Lifting Line Free Vortex Wake Research Articles

Vortex model of the aerodynamic wake of airborne wind energy systems

Abstract. Understanding and modeling the aerodynamic wake of airborne wind energy systems (AWESs) is crucial for estimating the performance and defining the design of such systems, as tight trajectories increase induced velocities and thus decrease the available power, while unnecessarily large trajectories increase power losses due to the gravitational potential energy exchange. The aerodynamic wake of crosswind AWESs flying circular trajectories is studied here with vortex methods. The velocities induced at the AWES from a generic helicoidal vortex filament, trailed by a position on the AWES wing, are modeled with an expression for the near vortex filament and one for the far vortex filament. The near vortex filament is modeled as the first half rotation of the helicoidal filament, with its axial component being neglected. The induced drag due to the near wake, built up from near vortex filaments, is found to be similar to the induced drag the AWES would have in forward flight. The far wake is modeled as two semi-infinite vortex ring cascades with opposite intensity. An approximate solution for the axial induced velocity at the AWES is given as a function of the radial (known) and axial (unknown) position of the vortex rings. An explicit and an implicit closure model are introduced to link the axial position of the vortex rings with the other quantities of the model. The aerodynamic model, using the implicit closure model for the far wake, is validated with the lifting-line free-vortex wake method implemented in QBlade. The model is suitable to be used in time-marching aero-servo-elastic simulations and in design and optimization studies.

Performance analysis of low Reynolds number vertical axis wind turbines using low-fidelity and mid-fidelity methods and wind conditions in the city of Nottingham

The aerodynamics of small-scale Darrieus vertical axis wind turbines (VAWT) is investigated at chord-based Reynolds number between 1 ×105 and 1 ×106. Initially, wind resource assessment is done for two locations in Nottingham, UK for 4 years. Both locations experience highly unsteady wind and the average wind speed is lower for the location within the city than outside the city. Next, two analytical aerodynamic methods are compared: low-fidelity Double Multiple Streamtube and mid-fidelity Lifting Line Free Vortex Wake methods. Five 3D design parameters are investigated: number of blades, blade shape, chord length, blade height and blade pitch angle. Overall, the power coefficient values and trends agree well between the two methods. The differences arise either in cases of very low solidity or high solidity. The unsteady flow field is visualized for each case using instantaneous vortices and streamwise velocity contours in the wake. The aim of the current work is twofold. Firstly, to investigate the difference between the two methods based on the physical principles modeled by each method. The second aim is to have a better understanding of the VAWT flow physics by studying the complex 3D force and flow field, and fluid dynamic interactions in the VAWT wake.

Rotational and blockage effects on a wind turbine model based on local blade forces

This paper describes the results of an extended experimental campaign, reporting surface pressure measurement over one of the blades of the Berlin Research Turbine (BeRT), placed in a closed-loop wind tunnel facility. BeRT is a three-bladed horizontal axis wind turbine with a 3m rotor diameter. The focus is, on the one side, on the three-dimensional effects experienced by the rotating blade, in comparison to 2D approaches by means of XFoil simulations and 2D blade section experiments. On the other side, the blockage effects are investigated between the wind turbine model, placed in the wind tunnel where a 40% blockage ratio is produced, and lifting line free vortex wake simulations, where wind tunnel walls are not considered. Additionally, CFD computations are added in the comparison, with simulations of the far-field and with the wind tunnel walls. The turbine model is studied at several operational conditions such as different blade pitch angles and turbine yaw misalignments. Results are presented in terms of local force components derived from the surface pressure measurements. It is shown that rotational augmentation is evident at the blade mid-span location despite the large blockage. Additionally, the blockage is noticed by means of an offset in both normal and tangential local forces conserving trends and features under axial inflow and yaw misalignments. It is found that the offset in forces can be counteracted by pitching the blades.

