Wake Deficit Research Articles

Monin–Obukhov Similarity Theory for Modeling of Wind Turbine Wakes under Atmospheric Stable Conditions: Breakdown and Modifications

Monin–Obukhov similarity theory (MOST) overestimates the mean vertical velocity gradient in some atmospheric stable conditions, i.e., Richardson number R f < 0.25 . To obtain a given hub-height inflow velocity for a certain roughness length, this overestimated velocity gradient underpredicts the friction wind speed and the turbulence intensity, potentially influencing wake modeling of a wind turbine. This work investigates the side effects of the breakdown of MOST on wake modeling under stable conditions and makes some modifications to the flow similarity functions to eliminate these side effects. Based on a field measurement in a wind farm, we first show that MOST predicts a larger velocity gradient for the atmospheric stability parameter ζ > 0.1 and proposes new flow similarity functions without constraining R f to limit the overestimated velocity gradient. Next, different turbulence models based on MOST and a modified one based on the new similarity functions are investigated through numerical simulations. These turbulence models are combined with the actuator disk model (AD) and Reynolds-averaged Navier–Stokes equations (RANS) to model wind turbine wakes under stable conditions. As compared to measurements, numerical results show that turbulence models based on MOST result in a larger wake deficit and a slower wake recovery rate with a root-mean-squared error (RSME) of wake deficit in the range of 0.07 to 0.20. This overestimated wake effect is improved by applying the new similarity functions, and the RSME of wake deficit is reduced by 0.05 on average.

Analysis of wake effects on global responses for a floating two-turbine case

While most existing modeling and analysis of floating wind turbines (FWTs) considers isolated systems, interactions among multiple FWTs arranged in an array have received little attention. In this study, two 10 MW semi-submersible FWTs, separated by 8 rotor diameters (D) in the wind direction, are simulated with an ambient wind speed of 10 m/s and in moderate wave conditions using FAST. Farm to investigate the effects of wakes on global responses. Synthetic inflow is generated using three methods: the Kaimal turbulence model, 1) without and 2) with spatial coherence in the lateral and vertical velocity components, and 3) the Mann turbulence model (where spatial coherence in all three dimensions is inherent to the model). The first method results in negligible wake meandering, a relatively uniform wake deficit, while the second and third methods result in meandering of the upstream turbine’s lateral wake center at the downstream turbine’s rotor plane of up to approximately 1D and 1.5D, respectively. The slow meandering behavior of the upstream turbine’s wake resulted in increased low-frequency platform motions for the downstream turbine. Yaw motions were especially susceptible to wake meandering as the standard deviation of the downstream turbine’s yaw motion increased by 28.0 % for the second method and 11.3 % for the third method. Increased low-frequency response in structural loading was also observed. Wake effects led to between 2 % and 30 % greater fatigue damage at the top of the tower for all three methods and at the base of the tower for the second method. However, other results were found to be sensitive to the blade-passing frequency.

Effect of Wake Meandering on Aeroelastic Response of a Wind Turbine Placed in a Park

A wind turbine operating inside a wind farm is subjected to increased turbulence intensity and reduced wind speeds resulting in increased fatigue loadings and reduced power production. Furthermore, meandering of the wakes results in increased dynamic loading of the wind turbine. In the present study, a standalone dynamic wake meandering (DWM) model has been developed and implemented in commercial code SIMA. The standalone DIWA model does not require a direct coupling with aeroelastic code, hence it is computationally fast. Although the standalone tool is a good alternative for power and thrust prediction, it does not have the capability to predict the turbine aeroelastic loads. The new DWM program is referred as “Disturbed Inflow Wind Analyzer” (DIWA). Benchmarking studies of DIWA with the literature data are presented and discussed. Overall the DIWA compares well with the literature data and the discrepancies between DIWA and the literature data are discussed. The present studies show that the wake deficit profiles are very sensitive to the eddy viscosity parameters. Finally, the turbulence boxes generated using DIWA have been used for understanding the aeroelastic behaviour of NREL 5MW turbine and one of the wind turbines from the Lillgrund wind park. The estimated power production using both aeroelastic coupled with DIWA turbulence boxes and standalone DIWA (without aeroelastic) are in good agreement with the literature data. The trends of fatigue loads are predicted well, with a few exceptions.

