Wake Dynamics Research Articles

Impact of rotational direction on wake replenishment mechanisms of counter-rotating paired vertical-axis wind turbines

Recent studies have shown that the placement of paired vertical-axis wind turbines (VAWTs) in close proximity is a promising approach to design efficient VAWT farm layouts, mainly due to the increased power output. This study aims to experimentally investigate the impact of the rotational direction of paired counter-rotating VAWTs on their wake characteristics and replenishment mechanisms through a quantitative analysis using the momentum balance equation. The results of this study enhance our understanding of the effect of rotational direction on wake dynamics of counter-rotating paired VAWTs and offer valuable insights for optimising the design of VAWT farm configurations.

Multi-fidelity actuator-line modelling of FOWT wakes

Large Eddy Simulations (LES) are considered the proper tool for predicting the physics of a wind turbine wake, thereby establishing a solid foundation for investigating the interaction among floating turbines within wind farms. In this work the Actuator Line Model, implemented in the OpenFoam environment, is combined with both U-RANS and LES simulations to underline the differences in accuracy when reproducing the near and far wake of a single turbine. Both a fixed-bottom and a surge motion case are tested to highlight the wake phenomena strictly generated by the platform motion. The use of LES simulation becomes fundamental by virtue of its ability to accurately simulate turbulence and mixing with free-stream flow, hence, this research aims at advancing the knowledge of wake dynamics from multiple perspectives while ensuring reliability thanks to the use of the experimental wake data from the UNAFLOW test campaign on the scaled laboratory model of the DTU 10 MW. In the near wake, limited flow unsteadiness and similar mean velocity are predicted by the two models. In the far wake, instead, the LES approach estimates a strong rise of flow unsteadiness which, in case of surge motion, affects the mean velocity value making evident the difference between LES and RANS estimation.

On the transitional wake past a streamwise rotating prolate spheroid

Direct numerical simulations are performed to study the behavior of the wake behind a 5:2 streamwise rotating prolate spheroid. The Reynolds number Re = 1000 under different rotational speeds over a large range of 0≤Ω≤3 is considered, where Ω is the non-dimensional rotational speed based on the freestream velocity and the volume-equivalent diameter of the prolate spheroid. By successively increasing the rotational speed, seven distinct flow regimes were identified and explored: steady state, low-speed steady rotation state, axisymmetric state, high-speed steady rotation state, twofold rotational symmetrical state (TFRS), quasi-periodic vortex shedding state (QVS), and weakly chaotic state. Among these wake regimes, the TFRS regime is reported for the first time, and it can be interpreted as an outcome of the stabilizing influence of the spheroid's rotation acting to restore the wake structure to an axisymmetric state. It is found that the rotation of the prolate spheroid has a stabilizing effect under low rotational speeds. Furthermore, the coupling mechanism between the rotational double helical structure and vortex shedding in the QVS regime has been revealed. The results of this study contribute to closing the knowledge gap regarding the wake dynamics of a streamwise rotating prolate spheroid.

Lift-Induced Wake Re-Energization for a VAWT-Based Multi-Rotor System

This study explores the performance and near-wake dynamics of a VAWT-based Multi-Rotor System in both its original configuration and in the presence of external lift-generating devices, specifically employed for wake control operations. The wake of a scaled VAWT-based MRS was measured in a wind tunnel using Particle Tracking Velocimetry. Lift-generating devices, including a 3-element cascading wing on top and a single-element wing in the middle of the MRS, were used to enhance wake control and deflection. Measurements in the near-wake revealed notable differences between configurations with and without these devices. Without them, the wake remained concentrated in the actuator surface’s projected downstream area, with minimal crossflow diffusion. Conversely, the configuration with lift-generating devices exhibited significant wake deformation, including axial expansion and lateral contraction, promoting streamwise momentum recovery. As a result, increased power recovery was found downstream of such a system compared to the clean MRS. These findings underscore the potential of such systems, particularly when equipped with lift-generating devices, to manipulate wake dynamics and enhance wind farm efficiency, thereby advancing innovative wind energy solutions.