Comparison of different fidelity aerodynamic solvers on the IEA 10 MW turbine including novel tip extension geometries

Lifting-line based solvers could supersede the blade element momentum (BEM) method as the industry standard in the near future as rotor sizes of modern wind turbines and computational resources continue to increase. A comparison study between both methods is presented where the IEA 10 MW wind turbine is evaluated in the aero-servo-elastic simulation tool QBlade, comparing the lifting-line free vortex wake method to an unsteady blade element momentum solver. Besides the baseline rotor of the IEA 10 MW turbine, the comparison includes several blade tip extensions, including a swept and a dihedral geometry, to further differentiate capabilities between both methods in aerodynamically complex flow fields. As a reference serve results from equivalent simulations performed with multiple fidelity solvers of the simulation tool HAWC2. Results of a rigid load case demonstrate considerable improvement regarding the aerodynamic accuracy of lifting-line based methods in below rated conditions over BEM codes. The aerodynamic loads on geometrically complex tip extensions in steady conditions prove good capabilities of lower fidelity codes to predict out-of-plane bend shapes but also clear limitations regarding loads on swept geometries. A quasi-steady aeroelastic load case further demonstrates the capability of both QBlade codes to produce comparable results to similar fidelity solvers of the HAWC2 tool on an integral level. A detailed comparison in the time domain shows a larger dependency of the results on the type of structural solver that is used in contrast to the fidelity level of the aerodynamic method.

Active flap control with the trailing edge flap hinge moment as a sensor: using it to estimate local blade inflow conditions and to reduce extreme blade loads and deflections

Abstract. Active trailing edge flaps are a promising technology that can potentially enable further increases in wind turbine sizes without the disproportionate increase in loads, thus reducing the cost of wind energy even further. Extreme loads and critical deflections of the blade are design-driving issues that can effectively be reduced by flaps. In this paper, we consider the flap hinge moment as a local input sensor for a simple flap controller that reduces extreme loads and critical deflections of the DTU 10 MW Reference Wind Turbine blade. We present a model to calculate the unsteady flap hinge moment that can be used in aeroelastic simulations in the time domain. This model is used to develop an observer that estimates the local angle of attack and relative wind velocity of a blade section based on local sensor information including the flap hinge moment of the blade section. For steady wind conditions that include yawed inflow and wind shear, the observer is able to estimate the local inflow conditions with errors in the mean angle of attack below 0.2∘ and mean relative wind speed errors below 0.4 %. For fully turbulent wind conditions, the observer is able to estimate the low-frequency content of the local angle of attack and relative velocity even when it is lacking information on the incoming turbulent wind. We include this observer as part of a simple flap controller to reduce extreme loads and critical deflections of the blade. The flap controller's performance is tested in load simulations of the reference turbine with active flaps according to the IEC 61400-1 power production with extreme turbulence group. We used the lifting line free vortex wake method to calculate the aerodynamic loads. Results show a reduction of the maximum out-of-plane and resulting blade root bending moments of 8 % and 7.6 %, respectively, when compared to a baseline case without flaps. The critical blade tip deflection is reduced by 7.1 %. Furthermore, a sector load analysis considering extreme loading in all load directions shows a reduction of the extreme resulting bending moment in an angular region covering 30∘ around the positive out-of-plane blade root bending moment. Further analysis reveals that a fast reaction time of the flap system proves to be critical for its performance. This is achieved with the use of local sensors as input for the flap controller. A larger reduction potential of the system is identified but not reached mainly because of a combination of challenging controller objectives and the simple controller architecture.

Implementation and Validation of an Advanced Wind Energy Controller in Aero-Servo-Elastic Simulations Using the Lifting Line Free Vortex Wake Model

Accurate and reproducible aeroelastic load calculations are indispensable for designing modern multi-MW wind turbines. They are also essential for assessing the load reduction capabilities of advanced wind turbine control strategies. In this paper, we contribute to this topic by introducing the TUB Controller, an advanced open-source wind turbine controller capable of performing full load calculations. It is compatible with the aeroelastic software QBlade, which features a lifting line free vortex wake aerodynamic model. The paper describes in detail the controller and includes a validation study against an established open-source controller from the literature. Both controllers show comparable performance with our chosen metrics. Furthermore, we analyze the advanced load reduction capabilities of the individual pitch control strategy included in the TUB Controller. Turbulent wind simulations with the DTU 10 MW Reference Wind Turbine featuring the individual pitch control strategy show a decrease in the out-of-plane and torsional blade root bending moment fatigue loads of 14% and 9.4% respectively compared to a baseline controller.