Wake modelling via actuator-line method for exergy analysis in openFOAM

ABSTRACT In this paper, first and second laws of thermodynamics are performed on MEXICO wind turbine based on a generalized Actuator Line method (ALM). In order to simulate the flow field around wind turbine’s rotor and to predict the wake’s field behind it, large eddy simulation (LES) coupled with a novel Gaussian spreading width is employed in ALM. Simulation has been done for two different conditions including design conditions and stalled conditions. Due to the wake deficit results, exergy analysis conducted. Some metrological variables such as velocity, pressure, and temperature which are measured in the wind tunnel are used to evaluate wind turbine’s performance based on energy and exergy efficiencies. Obtained results are compared to experimental data. It was observed that the ALM results agreed well with measurements. Stall condition’s results were in better agreement with experimental data. It is shown that the axial and radial wake velocities showed a difference of 5.2 and 11% respectively. Also, it is shown that output results from ALM have a good ability to analysis wind turbine based on the second law of thermodynamics. The maximum difference from exergy efficiency analysis compared to measurements were only 6.2%.

Full-scale 3D remote sensing of wake turbulence - a taster

The aim of the present paper is to investigate the wake turbulence as based on advanced full-scale measurements which, for the first time, makes it possible directly to resolve all three turbulence components in the wake behind an operating wind turbine with high spatial- and temporal resolution. The experimental setup will be described, and analysis of selected runs will be presented with a focus on the expected inhomogeneity of this turbulence field. The analyses are performed in a meandering frame of reference, and in addition to afore mentioned wake turbulence field, the wake deficit field will be resolved and analysed. Atmospheric stability is not considered but is, however, not expected to contribute noticeably to wake turbulence nor to the wake deficit field when expressed in the meandering frame of reference.

Development of a parameterized reduced-order vertical-axis wind turbine wake model

Analyzing or optimizing wind farm layouts often requires reduced-order wake models to estimate turbine wake interactions and wind velocity. We propose a wake model for vertical-axis wind turbines in streamwise and crosswind directions. Using vorticity data from computational fluid dynamic simulations and cross-validated Gaussian distribution fitting, we produced a wake model that can estimate normalized wake velocity deficits of an isolated vertical-axis wind turbine using normalized downstream and lateral positions, tip-speed ratio, and solidity. Compared with computational fluid dynamics, taking over a day to run one simulation, our wake model predicts a velocity deficit in under a second with an appropriate accuracy and computational cost necessary for wind farm optimization. The model agreed with two experimental studies producing percent differences of the maximum wake deficit of 6.3% and 14.6%. The wake model includes multiple wake interactions and blade aerodynamics to calculate power, allowing its use in wind farm layout analysis and optimization.

Local turbulence parameterization improves the Jensen wake model and its implementation for power optimization of an operating wind farm

Abstract. In this paper, a new calculation procedure to improve the accuracy of the Jensen wake model for operating wind farms is proposed. In this procedure, the wake decay constant is updated locally at each wind turbine based on the turbulence intensity measurement provided by the nacelle anemometer. This procedure was tested against experimental data at the Sole du Moulin Vieux (SMV) onshore wind farm in France and the Horns Rev-I offshore wind farm in Denmark. Results indicate that the wake deficit at each wind turbine is described more accurately than when using the original model, reducing the error from 15 % to 20 % to approximately 5 %. Furthermore, this new model properly calibrated for the SMV wind farm is then used for coordinated control purposes. Assuming an axial induction control strategy, and following a model predictive approach, new power settings leading to an increased overall power production of the farm are derived. Power gains found are on the order of 2.5 % for a two-wind-turbine case with close spacing and 1 % to 1.5 % for a row of five wind turbines with a larger spacing. Finally, the uncertainty of the updated Jensen model is quantified considering the model inputs. When checked against the predicted power gain, the uncertainty of the model estimations is seen to be excessive, reaching approximately 4 %, which indicates the difficulty of field observations for such a gain. Nevertheless, the optimized settings are to be implemented during a field test campaign at SMV wind farm in the scope of the national project SMARTEOLE.

