Wake Interaction Research Articles

Graph network heterogeneity predicts interplant wake losses

Wind plants generate large-scale wakes, which can affect the performance of neighboring installations. Such wakes are challenging to estimate due to the inherent complexity in modeling wake interactions between large quantities of turbines at various distances. Weighted directed graph networks can inform complex models by linking turbine pairs into chains of upstream and downstream neighbors for a given wind direction. A novel interpretation of the graph network adjacency matrix is proposed where each element of the matrix represents the cumulative impact of upstream turbines on an individual. In this study, wake losses were estimated with an engineering wake model across a range of inflow conditions for nine parametric variations of a system containing two neighboring wind plants. The parametric nature of the study isolates turbine spacing within the plant, separation distance between plants, and wind direction as the main drivers of wake losses. Spatial heterogeneity is computed from the weighted average adjacency matrix of each plant arrangement. The proposed method is orders of magnitude faster than wake modeling and does not require detailed turbine information or atmospheric conditions. The weighted average adjacency matrix provides insight on the spatial organization of wake losses at various scales. Plant heterogeneity is correlated with wake losses within and among plants. Framing wind plant wake interaction in terms of graph network spatial heterogeneity provides an efficient approach for predicting wake losses within and among neighboring wind plants with applications to other complex systems where wake interactions are key factor.

In situ airborne measurements of atmospheric parameters and airborne sea surface properties related to offshore wind parks in the German Bight during the project X-Wakes

Abstract. Between 14 March 2020 and 11 September 2021, meteorological measurement flights were conducted above the German Bight in the framework of the project X-Wakes. The scope of the measurements was to study the transition of the wind field and atmospheric stability from the coast to the sea, to study the interaction of wind park wakes, and to study the large-scale modification of the marine atmospheric boundary layer by the presence of wind parks. In total, 49 measurement flights were performed with the research aircraft Dornier 128 of the Technische Universität (TU) Braunschweig during different seasons and different stability conditions. Seven of the flights in the time period from 24 to 30 July 2021 were organised using a second research aircraft, the Cessna F406 of TU Braunschweig. The instrumentation of both aircraft consisted of a nose boom with sensors for measuring the wind vector, temperature and humidity and, additionally, a surface temperature sensor. The Dornier 128 was further equipped with a laser scanner for deriving sea state properties and two downward-looking cameras in the visible and infrared wavelength range. The Cessna F406 was additionally equipped with shortwave and longwave broadband radiation sensors for measuring upward and downward solar and terrestrial radiation. A detailed overview of the aircraft, sensors, data post-processing and flight patterns is provided here. Further, averaged profiles of atmospheric parameters illustrate the range of conditions. The potential use of the dataset has been already shown by the first few publications. The data of both aircraft are publicly available on the world data centre PANGAEA at https://doi.org/10.1594/PANGAEA.955382 (Rausch et al., 2023a).

Effects of Wake Separation on Aerodynamic Interference Between Rotors in Urban Low-Altitude UAV Formation Flight

In recent years, unmanned aerial vehicle (UAV) formation flight has become an effective strategy for urban air mobility (UAM). However, close rotor separation during formation flight leads to complex aerodynamic interference between rotors, significantly affecting UAV flight performance and operational safety. This study systematically examines the effects of axial and lateral rotor separation on the rotor’s thrust performance through wind tunnel experiments. The tests simulate horizontal, vertical, and hovering states by generating relative airflow in the wind tunnel, focusing primarily on the thrust coefficient changes of the bottom rotor at various separations. The results are compared with a single rotor operating under the same conditions without wake interference. Additionally, computational fluid dynamics (CFD) simulations using the Fluent software were conducted to investigate the effect of wake interactions by analyzing the velocity flow field between the two rotors in different separations. Both the experimental and simulation results demonstrate that rotor aerodynamic performance is notably influenced by wake interactions. Under hovering and vertical states, substantial aerodynamic interference occurs in the region directly beneath the top rotor, within 1D ≤ Z ≤ 3D. This interference gradually diminishes as the rotor separation increases. Additionally, the thrust coefficient of the bottom rotor decreases with increasing flight speed due to the wake, and at higher flight speeds, the wake tends to contract. When the lateral separation is X = 0D, the mid-sectional flow field of the two rotors exhibits symmetry; however, with lateral separation, the symmetry of the bottom rotor’s wake velocity field is disrupted. During the horizontal flight, the rotor wake tilts backward due to the relative airflow, and the extent of this influence is governed by both rotor rotational speed and flight velocity. Therefore, when UAVs operate in formation, it is crucial to account for these factors affecting aerodynamic performance, and rotor separation must be optimized to enhance flight safety and efficiency.