Predicting Wind Turbine Wake Breakdown Using a Free Vortex Wake Code

When modeling wind turbine wake recovery, the location of wake breakdown plays a crucial role. The breakdown is caused by a rapid deformation of the helical near-wake vortex structure that is triggered by the pairing of successive blade tip vortices. In this paper, the capability of a cost-efficient lifting-line free vortex wake code to accurately predict the wake breakdown location and its underlying mechanisms is demonstrated and validated against simulation results of a large-eddy simulation solver and additional data from the literature. Furthermore, this work investigates a technique to accelerate the breakdown of wind turbine wakes. The onset of wake breakdown is caused by perturbations that travel along the helical structure of the wake and grow via mutual-induction interaction between neighboring vortex filaments. To accelerate wake breakdown, the blade tip vortices are perturbed at different frequencies via trailing-edge flaps located in the outboard region of the rotor blades. Through the evaluation of the perturbation growth rates and the analysis of velocity fields, it is shown that for a multi-megawatt wind turbine operating in a turbulent wind field, the wake breakdown position can be significantly affected by a moderate flap actuation amplitude if excited at an appropriate frequency.

Comparison of the free vortex wake and actuator line methods to study the loads of a wind turbine in imposed surge motion

To enable the development of floating offshore wind farms, it is important to have a clear understanding of the aerodyamic forces applied on a floating offshore wind turbine. The paper presents comparisons between a lifting line free vortex wake method and an actuator line method in the case of a wind turbine in surge with blade-resolved CFD data as a reference. Each model is compared to a quasi-steady estimation of the loads to understand the variations due to the surge movement. The near-wake flow field is investigated in order to give an insight into the flow features leading to the observed behavior. Both methods predict a higher axial velocity at the position of the rotor and one radius downstream of the rotor in surge conditions compared to the fixed case.

Wind Turbine Tip Vortices under the influence of Wind Tunnel Blockage Effects

The current paper describes the characteristics of the tip vortex in the near wake of a three-bladed upwind horizontal axis wind turbine with a rotor diameter of 3 m. Phase-locked stereo particle image velocimetry measurements were carried out under the influence of the wind tunnel walls that create a high blockage ratio. The location of the vortex, convection velocity, core radius, and strength were investigated and compared with similar investigations, including different blockages cases. Additionally, the same performance of the wind turbine model was simulated in the open source wind turbine tool QBlade, using the lifting line free vortex wake module in the absence of the walls.The results showed that the location of the tip vortices was more inboard the tip and more downstream the tunnel compared to the simulations and similar experiments. The convection velocity remained similar in the axial direction and changed in the lateral direction, contributing to the delay of the movement of the tip vortex outboard the tip. The strength, based on the circulation, was found with a difference of 4% between simulation and experiment.

Is the Blade Element Momentum theory overestimating wind turbine loads? – An aeroelastic comparison between OpenFAST's AeroDyn and QBlade's Lifting-Line Free Vortex Wake method

Abstract. Load calculations play a key role in determining the design loads of different wind turbine components. To obtain the aerodynamic loads for these calculations, the industry relies heavily on the Blade Element Momentum (BEM) theory. BEM methods use several engineering correction models to capture the aerodynamic phenomena present in Design Load Cases (DLCs) with turbulent wind. Because of this, BEM methods can overestimate aerodynamic loads under challenging conditions when compared to higher-order aerodynamic methods – such as the Lifting-Line Free Vortex Wake (LLFVW) method – leading to unnecessarily high design loads and component costs. In this paper, we give a quantitative answer to the question of load overestimation of a particular BEM implementation by comparing the results of aeroelastic load calculations done with the BEM-based OpenFAST code and the QBlade code, which uses a particular implementation of the LLFVW method. We compare extreme and fatigue load predictions from both codes using sixty-six 10 min load simulations of the Danish Technical University (DTU) 10 MW Reference Wind Turbine according to the IEC 61400-1 power production DLC group. Results from both codes show differences in fatigue and extreme load estimations for the considered sensors of the turbine. LLFVW simulations predict 9 % lower lifetime damage equivalent loads (DELs) for the out-of-plane blade root and the tower base fore–aft bending moments compared to BEM simulations. The results also show that lifetime DELs for the yaw-bearing tilt and yaw moments are 3 % and 4 % lower when calculated with the LLFVW code. An ultimate state analysis shows that extreme loads of the blade root out-of-plane bending moment predicted by the LLFVW simulations are 3 % lower than the moments predicted by BEM simulations. For the maximum tower base fore–aft bending moment, the LLFVW simulations predict an increase of 2 %. Further analysis reveals that there are two main contributors to these load differences. The first is the different way both codes treat the effect of the nonuniform wind field on the local blade aerodynamics. The second is the higher average aerodynamic torque in the LLFVW simulations. It influences the transition between operating modes of the controller and changes the aeroelastic behavior of the turbine, thus affecting the loads.