Power curve and wake analyses of the Vestas multi-rotor demonstrator

Abstract. Numerical simulations of the Vestas multi-rotor demonstrator (4R-V29) are compared with field measurements of power performance and remote sensing measurements of the wake deficit from a short-range WindScanner lidar system. The simulations predict a gain of 0 %–2 % in power due to the rotor interaction at below rated wind speeds. The power curve measurements also show that the rotor interaction increases the power performance below the rated wind speed by 1.8 %, which can result in a 1.5 % increase in the annual energy production. The wake measurements and numerical simulations show four distinct wake deficits in the near wake, which merge into a single-wake structure further downstream. Numerical simulations also show that the wake recovery distance of a simplified 4R-V29 wind turbine is 1.03–1.44 Deq shorter than for an equivalent single-rotor wind turbine with a rotor diameter Deq. In addition, the numerical simulations show that the added wake turbulence of the simplified 4R-V29 wind turbine is lower in the far wake compared with the equivalent single-rotor wind turbine. The faster wake recovery and lower far-wake turbulence of such a multi-rotor wind turbine has the potential to reduce the wind turbine spacing within a wind farm while providing the same production output.

Development of a Computational System to Improve Wind Farm Layout, Part II: Wind Turbine Wakes Interaction

The second part of this work describes a wind turbine Computational Fluid Dynamics (CFD) simulation capable of modeling wake effects. The work is intended to establish a computational framework from which to investigate wind farm layout. Following the first part of this work that described the near wake flow field, the physical domain of the validated model in the near wake was adapted and extended to include the far wake. Additionally, the numerical approach implemented allowed to efficiently model the effects of the wake interaction between rows in a wind farm with reduced computational costs. The influence of some wind farm design parameters on the wake development was assessed: Tip Speed Ratio (TSR), free-stream velocity, and pitch angle. The results showed that the velocity and turbulence intensity profiles in the far wake are dependent on the TSR. The wake profile did not present significant sensitivity to the pitch angle for values kept close to the designed condition. The capability of the proposed CFD model showed to be consistent when compared with field data and kinematical models results, presenting similar ranges of wake deficit. In conclusion, the computational models proposed in this work can be used to improve wind farm layout considering wake effects.

Comparative study on a newly-developed three-dimensional wind turbine wake model

Abstract In this paper, an analytical three-dimensional wake model is developed to study the wind turbine wake effect and the model is compared with the existing one-dimensional wake model. With the fast development of both onshore and offshore wind energy, wind turbines are upsizing rapidly and the simple assumption of one-dimensional wake model is not suitable for large wind turbines. The commonly used one-dimensional wake model is impossible to describe the spatial distribution accurately as it assumes that the wind deficit is linear distributed along the downwind distance. While the three-dimensional wake model is an effective way to solve this problem. This wake model assumes the wake deficit as Gaussian shaped and considers wind speed variation along height direction as well. In this study, the wind tunnel measurement validation of the three-dimensional wake model is demonstrated which is used to calculate the wind deficit at a downstream position. Next, the results are compared to the one-dimensional wake model’s results. An error analysis and discussions are then conducted based on the comparisons. From this study, the new three-dimensional wake model contributes to the wake distribution study for researchers and a proper wake model can help developing optimized wind farm layouts as well.

Three-Dimensional Wake of Nonconventional Vortex Generators

The wakes of wishbone, doublet, and ramp-type vortex generators (VGs) were investigated. The VGs were placed in the thin laminar boundary layer of a flat plate at a Reynolds number of 930 based on the freestream velocity and VG height. The turbulence statistics of the wake were measured with high spatial resolution using planar particle image velocimetry (PIV) and stereoscopic PIV. Three-dimensional time-resolved tomographic PIV was also carried out to visualize the evolution of vortices. The fastest recovery of the wake deficit was observed for the wishbone VG. The peak of turbulence production in the wake of the wishbone and doublet VGs had a similar magnitude and was 1.5 times stronger than that of the ramp VG. The hairpin vortices generated by the ramp VG formed the largest percentage of the wake turbulent kinetic energy, and their size is about half of the hairpins produced by the wishbone and doublet VGs. The wishbone and ramp VGs had the best overall performance. The wishbone VG generated the strongest mixing in the wake region, whereas the ramp VG had the smallest drag coefficient. The doublet VG had the weakest overall performance due to low mixing and the largest drag.

