend on several parameters: flap structural characteristics, type of control, control gain factors and time lag. Copyright © 2009 John Wiley & Sons, Ltd.

The present work contains a deformable trailing edge flap controller integrated in a numerically simulated modern, variablespeed, pitch-regulated megawatt (MW)-size wind turbine. The aeroservoelastic multi-body code HAWC2 acts as a component in the control loop design. At the core of the proposed controller, all unsteady loads are divided by frequency content. Blade pitching and generator moment react to low-frequency excitations, whereas flaps deal with high-frequency excitations. The present work should be regarded as an investigation into the fatigue load reduction potential when applying trailing edge flaps on a wind turbine blade rather than a conclusive control design with traditional issues like stability and robustness fully investigated. Recent works have shown that the fatigue load reduction by use of trailing edge flaps may be greater than for traditional pitch control methods. By enabling the trailing edge to move independently and quickly along the spanwise position of the blade, local small flutuations in the aerodynamic forces can be alleviated by deformation of the airfoil flap. Strain gauges are used as input for the flap controller, and the effect of placing strain gauges at various radial positions on the blade is investigated. An optimization routine minimizes blade root fatigue loads. Calculations are based on the 5 MW reference wind turbine part of the UpWind project primarily with a mean turbulent wind speed close to rated power. A fatigue load reduction of 25% in the blade root moment was obtained for a continuous 6.3 m long flap. Copyright © 2009 John Wiley & Sons, Ltd.

In the present work, analytical expressions for distributed and integral unsteady two-dimensional forces on a variable geometry airfoil undergoing arbitrary motion are derived under the assumption of incompressible, irrotational, inviscid flow. The airfoil is represented by its camber line as in classic thin-airfoil theory, and the deflection of the airfoil is given by superposition of chord-wise deflection mode shapes. It is shown from the expressions for the forces that the influence from the shed vorticity in the wake is described by the same time lag for all chord-wise positions on the airfoil. This time-lag term can be approximated using an indicial function approach, making the practical calculation of the aerodynamic response numerically very efficient by use of Duhamel superposition. Furthermore, the indicial function expressions for the time-lag terms are formulated in their equivalent state-space form, allowing for use of the present theory in problems employing the eigenvalue approach, such as stability analysis. The analytical expressions for the integral forces can be reduced to Munk's steady and Theodorsen's unsteady results for thin airfoils, and numerical evaluation shows excellent agreement with other unsteady two-dimensional thin-airfoil results. Apart from the obvious applications within active load control/reduction, the present theory can be used for various applications which up to the formulation of the present theory have been possible only using much more computational costly methods. An example that highlights this feature is the propulsive performance of a soft heaving propulsor presented in this paper. Copyright © 2010 John Wiley & Sons, Ltd.

A wind tunnel test of the wind turbine airfoil Riso-B1-18 equipped with an Active Trailing Edge Flap (ATEF) was carried out. The ATEF was 9% of the total chord, made of piezo electric actuators attached to the trailing edge of a non-deformable airfoil and actuated using an (electric) amplifier. The airfoil was tested at Re = 1.66 × 106. Steady state and dynamic tests were carried out with prescribed deflections of the ATEF. The steady state tests showed that deflecting the ATEF towards the pressure side (positive β) translated the lift curve to higher lift values and deflecting the ATEF towards the suction side (negative β) translated the lift curve to lower lift values. Testing the airfoil for a step change of the ATEF from β = −3.0 to +1.8 showed that the obtainable Δcl was 0.10 to 0.13 in the linear part of the lift curve. Modeling the step response with an indicial function formulation showed that the time constant in the step change and in sinusoidal deflections in dimensionless terms was T0* = 0.6. Testing the ability of the ATEF to cancel out the load variations for an airfoil in sinusoidal pitch motion of ΔAOA = ±0.7 showed that it was possible to reduce the amplitude with around 80% from Δcl = 0.148 to Δcl = 0.032. Copyright © 2009 John Wiley & Sons, Ltd.

The present work contains an extension of the Beddoes–Leishman-type dynamic stall model. In this work, a deformable trailing-edge flap has been added to the dynamic stall model. The model predicts the unsteady aerodynamic forces and moments on an airfoil section undergoing arbitrary motion in heave, lead-lag, pitch, trailing-edge flapping. In the linear region, the model reduces to the inviscid model, which includes the aerodynamic effect of a thin airfoil with a deformable camberline in inviscid flow. Therefore, the proposed model can be considered a crossover between the work of Gaunaa for the attached flow region and Hansen et al. The model is compared qualitatively to wind tunnel measurements of a Riso/ B1-18 blade section equipped with deformable trailing-edge flap devices in the form of piezoelectric devices. Copyright © 2009 John Wiley & Sons, Ltd.

