Parabolic RANS solver for low‐computational‐cost simulations of wind turbine wakes

A numerical framework for simulations of wake interactions associated with a wind turbine column is presented. A Reynolds‐averaged Navier‐Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary‐layer approximations to reduce computational cost while capturing the essential wake physics. Turbulence effects on downstream evolution of the time‐averaged wake velocity field are taken into account through Boussinesq hypothesis and a mixing length model, which is only a function of the streamwise location. The calibration of the turbulence closure model is performed through wake turbulence statistics obtained from large‐eddy simulations of wind turbine wakes. This strategy ensures capturing the proper wake mixing level for a given incoming turbulence and turbine operating condition and, thus, accurately estimating the wake velocity field. The power capture from turbines is mimicked as a forcing in the RANS equations through the actuator disk model with rotation. The RANS simulations of the wake velocity field associated with an isolated 5‐MW NREL wind turbine operating with different tip speed ratios and turbulence intensity of the incoming wind agree well with the analogous velocity data obtained through high‐fidelity large‐eddy simulations. Furthermore, different cases of columns of wind turbines operating with different tip speed ratios and downstream spacing are also simulated with great accuracy. Therefore, the proposed RANS solver is a powerful tool for simulations of wind turbine wakes tailored for optimization problems, where a good trade‐off between accuracy and low‐computational cost is desirable.     

LiDAR measurements for an onshore wind farm: Wake variability for different incoming wind speeds and atmospheric stability regimes

Wind measurements were performed with the UTD mobile LiDAR station for an onshore wind farm located in Texas with the aim of characterizing evolution of wind‐turbine wakes for different hub‐height wind speeds and regimes of the static atmospheric stability. The wind velocity field was measured by means of a scanning Doppler wind LiDAR, while atmospheric boundary layer and turbine parameters were monitored through a met‐tower and SCADA, respectively. The wake measurements are clustered and their ensemble statistics retrieved as functions of the hub‐height wind speed and the atmospheric stability regime, which is characterized either with the Bulk Richardson number or wind turbulence intensity at hub height. The cluster analysis of the LiDAR measurements has singled out that the turbine thrust coefficient is the main parameter driving the variability of the velocity deficit in the near wake. In contrast, atmospheric stability has negligible influence on the near‐wake velocity field, while it affects noticeably the far‐wake evolution and recovery. A secondary effect on wake‐recovery rate is observed as a function of the rotor thrust coefficient. For higher thrust coefficients, the enhanced wake‐generated turbulence fosters wake recovery. A semi‐empirical model is formulated to predict the maximum wake velocity deficit as a function of the downstream distance using the rotor thrust coefficient and the incoming turbulence intensity at hub height as input. The cluster analysis of the LiDAR measurements and the ensemble statistics calculated through the Barnes scheme have enabled to generate a valuable dataset for development and assessment of wind farm models.     

Performance and near wake measurements of a model horizontal axis wind turbine

The performance characteristics and the near wake of a model wind turbine were investigated experimentally. The model tested is a three‐bladed horizontal axis type wind turbine with an upstream rotor of 0.90 m diameter. The performance measurements were conducted at various yaw angles, a freestream speed of about 10 m s ^?1, and the tip speed ratio was varied from 0.5 to 12. The time‐averaged streamwise velocity field in the near wake of the turbine was measured at different tip speed ratios and downstream locations. As expected, it was found that power and thrust coefficients decrease with increasing yaw angle. The power loss is about 3% when the yaw angle is less than 10° and increases to more than 30% when the yaw angle is greater than 30°. The velocity distribution in the near wake was found to be strongly influenced by the tip speed ratio and the yaw angle. At the optimum tip speed ratio, the axial velocity was almost uniform within the midsection of the rotor wake, whereas two strong peaks are observed for high tip speed ratios when the yaw angle is 0°. As the yaw angle increases, the wake width was found to be reduced and skewed towards the yawed direction. With increasing downstream distance, the wake velocity field was observed to depend on the tip speed ratio and more pronounced at high tip speed ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

Synthetic atmospheric turbulence and wind shear in large eddy simulations of wind turbine wakes