Revisiting a Drag Partition Model For Canopy-Like Roughness Elements

Turbulent flows over a large surface area (S) covered by n obstacles experience an overall drag due to the presence of the ground and the protruding obstacles into the flow. The drag partition between the roughness obstacles and the ground is analyzed using an analytical model proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992) and is hereafter referred to as R92. The R92 is based on the premise that the wake behind an isolated roughness element can be described by a shelter area A and a shelter volume V. The individual sizes of A and V without any interference from other obstacles can be determined from scaling analysis for the spread of wakes. To upscale from an individual roughness element to n/S elements where wakes may interact, R92 adopted a background stress re-normalizing instead of reducing A or V with each element addition. This work demonstrates that R92’s approach results in a linear background stress reduction in A and V only when the ratio of n/S is small, due to a low probability of wake interactions. This probabilistic nature suggests that up-scaling from individual to multiple roughness elements can be re-formulated using stochastic averaging methods proposed here. The two approaches are shown to recover R92 under plausible conditions. An alternative scaling for the shelter volume is also proposed here using thermodynamic arguments of work and dissipation though the final outcome remains similar to R92. Comparisons between R92 and available data spanning more than two decades after R92 on blocks and vegetation-like roughness elements confirm the practical utility of R92. The agreement between R92 and this updated databases of experiments and simulations confirm the potential use of R92 in large-scale models provided that the relevant parameters accommodate certain features of the roughness element type (cube versus vegetation-like) and, to a lesser extent, their configuration throughout S. Last, a comparison between R92 and models based on first-order closure principles with constant mixing length suggests that R92 can outperform such models when evaluated across a wide range of roughness densities.

Maximizing wind farm production through pitch control using graph neural networks and hybrid learning methods

AbstractThis article presents a novel methodology to maximize wind farm power generation by integrating graph neural networks (GNN), supervised learning, and reinforcement learning techniques. First, the article introduces a graph‐based representation of the wind farm, capturing wind turbines as vertices and the inter‐turbine wake interactions as edges. The construction of this graph representation integrates the Jensen wake model, which includes insights derived from prior knowledge of wind farm aerodynamics. Subsequently, a detailed description of the GNN model's architecture, incorporating a message passing mechanism, is outlined. This GNN model is trained initially with supervised learning using a dataset of optimal pitch angles generated from the analytical results derived from Jensen wake model. Moreover, to improve the GNN model's accuracy and adaptability, reinforcement learning techniques are employed. The GNN model interacts with a high‐fidelity wind farm simulation environment, receiving feedback in the form of rewards derived from the wind farm's actual power output. Through a policy gradient approach, the GNN parameters undergo iterative updates, enabling the model to learn and adapt to dynamic wind conditions and intricate turbine interactions. The effectiveness and advantages of the proposed methodology are demonstrated through comprehensive case studies across various wind farm layouts.