NUMERICAL ANALYSES OF A STRAIGHT BLADED VERTICAL AXIS DARRIEUS WIND TURBINE: VERIFICATION OF DMS ALGORITHM AND QBLADE CODE

Wind energy is among the most cost-effective renewable energies. Till date, turbines with different configurations had been designed to harness wind power, each having unique superiorities. Darrieus turbines are one of the mostly investigated vertical axis wind turbines using either experimental or numerical methods. Experimental analyses are time consuming works which requires high amount of effort and expenses. Thus, computational fluid dynamics (CFD) methods have been commonly used by scientists and engineers in order of obtaining detailed performance and illustration of the fluid flow. Contrary to the horizontal axis machines, Darrieus turbines are difficult to be analyzed by CFD algorithms due to high pressure and velocity variations which arise from extreme changes in the angle of attack beyond the stall condition at different azimuthal position of the blades. Therefore, more simplified numerical models are generated employing double multiple streamtube (DMS) theory together with additional improvements. QBlade is one of the mostly used numerical methods based on the lifting line free vortex wake method developed for calculating rotor aerodynamics. The main objective of this study is to verify the double multiple streamtube theory and QBlade algorithm with the experimental and computational results reported in the scientific literature. Analysis results represented good agreement with the previous studies especially at lower TSR ranges. Compare to the experimental results, an overestimation in the power coefficient is obtained at low free stream speed and high TSR ranges after exceeding the peak point. Sensitivity of the model to the Re number variations have also been outlined.

Benchmark of a Novel Aero-Elastic Simulation Code for Small Scale VAWT Analysis

After almost 20 years of absence from research agendas, interest in the vertical axis wind turbine (VAWT) technology is presently increasing again, after the research stalled in the mid 90's in favor of horizontal axis wind turbines (HAWTs). However, due to the lack of research in past years, there are a significantly lower number of design and certification tools available, many of which are underdeveloped if compared to the corresponding tools for HAWTs. To partially fulfill this gap, a structural finite element analysis (FEA) model, based on the Open Source multiphysics library PROJECT::CHRONO, was recently integrated with the lifting line free vortex wake (LLFVW) method inside the Open Source wind turbine simulation code QBlade and validated against numerical and experimental data of the SANDIA 34 m rotor. In this work, some details about the newly implemented nonlinear structural model and its coupling to the aerodynamic solver are first given. Then, in a continuous effort to assess its accuracy, the code capabilities were here tested on a small-scale, fast-spinning (up to 450 rpm) VAWT. The study turbine is a helix shaped, 1 kW Darrieus turbine, for which other numerical analyses were available from a previous study, including the results coming from both a one-dimensional beam element model and a more sophisticated shell element model. The resulting data represented an excellent basis for comparison and validation of the new aero-elastic coupling in QBlade. Based on the structural and aerodynamic data of the study turbine, an aero-elastic model was then constructed. A purely aerodynamic comparison to experimental data and a blade element momentum (BEM) simulation represented the benchmark for QBlade aerodynamic performance. Then, a purely structural analysis was carried out and compared to the numerical results from the former. After the code validation, an aero-elastically coupled simulation of a rotor self-start has been performed to demonstrate the capabilities of the newly developed model to predict the highly nonlinear transient aerodynamic and structural rotor response.