The design of a three-bladed wind turbine rotor is described, where the main focus has been highest possible mechanical power coefficient, CP, at a single operational condition. Structural, as well as off-design, issues are not considered, leading to a purely theoretical design for investigating maximum aerodynamic efficiency.The rotor is designed assuming constant induction for most of the blade span, but near the tip region, a constant load is assumed instead. The rotor design is obtained using an actuator disc model, and is subsequently verified using both a free-wake lifting line method and a full three-dimensional Navier-Stokes solver.Excellent agreement is obtained using the three models. Global CP reaches a value of slightly above 0.51, while global thrust coefficient CT is 0.87. The local power coefficient C-p increases to slightly above the Betz limit on the inner part of the rotor; the local thrust coefficient C, increases to a value above 1.1. This agrees well with the theory of de Vries, which states that including the effect of the low pressure behind the centre of the rotor stemming from the increased rotation, both C-p and C-t will increase towards the root. Towards the tip, both C-p and C-t decrease due to tip corrections as well as drag. Udgivelsesdato: Sep

Vertical Axis Wind Turbines (VAWT) are competitive concepts for very large scale (1020 MW) floating offshore applications. Rotor circulation control (loading control) opens a wide design space to enhance the aerodynamic and operational features of VAWT. The modified linear derivation of the Actuator Cylinder Model (Mod-Lin ACM) is used as the aerodynamic model to assess VAWT performance throughout the work. As the first step, optimum aerodynamic loadings of a VAWT with infinite number of blades are studied. Next, for the case of finite number of blades, direct and inverse optimization approaches are used. The direct method is coupled with a hybrid numerical optimizer to serve as a global method for designing flap sequences. The effectiveness of trailing edge flap on VAWT is investigated for three aerodynamic objectives which lead to improved power efficiency, rated power control and peak load control. The aerodynamic gains for various solidity, tip-speed ratio, maximum flap deflection and flap size are quantified in inviscid flow. This extensive work presents new insights on the performance of a VAWT with infinite number of blades as well as it provides a solid foundation for flap usage on a real VAWT rotor to enhance its capabilities.

This paper presents an investigation of the potential for reduction of fluctuating loads on wind turbine blades with the use of flaplike deflectable trailing edges. More specifically, the aeroelastic response of an elastically mounted airfoil section with a deflectable trailing edge is investigated. This is done by coupling a model for the aerodynamic forces on a deforming airfoil with a linear spring/damper model for the elastic deformation of a rigid airfoil to which the forces associated with the deflection of the trailing edge are added. The analysis showed that when the airfoil experienced a wind step from 10to12m∕s the standard deviation of the normal force could be reduced by up to 85% when the flap was controlled by the reading of the airfoil flapwise position and velocity, while reductions of up to 95% could be obtained when the flap was controlled by the reading of the angle of attack. When the airfoil experienced a turbulent wind field, the standard deviation of the normal force could be reduced by 81% for control based on measured angle of attack. The maximum reduction using a combination of flapwise position and velocity was 75%. The maximum deflection of the trailing edge geometry was, in all the considered cases, small enough to justify the use of a potential flow code for calculation of the aerodynamic forces. Calculations showed that the effect of a time lag in the actuators and sensors may drastically reduce the efficiency of the control algorithm. Likewise, the effect of a low maximum actuation velocity reduces the efficiency of the control algorithm. The analysis of the two-dimensional (2D) aeroservoelastic system shown in this paper indicates that the potential of using trailing edge flaps for reduction of fluctuating loads is significant.

Aerodynamic modelling of HAWT rotors by means of “engineering methods” has reached a saddle point, where no further development can be expected without a breakthrough in understanding the physics of unsteady, rotating three-dimensional flows. However, such a breakthrough becomes ever more necessary, as the size of the wind turbines increases. With the experimental work in that direction being mostly limited to observing the phenomena and interpreting the associated mechanisms, and its increased cost, alternatives are being sought. The use of CFD techniques and state-of-the-art Navier–Stokes solvers is considered a very serious contender, a belief shared by the members of the present consortium, which has worked on the VISCEL JOR3-CT98-0208 Joule III project. This project's goal was to determine the aerodynamic characteristics as well as the aeroelastic behaviour of wind turbine blades across their broad range of operational conditions, from attached to highly separated flow regimes. The work programme included specific tasks for the validation and assessment of existing 3D solvers, for the parametric study of 3D flow around realistic blades and for the investigation of aeroelastic stability, at the blade section level. Copyright © 2003 John Wiley & Sons, Ltd.