Canard-configured underwater gliders lift enhancement investigation

ABSTRACT To enhance the lift performance of underwater gliders, this study investigates the application of the canard configuration. Initial experiments conducted in the towing tank confirm the feasibility of the canard configuration in enhancing lift on underwater gliders. Numerical simulations were conducted to determine the effects of canard shape and position on lift. The findings show that the canard vortex induces beneficial upwash, enhancing lift by facilitating flow separation and expanding the negative pressure region on the wing. Specifically, smaller canard sweep angles result in stronger canard vortices, increasing the impact of canards on the wings. A 45° canard sweep angle optimizes both lift and stability for underwater gliders. Positioning canards above and away from wings minimize adverse wake interactions with wing vortices, enhancing glider performance. Compared with the canard-off underwater glider, the lift-to-drag ratio of the canard-on underwater glider was improved by a maximum of 9.8%.

Data-driven multi-objective optimization of aerodynamics and aeroacoustics in dual Savonius wind turbines using large eddy simulation and machine learning

Savonius rotor is a popular form of vertical-axis wind turbine (VAWT) for small-scale and urban applications because of its straightforward design and self-starting ability. Dual VAWTs present challenges in terms of wake interactions and noise, particularly in urban areas. Optimizing these parameters is essential for future wind energy adoption. This research is the first to analyze how the interaction of wakes from adjacent rotors, combined with a deflector, affects both the aerodynamic performance and noise levels of dual Savonius rotors. Large Eddy Simulation is applied, as it effectively captures detailed turbulent wind flows and their interactions with wind turbines. A multi-objective optimization method combining Machine Learning and Computational Fluid Dynamics (CFD) is developed to optimize rotors for maximum power efficiency and minimum noise, considering their wake interactions with a unique deflector system. First, the influence of geometric parameters on aerodynamics and aeroacoustics characteristics of rotors is analyzed, and the database is generated using Design of Experiment approach. Next, the CFD model is replaced by Artificial Neural Network (ANN) model established for predicting rotor performances. A Multi-Objective Genetic Algorithm method is used to optimize aerodynamics and aeroacoustics characteristics of rotors. Finally, optimal design parameters are identified from the Pareto front using the technique for order of preference by similarity to ideal solution decision-making method. The ANN model demonstrated high accuracy with an RANN2 of 0.995 and 0.971 for the average power coefficient (CP) and overall sound pressure level (OSPL) predictions, respectively. Multi-objective optimization revealed the best configuration of the deflector with bleed jets, improving the average CP up to 57.5% and reducing OSPL to an almost 5.2% compared to the dual rotor case at TSR = 0.8.

Quasi-steady aerodynamic theory under-predicts glide performance in flying snakes.

Flying snakes (genus Chrysopelea) glide without the use of wings. Instead, they splay their ribs and undulate through the air. A snake's ability to glide depends on how well its morphing wing-body produces lift and drag forces. However, previous kinematics experiments under-resolved the body, making it impossible to estimate the aerodynamic load on the animal or to quantify the different wing configurations throughout the glide. Here, we present new kinematic analyses of a previous glide experiment, and use the results to test a theoretical model of flying snake aerodynamics using previously measured lift and drag coefficients to estimate the aerodynamic forces. This analysis is enabled by new measurements of the center of mass motion based on experimental data. We found that quasi-steady aerodynamic theory under-predicts lift by 35% and over-predicts drag by 40%. We also quantified the relative spacing of the body as the snake translates through the air. In steep glides, the body is generally not positioned to experience tandem effects from wake interaction during the glide. These results suggest that unsteady 3D effects, with appreciable force enhancement, are important for snake flight. Future work can use the kinematics data presented herein to form test conditions for physical modeling, as well as computational studies to understand unsteady fluid dynamics effects on snake flight.