Three-dimensionality of the wake recovery behind a vertical axis turbine

The wake recovery downstream of a vertical axis turbine operating in a turbulent channel flow is investigated via detailed velocity measurements using an Acoustic Doppler Velocimeter. Three distinct wake regions are identified: (i) a near-wake region which extends until two rotor diameters (2D) downstream and characterised by a low-momentum area isolated from the ambient flow and the presence of energetic dynamic stall vortices; (ii) a transition region (2D-5D), characterised by a fast momentum recovery, high levels of turbulence and vertical expansion of the wake; and (iii) a far-wake region beyond 5D where the velocity recovers to approximately 95% of the free-stream velocity. Albeit the wake deficit recovery is mostly accomplished at 5D behind the turbine, rotor-induced effects are still present beyond 10D as indicated by high-order flow statistics, such as high velocity fluctuations and flow skewness. The analysis of the streamwise momentum budget reveals that advection is the main mechanism for momentum replenishment through most of the wake and turbulent transport terms play only a minor role. This study evidences the anisotropic nature of the turbulence and asymmetry of the flow in horizontal, vertical and cross-sectional planes downstream of the vertical axis turbine.

The Influence of Intra-Array Wake Dynamics on Depth-Averaged Kinetic Tidal Turbine Energy Extraction Simulations

Assessing the tidal stream energy resource, its intermittency and likely environmental feedbacks due to energy extraction, relies on the ability to accurately represent kinetic losses in ocean models. Energy conversion has often been implemented in ocean models with enhanced turbine stress terms formulated using an array-averaging approach, rather than implementing extraction at device-scale. In depth-averaged models, an additional drag term in the momentum equations is usually applied. However, such array-averaging simulations neglect intra-array device wake interactions, providing unrealistic energy extraction dynamics. Any induced simulation error will increase with array size. For this study, an idealized channel is discretized at sub 10 m resolution, resolving individual device wake profiles of tidal turbines in the domain. Sensitivity analysis is conducted on the applied turbulence closure scheme, validating results against published data from empirical scaled turbine studies. We test the fine scale model performance of several mesh densities, which produce a centerline velocity wake deficit accuracy (R2) of 0.58–0.69 (RMSE = 7.16–8.28%) using a k-Ɛ turbulence closure scheme. Various array configurations at device scale are simulated and compared with an equivalent array-averaging approach by analyzing channel flux differential. Parametrization of array-averaging energy extraction techniques can misrepresent simulated energy transfer and removal. The potential peak error in channel flux exceeds 0.5% when the number of turbines nTECs ≈ 25 devices. This error exceeds 2% when simulating commercial-scale turbine array farms (i.e., >100 devices).

Investigation of wake characteristics for the offshore floating vertical axis wind turbines in pitch and surge motions of platforms

Pitch and surge motions of platforms are two main movements of offshore floating vertical axis wind turbines when they are faced with wind and wave loads. These two movements can not only affect the aerodynamic loads, but also may influence the wake characteristics of the wind turbines. In the present study, the computational fluid dynamics approach with the improved delayed detached eddy simulation (IDDES) and the overset mesh are employed to investigate the wake characteristics of an H-rotor floating vertical axis wind turbine under the platform’s pitch and surge motions. The wake profiles and structures between pitch and non-pitch conditions, and surge and non-surge conditions are compared. Then, the wake characteristics under different pitching amplitudes and periods and different surging amplitudes and periods are investigated. It is shown that pitch motion can enlarge the peak values of wake deficits and shift the positions of the mainstream of the wake in the vertical direction. The amplitudes and periods of the ‘wake wave’ under different pitching amplitudes and periods show regular variations. A ‘Spindle’ -type of wake structure is formed in the wake region under a platform’s surge motion, and the strength and core zone of the ‘Spindle’ also regularly change with different surging amplitudes and periods. These changes cause wake profile’s diversity at certain motion stages for the same downwind distance under different periods and amplitudes of surge and pitch.