Towards an automated framework for Aero-Servo-Elastic Large Eddy Simulation of wind turbine wakes

During the last two decades, wind turbine wakes have been extensively studied in academia by implementing the Actuator Line method in numerous Large Eddy Simulation solvers tailored for atmospheric flows. However, and while being computationally affordable for ad hoc deep investigations, this approach remains barely used in industry. One of the leading causes is the complexity of the simulation process, which still involves several aspects to be carefully looked at to get valuable results in output. This paper aims to present a workflow that merges and automates the different steps required to conduct aero-servo-elastic Large Eddy Simulations of wind turbines. In particular, a strategy based on an Accurate Conservative Level Set function is used to flag the regions where wakes propagate. This allows to automatically derive refinement zones that cover the wakes at all times. This generic procedure can be seamlessly applied to various farm layouts and inflow conditions. To display the capabilities of the workflow, it is applied to several configurations, including one to seven wind turbines for different inflow conditions. It is observed that lower wind speeds require larger mesh to capture the wake dynamics adequately. Overall, the workflow offers the added advantage of significantly reducing the required human effort while standardizing the process. This is important from an industrial perspective, wherein parametric studies are usually carried out as part of the design process.

An improved statistical wake meandering model

A new statistical wake meandering (SWM) model is proposed that improves on existing models in the literature. Compared to the existing SWM models, the proposed model has a closed description that does not require simulations to create look-up tables while maintaining applicability to a wide range of flow conditions. The proposed SWM model is compared to the predictions of the Dynamic Wake Meandering (DWM) model and to wind speed measurements from a scanning Doppler lidar mounted on the nacelle of a utility-scale wind turbine for validation. The results show that the proposed model has a similar performance as the DWM model for the effect of wake meandering on the mean velocity deficit and the turbulence intensity, while being significantly faster to compute.

Closed-loop coupling of a dynamic wake model with a wind inflow estimator

The estimation of turbine flow evolution provided by low-fidelity dynamic wake models, such as FLORIDyn, can be improved by the introduction of a Kalman filter based on power production measurements. However, it is not possible to infer any information about which side of an impinged rotor is affected by the wake only by the observed power, being itself a single scalar quantity. In this paper, a new closed-loop formulation of the FLORIDyn model is investigated: wind speed estimates, given by a blade load-based wind observer, are implemented into a Kalman Filter, providing information about the position of the wake over the rotor plane. The FLORIDyn model augmented with the wind flow estimator is tested in a layout of two aligned turbines and compared to a corresponding CFD simulation. The results of the proposed approach show an improved ability to predict wind flow quantities and the wake centerline position compared to the open-loop version of the model.

Wake Modelling Based on the Stokes Stream Function and the Toroidal-Poloidal Decomposition

The Stokes stream function and its generalisation, the Toroidal-Poloidal decomposition, are well-suited for the derivation of axisymmetric engineering wake models, as they are solenoidal and fulfil conservation of mass of an incompressible fluid by construction. The presented model consists of a time-independent contribution based on Laguerre basis functions with a simple parametrisation that is well-suited for the diffusion-dominated far wake. A time-dependent part can be added based on a poloidal component that can model either helical or toroidal vortex structures, and its parametrisation can be closed towards the total thrust force on the rotor. Despite requiring an external solver, the presented model shows potential as a drop-in replacement for the Ainslie wake model that is widely used in the Wind Energy industry as part of the Dynamic Wake Meandering model.

Fluid-structure interaction simulation of dynamic response and wake of floating offshore wind turbine considering tower shadow effect

Fluid-structure interaction simulation of dynamic response and wake of floating offshore wind turbine considering tower shadow effect

Local and regional interactions between tidal stream turbines and coastal environment

An extended three-dimensional unstructured ocean model for simulating impacts of tidal stream turbines on tidal current, turbulence and surface waves has been applied to study the interactions between a tidal turbine farm and its surrounding environment. The present study aims to reveal three-dimensional local and regional changes due to the operation of a proposed turbine farm in natural coastal environment. Fine mesh size is assigned at the turbine farm location to capture the details of local wake dynamics, hydrodynamics and suspended sediment transport. Large geographic coverage of the model provides details of changes in regional features. Results showed that the proposed turbine farm comprised of 18 turbines (15–20 m in diameter) with approximately 20% power extraction from the average available power (averaged over five and half tidal cycles) led to local variation of surface elevation within the range of −10 to 3 mm, flow acceleration on both sides of the turbine farm, flow acceleration of ∼ 0.4 m/s near the bed in the vicinity of the turbine farm which caused bed shear stress to rise up to 2.5 N/m2 (corresponding to the critical stress of a range of fine gravel and finer sediment particles), locally increased TKE of 0.09 m2/s2, reduced wave height of 0.01–0.05 m, and upward sediment transport in the water column. On a regional scale, most of the changes on amplitude and phase of M2 constituent were observed within 10 km (∼ 15 times the array width) from the centre of the turbine farm, and the wake in terms of 95% flow rate recovery was found to be 9 km long (∼ 14 times the array width). Noticeable changes were also found in surface waves, bed shear stress and suspended sediment transport on regional scale as result of moderation in tidal and flow dynamics, although much less prominent than the local effects. It is recommended that consideration during the Environmental Impact Assessment stage of tidal stream energy projects should be given to an area that extends beyond the immediate vicinity of the planned turbine farm.