Effect of yaw on wake and load characteristics of two tandem offshore wind turbines under neutral atmospheric boundary layer conditions

In this work, we numerically investigated the effects of yaw angle on the wake and power characteristics of two National Renewable Energy Laboratory (NREL) 5 MW wind turbines based on actuator line method (ALM) and large eddy simulation (LES) under a neutral atmospheric boundary layer (ABL) with specified offshore surface roughness. The turbines are placed in tandem, with a spacing of seven rotor diameters, and the yaw angles range from 0° to 30°. The results indicate that under coordinated yaw conditions, the wakes of the two turbines significantly shift with increasing yaw angles, encroaching on the trailing edge of the turbines. The expansion of the wakes also gradually weakens, leading to a reduction in width. The superposition of the wake generated by the downstream turbine diminishes, leading to both turbines exhibiting approximately comparable physical characteristics within their respective wakes. As the wake of the upstream turbine propagates downstream, a secondary low-speed region emerges between the primary low-speed zone of the wake of downstream turbine and the surrounding atmosphere. With the increase in yaw angle, this secondary low-speed region significantly enhances the rate of wake recovery while also inducing a more pronounced deflection of the wake, thereby demonstrating a stronger entrainment effect. Regarding load characteristics, the time history of power characteristics and the power spectral density (PSD) spectra indicate a good turbine response to the inflow. The power characteristics of the upstream turbine exhibit a scaling law is closely related to the yaw angle. The quantitative relationship is established between yaw angle and the power distribution of the turbines, alongside a proposed correlation between the yaw angle and the cos 2(γ) scaled power curve. The power of upstream turbine decreases and the power of downstream turbine gradually increases with the increase in yaw angle. It is further found that the downstream turbine demonstrates optimal performance at a yaw angle of 20°due to the influence of the yawed upstream turbine. These analyses provide insights into the characteristics of wind turbine arrays under yaw conditions from the perspective of unsteady wake features, interactions, and aerodynamic performance, which can aid in wind farm unit planning and control strategies.

Detachment of leading-edge vortex enhances wake capture force production

During stroke reversals, insect wings interact with their own wake flow from the preceding half-stroke, resulting in an unsteady aerodynamic mechanism known as ‘wing–wake interaction’ or ‘wake capture’. To better elucidate this mechanism, we numerically solved the incompressible Navier–Stokes equations at Reynolds numbers $10^2$ and $10^3$ . Simulations were conducted for wing planforms defined using the beta function distribution with varying aspect ratios ( $AR=2\unicode{x2013}6$ ) and radial centroid locations ( $\hat {r}_1=0.4\unicode{x2013}0.6$ ), whilst employing representative normal hovering kinematics. The wake development from the considered flapping wing planforms was investigated, and the wake capture contribution to aerodynamic force production was quantified by comparing the force generation between the fifth and first stroke cycles at multiple sections along the wingspan. Our results revealed that on the inboard wing region experiencing an attached leading-edge vortex (LEV) structure, wing–wake interaction is dominated by an unsteady downwash effect, resulting in a reduction in local force production. However, in regions closer to the wingtip experiencing detachment of the LEV, wing–wake interaction is dominated by an unsteady upwash effect, leading to an increase in local force production. Consequently, the global wake capture force production is controlled by the extent of LEV detachment, which primarily increases with the increase of wing aspect ratio. This suggests that for normal hovering flapping wings, the typical loss in translational force production due to wingtip stall is partially mitigated by wake capture effects.

Comparison of aerodynamic and aeroacoustic characteristics of fixed-pitch and variable-pitch rotors

This research conducts a comparative analysis of the aerodynamic and aeroacoustic characteristics of fixed-pitch and variable-pitch controlled multirotors [i.e., revolution per minute (RPM) and collective pitch control]. The study encompasses single-, twin-, and quad-rotor configurations under hovering flight conditions. The unsteady blade motion is modeled as a function of RPM and pitch, fluctuating with frequency and amplitude. To comprehensively account for wake interaction effects, a free-wake vortex lattice method combined with acoustic analogy is utilized. The findings reveal that unsteady blade motion and wake interaction effects cause fluctuations in thrust and tip vortex trajectory. The thrust and tip vortex behavior exhibited greater instability in response to RPM fluctuations than to pitch fluctuations. Consequently, the axial unsteady loading noise was more pronounced under RPM fluctuations compared to pitch fluctuations. In both twin- and quad-rotor configurations, the wake interaction significantly influenced the characteristics of thrust and tip vortex behavior. In addition, spectral analysis demonstrated that the frequencies of unsteady blade motion and wake interaction determine the frequencies of thrust and tip vortex fluctuations as well as unsteady loading noise.