A method of generating a synthetic ambient wind field in neutral atmosphere is described and verified for modelling the effect of wind shear and turbulence on a wind turbine wake using the flow solver EllipSys3D. The method uses distributed volume forces to represent turbulent fluctuations, superimposed on top of a mean deterministic shear layer consistent with that used in the IEC standard for wind turbine load calculations. First, the method is evaluated by running a series of large‐eddy simulations in an empty domain, where the imposed turbulence and wind shear is allowed to reach a fully developed stage in the domain. The performance of the method is verified by comparing the turbulence intensity and spectral distribution of the turbulent energy to the spectral distribution of turbulence generated by the IEC suggested Mann model. Second, the synthetic turbulence and wind shear is used as input for simulations with a wind turbine, represented by an actuator line model, to evaluate the development of turbulence in a wind turbine wake. The resulting turbulence intensity and spectral distribution, as well as the meandering of the wake, are compared to field data. Overall, the performance of the synthetic methods is found to be adequate to model atmospheric turbulence, and the wake flow results of the model are in good agreement with field data. An investigation is also carried out to estimate the wake transport velocity, used to model wake meandering in lower‐order models. The conclusion is that the appropriate transport velocity of the wake lies somewhere between the centre velocity of the wake deficit and the free stream velocity. Copyright © 2013 John Wiley & Sons, Ltd.     

The near wake of a model horizontal-axis wind turbine—II. General features of the three-dimensional flowfield

The three-dimensional near-wake of a model horizontal-axis wind turbine has been measured for three operating conditions: stalled flow over the blades, close to optimum performance, and approaching runaway. The measurements of the mean velocity and turbulence at six axial locations document the formation and development of the near-wake. For the two highest tip speed ratios, the tip vortices are clearly identifiable from the contours of axial velocity and vorticity, and turbulent kinetic energy. At the lowest tip speed ratio, the turbulence level is also high within the blade wakes and these wakes are larger, because of separation in the flow over the blades. The wake structure is simplest for the condition closest to the optimum where the bound vorticity is almost constant with radius. As the tip speed ratio increases, the pitch of the tip vortices decreases and the angular momentum within them increases. This angular momentum reduces the power available from the turbine. The implication is that the structure of the tip vortices must be included in computational models intended to cover the entire operating range of a turbine.     

Coupled multi-body dynamics and CFD for wind turbine simulation including explicit wind turbulence

A high fidelity approach for wind turbine aero-elastic simulations including explicit representation of the atmospheric wind turbulence is presented. The approach uses a dynamic overset computational fluid dynamics (CFD) code for the aerodynamics coupled with a multi-body dynamics (MBD) code for the motion responses to the aerodynamic loads. Mann's wind turbulence model was implemented into the CFD code as boundary and initial conditions. The wind turbulence model was validated by comparing the theoretical one-point spectrum for the three components of the velocity fluctuations, and by comparing the expected statistics from the CFD simulated wind turbulent field with the explicit wind turbulence inlet boundary from Mann model. Extensive simulations based on the proposed coupled approach were conducted with the conceptual NREL 5-MW offshore wind turbine in an increasing level of complexity, analyzing the turbine behavior as elasticity, wind shear and atmospheric wind turbulence are added to the simulations. Results are compared with the publicly available simulations results from OC3 participants, showing good agreement for the aerodynamic loads and blade tip deflections in time and frequency domains. Wind turbulence/turbine interaction was examined for the wake flow. It was found that explicit turbulence addition results in considerably increased wake diffusion. The coupled CFD/MBD approach can be extended to include multibody models of the shaft, bearings, gearbox and generator, resulting in a promising tool for wind turbine design under complex operational environments.     

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.     

The velocity of the tip vortex of a horizontal-axis wind turbine at high tip speed ratio

An equation is derived for the streamwise velocity of the tip vortex of a horizontal-axis wind turbine as the pitch of the vortex tends to zero. The equation is applicable at high tip speed ratios provided the vortex core remains of constant size and there is no flow along the vortex axis. Under these conditions, the vortex velocity is the average of the velocity in the wake and the external wind speed. This result appears to conflict with the computational need to have the vortex velocity approach the wind speed in the high thrust region. It is suggested that the conflict could be resolved by considering the axial flow within the tip vortex.     