Experimental investigation of rear flexible flaps interacting with the wake dynamics behind a squareback Ahmed body

We have conducted an experimental study on the use of rear flexible vertical flaps as adaptive solutions to reduce the drag of a squareback Ahmed body, and on the fluid–structure interaction mechanisms at the turbulent wake. To that aim, wind tunnel experiments were conducted to compare the performance of various configurations including the baseline body, the body with rigid flaps and with flexible flaps. These configurations were tested under different aligned and cross-flow conditions. The results reveal that the flexible adaptive devices effectively reduce the drag within for low values of the dimensionless stiffness quantified through the Cauchy number, Ca. Thus, the two-dimensional deformation of the flexible flaps, which undergo progressive inwards reconfiguration (with an averaged tip deflection angle of Θ≃4°), reduces the bluffness of the flow separation at the body base, thus shrinking the recirculation region. This reconfiguration leads to increased base pressure, resulting into a 8.3% decrease in the global drag, CD, under aligned conditions. Similar drag reductions are observed under yawed conditions.Two regimes are identified in terms of the coupled fluid–structure dynamics. For low Ca, the passive reconfiguration of the flaps include small amplitude, periodic oscillations corresponding to the first free deformation mode of a cantilevered beam. Alongside these weak oscillations, the flaps are deformed guided by the changes in the value of the horizontal base pressure gradient, depicting bi-stable behavior which is caused by the synchronization between the Reflectional Symmetry Breaking (RSB) mode, typically present in the wake of three-dimensional bluff bodies, and the flaps deformation. For higher values of Ca, the flexible flaps deflect inwardly by about Θ≃20° on average, but exhibit vigorous oscillations combining the first and second free deformation modes of a cantilevered beam. These large amplitude oscillations excite the flow separation at the model’s trailing edges, leading to significant fluctuations in the separated shear layers and a consequent 31% increase in the global drag. Under yawed conditions, the flaps responses for large values of Ca are different due to the asymmetry of the corresponding recirculation region.

Influence of the tip speed ratio on the wake dynamics and recovery of axial-flow turbines

Detached eddy simulation is employed to investigate the wake development downstream of the rotor of an axial-flow turbine and its dependence on the tip speed ratio. In this study, we found that the trend of the momentum deficit as a function of the rotational speed shows opposite directions in the near wake and further downstream. While the momentum deficit in the near wake increases with the rotational speed, it decreases further downstream. For instance, we found that at six diameters downstream of the rotor the streamwise velocity in its wake recovered to about 30% of its free-stream value at the lowest simulated tip speed ratio of 4, while its recovery was equal to about 65% at the largest tip speed ratio of 10. This is due to the earlier breakdown of the tip vortices. The results of the computations demonstrate indeed that mutual inductance phenomena between tip vortices, promoting pairing events and the eventual instability of the helical structures, occur at shorter downstream distances for higher values of tip speed ratio. Wake instability enhances the process of wake recovery, especially due to radial advection. Therefore, higher rotational speeds do not promote wake recovery through more intense tip vortices, but through their greater instability. Implications are important, affecting the optimal distance between rows of axial-flow turbines in array configurations: the operation at higher rotational speeds allows for smaller distances between turbines, decreasing the cost and environmental impact of farms consisting of several devices.

Unsteady cylinder wakes from arbitrary bodies with differentiable physics-assisted neural network.