Research on Aerodynamic Characteristics of Three Offshore Wind Turbines Based on Large Eddy Simulation and Actuator Line Model

Investigating the aerodynamic performance and wake characteristics of wind farms under different levels of wake effects is crucial for optimizing wind farm layouts and improving power generation efficiency. The Large Eddy Simulation (LES)–actuator line model (ALM) method is widely used to predict the power generation efficiency of wind farms composed of multiple turbines. This study employs the LES-ALM method to numerically investigate the aerodynamic performance and wake characteristics of a single NREL 5 MW horizontal-axis wind turbine and three such turbines under different wake interaction conditions. For the single turbine case, the results obtained using the LES-ALM method were compared with the existing literature, showing good agreement and confirming its reliability for single turbine scenarios. For the three-turbine wake field problem, considering the aerodynamic performance differences under three cases, the results indicate that spacing has a minor impact on the power coefficient and thrust coefficient of the middle turbine but a significant impact on the downstream turbine. For staggered three-turbine arrangements, unilateral turbulent inflow to the downstream turbine causes significant fluctuations in thrust and torque, while bilateral turbulent inflow leads to more stable thrust and torque. The presence of two upstream turbines causes an acceleration effect at the inflow region of the downstream single turbine, significantly increasing its power coefficient. The findings of this study can provide methodological references for reducing wake effects and optimizing the layout of wind farms.

On the unsteady aerodynamics of flapping wings under dynamic hovering kinematics

Hummingbirds and insects achieve outstanding flight performance by adapting their flapping motion to the flight requirements. Their wing kinematics can change from smooth flapping to highly dynamic waveforms, generating unsteady aerodynamic phenomena such as leading-edge vortices (LEV), rotational circulation, wing wake capture, and added mass. This article uncovers the interactions of these mechanisms in the case of a rigid semi-elliptical wing undergoing aggressive kinematics in the hovering regime at Re∼O(103). The flapping kinematics were parametrized using smoothed steps and triangular functions and the flow dynamics were simulated by combining the overset method with large eddy simulations. The analysis of the results identifies an initial acceleration phase and a cruising phase. During the former, the flow is mostly irrotational and governed by the added mass effect. The added mass was shown to be responsible for a lift first peak due to the strong flapping acceleration. The dynamic pitching and the wing wake interaction generate a second lift peak due to a downwash flow and a vortex system on the proximal and distal parts of the wing's pressure side. Conversely, aerodynamic forces in the cruising phase are mainly governed by the growth and the establishment of the LEV. Finally, the leading flow structures in each phase and their impact on the aerodynamic forces were isolated using the extended proper orthogonal decomposition.

Vortex-induced vibration of a rotating cylinder with dual splitter plates

To explore suppression method on vortex-induced vibrations (VIVs) response of the rotating cylinders, the VIVs of two-degree-of-freedom rotating cylinders with dual splitter plates at a Reynolds number of 200 and a mass ratio of 2.6 are investigated via numerical simulations. The numerical results show that splitter plates are more effective at suppressing VIV in the cylinders with low rotation rates, and the suppression effect decreases with increasing rotation rate. Three flow patterns are defined [overshoot, merge shedding, and individual shedding], and the distributions of the flow patterns and wake patterns under different rotation rates and gap distances are discussed. The vibration–fluid force–wake interaction is analyzed, and the variation of flow patterns is accompanied by the sudden increase in amplitude and fluid force. In addition, the directional sensitivity of the lift and drag is discussed, the lift is more sensitive to the rotation rate, and the drag is more sensitive to the gap distance.

