Blade‐resolved simulations of a model wind turbine: effect of temporal convergence

Simulations of a model wind turbine at various tip‐speed‐ratios were carried out using Tenasi, a node‐centered, finite volume unstructured flow solver. The simulations included the tunnel walls, tower, nacelle, hub and the blades. The effect of temporal convergence on the predicted thrust and power coefficients is evaluated and guidelines for best practices are established. The results presented here are for tip‐speed‐ratios of 3, 6 and 10, with 6 being the design point. All simulations were carried out at a freestream velocity of 10 m s^?1 with an incoming boundary layer present and the wind turbine RPM was varied to achieve the desired tip‐speed‐ratio. The performance of three turbulence models is evaluated. The models include a one‐equation model (Spalart–Allmaras), a two‐equation model (Menter SST) and the DES version of the Menter SST. Turbine performance as well as wake data at various locations is compared to experiment. All the turbulence models performed well in terms of predicting power and thrust coefficients. The DES model was significantly better than the other two turbulence models for predicting the mean and fluctuating components of the velocity in the wake. Copyright © 2015 John Wiley & Sons, Ltd.     

Wind tunnel investigation on the effect of the turbine tower on wind turbines wake symmetry

In wind farms, the wake of the upstream turbines becomes the inflow for the downstream machines. Ideally, the turbine wake is a stable vortex system. In reality, because of factors like background turbulence, mean flow shear, and tower‐wake interaction, the wake velocity deficit is not symmetric and is displaced away from its mean position. The irregular velocity profile leads to a decreased efficiency and increased blade stress levels for the downstream turbines. The object of this work is the experimental investigation of the effect of the wind turbine tower on the symmetry and displacement of the wake velocity deficit induced by one and two in‐line model wind turbines (,D= 0.9 m). The results of the experiments, performed in the closed‐loop wind tunnel of the Norwegian University of Science and Technology in Trondheim (Norway), showed that the wake of the single turbine expanded more in the horizontal direction (side‐wall normal) than in the vertical (floor normal) direction and that the center of the wake vortex had a tendency to move toward the wind tunnel floor as it was advected downstream from the rotor. The wake of the turbine tandem showed a similar behavior, with a larger degree of non‐symmetry. The analysis of the cross‐stream velocity profiles revealed that the non‐symmetries were caused by a different cross‐stream momentum transport in the top‐tip and bottom‐tip region, induced by the turbine tower wake. In fact, when a second additional turbine tower, mirroring the original one, was installed above the turbine nacelle, the wake recovered its symmetric structure. Copyright © 2017 John Wiley & Sons, Ltd.     

A new class of actuator surface models for wind turbines

Actuator line model has been widely used in wind turbine simulations. However, the standard actuator line model does not include a model for the turbine nacelle which can significantly impact turbine wake characteristics. Another disadvantage of the standard actuator line model is that more geometrical features of turbine blades cannot be resolved on a finer mesh. To alleviate these disadvantages of the standard model, we develop a new class of actuator surface models for turbine blades and nacelle to take into account more geometrical details of turbine blades and include the effect of turbine nacelle. The actuator surface model for nacelle is evaluated by simulating the flow over periodically placed nacelles. Both the actuator surface simulation and the wall‐resolved large‐eddy simulation are conducted. The comparison shows that the actuator surface model is able to give acceptable results especially at far wake locations on a very coarse mesh. It is noted that although this model is used for the turbine nacelle in this work, it is also applicable to other bluff bodies. The capability of the actuator surface model in predicting turbine wakes is assessed by simulating the flow over the MEXICO (Model experiments in Controlled Conditions) turbine and the hydrokinetic turbine of Kang, Yang, and Sotiropoulos (Journal of Fluid Mechanics 744 (2014): 376‐403). Comparisons of the computed results with measurements show that the proposed actuator surface model is able to predict the tip vortices, turbulence statistics, and meandering of turbine wake with good accuracy.     