This work describes a hybrid predictive framework configured as a coarse-grained surrogate for reconstructing unsteady fluid flows around multiple cylinders of diverse configurations. The presence of cylinders of arbitrary nature causes abrupt changes in the local flow profile while globally exhibiting a wide spectrum of dynamical wakes fluctuating in either a periodic or chaotic manner. Consequently, the focal point of the present study is to establish predictive frameworks that accurately reconstruct the overall fluid velocity flowfield such that the local boundary layer profile, as well as the wake dynamics, are both preserved for long time horizons. The hybrid framework is realized using a base differentiable flow solver combined with a neural network, yielding a differentiable physics-assisted neural network (DPNN). The framework is trained using bodies with arbitrary shapes, and then it is tested and further assessed on out-of-distribution samples. Our results indicate that the neural network acts as a forcing function to correct the local boundary layer profile while also remarkably improving the dissipative nature of the flowfields. It is found that the DPNN framework clearly outperforms the supervised learning approach while respecting the reduced feature space dynamics. The model predictions for arbitrary bodies indicate that the Strouhal number distribution with respect to spacing ratio exhibits similar patterns with existing literature. In addition, our model predictions also enable us to discover similar wake categories for flow past arbitrary bodies. For the chaotic wakes, the present approach predicts the chaotic switch in gap flows up to the mid-time range.

Quantifying wake dynamics subjected to stream vegetation patch elongation: The influence of patch-edge vortices

Vortices are generated across a wide range of scales due to the interaction between in-stream vegetation and surrounding flows, significantly influencing hydro-geomorphodynamics in earth surface water systems. Recent advance in vegetation patch hydrodynamics has revealed that the elongation of the middle channel patch can generate complex wake flow patterns by adjusting the bleed flow from the patch and triggering the patch-edge Kelvin–Helmholtz (KH) vortices. With a broader range of experimental configurations, this study reveals how the patch wake mixing is apparently strengthened by the presence of KH vortices, indicated by a larger steady wake velocity, a shorter steady wake length, and a damped energy of wake von Karman vortex. Furthermore, we quantify these characteristic metrics of patch wake behavior with and without the influence of KH vortices. Our findings provide insights into the role of vegetation-induced vortex interactions in regulating mixing processes, thereby promoting informed practices in environmental flows.

Enhanced recovery caused by nonlinear dynamics in the wake of a floating offshore wind turbine

An experimental study in a wind tunnel is presented to explore the wake of a floating wind turbine subjected to harmonic side-to-side and fore–aft motions under laminar inflow conditions. The wake recovery is analysed as a function of the frequency of motion $f_p$ , expressed by the rotor-based Strouhal number, $St = f_p D / U_{\infty }$ ( $D$ is the rotor diameter, $U_{\infty }$ the inflow wind speed). Our findings indicate that both directions of motion accelerate the transition to the far-wake compared with the fixed turbine. The experimental outcomes confirm the computational fluid dynamics results of Li et al. (J. Fluid Mech., vol. 934, 2022, p. A29) showing that sideways motions lead to faster wake recovery, especially for $St \in [0.2, 0.6]$ . Additionally, we find that fore–aft motions also lead to better recovery for $St \in [0.3, 0.9]$ . The recovery is closely linked to nonlinear spatiotemporal dynamics found in the shear layer region of the wake. For both directions of motion and $St \in [0.2, 0.55]$ , the noisy wake dynamics lock in to the frequency of the motion. In this synchronised-like state, sideways motions result in large coherent structures of meandering, and fore–aft movements induce coherent pulsing of the wake. For fore–aft motion and $St \in [0.55, 0.9]$ , the wake shows a more complex quasiperiodic dynamic, namely, a self-generated meandering mode emerges, which interacts nonlinearly with the excitation frequency $St$ , as evidenced by the occurrence of mixing components. The coherent structures grow nonlinearly, enhance wake mixing and accelerate the transition to the far-wake, which, once reached, exhibits universal behaviour.

