Wake Growth Research Articles

Influence of wind direction on flow over a cliff and its interaction with a wind turbine wake

This work investigates the effect of wind direction on the flow over a cliff and its interaction with the wake of a wind turbine sited on the cliff. The cliff is modeled as a forward-facing step, and five wind directions are tested (θ=0∘, 15∘, 30∘, 45∘, and −45∘), where 0∘ represents a wind direction perpendicular to the cliff edge. The flow becomes increasingly three-dimensional with the increase in the wind direction magnitude and a cross-stream flow separation develops from the cliff leading edge. The turbulence kinetic energy decreases for wind directions higher than 15∘, which is due to the absence of the streamwise flow separation for higher wind directions. The cross-stream flow development in the base flow affects the shape of the turbine wake. A two-dimensional Gaussian fit is performed on the wake velocity deficit, which shows a slight departure from self-similarity in the lateral direction. The wake recovery slows down for wind directions higher than 15∘, which is consistent with the decrease in the wake growth rate for θ>15∘. The wake shows higher deflection and tilt angle for higher wind directions. Analysis of the streamwise momentum in the wake reveals that the advection terms play a role in slowing the wake recovery for higher wind directions. Published by the American Physical Society 2024

Prediction of multiple-wake velocity and wind power using a cosine-shaped wake model

It is well accepted the wakes induced by upstream turbines have an adverse impact on the power production of downstream turbines and this ubiquitous phenomenon severely affects wind farm performance. The aim of the study is to apply a new analytical wake model to prediction of multiple-wake velocity and power output inside wind farms and evaluate its performance. Unlike the classical top-hat model (Jensen model) widely embedded in industry-standard software, the newly proposed analytical wake model, which is derived based on the conservation of both mass and momentum, assumes a trigonometric distribution for the velocity deficit in the wakes of a stand-alone wind turbine and adopts a variable wake growth rate relating ambient turbulence as well as rotor-generated turbulence. Two superposition models including the SED (superposition of energy deficits) and the SVD (superposition of velocity deficits) are employed to simulate the wake-interaction flows and the performance of the new model with the superposition methods is evaluated in two cases: (1) wake interactions of two wind turbines; (2) power prediction of the Horns Rev offshore wind farm. The open-source wind-farm simulation tool FLORIS is employed to make a further comparison of different wake models. It is found that the new and the Gaussian models with the SED are in reasonably good agreement with large-eddy simulation (LES) and measurements compared with other wake models, whereas lower velocity as well as power output is predicted when using the SVD counterpart. This research proposes the SED model as an effective selection strategy for evaluating power output in wind farms when using the cosine and Gaussian models.

Analytical Descriptions of Swirling Wake Profiles

Wake behavior significantly affects the performance and lifetime of wind turbines on which it impacts. This study considers wake profile fits applied to velocity data gathered in a swirling turbulent wake. Wake rotation or swirl has been found to impact wake growth and evolution, and thus both wake deficit and swirl profiles are fit. Specifically, Gaussian and double Gaussian functions are applied to the wake deficit profiles, and Lamb-Oseen and Taylor distributions are used for the tangential velocity profiles. Fits that accurately represent the wake profiles promise to improve wake representations that can be used, for example, in stability theory analyses and wake modeling. The double Gaussian and Taylor vortex distributions were found to best represent the distributions, but Taylor vortex distribution failed to capture the true distribution at some radial locations. An example use of these fits to quantify the impact of swirl on wake evolution is provided.

An experimental and analytical study of wind turbine wakes under pressure gradient

This work is dedicated to the systematic investigation of wind turbine wakes under the effect of pressure gradients. Wind tunnel experiments are carried out with a wind turbine positioned on straight ramps of increasing angle such that it experiences an approximately linear flow speed-up/slow-down from the induction region into the far wake. Fifteen ramp angles are studied: 7 favorable (FPG), 7 adverse (APG), and 1 zero pressure gradient. The wake center is shown to follow the base flow streamline originating from a virtual turbine hub height. A quasi-linear relationship between the pressure gradient and near wake length is demonstrated. Far wake characteristics, such as the recovery of the wake center velocity deficit and wake growth rate, are observed to systematically vary with the pressure gradient. The wake recovery rate increases (decreases) with the increase in the FPG (APG), and the wake growth rate shows a linear increase from most favorable to most adverse pressure gradient. The turbine power coefficient decreases significantly with increasing APG to a greater degree than the increase in power coefficient under FPG. The engineering approach of superposing the wake deficit predicted by the standard Gaussian model on the modified base flow is shown to work for very moderate pressure gradients. In light of this, a threshold in terms of flow speed-up/slow-down along the wake trajectory is established, below which the engineering approach can be reasonably employed. Finally, a physics-based model for wakes under the pressure gradient is tested. A new theoretical relation for near wake length under the pressure gradient is proposed. Using the theoretical near wake length, the pressure gradient model predicts the turbine wakes for all cases with good accuracy and shows a significant improvement from the engineering approach.