Aerodynamic and acoustic investigations of rotor-rotor wake interaction

The paper presents part of the experimental activities carried out in the GARTEUR Action Group RC/AG-26 to study the acoustic and aerodynamic characteristics of small rotor configurations, including the influence of the rotor-rotor interactions. Two rotors, equipped with two-bladed propellers of a diameter of D=330.2 mm, were operated at two rotating speeds of 8025 RPM and 10120 RPM and arranged in different configurations. Isolated rotor and two different coaxial configurations in hover conditions were assessed. The aerodynamic loads and the rotor slipstream characterisation, in terms of flow field velocity, tip vortex characterization as well as acoustics emissions, were performed using a six-component load cell, Particle Image Velocimetry and microphone measurements. The isolated pusher rotor presented better aerodynamic performance with respect to the puller one. The coaxial configurations result in a loss of thrust and an increase in torque compared to the isolated rotors. The upper rotor is barely affected by the presence of the lower one, while the lower rotor experiences a thrust loss ranging from 17 to 19%. The configuration with the larger rotor distance experiences greater performance loss. The mean velocity fields of the isolated rotors are measured and compared with the coaxial configurations for assessing the roto-rotor interaction, the results support the aerodynamic behaviour. The isolated rotor slipstream characterisation was carried out by phase-locked measurements covering the full rotor azimuth angle range from 0° to 350° with an increment of 30°. Tip vortex paths are followed up to a vortex age of 3.5 rotor revolutions. The 3D reconstruction of the tip vortices is conducted to gain insight into the slipstream behaviour and enhance the occurring vortex roll-up during the second revolution. The tip vortex jitter is investigated and the anisotropic distribution is confirmed along the slipstream. Furthermore, the noise emission intensifies in magnitude for the coaxial configuration with increasing relative gap between the rotors. The turbulent kinetic energy and the meandering of the blade tip vortices support the findings of the acoustics results.

Wind farm structural response and wake dynamics for an evolving stable boundary layer: computational and experimental comparisons

Abstract. The wind turbine design process requires performing thousands of simulations for a wide range of inflow and control conditions, which necessitates computationally efficient yet time-accurate models, especially when considering wind farm settings. To this end, FAST.Farm is a dynamic-wake-meandering-based mid-fidelity engineering tool developed by the National Renewable Energy Laboratory targeted at accurately and efficiently predicting wind turbine power production and structural loading in wind farm settings, including wake interactions between turbines. This work is an extension of a study that addressed constructing a diurnal cycle evolution based on experimental data (Quon, 2024). Here, this inflow is used to validate the turbine structural and wake-meandering response between experimental data, FAST.Farm simulation results, and high-fidelity large-eddy simulation results from the coupled Simulator fOr Wind Farm Applications (SOWFA)–OpenFAST tool. The validation occurs within the nocturnal stable boundary layer when corresponding meteorological and turbine data are available. To this end, we compared the load results from FAST.Farm and SOWFA–OpenFAST to multi-turbine measurements from a subset of a full-scale wind farm. Computational predictions of blade-root and tower-base bending loads are compared to 10 min statistics of strain gauge measurements during 3.5 h of the evolving stable boundary layer, generally with good agreement. This time period coincided with an active wake-steering campaign of an upstream turbine, resulting in time-varying yaw positions of all turbines. Wake meandering was also compared between the computational solutions, generally with excellent agreement. Simulations were based on a high-fidelity precursor constructed from inflow measurements and using state-of-the-art mesoscale-to-microscale coupling.