Wind turbine performance in shear flow and in the wake of another turbine through high fidelity numerical simulations with moving mesh technique

We present numerical simulations of two horizontal axis wind turbines, one operating under the wake of the other, under an incoming sheared velocity profile. We use a moving mesh technique to represent the rotation of the turbine blades and solve the unsteady Reynolds averaged Navier–Stokes equations with a shear stress transport k ? ω turbulence model. Temporal evolution of the lift and drag coefficients of the front turbine show a phase shift in the periodic cycle due to the non‐uniform incoming free stream velocity. Comparisons of the lift and drag coefficients for the back turbine with the unperturbed behaviour of the front demonstrate the complex non‐linear interactions of the blades with the wake, with a significant decrease in overall performance and two peaks at specific points in the cycle associated with local angle of attack modification in the wake. The vorticity field in the near wake shows tilting of the vortex lines in the wake due to the shear and a faster diffusion of the tip vortical signature compared with the uniform free stream velocity case. Observations of the wake–wake interaction show good agreement with recent studies that use different methodologies. Copyright © 2012 John Wiley & Sons, Ltd.     

基于Frandsen尾流半径假设的风力机尾流模型研究

在Frandsen非线性尾流半径假设的基础上,推导得出考虑环境湍流强度和风力机推力系数影响的Frandsen高斯修正尾流速度模型,并提出Frandsen双高斯湍流强度模型。以600 kW单风力机为案例,通过开展风洞试验和大涡模拟2种研究手段验证2个修正模型的预测效果。结果表明,Frandsen高斯修正尾流速度模型在径向尾流上预测效果更好,模型平均误差下降至7%,优于Frandsen速度模型。Frandsen双高斯湍流强度模型则能更好反映实际湍流强度在尾流场的变化特征。2种修正模型均比传统模型具有更好的预测效果,为风力机设计提供了新的尾流模型。     

Evaluation of the effects of turbulence model enhancements on wind turbine wake predictions

The modelling of wind turbine wakes is investigated in this paper using a Navier–Stokes solver employing the k–ω turbulence model appropriately modified for atmospheric flows. It is common knowledge that even single‐wind turbine wake predictions with computational fluid dynamic methods underestimate the near wake deficit, directly contributing to the overestimation of the power of the downstream turbines. For a single‐wind turbine, alternative modelling enhancements under neutral and stable atmospheric conditions are tested in this paper to account for and eventually correct the turbulence overestimation that is responsible for the faster flow recovery that appears in the numerical predictions. Their effect on the power predictions is evaluated with comparison with existing wake measurements. A second issue addressed in this paper concerns multi‐wake predictions in wind farms, where the estimation of the reference wind speed that is required for the thrust calculation of a turbine located in the wake(s) of other turbines is not obvious. This is overcome by utilizing an induction factor‐based concept: According to it, the definition of the induction factor and its relationship with the thrust coefficient are employed to provide an average wind speed value across the rotor disk for the estimation of the axial force. Application is made on the case of five wind turbines in a row. Copyright © 2010 John Wiley & Sons, Ltd.     

Measurements behind model wind turbines: further evidence of wake meandering

The frequency of wind turbine wake meandering was studied using wind turbine models with one, two and three blades. The one‐bladed turbine did not give rise to any meandering motion, whereas meandering was observed for both the two‐ and three‐bladed turbines at high enough rotational speeds. It was shown that both the thrust of the turbine and the tip‐speed ratio influence the meandering. Copyright © 2007 John Wiley & Sons, Ltd.     

Another engineering wake model variant for horizontal axis wind turbines

An engineering model is presented for predicting the performance of a single turbine located in an incoming turbulent, sheared, wind velocity field. The approach used is a variant of the well‐known and documented Ainslie eddy viscosity approach as also employed in the Direct Wake Meandering model. It incorporates a new and simple means of representing the rotor's loading profile, initializing the calculations, simplifying the wakes' shear layer mixing model and accounting for wind shear effects. Additionally, two figures of merit are employed for assessing the reliability of all data used and predictions provided. The first, a wake momentum‐flux/thrust parameter, is used for quantitatively assessing the accuracy and utility of both measured and/or computational wake data. The second, a rotor swept area wake‐averaged velocity, is employed as a single quantitative measure of a turbine's impact on its downstream neighbor. Through detailed comparisons with three independent state‐of‐the‐art Computational Fluid Dynamic generated datasets and a field‐measured dataset, the current model is shown to be accurate for turbine rated power levels from 100 kW to 2.3 MW, wind speeds of 6 to 22 m s^?1 (corresponding to turbine thrust coefficient levels of 0.14 to 0.8) and free‐stream turbulence levels from 0% to 16%. Copyright © 2015 John Wiley & Sons, Ltd.     