The impact of swirl and wake strength on turbulent axisymmetric wake evolution

An experimental investigation of swirl and wake strength influence on axisymmetric turbulent wake evolution was conducted. A novel wake generator design wire mounted in a wind tunnel test section with low free-stream turbulence produced wake Reynolds numbers based on momentum thickness and free-stream velocity in excess of 14 000 and swirl numbers up to 0.4 with minimal blockage. Steady-state blade element momentum simulations of reference wind turbine designs indicated that wind turbines operate in the flow regimes studied, indicating the practical aspects of this work. Stereoscopic particle image velocimetry was used to acquire three components of velocity in the swirling wake at locations up to approximately ten diameters downstream. Quantitative measures of wake growth and decay were deduced using available equilibrium similarity scaling for the swirling wake. The results show an increase above 50% in growth and axial velocity decay rate constants over the range of swirl strength studied compared to those of the non-swirling wake. Tangential velocity decay constants were shown to decrease with swirl strength over the range of conditions studied. Notably, changes in wake strength have little influence on growth and decay rates when compared to changes in swirl strength for the flow regimes studied in this work.

A physical wind‐turbine wake growth model under different stratified atmospheric conditions

AbstractThe wind‐turbine wake growth is crucial for wake assessment. At present, it can only be determined empirically, which is the primary source of prediction errors in the analytical wake model, and a physically‐based method is urgently needed. Recently, the plume model is proposed for wake width prediction in the neutral boundary layer based on Taylor's diffusion theory. However, this model is not applicable for high‐roughness neutral and strongly convective conditions, which is mainly related to the fact that the specified far wake point in the plume model is too close to the virtual wake origin. In this condition, the wake width prediction has evident convex function characteristics, which is inconsistent with the actual linear expansion of wake width. To this end, we propose a coupled model of the plume model and the traditional wake model (CPT model) to calculate the wake growth rate iteratively, thereby obtaining the wake width and velocity deficits in the far‐wake region. The average wake width prediction error decreases from 11.75% to 3.1% in these conditions. Since the wind‐turbine‐induced‐turbulence contribution is dominant in the wake recovery in the very stable boundary layer, both models have low but engineering acceptable prediction accuracy. Except for the above conditions, both the plume and CPT models can predict the wake width well, and their average wake width prediction errors are 2.5% and 1.9%, respectively. This implies that the proposed CPT model has higher prediction accuracy and a broader application range.

A physics-based model for wind turbine wake expansion in the atmospheric boundary layer

Analytical wind turbine wake models are widely used to predict the wake velocity deficit. In these models, the wake growth rate is a key parameter specified mainly with empirical formulations. In this study, a new physics-based model is proposed and validated to predict the wake expansion downstream of a turbine based on the incoming ambient turbulence and turbine operating conditions. The new model utilises Taylor diffusion theory, the Gaussian wake model, turbulent mixing layer theory and the analogy between wind turbine wake expansion and scalar diffusion. These components ensure that the model conserves mass and momentum in the far wake and accounts for the ambient turbulence and turbine-induced turbulence effects on the wake expansion. To account for the turbulence relevant scales that contribute to the wake expansion, the model uses the root-mean-square of the low-pass filtered radial velocity component. A simplified version that only requires the unfiltered velocity standard deviation and turbulence integral scale is also proposed. In addition, a new relation for the near-wake length is derived. The model performance is validated using large-eddy simulation data of a wind turbine wake under neutral atmospheric conditions with a wide range of incoming turbulence levels. The results show that the proposed model yields reasonable predictions of the wake width, maximum velocity deficit and near-wake length. In the case with a relatively low incoming streamwise turbulence intensity of 0.05, the ambient and turbine-induced terms in the model contribute almost equally to the wake width, rendering them both crucial for reasonable wake predictions.