Development of a floating Vertical Axis Wind Turbine for the Mediterranean Sea

Differently from Horizontal Axis Wind Turbines (HAWTs), which are the reference technologies in the wind market for their reliability and maturity, Vertical Axis Wind Turbine (VAWT) applications are related to small-scale contexts, such as providing electricity in isolated areas or urban settings. Consequently, the capacity of VAWTs results significantly lower than the order of megawatts and does not exceed a few tens of kilowatts. A promising field of application for VAWTs is the floating offshore: among the main advantages there are an increased static stability, by placing the rotor-nacelle assembly (RNA) at the base of the VAWT and reduced operational and maintenance (O&M) costs. Moreover, the different wake dynamics allows to reduce the aerodynamic losses, allowing closer turbine installations. However, to be competitive with floating HAWTs, it is necessary to have numerical models for the analysis and simulation of multi-megawatt VAWTs. This paper aims to introduce a time domain model of a floating vertical axis wind turbine, developed within the Matlab-Simscape environment. The model comprises an aerodynamics module, based on Double Multiple Stream Tube theory while hydrodynamics is modelled using WEC-Sim. A case study, involving a Darrieus H-rotor VAWT tested in the Mediterranean Sea and supported by a semi-sub foundation, the OC4-DeepCwind, is introduced. The results obtained are compared with those from QBlade, an software developed by TU Berlin, demonstrating a good agreement between the two codes.

Coherence analysis of geophysical wakes in flow past a three-dimensional hill

Wakes generated by topographies are ubiquitous in nature. The formation and evolution mechanism of wake-generated eddies is essential to understanding the effect of topography on oceanic bottom flow. In this study, we analyze the temporally resolved numerical database [1] of stratified wakes past an isolated three-dimensional hill, via proper orthogonal decomposition (POD) of the vertical vorticity field. We study the dynamics of the near wake (x/D < 3) and the far wake (x/D ≥ 3) separately, where x is the downstream distance from the center of the hill. The aim is to understand how rotation influences the change of coherence from the near to the far wake and also the coherence across heights.

Numerical investigation of the cavitation effects on the wake dynamics behind a blunt trailing edge hydrofoil

The influence of cavitation on the wake behind a NACA 0009 hydrofoil with a truncated trailing edge has been numerically investigated using a homogeneous mixture model coupled with a controlled decay SST γ-Reθt turbulence model. Using optimal definitions of the inlet turbulent intensity and the empirical condensation and vaporization coefficients of the cavitation model, simulated results have shown a good agreement with experimental data. Notably, the numerical results exhibit negligible deviations of less than 0.7% in vortex shedding frequencies for different cavitation levels. If the size of the vortex cavitation grows, a substantial increase in both lift and drag coefficients on the hydrofoil is observed. Furthermore, the influence of cavitation on the trajectories of vortex centers and the morphology of the primary shedding vortices has been revealed using a vortex identification method. The findings highlight that the cavitation development enhances the advected velocity of the shedding vortices while decreasing the streamwise inter-vortex spacing. Consequently, both factors are found to contribute to the increase of the vortex-shedding frequency behind the NACA 0009 hydrofoil with the truncated trailing edge when cavitation appears and develops.

Numerical analysis of aero-hydrodynamic wake flows of a floating offshore wind turbine subjected to atmospheric turbulence inflows

The influence of atmospheric turbulence inflow on coupled dynamic behaviors and wakes of floating offshore wind turbine (FOWT) is pronounced, especially as blade size increases. In this study, we explore the effects of atmospheric inflow on aero-hydrodynamics and wake characteristics of a spar-type FOWT. A well-validated in-house computational fluid dynamic (CFD) solver, FOWT-UALM-SJTU, is utilized to conduct the numerical simulations. To generate the realistic atmospheric inflow condition, the large eddy simulation (LES) with long-duration is employed. Two other cases involving uniform inflow and shear inflow are conducted to provide some comparable results. Compared to uniform inflow and shear inflow, the power and thrust of FOWT under atmospheric inflow display greater instability, with their power spectrums exhibiting higher intensity in high frequency region. The variation of yaw moment in atmospheric scenario is significantly drastic, leading to a remarkable response in platform yaw motion. Notably, the dominant frequency in this scenario is the blade passage frequency, as opposed to the incident wave frequency observed in the uniform and shear scenarios. The atmospheric inflow promotes the manifestation of wake breakdown and wake meandering, resulting in the faster wake recovery of FOWT. Besides, the meandering in the far wake is more significant compared to uniform and shear scenarios. The absence of vortex rings in atmospheric scenario is observed, along with the presence of more complex and smaller vortices in far wake. Our findings highlight the remarkable impacts of atmospheric inflow on dynamic responses and wake evolution of FOWT, and it is recommended that the atmospheric inflow be taken into account when assessing wake interactions between multiple FOWTs.

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.