Wake Model Research Articles

Energy extraction and optimization studies on vortex-induced vibration of the elastically mounted rigid cylinder using wake oscillator model

The vortex-induced vibration (VIV) response of an elastically mounted rigid cylinder from the standpoint of energy harvesting is analyzed with the aid of the wake oscillator model (WOM). A model of an elastically mounted rigid cylinder free to oscillate in the in-line (IL) and cross-flow (CF) directions subjected to different uniform flow velocities is considered and its responses under different mass ratios are predicted using the modified wake oscillator model. For modeling structure motion, the dynamic equilibrium equation, and for modeling the fluid part, the Van der Pol wake oscillator is utilized and they are coupled together to get the response in IL and CF directions. A comparative study is performed between the numerical and the experimental results and they are found to be in good agreement. The study is then probed into the scope of energy extraction from VIV which will presumably throw light into the development of VIV-based energy harvesting methods which is a potential future hope for the renewable energy sector. Parametric optimization study is carried out to determine the maximum harnessable energy from VIV. The response of the cylinder for the optimal parametric combination is analyzed in the time and frequency domain. It is observed that damping and reduced velocity play a crucial role in the energy extraction.

Wind Farm Layout Optimization Subject to Cable Cost, Hub Height, and a Feasible 3D Gaussian Wake Model Implementation

We address the Wind Farm Layout Optimization (WFLO) problem and tackle the optimal placement of several turbines within a specific (wind farm) area by incorporating additional aspects of an economically driven target function. With this, we contribute three refinements for WFLO research: First, while many research contributions optimize the turbines’ locations subject to maximum energy production or energy efficiency, we instead pursue a strategy of maximizing a profit objective. This enables us to incorporate inner-farm wiring costs (underground cable installation). For this, we explore the impact of using MSTs (Minimum Spanning Trees) and adding junction (so-called “Steiner”) points to the terrain plane. Second, while most research focuses on finding optimal x and y coordinates (i.e., address two-dimensional turbine placement), we also optimize the turbines’ hub heights z. Third, we also provide a software implementation of the Gaussian wake model. The latter finds entrance to the open-source WFLO research framework that comes as package <strong>wflo</strong> for statistical software R. We find that taking wiring cost into account may lead to very different turbine placements, however, increasing overall profit significantly. Allowing the optimizer to vary the hub heights may have an ambiguous impact on the wind farm profit.

Site-specific wake steering strategy for combined power enhancement and fatigue mitigation within wind farms

Wind energy plays a crucial role in the quest for sustainable energy solutions. However, optimizing the efficiency of wind energy utilization remains a significant challenge. Wake steering, a key strategy in the field, offers the potential to address this challenge. This study introduces an innovative site-specific wake steering framework that incorporates a wake superposition model for wake steering, a machine-learning based fatigue and power predictor and a multi-objective optimizer to both enhance total power generation and mitigate fatigue loads within wind farms. The wake superposition model, developed and validated here, successfully replicates secondary wake steering effects and provides a new solution for calculating superimposed transverse velocity. The study comprehensively considers and implements constraints based on physical laws. Analysis of inflow speed and turbulence levels reveals that wake steering can continue to enhance total power output. Power enhancement can reach up to 18% at lower turbulence levels and still achieve significant increases even when inflow speeds exceed rated values, with only marginal increases in fatigue loads. Lower turbulence levels improve optimization results at the expense of heightened structural loads, while higher turbulence levels lead to diminishing power enhancement and additional fatigue loads. Examination of wind turbine spacing shows that smaller intervals yield substantial power enhancement, with improvements of up to 51.7%, although the effect diminishes as intervals increase and wake recovery takes place. In conclusion, the proposed site-specific wake steering framework offers an efficient means of balancing enhanced wind farm power output and structural integrity, representing a significant advancement in wind energy optimization.