Wind turbine boundary layer arrays for Cartesian and staggered configurations‐Part I,flow field and power measurements

Model wind turbine arrays were developed for the purpose of investigating the wake interaction and turbine canopy layer in a standard cartesian and row‐offset turbine array configurations. Stereographic particle image velocimetry was used to collect flow data upstream and downstream of entrance and exit row turbines in each configuration. Wakes for all cases were analyzed for energy content and recovery behavior including entrainment of high‐momentum flow from above the turbine canopy layer. The row‐offset arrangement of turbines within an array grants an increase in streamwise spacing of devices and allows for greater wake remediation between successive rows. These effects are seen in exit row turbine wakes as changes to statistical quantities including the in‐plane Reynolds stress, , and the production of turbulence. The recovery of wakes also strongly mitigates the perceived underperformance of wind turbines within an array. The flux of kinetic energy is demonstrated to be more localized in the entrance rows and in the offset arrangement. Extreme values for the flux of kinetic energy are about 7.5% less in the exit row of the cartesian arrangement than in the offset arrangement. Measurements of mechanical torque at entrance and exit row turbines lead to curves of power coefficient and demonstrate an increase in efficiency in row‐offset configurations. Copyright © 2014 John Wiley & Sons, Ltd.     

Performance losses due to ice accretion for a 5 MW wind turbine

A numerical study of power performance losses due to ice accretion on a large horizontal axis wind turbine blade has been carried out using computational fluid dynamics (CFD) and blade element momentum (BEM) calculations for rime ice conditions. The computed aerodynamic coefficients for the normal and iced blades from the CFD calculations were used together with the BEM method to calculate the torque, power and curves of the wind turbine for both normal and icing conditions. The results are compared with the published data. It is shown that icing results in a reduced power production from the turbine and that changing the turbine controller could improve the power production with iced blades. Copyright © 2011 John Wiley & Sons, Ltd.     

Blind Test 2 calculations for two in-line model wind turbines where the downstream turbine operates at various rotational speeds

In this paper we report on the results of the Blind Test 2 workshop, organized by Norcowe and Nowitech in Trondheim, Norway in October 2012. This workshop was arranged in order to find out how well wind turbine simulation models perform when applied to two turbines operating in line. Modelers with a suitable code were given boundary conditions of a wind tunnel test performed in the large wind tunnel facility at the Department of Energy and Process Engineering, at NTNU Trondheim, where two almost identical model turbines with a diameter of about 0.9∼m had been tested under various operating conditions. A detailed geometry specification of the models could be downloaded and the modelers were invited to submit the calculation without knowing the experimental results in advance.Nine different contributions from eight institutions were received, representing a wide range of simulation models, such as a LES coupled with an actuator line rotor model, RANS using an actuator disc, U-RANS models applied to fully resolved turbine model geometries, as well as a vortex panel method. The comparison showed a larger than expected scatter on the performance calculation of the upstream turbine (±20%), and an even higher uncertainty for the downstream turbine, especially at operating conditions close to the runaway point. The modelers were requested to document the wake development downstream of the second turbine, the development behind the first turbine had been the challenge for a previous blind test (see Krogstad and Eriksen [17]).Mean flow calculations reported at X = 1D downstream of the second turbine showed that the models which fully resolved boundary layers on the rotor surface performed best. Including the tower and the hub in the simulation improved the accuracy of the predictions and is essential in capturing the important asymmetries that develop in the wake. These turbine details strongly influence the development near the center of the wake, but are often omitted in simulations in order to incorporate simplifying symmetry conditions in the calculations. Further from the rotor, at X = 4D, the LES simulations coupled to actuator line rotor models performed well and were able to capture the main features of the mean and turbulent flows, while RANS models using actuator disc models showed limitations especially in predicting correctly the turbulent kinetic energy.     

Aerodynamic performance of a dual turbine concept characterized by a relatively close distance between rotors

In this work, a closely spaced dual turbine concept is studied. The distance between the two side-by-side hubs is 1.05 $D$, where $D$ is the rotor diameter. This configuration has a potential benefit for offshore wind developments in which power density can be maximized. The main goal is to evaluate the overall aerodynamic performance, blade loads, and wake structure of a reference wind turbine generator operating within this dual turbine configuration and to compare the effects against those for the typical single turbine configuration. For this purpose, an actuator line model has been employed together with the large eddy simulation approach for predicting the turbulence effects. This model was implemented by using the open-source computational fluid dynamics toolbox OpenFOAM. Results show a better performance for the dual turbine concept. Under same operating conditions, the aerodynamic power of each turbine within the dual concept is higher than the power of the stand alone turbine, particularly at lower operating wind speeds (approximately 2% to 3% of extra power per turbine). Comparison between the two configurations shows similar character of the tangential and normal forces acting on the blades in terms of magnitude and fluctuation, eliminating potential concerns regarding fatigue and blade design. The largest difference in the tangential and normal root bending moments are approximately 3% and 2%, respectively, between single and dual turbine configurations. Finally, wake recovery analysis shows a downwind velocity deficit that is not enhanced streamwise in the dual turbine configuration with no considerable difference after 7 $D$.     