The crossflow principle is one of the key elements used in engineering models for prediction of the aerodynamic loads on wind turbine blades in standstill or blade installation situations, where the flow direction relative to the wind turbine blade has a component in the direction of the blade span direction. In the present work, the performance of the crossflow principle is assessed on the DTU 10MW reference blade using extensive 3D CFD calculations. Analysis of the computational results shows that there is only a relatively narrow region in which the crossflow principle describes the aerodynamic loading well. In some conditions the deviation of the predicted loadings can be quite significant, having a large influence on for instance the integral aerodynamic moments around the blade centre of mass; which is very important for single blade installation applications. The main features of these deviations, however, have a systematic behaviour on all force components, which in this paper is employed to formulate the first version of an engineering correction method to the crossflow principle applicable for wind turbine blades. The new correction model improves the agreement with CFD results for the key aerodynamic loads in crossflow situations. The general validity of this model for other blade shapes should be investigated in subsequent works.

Vortex-induced integral loading fluctuations on a single suspended blade at various inflow angles were modeled in the presents work by means of stochastic modelling methods. The reference time series were obtained by 3D DES CFD computations carried out on the DTU 10MW reference wind turbine blade. In the reference time series, the flapwise force component, Fx, showed both higher absolute values and variation than the chordwise force component, Fz, for every inflow angle considered. For this reason, the present paper focused on modelling of the Fx and not the Fz whereas Fz would be modelled using exactly the same procedure. The reference time series were significantly different, depending on the inflow angle. This made the modelling of all the time series with a single and relatively simple engineering model challenging. In order to find model parameters, optimizations were carried out, based on the root-mean-square error between the Single-Sided Amplitude Spectra of the reference and modelled time series. In order to model well defined frequency peaks present at certain inflow angles, optimized sine functions were superposed on the stochastically modelled time series. The results showed that the modelling accuracy varied depending on the inflow angle. None the less, the modelled and reference time series showed a satisfactory general agreement in terms of their visual and frequency characteristics. This indicated that the proposed method is suitable to model loading fluctuations on suspended blades.

Measurements on a heavily instrumented pitch regulated variable speed Vestas V52 850 kW wind turbine situated at the DTU Riso Campus are carried out, where the effect of vortex generators mounted on almost the entire blade is tested with and without leading edge roughness. The measurements are compared to the predictions carried out by a developed design tool, where the effect of vortex generators and leading edge roughness is simulated using engineering models. The measurements showed that if vortex generators are mounted there is an increase in flapwise blade moments if the blades are clean, but also that the loads are almost neutral when vortex generators are installed if there is leading edge roughness on the blades. Finally, it was shown that there was a good agreement between the measurements and the predictions from the design tool.

A new analytical formulation of the tip-loss factor is established based on helical vortex filament solutions. The derived tip-loss factor can be applied to wind-turbines, propellers or other rotary wings. Similar numerical formulations are used to assess the influence of wake expansion on tip-losses. Theodorsen's theory is successfully applied for the first time to assess the wake expansion behind a wind turbine. The tip-loss corrections obtained are compared with the ones from Prandtl and Glauert and implemented within a new Blade Element Momentum(BEM) code. Wake expansion is seen to reduce tip-losses and have a greater influence than wake distortion.

In this work a 2D CFD solver has been used to optimize the shape of a leading edge slat with a chord length of 30% of the main airfoil which was 40% thick. The airfoil configuration was subsequently tested in a wind tunnel and compared to numerical predictions. The multi-element airfoil was predicted to achieve a Cl−max of 3.1 based on the main airfoil chord length, which was confirmed in the wind tunnel campaign. Using wake rake traversal and wool tuft flow visualization wall interference effects were investigated, which were found to be a source of considerable uncertainty when measuring on thick airfoils.

CFD (Computational Fluid Dynamics) analysis of the temporal response of the microtab show that it has two disadvantages compared with a trailing edge flap, when considering it for active load control of a wind turbine. First of all the microtab has a reverse control phenomenon in the initial phase of deployment, and second of all the response is delayed, compared with the flap, due to buildup of flow structures. This motivated us to find an engineering model for the temporal response of the microtab to investigate the behavior of the microtab in an aeroelastic model of a wind turbine. Before we attempted to model the microtab in detail, we inserted temporal response of the microtab found with CFD directly into the aeroelastic code FLEX5. We found that the reverse control was not important for the response of the blade. We propose to use a simple queue delay to model the flow physics of the microtab. Finally, we calculated the load reduction potential of the microtab, assuming that we could model it as a delay, and compared it to that of a trailing edge flap. In our calculation the trailing edge flap had a load reduction potential twice as big as the microtab solution on the UPWIND reference turbine.

The present work includes analysis of the results obtained with a free wake code to determine two simple, non-iterative prescribed wake models aimed for use in steady load and design calculations for rotors with winglets. The results show that results from a prescribed wake model using only the integral axial load on the rotor and the main geometry of the wing/winglet can produce results in qualitative agreement with the physically more correct free wake model. The results indicate, however, that the power production estimated from the prescribed wake models using only the integral loads and no local loadings and/or induced velocities along the blade will be erroneous if the load distribution along the wing is not similar to the one the model was calibrated for.