A new 3D asymmetric double-Gaussian wake analytical model for horizontal-axis wind turbines

A new three-dimensional analytical model named 3DADG that is able to describe asymmetric evolution of wind turbine wake is proposed in this paper. Due to the combined effects of wind wheel rotation and wind shear effects wake attenuation shows asymmetric properties. However, existing wake analytical models fail to describe such unique properties. To solve this problem, spatial dependencies of the wake expansion rate and deficit coefficient are revealed to successfully present horizontal attenuations of the wake varying from asymmetric-double-Gaussian in the near and transition wake regions, and then to single-Gaussian in the far wake region. The wind shear effect is also considered in the model to include asymmetric vertical wake speed attenuation. This model is derived from the laws of mass and momentum conservation. It is verified through comparisons with the results of wind tunnel “blind test” and LES simulation. The model proposed is capable to show spatial evolution of wind turbine wake from a three-dimensional perspective. Sensitivities of thrust coefficient and turbulence intensity to the model are also investigated. It not only promotes development of wake analytical model but also provides a useful tool for power prediction and wake control of wind farms under wake effects.

Measurement-driven large-eddy simulations of a diurnal cycle during a wake-steering field campaign

Abstract. High-fidelity flow modeling with data assimilation enables accurate representation of the wind farm operating environment under realistic, nonstationary atmospheric conditions. Capturing the temporal evolution of the turbulent atmospheric boundary layer is critical to understanding the behavior of wind turbines under operating conditions with simultaneously varying inflow and control inputs. This paper has three parts: the identification of a case study during a field evaluation of wake steering; the development of a tailored mesoscale-to-microscale coupling strategy that resolved local flow conditions within a large-eddy simulation (LES), using observations that did not completely capture the wind and temperature fields throughout the simulation domain; and the application of this coupling strategy to validate high-fidelity aeroelastic predictions of turbine performance and wake interactions with and without wake steering. The case study spans 4.5 h after midnight local time, during which wake steering was toggled on and off five times, achieving yaw offset angles ranging from 0 to 17°. To resolve nonstationary nighttime conditions that exhibited shear instabilities, the turbulence field was evolved starting from the diurnal cycle of the previous day. These background conditions were then used to drive wind farm simulations with two different models: an LES with actuator disk turbines and a steady-state engineering wake model. Subsequent analysis identified two representative periods during which the up- and downstream turbines were most nearly aligned with the mean wind direction and had observed yaw offsets of 0 and 15°. Both periods corresponded to partial waking on the downstream turbine, which had errors in the LES-predicted power of 4 % and 6 %, with and without wake steering. The LES was also able to capture conditions during which an upstream turbine wake induced a speedup at a downstream turbine and increased power production by up to 13 %.

An improved analytical framework for flow prediction inside and downstream of wind farms

This study evaluates available analytical wake models for flow prediction inside and downstream of wind farms of different sizes and layouts using large-eddy simulation (LES), and introduces an enhanced analytical framework. All the tested analytical wake models, based on the superposition of individual turbine wakes, systematically overestimate the wake recovery both inside and downstream of the wind farms. The results indicate that the overestimation is linked to the assumption of linear or quasilinear wake expansion, which does not hold at large downstream distances. To address this issue, an enhanced analytical framework is proposed based on the extension of a recently developed streamwise scaling model for single wakes that eliminates the need for the linear wake expansion assumption. Since the new framework computes the wake expansion based on the near-wake length and the local turbulence intensity, different methods for their calculation and the superposition of turbulence intensity within wind farms are evaluated against the LES data. The identified best methods are incorporated into the new analytical framework. The proposed framework consistently yields more accurate power estimates and flow predictions inside and downstream of finite-size wind farms with different sizes and configurations.