Impact on wind turbine loads from different down regulation control strategies

This paper presents a study on derating wind turbine power levels in a wind farm and the associated loads on down wind placed wind turbines. This is done by derating the wind farm power output for certain periods of time. Derating can be done in different ways by adjusting the rotor speed and blade pitch on the individual turbines which also has a direct impact on the turbine component loads. The paper studies three characteristic derating strategies on the upstream wind Turbine (WT) and the corresponding load impact on the downstream one. These are defined as minimum/maximum rotor speeds (minRS, maxRS) and minimum thrust (minT) modes. Derating factors of 20% and 40% on available power are applied together with 4 and 7 diameters WT interspace. The study is based on aeroelastic simulations of a 2MW generic WT model including wake effects. The results show that below rated wind speed (8m/s) the downstream WT blade flap fatigue loads are minimized when the upfront WT is derated with the minRS or minT strategy. The maxRS mode returns around 2% percent higher loads. The load levels for minRS and minT strategies are almost equal. Above rated wind speed (16m/s) the trend is the same as at 8m/s with a bit higher difference on load levels, up to 6% percent at tighter interspace bewteen maxRS strategy and the other two. The fore-aft fatigue loads on the tower base and the main bearing yaw moment follow the same trends as the blade for both below and above rated wind speed.Finally, it is also found that there is a correlation on the load levels and the wind deficit values. In all cases up to around ±10 degrees incoming wind direction the wake deficit from the maxRS control strategy is higher and the load levels follow the same trend. This is an important outcome and links the control strategies directly to the wake deficit due to the upstream WT operation.

Vortex simulations of wind turbines operating in atmospheric conditions using a prescribed velocity‐vorticity boundary layer model

AbstractA prescribed velocity‐vorticity boundary layer model for the vorticity transport equation is proposed, which corrects the unphysical upward deflection of the wake seen in a simpler prescribed velocity shear approach. A Lagrangian implementation of the boundary layer model has been investigated using our in‐house vortex solver MIRAS. The MIRAS code contains both an aerodynamic part and a structural‐mechanical part taking into account aeroelastic phenomena. The solver is employed to simulate flows around wind turbines and uses a combination of filaments and particles in order to mimic the vorticity released by the wind turbine blades. The vorticity is interpolated onto a uniform Cartesian mesh, where the interaction is efficiently calculated by an fast Fourier transform‐based method. Simulations of wind turbines operating in an atmospheric boundary layer flow are carried out and analysed in detail for a range of scenarios. The manuscript focuses on studying the influence of wind shear and turbulence, which is varied to mimic natural atmospheric conditions. A traverse virtual probe up to 30 diameters downstream of the rotor plane is used to investigate the properties of the turbulent wake flow for the different cases. This includes mean and standard deviation of the streamwise velocity component, wake deficit, Reynolds stresses, and power spectral density of the velocity signal. The results show that combining a prescribed boundary layer approach with a vortex method gives consistent and physically correct results if properly implemented.

Numerical investigation of flow around hairy flaps cylinder using FSI Capabilities

Flow around a cylinder has been extensively studied due to its practical importance in engineering; much attention has been devoted to drag reduction and vortex shedding suppression using active and passive control devices. A strong motivation for studying such practical problems come from the fact that large amplitude of lift fluctuation and alternate vortex shedding are generally design concerns for engineers. Several numerical and experimental studies have been devoted for studying flow around a cylinder with a flexible plate attached to its centerline. This investigation has been known to be one of the most successful ways of controlling vortex shedding. Other active device for vortex shedding cycle reduction in order to minimize sound pressure is a cylinder equipped with hairy flaps. Experimental studies of air around a cylinder equipped with hairy flaps show that hairy flaps can reduce the wake deficit by modifying the shedding cycle behind the cylinder. For the modelisation and simulation of such a coupling problem, fluid structure capabilities need to be performed. Fluid structure coupling problems can be solved using different solvers; a monolithic solver and a partitioned process. Monolithic process is a fully implicit method preserving energy at the fluid structure interface. However its implementation is more complex when specific methods are required for both fluid and structure solvers. When efficient fluid and structure software packages are available, a partitioned procedure can be used in order to couple the two codes. The present work is devoted to simulation of fluid structure interaction problems and flow around thin flexible hairy flaps, using a partitioned procedure. One of the main problems encountered in the simulation is the automatic remeshing when the flaps come into contact and the fluid mesh between the flaps undergoes high mesh distortion. . In this paper, numerical simulation has been performed and Strouhal number for two different Reynolds number Re=1.46 10 4 and 1.89 10 4 have been investigated. For both Reynolds number experimental data is available. For comparison with flow around a plain cylinder, numerical simulation were also performed and Strouhal number compared to experimental value