A generalized framework for reduced‐order modeling of a wind turbine wake

A reduced‐order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode. Back‐projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced‐order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large‐scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open‐loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root‐mean‐square error.  A high‐level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM.     

Effect of tower and nacelle on the flow past a wind turbine

Large eddy simulations (LES) of the flow past a wind turbine with and without tower and nacelle have been performed at 2 tip speed ratios (TSR, ), λ=3 and 6, where the latter corresponds to design conditions. The turbine model is placed in a virtual wind tunnel to reproduce the “Blind test 1” experiment performed at the Norwegian University of Science and Technology (NTNU) closed‐loop wind tunnel. The wind turbine was modeled using the actuator line model for the rotor blades and the immersed boundary method for the tower and nacelle. The aim of the paper is to highlight the impact of tower and nacelle on the turbine wake. Therefore, a second set of simulations with the rotating blades only (neglecting the tower and nacelle) has been performed as reference. Present results are compared with the experimental measurements made at NTNU and numerical simulations available in the literature. The tower and nacelle not only produce a velocity deficit in the wake but they also affect the turbulent kinetic energy and the fluxes. The wake of the tower interacts with that generated by the turbine blades promoting the breakdown of the tip vortex and increasing the mean kinetic energy flux into the wake. When tower and nacelle are modeled in the numerical simulations, results improve significantly both in the near wake and in the far wake.     

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.     

垂直轴风力机气动特性与涡脱落模态分析

垂直轴风力机运行过程中,叶片上下表面边界层与剪切层的相互作用使风力机下游尾迹形成周期性涡结构,这种尾迹涡结构对风力机空气动力学特性具有重要影响。基于此,该文采用计算流体力学方法对不同工况下垂直轴风力机尾迹涡结构展开研究,利用快速傅里叶变换与相空间轨迹分析不同尖速比下风力机叶片涡脱落现象和尾迹涡结构,并通过分形维数研究转矩与尾迹流场速度变化。结果表明：风力机尾迹涡结构随尖速比变化呈现不同特征,当尖速比为3.6时,风力机尾迹两侧呈规则性反向脱落涡模态;低尖速比垂直轴风力机尾迹具有明显的混沌特性,且随尖速比的增加混沌特性逐渐减弱;随着尖速比的增加,风力机转矩与下游速度分形维数不断降低,且当尖速比为3.6时,风力机下游速度分形维数仅为1.07。     

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.     

Measurements on a wind turbine wake: 3D effects and bluff body vortex shedding

The velocity field in the wake of a two‐bladed wind turbine model (diameter 180 mm) has been studied under different conditions using a two‐component hot wire. All three velocity components were measured both for the turbine rotor normal to the oncoming flow as well as with the turbine inclined to the freestream direction (the yaw angle was varied from 0° to 20°). The measurements showed, as expected, a wake rotation in the opposite direction to that of the turbine. A yawed turbine is found to clearly deflect the wake flow to the side, showing the potential of controlling the wake by yawing the turbine. An unexpected feature of the flow was that spectra from the time signals showed the appearance of a low‐frequency fluctuation both in the wake and in the flow outside the wake. This fluctuation was found both with and without freestream turbulence and also with a yawed turbine. The frequency expressed as a Strouhal number was shown to be independent of the freestream velocity or turbulence level, but the low frequency was only observed when the tip speed ratio (or equivalently the drag coefficient) was high. The shedding frequency changed also with the yaw angle. This is in agreement with the idea that the turbine sheds structures as a bluff body. The phenomenon, noticeable in all the velocity components, was further investigated using two‐point cross‐correlations of the velocity signals. Copyright © 2005 John Wiley & Sons, Ltd.