Inviscid analysis of horizontal axis wind turbines using distributed vorticity elements

The primary tool currently used for a wind turbine preliminary design is the blade element momentum method, which lacks a detailed wake model and relies on an assumption of non-interacting streamtubes. These simplifications limit the designer's ability to tailor the blade shape to minimize the induced power loss of the rotor. Improved prediction of the induced velocity distribution on the blades can be achieved through the use of vortex-based models at a computational cost low enough for use in design processes requiring many iterations. This paper presents the implementation of a potential flow, lifting-surface methodology using elements of distributed vorticity. The use of such elements provides several advantages including higher resolution than filament-based methods, simulation of non-planar blade planforms, and avoids the need for empirical corrections. Because the wake has a strong influence on the flow at the rotor, the accurate prediction of its geometry is highly important for wind turbine analysis. To this end, a force-free relaxed-wake model is presented as well as less numerically intensive fixed-wake and hybrid-wake models. Comparison is made to the blade element momentum method and Goldstein's theoretical solution for the ideal lightly loaded rotor.

A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines

Efficient and accurate prediction of the wind turbine dynamic wake is crucial for active wake control and load assessment in wind farms. This paper proposes a real-time dynamic wake prediction model for wind turbines based on a physics-guided neural network. The model can predict the instantaneous dynamic wake field under various operating conditions using only the inflow wind speed as input. The model utilizes Taylor's frozen-flow hypothesis and a steady-state wake model to convert instantaneous inflow wind speed and turbine parameters into neural network input features. A deep convolutional neural network then maps these features to desired wake field snapshots, enabling dynamic wake predictions for wind turbines. To train the model, we generated approximately 255 000 instantaneous flow field snapshots of single-turbine wakes using the large eddy simulation, covering different thrust coefficients and yaw angles. The model was trained using the supervised learning method and verified on the test set. The results indicate that the model can effectively predict the dynamic wake characteristics, including the dynamic wake meandering and the wake deflection of the yawed turbines. The model can also assess both the instantaneous wake velocity and the instantaneous wake center of a wind turbine. At a thrust coefficient of 0.75, the root mean square error for the predicted instantaneous wake velocity is around 6.53%, while the Pearson correlation coefficient for the predicted instantaneous wake center can reach 0.624. Furthermore, once the model is trained, its prediction accuracy does not decrease with the increase in the time span.

Analysis of the Effect on Wake Decay Constant of Jensen Wake Model in a Wind Farm

Analysis of the Effect on Wake Decay Constant of Jensen Wake Model in a Wind Farm

Quantification of three-dimensional added turbulence intensity for the horizontal-axis wind turbine considering the wake anisotropy

The accurate evaluation of wake turbulence intensity (TI) is of great significance for the layout optimization of wind farms and research on control strategies. However, the existing engineering wake models still have many shortcomings in evaluating the TI in the wake of horizontal-axis wind turbines (HAWTs), especially in the near wake region. In response to this, this article proposed an analytical model based on the double-Gaussian ellipse function that can describe the three-dimensional added TI distribution in the entire wake region. Firstly, the anisotropy of wake expansion is taken into account in both the horizontal and vertical directions, assuming that the added TI distribution downstream of the HAWT is a double-Gaussian elliptical shape. Secondly, taking into account the self-similarity characteristics of flow TI, the maximum added TI and its position in the entire wake region are evaluated. In addition, considering the influence of the ground effect, the vertical turbulence distribution was corrected. Finally, the proposed added turbulence model was validated and relative error analysis was conducted using large eddy simulation (LES) data, wind field measurement data, and wind tunnel experimental data. The results show that the model had good prediction accuracy in the entire wake region, and its prediction performance was significantly improved compared to traditional models, especially in the near wake region, with the lowest even relative error of 3.66%. This model has significant advantages such as low computational cost, wide applicability, and high accuracy. It can reduce energy losses in wind farms, improve wind energy utilization efficiency, and has great potential for widespread application in large-scale wind farms.