Effects of freestream turbulence on the wake growth rate of a model wind turbine and a porous disc

This study presents the results of an experimental investigation that focuses on quantifying the differences between the spreading rates of a model wind turbine wake and a porous disc wake at different freestream turbulence intensity levels. Two-dimensional two-component particle image velocimetry (2D2C PIV) measurements are performed within the wakes of a model wind turbine and a porous disc (up to 7D downstream) of the same diameter and a matching thrust coefficient. The wind turbine is operated at a Tip Speed Ratio (TSR) of 2 in order to have matching thrust coefficient conditions for a consistent wake comparison. The results show that the mean wake flow field (both near and far wake) is significantly different for the wind turbine compared to the porous disc even if they are operating at similar, high or low, freestream turbulence levels. The wake of the wind turbine recovers much faster than that of a porous disc with a matching thrust coefficient especially in the far wake region at both low and high freestream turbulence levels. On the other hand, the data shows that the far wake of the turbine operating at low freestream turbulence is very similar to that of the disc operating at high freestream turbulence. This suggests caution and stresses the importance in choosing the freestream turbulence intensity level when using porous discs to represent wind turbines in wind tunnel studies.

Anisotropic double‐Gaussian analytical wake model for an isolated horizontal‐axis wind turbine

AbstractAn anisotropic double Gaussian (DG) model for analytical wake modeling to predict the streamwise wake velocity behind an isolated non‐yawed horizontal‐axis wind turbine is proposed. The proposed model is based upon the conservation of mass and momentum inside a streamtube control volume. The wake growth rate parameters to distinguish the wake expansion rate between lateral and vertical directions were tuned based on numerical and measurement data of utility‐scale turbines. It was found that the proposed model can give feasible predictions within the full‐wake region under different inflow conditions. In addition, the other analytical models based on top‐hat shape and single Gaussian approaches were evaluated for comparison. The root‐mean‐square error statistical analysis was used to evaluate the performance of each examined model under different flow conditions. In general, the proposed model outperformed the other examined models in all wake region categories, particularly within the near‐wake region and the onset of the far‐wake region, which are beyond the scope of the conventional approach for analytical wake modeling. This advantage gives the potential for the proposed model to provide a better prediction for the wake flow estimation within tightly packed wind farms.

Numerical Investigations of Wake Expansion in the Offshore Wind Farm Using a Large Eddy Simulation

Due to abundant wind resources and land saving, offshore wind farms have been vigorously developed worldwide. The wake of wind turbines is an important topic of offshore wind farms, in which the wake expansion is a key issue for the wake model and the layout optimization of a wind farm. The large eddy simulation (LES) is utilized to investigate various offshore wind farms under different operating conditions. The numerical results indicate that it is more accurate to calculate the wake growth rate using the streamwise turbulence intensity or the total turbulence intensity in the environment. By fitting the results of the LES, two formulae are proposed to calculate the wake growth rate of the upstream wind turbine. The wake expansion of the downstream wind turbine is analyzed, and the method of calculating the wake growth rate is introduced. The simulation indicates that the wake expansion of the further downstream wind turbines is significantly reduced. The smaller lateral distance of wind turbines in the offshore wind farm has the less wake expansion of the wind turbines. The wake expansion under different inflow wind speeds is also analyzed, while the wake expansion of wind turbines under more complex conditions needs to be further studied.

Wake behind a discontinuous cylinder: unveiling the role of the large scales in wake growth and entrainment

The turbulent flow in the wake of a discontinuous cylinder (DC) was investigated. The DC geometry consisted of cylinder segments $5D$ long (with $D$ being the diameter of the cylinder) separated by gaps of width $2.5D$ . Particle image velocimetry and hot-wire anemometry were used to analyse the flow at two Reynolds numbers, $Re = 4000$ and $10\,000$ , for $x/D \le 180$ . Large eddy simulations for both the DC and the infinite continuous cylinder (CC) wakes were also carried out at $Re = 10\,000$ . The DC configuration was devised to trigger the shedding of horseshoe vortices (HSV) in the very-near-wake region with the intent of illustrating the role that these three-dimensional HSVs, previously identified in the far-wake region of CC, play in the entrainment process in turbulent wakes. The DC geometry produced HSVs by the interaction between the high momentum flow through the gaps and the main spanwise vortex shed behind each cylinder segment, while in the CC wake they evolve from near-wake instabilities straddled with hairpin vortices that detach spanwise vorticity from the shed Kármán vortices. The DC wake was found to grow and spread in the transverse direction with a much faster rate than for the CC wake, up until approximately $x/D \approx 50$ . Prior to this location, the enhanced growth rate caused by the shear-aligned HSV led to a wake width of approximately 3 times that of the CC wake, with a maximum mean velocity deficit that was approximately half.