Aeroelastic validation and Bayesian updating of a downwind wind turbine

Downwind wind turbine blades are subjected to tower wake forcing at every rotation, which can lead to structural fatigue. Accurate characterisation of the unsteady aeroelastic forces in the blade design phase requires detailed representation of the aerodynamics, leading to computationally expensive simulation codes, which lead to intractable uncertainty analysis and Bayesian updating. In this paper, a framework is developed to tackle this problem. Full, detailed aeroelastic model of an experimental wind turbine system based on 3‐D Reynolds‐averaged Navier‐Stokes is developed, considering all structural components including nacelle and tower. This model is validated against experimental measurements of rotating blades, and a detailed aeroelastic characterisation is presented. Aerodynamic forces from prescribed forced‐motion simulations are used to train a time‐domain autoregressive with exogenous input (ARX) model with a localised forcing term, which provides accurate and cheap aeroelastic forces. Employing ARX, prior uncertainties in the structural and rotational parameters of the wind turbine are introduced and propagated to obtain probabilistic estimates of the aeroelastic characteristics. Finally, the experimental validation data are used in a Bayesian framework to update the structural and rotational parameters of the system and thereby reduce uncertainty in the aeroelastic characteristics.     

Simultaneous identification of wind turbine vibrations by using seismic data,elastic modeling and laser Doppler vibrometry

This work compares continuous seismic ground motion recordings over several months on top of the foundation and in the near field of a wind turbine (WT) at Pfinztal, Germany, with numerical tower vibration simulations and simultaneous optical measurements. We are able to distinguish between the excitation of eigenfrequencies of the tower‐nacelle system and the influence of the blade rotation on seismic data by analyzing different wind and turbine conditions. We can allocate most of the major spectral peaks to either different bending modes of the tower, flapwise, and edgewise bending modes of the blades or multiples of the blade‐passing frequency after comparing seismic recordings with tower simulation models. These simulations of dynamic properties of the tower are based on linear modal analysis performed with finite beam elements. To validate our interpretations of the comparison of seismic recordings and simulations, we use optical measurements of a laser Doppler vibrometer at the tower of the turbine at a height of about 20 m. The calculated power spectrum of the tower vibrations confirms our interpretation of the seismic peaks regarding the tower bending modes. This work gives a new understanding of the source mechanisms of WT‐induced ground motions and their influence on seismic data by using an interdisciplinary approach. Thus, our results may be used for structural health purposes as well as the development of structural damping methods, which can also reduce ground motion emissions from WTs. Furthermore, it demonstrates how numerical simulations of wind turbines can be validated by using seismic recordings and laser Doppler vibrometry.     

Large eddy simulations of the flow past wind turbines: actuator line and disk modeling

Large eddy simulations of the flow through wind turbines have been carried out using actuator disk and actuator line models for the turbine rotor aerodynamics. In this study, we compare the performance of these two models in producing wind turbine wakes. We also examine parameters that strongly affect the performance of these models, namely, grid resolution and the way in which the actuator force is projected onto the flow field. The proper choice of these two parameters has not been adequately addressed in previous works. We see that as the grid is coarsened, the predicted power decreases. As the width of the body force projection function is increased, the predicted power increases. The actuator disk and actuator line models produce similar wake profiles and predict power within 1% of one another when subject to the same uniform inflow. The actuator line model is able to generate flow structures near the blades such as root and tip vortices which the actuator disk model does not, but in the far wake, the predicted mean wakes are very similar. In order to perform validation against experimental data, the actuator line model output was compared with data from the wind tunnel experiment conducted at the Norwegian University of Science and Technology, Trondheim. Agreement between measured and predicted power, wake profiles, and turbulent kinetic energy has been observed for most tip speed ratios; larger discrepancies in power and thrust coefficient, though, have been found for tip speed ratios of 9 and 12. Copyright © 2014 John Wiley & Sons, Ltd.     