Aerodynamic model comparison for an X-shaped vertical-axis wind turbine

Abstract. This article presents a comparison study of different aerodynamic models for an X-shaped vertical-axis wind turbine and offers insight into the 3D aerodynamics of this rotor at fixed pitch offsets. The study compares six different numerical models: a double-multiple streamtube (DMS) model, a 2D actuator cylinder (2DAC) model, an inviscid free vortex wake model (from CACTUS), a free vortex wake model with turbulent vorticity (from QBlade), a blade-resolved unsteady Reynolds-averaged Navier–Stokes (URANS) model, and a lattice Boltzmann method (from PowerFLOW). All models, except URANS and PowerFLOW use the same blade element characteristics other than the number of blade elements. This comparison covers the present rotor configuration for several tip-speed ratios and fixed blade pitch offsets without unsteady corrections, except for the URANS and PowerFLOW which cover a single case. The results show that DMS and 2DAC models are inaccurate – especially at highly loaded conditions, are unable to predict the downwind blade vortex interaction, and do not capture the vertical/axial induction this rotor exhibits. The vortex models are consistent with each other, and the differences when compared against the URANS and PowerFLOW mostly arise due to the unsteady and flow curvature effects. Furthermore, the influence of vertical induction is very prominent for this rotor, and this effect becomes more significant with fixed pitch offsets where the flow at the blade root is considerably altered.

MORSA: Multi-objective reptile search algorithm based on elite non-dominated sorting and grid indexing mechanism for wind farm layout optimization problem

The proposal of the wind farm layout optimization (WFLO) problem aims to better utilize wind energy. A multi-objective reptile search algorithm (MORSA) based on elite non-dominated sorting and grid indexing mechanism was proposed to solve the multi-objective optimization problem of wind farm layout under the Jansen wake model to maximize power generation while minimizing costs. Firstly, the elite non-dominated sorting method was used to sort the population, and then the crowding distance method was used to maintain the diversity between the optimal sets. By calculating the crowding distance, the same level of non-dominated populations are sorted. Then, the grid index mechanism is added to the archive for selection and deletion. Leaders can use the roulette wheel to select and delete some solutions in high-density grids. By obtaining the optimal Pareto solution set while maintaining the diversity of the population, the effectiveness of solving multi-objective optimization problems is improved. The improved algorithm solves the WFLO problem based on the Jansen wake model by using two different initial self-flow winds for performance testing while considering the effects of single wake and multiple wake with or without partial wake occlusion. The performance of the WFLO (output power and cost) was compared without considering wake obstruction, MORSA can obtain the minimum turbine cost of 26.3601 and the maximum power generation of 2.3078E-08 with a single wake flow of 16 m/s. The experimental results show that the proposed MORSA has better convergence and applicability, and has shown good results in multi-objective layout optimization of wind farms.

Predicting wind farm wake losses with deep convolutional hierarchical encoder–decoder neural networks

Wind turbine wakes are the most significant factor affecting wind farm performance, decreasing energy production and increasing fatigue loads in downstream turbines. Wind farm turbine layouts are designed to minimize wake interactions using a suite of predictive models, including analytical wake models and computational fluid dynamics simulations (CFD). CFD simulations of wind farms are time-consuming and computationally expensive, which hinder their use in optimization studies that require hundreds of simulations to converge to an optimal turbine layout. In this work, we propose DeepWFLO, a deep convolutional hierarchical encoder–decoder neural network architecture, as an image-to-image surrogate model for predicting the wind velocity field for Wind Farm Layout Optimization (WFLO). We generate a dataset composed of image representations of the turbine layout and undisturbed flow field in the wind farm, as well as images of the corresponding wind velocity field, including wake effects generated with both analytical models and CFD simulations. The proposed DeepWFLO architecture is then trained and optimized through supervised learning with an application-tailored loss function that considers prediction errors in both wind velocity and energy production. Results on a commonly used test case show median velocity errors of 1.0%–8.0% for DeepWFLO networks trained with analytical and CFD data, respectively. We also propose a model-fusion strategy that uses analytical wake models to generate an additional input channel for the network, resulting in median velocity errors below 1.8%. Spearman rank correlations between predictions and data, which evidence the suitability of DeepWFLO for optimization purposes, range between 92.3% and 99.9%.