Influence of the Fluctuating Velocity Field on the Surface Pressures in a Jet/Fin Interaction

The mechanism by which aerodynamic effects of jet/fin interaction arise from the flow structure of a jet in crossflow is explored using particle image velocimetry measurements of the crossplane velocity field as it impinges on a downstream fin instrumented with high-frequency pressure sensors. A Mach 3.7 jet issues into a Mach 0.8 crossflow from either a normal or inclined nozzle, and three lateral fin locations are tested. Conditional ensemble-averaged velocity fields are generated based upon the simultaneous pressure condition. Additional analysis relates instantaneous velocity vectors to pressure fluctuations. The pressure differential across the fin is driven by variations in the spanwise velocity component, which substitutes for the induced angle of attack on the fin. Pressure changes at the fin tip are strongly related to fluctuations in the streamwise velocity deficit, wherein lower pressure is associated with higher velocity and vice versa. The normal nozzle produces a counter-rotating vortex pair that passes above the fin, and pressure fluctuations are principally driven by the wall horseshoe vortex and the jet wake deficit. The inclined nozzle produces a vortex pair that impinges the fin and yields stronger pressure fluctuations driven more directly by turbulence originating from the jet mixing.

Interaction of Wind Turbine Wakes under Various Atmospheric Conditions

We present a numerical study of two utility-scale 5-MW turbines separated by seven rotor diameters. The effects of the atmospheric boundary layer flow on the turbine performance were assessed using large-eddy simulations. We found that the surface roughness and the atmospheric stability states had a profound effect on the wake diffusion and the Reynolds stresses. In the upstream turbine case, high surface roughness increased the wind shear, accelerating the decay of the wake deficit and increasing the Reynolds stresses. Similarly, atmospheric instabilities significantly expedited the wake decay and the Reynolds stress increase due to updrafts of the thermal plumes. The turbulence from the upstream boundary layer flow combined with the turbine wake yielded higher Reynolds stresses for the downwind turbine, especially in the streamwise component. For the downstream turbine, diffusion of the wake deficits and the sharp peaks in the Reynolds stresses showed faster decay than the upwind case due to higher levels of turbulence. This provides a physical explanation for how turbine arrays or wind farms can operate more efficiently under unstable atmospheric conditions, as it is based on measurements collected in the field.

An annual energy production estimation methodology for onshore wind farms over complex terrain using a RANS model with actuator discs

This work presents a new methodology for the interpolation and extrapolation of the wind power generated by each wind turbine in a wind farm at different wind speeds for a given wind direction, running only three RANS-CFD simulations, two with and one without wind turbines. The wind turbines are modeled as uniformly loaded actuator discs with an adaptation for wake interaction cases. Three RANS turbulence models are used, standard k-ε, k-ε-fP and the realizable k-ε model modified to account for Coriolis forces and with appropriate coefficients for the simulation of ABL flows. The turbulence models are validated against wake deficit and power output measurements from the wind turbine test site Wieringermeer. Then, the new methodology proposed to predict the wind turbine power is detailed and evaluated with simulation results and measurements for a large onshore wind farm, particularly for a strong wake interaction case. It is observed that the power predictions using the proposed strategy are in good agreement with the obtained from different wind velocity simulations and power measurements. The methodology is a useful tool for wind farm annual energy production estimation.