Comparison of Experimental and Numerically Predicted Three-Dimensional Wake Behavior of Vertical Axis Wind Turbines

The evolution of the wake of a wind turbine contributes significantly to its operation and performance, as well as to those of machines installed in the vicinity. The inherent unsteady and three-dimensional (3D) aerodynamics of vertical axis wind turbines (VAWT) have hitherto limited the research on wake evolution. In this paper, the wakes of both a troposkien and a H-type VAWT rotor are investigated by comparing experiments and calculations. Experiments were carried out in the large-scale wind tunnel of the Politecnico di Milano, where unsteady velocity measurements in the wake were performed by means of hot wire anemometry. The geometry of the rotors was reconstructed in the open-source wind-turbine software QBlade, developed at the TU Berlin. The aerodynamic model makes use of a lifting line free-vortex wake (LLFVW) formulation, including an adapted Beddoes-Leishman unsteady aerodynamic model; airfoil polars are introduced to assign sectional lift and drag coefficients. A wake sensitivity analysis was carried out to maximize the reliability of wake predictions. The calculations are shown to reproduce several wake features observed in the experiments, including blade-tip vortex, dominant and minor vortical structures, and periodic unsteadiness caused by sectional dynamic stall. The experimental assessment of the simulations illustrates that the LLFVW model is capable of predicting the unsteady wake development with very limited computational cost, thus making the model ideal for the design and optimization of VAWTs.

About the suitability of different numerical methods to reproduce model wind turbine measurements in a wind tunnel with a high blockage ratio

Abstract. In the present paper, numerical and experimental investigations of a model wind turbine with a diameter of 3.0 m are described. The study has three objectives. The first one is the provision of validation data. The second one is to estimate the influence of the wind tunnel walls by comparing measurements to simulated results with and without wind tunnel walls. The last objective is the comparison and evaluation of methods of high fidelity, namely computational fluid dynamics, and medium fidelity, namely lifting-line free vortex wake. The experiments were carried out in the large wind tunnel of the TU Berlin where a blockage ratio of 40 % occurs. With the lifting-line free vortex wake code QBlade, the turbine was simulated under far field conditions at the TU Berlin. Unsteady Reynolds-averaged Navier–Stokes simulations of the wind turbine, including wind tunnel walls and under far field conditions, were performed at the University of Stuttgart with the computational fluid dynamics code FLOWer. Comparisons among the experiment, the lifting-line free vortex wake code and the computational fluid dynamics code include on-blade velocity and angle of attack. Comparisons of flow fields are drawn between the experiment and the computational fluid dynamics code. Bending moments are compared among the simulations. A good accordance was achieved for the on-blade velocity and the angle of attack, whereas deviations occur for the flow fields and the bending moments.

Numerical simulations of a large offshore wind turbine exposed to turbulent inflow conditions

This work is intended to investigate the aerodynamic responses of a large generic 10-MW offshore wind turbine under turbulent inflow conditions. The nonlinear lifting line free vortex wake simulations approach is employed for this purpose, computed using the QBlade code. In these studies, the effects of a three-dimensional correction model for the airfoil polars were studied in advance. For this purpose, the blade element momentum computations employing the corrected polars are performed and compared to computational fluid dynamics simulations, and a good agreement is obtained between both employed approaches. Background turbulence is then imposed in the QLLT simulations with the turbulence intensities ranging from low to high turbulence levels (3%–15%). Furthermore, the impact of wind shear from different locations (offshore and onshore) is investigated in this work.

Modern methods for investigating the stability of a pitching floating platform wind turbine

Abstract. The QBlade implementation of the lifting-line free vortex wake (LLFVW) method was tested in conditions analogous to floating platform motion. Comparisons against two independent test cases using a variety of simulation methods show good agreement in thrust forces, rotor power, blade forces and rotor plane induction. Along with the many verifications already undertaken in the literature, it seems that the code performs solidly even in these challenging cases. Further to this, the key steps are presented from a new formulation of the instantaneous aerodynamic thrust damping of a wind turbine rotor. A test case with harmonic platform motion and collective blade pitch is used to demonstrate how combining such tools can lead to a better understanding of aeroelastic stability. A second case demonstrates a non-harmonic blade pitch manoeuvre showing the versatility of the instantaneous damping method.