Synchronized optimization of wind farm start-stop and yaw control based on 3D wake model

In existing wind farms, the overall power output can be increased through yaw control. However, the cooperative control of start/stop, yaw and turbines positions is often overlooked, leading to wake superposition to downstream wind turbines and suboptimal power output. This paper proposes a synchronized optimized method that considers start/stop, yaw and turbines positions control based on a three-dimensional wake model and yaw flow superposition model. The objective function of the proposed strategy is to maximize the power output of the Chapman Ranch (CR) wind farm. Four cases are considered: start-stop, yaw control, start-stop & yaw control and start-stop & yaw & turbines positions control. The particle swarm algorithm is introduced to optimize the wind farm layout. According to the results, considering start-stop, yaw and turbines positions optimization can not only increase the annual power output of the wind farm by 8.85 %, but also avoid the colliding wake in the CR wind farm. However, the other three cases will cause colliding wake in some fields of the CR wind farm. This study provides important guidance on improving the overall power output of existing wind farms.

An advanced three-dimensional analytical model for wind turbine near and far wake predictions

Most existing analytical wake models have been designed to represent the velocity distribution of the far wake region behind a wind turbine, but fail to reproduce the trend of the near wake. In order to meet the demand for both near and far wake velocity predictions, a concise three-dimensional dual-cosine shape (3D-COU) model is proposed. Moreover, by taking into account the wind shear and ground effects in the vertical direction, this model is capable of describing the anisotropic property of the 3-D wake field and is much closer to the reality. The proposed model is then calibrated and validated through a series of test cases, including different scales of turbines that are operating under a wide range of inflow conditions, and meanwhile the reference data resource is diverse. Overall, the results demonstrate that the 3D-COU model can accurately predict the variations of the wake velocity in both the vertical and horizontal directions throughout the whole wake region. Given its good accuracy, simplicity and applicability, this model provides the potential to effectively address practical problems in wind energy projects.

Impact of turbine availability and wake effect on the application of dynamic thermal rating of wind farm export transformers

Dynamic thermal rating allows transformers to operate beyond the nameplate rating according to the actual weather and loading conditions. This paper proposes a methodology to improve the application of this technology in the design of new transformers or in the operation of existing transformers connected to wind farms by accurately predicting their load profiles, accounting for the influence of wake effect and turbine availability. Specifically, the variation of turbine availability due to the intermittent wind is considered in the load profile estimation. Additionally, a correction method, which can be incorporated into any wake model, is proposed to improve the accuracy of wake loss computation. A case study shows that the wake effect and the changing turbine availability shorten the time that the transformers maintain at full load, thereby reducing the aging rate of the wind farm export transformers. The findings suggest that considering these two factors in the DTR application can benefit the longevity and efficiency of wind farm exported transformers.

Modeling of the internal wave wake of a self-propelled body for radar scattering cross sections

The motion of a self-propelled body excites internal waves that modulate wind-induced microscale waves and affect the radar scattering cross section of rough sea surfaces. This process is closely related to factors such as stratification, propulsion effect, and radar parameters. Based on this, this study establishes and partially verifies a computational model for the scattering cross section of the internal wave wake left by an underwater self-propelled body. The model incorporates the first-order resonant internal waves of the stratified flow field as the dominant component of the wake-effect internal waves and determines the equivalent source size using the wake evolution model, thereby effectively simulating the characteristics of the surface flow field when the net momentum of the underwater vessel is nonzero. By solving the wave-action conservation equations, the wave spectrum of the modulated surface is derived, and the tilt and convergence/divergence effects caused by internal waves are comprehensively considered through the facet scattering model to assess their impact on the synthetic aperture radar (SAR) scattering cross section. Overall, this study systematically elucidates the correlation mechanism between the flow field and the radar system.