Passive control of wind turbine vibrations including blade/tower interaction and rotationally sampled turbulence

This paper investigates the use of a passive control device, namely, a tuned mass damper (TMD), for the mitigation of vibrations due to the along‐wind forced vibration response of a simplified wind turbine. The wind turbine assembly consists of three rotating uniform rotor blades connected to the top of a flexible uniform annular tower, constituting a multi‐body dynamic system. First, the free vibration properties of the tower and rotating blades are each obtained separately using a discrete parameter approach, with those of the tower including the presence of a rigid mass at the top, representing the nacelle, and those of the blade including the effects of centrifugal stiffening due to blade rotation and self‐weight. Drag‐based loading is assumed to act on the rotating blades, in which the phenomenon of rotationally sampled wind turbulence is included. Blade response time histories are obtained using the mode acceleration method, allowing base shear forces due to flapping motion for the three blades to be calculated. The resultant base shear is imparted into the top of the tower. Wind drag loading on the tower is also considered, and includes Davenport‐type spatial coherence information. The tower/nacelle is then coupled with the rotating blades by combining their equations of motion. A TMD is placed at the top of the tower, and when added to the formulation, a Fourier transform approach allows for the solution of the displacement at the top of the tower under compatibility of response conditions. An inverse Fourier transform of this frequency domain response yields the response time history of the coupled blades/tower/damper system. A numerical example is included to qualitatively investigate the influence of the damper. Copyright © 2007 John Wiley & Sons, Ltd.     

A CFD study into the influence of unsteady aerodynamic interference on wind turbine surge motion

To improve knowledge of the unsteady aerodynamic characteristics and interference effects of a floating offshore wind turbine (FOWT), this article focuses on the platform surge motion of a full configuration wind turbine with the rotating blades, hub, nacelle, and tower shapes. Unsteady aerodynamic analyses considering the moving motion of an entire configuration wind turbine have been conducted using an advanced computational fluid dynamics (CFD) and a conventional blade element momentum (BEM) analyses. The present CFD simulation is based on an advanced overset moving grid method to accurately consider the local and global motion of a three-dimensional wind turbine. The effects of various oscillation frequencies and amplitudes of the platform surge motion have been widely investigated herein. Three-dimensional unsteady flow fields around the moving wind turbine with rotating blades are graphically presented in detail. Complex flow interactions among blade tip vortices, tower shedding vortices, and turbulent wakes are physically observed. Comparisons of different aerodynamic analyses under the periodic surge motions are summarized to show the potential distinction among applied numerical methods. The present result indicates that the unsteady aerodynamic thrust and power tend to vary considerably depending on the oscillation frequency and amplitude of the surge motion.     

Reynolds number dependence of turbulence statistics in the wake of wind turbines

A wind tunnel experiment has been performed to quantify the Reynolds number dependence of turbulence statistics in the wake of a model wind turbine. A wind turbine was placed in a boundary layer flow developed over a smooth surface under thermally neutral conditions. Experiments considered Reynolds numbers on the basis of the turbine rotor diameter and the velocity at hub height, ranging from Re = 1.66 × 10⁴ to 1.73 × 10⁵. Results suggest that main flow statistics (mean velocity, turbulence intensity, kinematic shear stress and velocity skewness) become independent of Reynolds number starting from Re ≈ 9.3 × 10⁴. In general, stronger Reynolds number dependence was observed in the near wake region where the flow is strongly affected by the aerodynamics of the wind turbine blades. In contrast, in the far wake region, where the boundary layer flow starts to modulate the dynamics of the wake, main statistics showed weak Reynolds dependence. These results will allow us to extrapolate wind tunnel and computational fluid dynamic simulations, which often are conducted at lower Reynolds numbers, to full‐scale conditions. In particular, these findings motivates us to improve existing parameterizations for wind turbine wakes (e.g. velocity deficit, wake expansion, turbulence intensity) under neutral conditions and the predictive capabilities of atmospheric large eddy simulation models. Copyright © 2011 John Wiley & Sons, Ltd.     

Self‐similarity and turbulence characteristics of wind turbine wakes via large‐eddy simulation

Mean and turbulent properties of the wake generated by a single wind turbine are studied in this paper with a new large eddy simulation (LES) code, the wind turbine and turbulence simulator (WiTTS hereafter). WiTTS uses a scale‐dependent Lagrangian dynamical model of the sub‐grid shear stress and actuator lines to simulate the effects of the rotating blades. WiTTS is first tested by simulating neutral boundary layers without and with a wind turbine and then used to study the common assumptions of self‐similarity and axisymmetry of the wake under neutral conditions for a variety of wind speeds and turbine properties. We find that the wind velocity deficit generally remains self similarity to a Gaussian distribution in the horizontal. In the vertical, the Gaussian self‐similarity is still valid in the upper part of the wake, but it breaks down in the region of the wake close to the ground. The horizontal expansion of the wake is always faster and greater than the vertical expansion under neutral stability due to wind shear and impact with the ground. Two modifications to existing equations for the mean velocity deficit and the maximum added turbulence intensity are proposed and successfully tested. The anisotropic wake expansion is taken into account in the modified model of the mean velocity deficit. Turbulent kinetic energy (TKE) budgets show that production and advection exceed dissipation and turbulent transport. The nacelle causes significant increase of every term in the TKE budget in the near wake. In conclusion, WiTTS performs satisfactorily in the rotor region of wind turbine wakes under neutral stability. Copyright © 2014 John Wiley & Sons, Ltd.     