Nonlinear Lifting Line Theory Applied to Vertical Axis Wind Turbines: Development of a Practical Design Tool

Recently, a new interest in vertical axis wind turbine (VAWT) technology is fueled by research on floating support structures for large-scale offshore wind energy application. For the application on floating structures at multimegawatt size, the VAWT concept may offer distinct advantages over the conventional horizontal axis wind turbine (HAWT) design. As an example, VAWT turbines are better suited for upscaling, and at multimegawatt size, the problem of periodic fatigue cycles reduces significantly due to a very low rotational speed. Additionally, the possibility to store the transmission and electricity generation system at the bottom, compared to the tower top as in a HAWT, can lead to a considerable reduction of material logistics costs. However, as most VAWT research stalled in the mid 1990s, no sophisticated and established tools to investigate this concept further exist today. Due to the complex interaction between unsteady aerodynamics and movement of the floating structure, fully coupled simulation tools modeling both aero and structural dynamics are needed. A nonlinear lifting line free vortex wake (LLFVW) code was recently integrated into the open source wind turbine simulation suite qblade. This paper describes some of the necessary adaptions of the algorithm, which differentiates it from the usual application in HAWT simulations. A focus is set on achieving a high robustness and computational efficiency. A short validation study compares LLFVW results with those of a two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) simulation.

Three-Dimensional Aerodynamic Analysis of a Darrieus Wind Turbine Blade Using Computational Fluid Dynamics and Lifting Line Theory

Due to the rapid progress in high-performance computing and the availability of increasingly large computational resources, Navier–Stokes (NS) computational fluid dynamics (CFD) now offers a cost-effective, versatile, and accurate means to improve the understanding of the unsteady aerodynamics of Darrieus wind turbines and deliver more efficient designs. In particular, the possibility of determining a fully resolved flow field past the blades by means of CFD offers the opportunity to both further understand the physics underlying the turbine fluid dynamics and to use this knowledge to validate lower-order models, which can have a wider diffusion in the wind energy sector, particularly for industrial use, in the light of their lower computational burden. In this context, highly spatially and temporally refined time-dependent three-dimensional (3D) NS simulations were carried out using more than 16,000 processor cores per simulation on an IBM BG/Q cluster in order to investigate thoroughly the 3D unsteady aerodynamics of a single blade in Darrieus-like motion. Particular attention was paid to tip losses, dynamic stall, and blade/wake interaction. CFD results are compared with those obtained with an open-source code based on the lifting line free vortex wake model (LLFVW). At present, this approach is the most refined method among the “lower-fidelity” models, and as the wake is explicitly resolved in contrast to blade element momentum (BEM)-based methods, LLFVW analyses provide 3D flow solutions. Extended comparisons between the two approaches are presented and a critical analysis is carried out to identify the benefits and drawbacks of the two approaches.

Modern methods for investigating the stability of a pitching floating platform wind turbine

The QBlade implementation of the Lifting Line Free Vortex Wake method(LLFVW) was tested in conditions analogous to floating platform motion. Comparisons against two independent test cases, using a variety of simulation methods show excellent agreement in thrust forces, rotor power, blade forces and rotor plane induction. Along with the many verifications already undertaken in literature, it seems that the code performs solidly even in these challenging cases. Further to this, the key steps are presented from a new formulation of the instantaneous aerodynamic thrust damping of a wind turbine rotor. A test case with harmonic platform motion and collective pitch is used to demonstrate how combining such tools can lead to better understanding of aeroelastic stability.

Aeroelastic simulation of multi-MW wind turbines using a free vortex model coupled to a geometrically exact beam model

The current paper investigates the aeroelastic modelling of large, flexible multi- MW wind turbine blades. Most current performance prediction tools make use of the Blade Element Momentum (BEM) model, based upon a number of simplifying assumptions that hold only under steady conditions. This is why a lifting line free vortex wake (LLFVW) algorithm is used here to accurately resolve unsteady wind turbine aerodynamics. A coupling to the structural analysis tool BeamDyn, based on geometrically exact beam theory, allows for time-resolved aeroelastic simulations with highly deflected blades including bend-twist, coupling. Predictions of blade loading and deformation for rigid and flexible blades are analysed with reference to different aerodynamic and structural approaches. The emergency shutdown procedure is chosen as an examplary design load case causing large deflections to place emphasis on the influence of structural coupling and demonstrate the necessity of high fidelity structural models.