An optimization framework for wind farm layout design using CFD-based Kriging model

Wind farm layout optimization (WFLO) seeks to alleviate the wake loss and maximize wind farm power output efficiency, and is a crucial process in the design and planning of wind energy projects. Since the optimization algorithms typically require thousands of numerical evaluations of the wake effects, conventional WFLO studies are usually carried out with the low-fidelity analytical wake models, while the higher-fidelity computational-fluid-dynamics-based (CFD-based) methods are seldom used due to the excessive computational cost. In this paper, we develop a self-adaptive optimization framework for wind farm layout design using CFD-based Kriging model to maximize the annual energy production (AEP) of wind farms. This surrogate-based optimization (SBO) framework uses latin hypercube sampling to generate a group of wind farm layout samples, based on which CFD simulations with the turbines modeled as actuator disks are carried out to obtain the corresponding AEPs. This initial wind farm layout dataset is used to train the Kriging model, which is then integrated with an optimizer based on genetic algorithm (GA). As the optimization progresses, the intermediate optimal layout designs are again fed into the dataset to re-train the Kriging model. Such adaptive update of wind farm layout dataset continues until the algorithm converges to the optimal layout design. To evaluate the performance of the proposed SBO framework, we apply it to four representative wind farm cases. Compared to the conventional staggered layout along the dominant wind direction, the optimized wind farm produces significantly higher total AEP, which is more evenly distributed among the turbines. In particular, the SBO framework requires significantly smaller number of CFD calls to yield the optimal layouts that generates almost the same AEP with the direct CFD-GA method. Further analysis on the velocity fields show that the optimization framework always attempts to locate the downstream turbines away from the wakes of upstream ones along the dominant wind directions. The proposed CFD-based surrogate model provides a more accurate and flexible alternative to the conventional analytical-wake-model-based methods in WFLO tasks, and has the potential to be used for designing efficient wind farm projects.

Leading effect for wind turbine wake models

As wind energy expands worldwide, the demand of reliable, fast, cost-efficient wind turbine wake models is growing. This is a significant challenge as wind turbines face various inflow conditions that include turbulence, inhomogeneities/instationarities and upstream wakes. In consequence, an enormous number of engineering models, each one based on different physical concepts, has been proposed. The majority focuses on the far wake where the mean velocity recovers and turbulence decays after it built up. We argue that the most important, or the leading, parameter for wake modeling is the length scale of a virtual origin. Testing different models from the literature for data sets from laboratory wind turbines and multi-megawatt turbines obtained by LiDAR, we find that all models perform significantly better when such a virtual origin is added. Our results can therefore be used for a yet missing definition of a near wake zone.

Evaluation of wind resource uncertainty on energy production estimates for offshore wind farms

Wind farm design generally relies on the use of historical data and analytical wake models to predict farm quantities, such as annual energy production (AEP). Uncertainty in input wind data that drive these predictions can translate to significant uncertainty in output quantities. We examine two sources of uncertainty stemming from the level of description of the relevant meteorological variables and the source of the data. The former comes from a standard practice of simplifying the representation of the wind conditions in wake models, such as AEP estimates based on averaged turbulence intensity (TI), as opposed to instantaneous. Uncertainty from the data source arises from practical considerations related to the high cost of in situ measurements, especially for offshore wind farms. Instead, numerical weather prediction (NWP) modeling can be used to characterize the more exact location of the proposed site, with the trade-off of an imperfect model form. In the present work, both sources of input uncertainty are analyzed through a study of the site of the future Vineyard Wind 1 offshore wind farm. This site is analyzed using wind data from LiDAR measurements located 25 km from the farm and NWP data located within the farm. Error and uncertainty from the TI and data sources are quantified through forward analysis using an analytical wake model. We find that the impact of TI error on AEP predictions is negligible, while data source uncertainty results in 0.4%–3.7% uncertainty over feasible candidate hub heights for offshore wind farms, which can exceed interannual variability.