Four-quadrant propeller hydrodynamic performance mapping for improving ship motion predictions

On the path toward fully autonomous sea vessels, forecasting a ship’s exact velocity and position during its route plays a crucial role in dynamic positioning, target tracking, and autopilot operations of the unmanned body navigating toward predetermined locations. This paper addresses the prediction of the operational performance of a free-running submarine advancing in a straight route (in surge motion). Along with the forward advancing vessel (straight-ahead motion) the study covers all possible scenarios of ship’s surge, including crash-ahead, crash-back, and astern motions. Conventional maneuvering models cannot handle motions other than forward advancement due to the absence of propeller data in all four quadrants of hydrodynamic performance map. This study proposes an approach for predicting submarine performance in all these surge conditions by utilizing four-quadrant propeller performance and resistance test data. We developed an in-house code, SMot4QP, to simulate ship speed and position in the time domain. We obtained satisfying results for the straight-ahead and crash-ahead motions, while the crash-back and astern maneuvers require further refinement due to propeller wake interaction with the hull. The proposed method is capable of predicting the motions of all types of vessels using the ship’s resistance and four-quadrant propeller test results. Thus, SMot4QP offers a fast and robust alternative to computationally expensive free-running self-propulsion simulations for operational performance prediction in broader naval applications.

Unsteady Surface Pressure Characterization on Launch Vehicle in Liftoff Configuration

Acquisition of unsteady pressure using remote scanners can provide practical advantages over making the same measurements directly using flush-mounted pressure transducers. However, pneumatic distortion of the signal is introduced by the tubing between the sensing module and surface port. This typically limits the usefulness of such measurements to averaged, steady data only, restricting the application of pressure scanners for unsteady pressure measurements in wind-tunnel and flight-testing applications. In this work, unsteady pressure on the surface of a 1.75%-scale model of the NASA Space Launch System Block 1B Cargo vehicle was remotely measured using an electronic scanning pressure module at the NASA Langley Research Center 14-by 22-Foot Subsonic Tunnel. Subsequent reconstruction using an empirically tuned, Wiener-filtered inverse transfer function produced excellent agreement compared to nearby surface-mounted transducers within a usable bandwidth of approximately 500 Hz. Interactions between the launch vehicle and the support tower produced strong oscillations that were absent in the vehicle-alone configuration, and it is likely that the wake interaction leads to a resonant flow response when the launch tower is immediately downstream of the vehicle.

It pays to follow the leader: Metabolic cost of flight is lower for trailing birds in small groups

Many bird species commonly aggregate in flocks for reasons ranging from predator defense to navigation. Available evidence suggests that certain types of flocks-the V and echelon formations of large birds-may provide a benefit that reduces the aerodynamic cost of flight, whereas cluster flocks typical of smaller birds may increase flight costs. However, metabolic flight costs have not been directly measured in any of these group flight contexts [Zhang and Lauder, J. Exp. Biol. 226, jeb245617 (2023)]. Here, we measured the energetic benefits of flight in small groups of two or three birds and the requirements for realizing those benefits, using metabolic energy expenditure and flight position measurements from European Starlings flying in a wind tunnel. The starlings continuously varied their relative position during flights but adopted a V formation motif on average, with a modal spanwise and streamwise spacing of [0.81, 0.91] wingspans. As measured via CO2 production, flight costs for follower birds were significantly reduced compared to their individual solo flight benchmarks. However, followers with more positional variability with respect to leaders did less well, even increasing their costs above solo flight. Thus, we directly demonstrate energetic costs and benefits for group flight followers in an experimental context amenable to further investigation of the underlying aerodynamics, wake interactions, and bird characteristics that produce these metabolic effects.

Optimal control of a wind farm in time-varying wind using deep reinforcement learning

A deep-reinforcement-learning (DRL) based control method to take the advantage of complex wake interactions in a wind farm is developed. Although the wind over a wind farm is changing, steady wind has been assumed in the most conventional methods for wind farm control. Under unsteady wind, the generated power of a wind farm becomes stochastic due to intermittent and fluctuating wind. To tackle the difficulty, a DRL-based method with which the pitch and yaw angles of wind turbines in a wind farm are strategically controlled is developed. Time-histories of the past wind and the predicted future wind are both utilized to identify the relation between the generated power and control. The present neural network is trained and validated using an experimental wind farm. A multi-fan wind tunnel is developed to generate unsteady wind for experiments with miniature wind farms, where the improvement in the generated power by the present DRL-based control method is demonstrated.