A simple improvement of a tip loss model for actuator disc simulations

The loading of a wind turbine decreases towards the blade tip because of the velocities induced by the tip vortex. This tip loss effect has to be taken into account when performing actuator disc simulations, where the single blades of the turbine are not modeled. A widely used method applies a factor on the axial and tangential loading of the turbine. This factor decreases when approaching the blade tip. It has been shown that the factor should be different for the axial and tangential loading of the turbine to model the rotation of the resulting force vector at the airfoil sections caused by the induced velocity. The present article contains the derivation of a simple correction for the tangential load factor that takes this rotation into account. The correction does not need any additional curve fitting but just depends on the local airfoil characteristics and angle of attack. Actuator disc computations with the modified tip loss correction show improved agreement with results from actuator line, free wake lifting line, and blade element momentum simulations.     

Data-driven modelling of turbine wake interactions and flow resistance in large wind farms

Turbine wake and local blockage effects are known to alter wind farm power production in two different ways: (1) by changing the wind speed locally in front of each turbine and (2) by changing the overall flow resistance in the farm and thus the so-called farm blockage effect. To better predict these effects with low computational costs, we develop data-driven emulators of the ‘local’ or ‘internal’ turbine thrust coefficient $C_T^{\ast }$ as a function of turbine layout. We train the model using a multi-fidelity Gaussian process (GP) regression with a combination of low (engineering wake model) and high-fidelity (large eddy simulations) simulations of farms with different layouts and wind directions. A large set of low-fidelity data speeds up the learning process and the high-fidelity data ensures a high accuracy. The trained multi-fidelity GP model is shown to give more accurate predictions of $C_T^{\ast }$ compared to a standard (single-fidelity) GP regression applied only to a limited set of high-fidelity data. We also use the multi-fidelity GP model of $C_T^{\ast }$ with the two-scale momentum theory (Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to demonstrate that the model can be used to give fast and accurate predictions of large wind farm performance under various mesoscale atmospheric conditions. This new approach could be beneficial for improving annual energy production (AEP) calculations and farm optimization in the future.     

大型风力机风轮气动不平衡的特性研究与验证

为了研究和探索风轮气动不平衡的物理特性,以某2.0 MW三叶片水平轴风力机为研究对象,采用计算机仿真及试验相结合的方法,研究风轮气动不平衡对机组动力学特性、气动性能及气动载荷的影响研究。通过气动特性分析和动力学分析表明,随着风轮叶片安装角的不平衡度增大,其机组性能逐渐下降,塔顶的载荷波动逐渐增大,叶片的挥舞载荷出现明显差异,机舱振动加速度变大。对塔顶振动加速度进行快速傅里叶变换分析,出现明显特征变化。研究过程表明,监测机舱振动加速度和机组功率曲线能有效识别机组气动不平衡程度。     

Characterization of the unsteady flow in the nacelle region of a modern wind turbine

A three‐dimensional Navier–Stokes solver has been used to investigate the flow in the nacelle region of a wind turbine where anemometers are typically placed to measure the flow speed and the turbine yaw angle. A 500 kW turbine was modelled with rotor and nacelle geometry in order to capture the complex separated flow in the blade root region of the rotor. A number of steady state and unsteady simulations were carried out for wind speeds ranging from 6 m s^?1 to 16 m s^?1 as well as two yaw and tilt angles. The flow in the nacelle region was found to be highly unsteady, dominated by unsteady vortex shedding from the cylindrical part of the blades, which interacted with the root vortices from each blade, generating high‐velocity gradients. As a consequence, the nacelle wind speed and the nacelle flow angle were found to vary significantly with the height above the nacelle surface. The nacelle anemometry showed significant dependence on both yaw and tilt angles with yaw errors of up to 10 degrees when operating in a tilted inflow. Copyright © 2010 John Wiley & Sons, Ltd.