Wind turbine wakes on escarpments: A wind-tunnel study

In this study, the wake behind a wind turbine located on an escarpment is investigated using particle-image velocimetry in a wind tunnel. Five different escarpment models are used, which vary in the windward side shape from forward facing steps (FFS) with different curvatures at the leading-edge to sinusoidal ramp shapes with varying slopes. The difference in the base flow (flow without the turbine) resulting from the change in the geometry of the escarpment leads to significant differences in the average and dynamic characteristics of the turbine wake. The relatively high level of turbulence intensity in the base flow induced by the FFS escarpments leads to a faster wake recovery accompanied by higher turbulence kinetic energy, compared with the ramp-shaped ones. The self-similar behavior of the velocity deficit profiles in the far wake is confirmed for all the cases; unlike turbine wakes over flat terrain, the wake growth rate is found to be larger in the vertical direction than in the lateral direction. Meandering of the wake is observed to be higher on the FFS escarpment with an upward wake trajectory, compared to the ramp-shaped one. Finally, an analytical model is assessed to predict the wake velocity deficit of the turbine.

Off- and on-surface studies on flow development from various vortex generators configurations at Mach 2.0

An experimental investigation was conducted to study off- and on-surface flow developments behind various mechanical vortex generators configurations at Mach 2.0. The control configurations used in this study include rectangular vane, ramp vane, delta-ramp, and split delta-ramp. The primary objective of this study was to understand the effectiveness of control in terms of adding fullness to the boundary layer, wake liftoff, and spanwise uniformity when placed in an array. Pitot rake surveys were carried out both in spanwise and three streamwise locations, namely, x/δ = 5, 10, and 15. The velocity profile is found to be much fuller for rectangular vane relative to other control configurations. The iso-velocity contours captured the wake growth and vortex liftoff features for all the control configurations. The surface oil visualization shows the vortex trail for the rectangular vane to be the widest and for delta-ramp to be the least. The Pressure Sensitive Paint tests show surface flow features similar to that from oil flow visualization results for all control configurations. The quantitative data from these tests further helped to understand the flow development features in detail.

Spatial wake transition past a thin pitching plate.

The spatial transition of the wake behind a thin pitching plate in the thrust regime is studied. The drag-to-thrust transition is seen to occur at a threshold pitching frequency which becomes smaller for higher pitching angle and aspect ratio. The reverse von Kármán wake shows deflected asymmetric vortex pairing in two dimensions, while a bifurcated wake with a swirling ring is the signature in three dimensions, both resulting in nearly the same scaling for the power coefficient. The wake transition in the thrust regime occurs through three spatial regions comprising the reverse von Kármán vortex street, transitional zone, and twin jet region. Near the trailing edge, reverse von Kármán shedding is marked by linear decay of the spanwise wake width and growth of secondary instability. A large volume of fluid resulting from inward horizontal acceleration renders a weak form drag in the subsequent transition zone which is followed by vertical bifurcation into twin jet formation in the far wake. The spanwise pressure gradient is seen to guide the wake compression, with a streamwise adverse pressure gradient aiding it in the near wake.

Modelling Yawed Wind Turbine Wakes: Extension of a Gaussian-Based Wake Model

Yaw-based wake steering control is a potential way to improve wind plant overall performance. For its engineering application, it is crucial to accurately predict the turbine wakes under various yawed conditions within a short time. In this work, a two-dimensional analytical model is proposed for far wake modeling under yawed conditions by taking the self-similarity assumption for the streamwise velocity deficit and skewness angle at hub height. The proposed model can be applied to predict the wake center trajectory, streamwise velocity, and transverse velocity in the far-wake region downstream of a yawed turbine. For validation purposes, predictions by the newly proposed model are compared to wind tunnel measurements and large-eddy simulation data. The results show that the proposed model has significantly high accuracy and outperforms other common wake models. More importantly, the equations of the new proposed model are simple, the wake growth rate is the only parameter to be specified, which makes the model easy to be used in practice.

Self-similar decay of the drag wake of a dimpled sphere

Recent experimental results from the drag wake of a dimpled sphere show that the observed wake growth and decay are inconsistent with a widely accepted, 100-year-old scaling law for these quantities. While previous experiments have found a similar discrepancy just behind the wake source, this work shows that the new law holds over a full decade in scaling of distance. The theory behind the existing wake scaling law is revisited, and a faulty assumption which may account for the discrepancy is identified.

Anisotropic RANS Turbulence Modeling for Wakes in an Active Ocean Environment

The problem of simulating wakes in a stratified oceanic environment with active background turbulence is considered. Anisotropic RANS turbulence models are tested against laboratory and eddy-resolving models of the problem. An important aspect of our work is to acknowledge that the environment is not quiescent; therefore, additional sources are included in the models to provide a non-zero background turbulence. The RANS models are found to reproduce some key features from the eddy-resolving and laboratory descriptions of the problem. Tests using the freestream sources show the intuitive result that background turbulence causes more rapid wake growth and decay.

Impact of Tip-Vortex Modeling Uncertainty on Helicopter Rotor Blade–Vortex Interaction Noise Prediction

Free-wake models are routinely used in aeroacoustic analysis of helicopter rotors; however, their semiempiricism is accompanied with uncertainty related to the modeling of physical wake parameters. In some cases, analysts have to resort to empirical adaption of these parameters based on previous experimental evidence. This paper investigates the impact of inherent uncertainty in wake aerodynamic modeling on the robustness of helicopter rotor aeroacoustic analysis. A free-wake aeroelastic rotor model is employed to predict high-resolution unsteady airloads, including blade–vortex interactions. A rotor aeroacoustics model, based on integral solutions of the Ffowcs Williams–Hawkings equation, is utilized to calculate aerodynamic noise in the time domain. The individual analytical models are incorporated into an uncertainty analysis numerical procedure, implemented through nonintrusive Polynomial Chaos expansion. The potential sources of uncertainty in wake tip-vortex core growth modeling are identified and their impact on noise predictions is systematically quantified. When experimental data to adjust the tip-vortex core model are not available the uncertainty in acoustic pressure and noise impact at observers dominated by blade–vortex interaction noise can reach up to 25% and 3.50 dB, respectively. A set of generalized uncertainty maps is derived, for use as modeling guidelines for aeroacoustic analysis in the absence of the robust evidence necessary for calibration of semiempirical vortex core models.

Multi-rotor Wind Farm Layout Optimization

Multi-rotor wind turbines have shown a faster wake recovery than equivalent single-rotor turbines. In this work the potential benefit of a wind farm with multi-rotor turbines is assessed through the optimization of the turbine positions using the CEGA wind farm optimization algorithm, for different power densities. The EPFL analytical wake model is used to compute the power output at each turbine. The wake growth rate in this model depends on the incoming turbulence intensity. However, added turbulence intensities caused by multi-rotors affecting downstream turbines in a wind farm have recently been shown to be different from those by single-rotors. Here, two simple expressions are derived, one for the added turbulence intensity behind a multi-rotor and another for its relationship with the wake growth rate in a downstream turbine. Results on fixed layouts show multi-rotor power output improvements between 6% (3D spacings) and 0.3% (10D spacings). This benefit is bigger under relatively low ambient turbulent levels. The optimization of a full-scale wind farm layout (Horns Rev, 80-turbines) using multi-rotors provides an advantage of 0.66% and 0.79% against the optimized and the baseline single-rotor layouts, respectively. Optimizations of power densities with average inter-turbine distances of 4D and 10D show 2.75% and 0.1% improvements, respectively.

A Calibration Procedure for an Analytical Wake Model Using Wind Farm Operational Data

Wind energy is one of the fastest growing renewable energy sources in the U.S. Wind turbine wakes change the flow field within wind farms and reduce power generation. Prior research has used experimental and computational methods to investigate and model wind farm wake effects. However, these methods are costly and time-consuming to use commercially. In contrast, a simple analytical approach can provide reasonably accurate estimates of wake effects on flow and power. To reducing errors in wake modeling, one must calibrate the model based on a specific wind farm setting. The purpose of this research is to develop a calibration procedure for wind farm wake modeling using a simple analytical approach and wind turbine operational data obtained from the Supervisory Control And Data Acquisition (SCADA) system. The proposed procedure uses a Gaussian-based analytical wake model and wake superposition model. The wake growth rate varies across the wind farm based on the local streamwise turbulence intensity. The wake model was calibrated by implementing the proposed procedure with turbine pairs within the wind farm. The performance of the model was validated at an onshore wind farm in Iowa, USA. The results were compared with the industry standard wind farm wake model and shown to result in an approximate 1% improvement in sitewide total power prediction. This new SCADA-based calibration procedure is useful for real-time wind farm operational optimization.