ABSTRACT Yaw engineering models are commonly used as add-ons to the industrial blade element momentum (BEM) framework to improve load and power predictions by accounting for the skewed wake effect. However, existing yaw engineering models show noticeable limitations in accurately predicting the induced velocity distribution across the blade span. In this study, we employ a genetic symbolic regression （SR） approach to develop a new set of yaw engineering models for both the normal and tangential induced velocities of a static yawed wind turbine. The model regression is performed using simulation data from Reynolds-averaged Navier–Stokes (RANS) simulations with an actuator line model (ALM) of the NREL 5-MW wind turbine, covering a range of yaw angles ( gamma ) and thrust coefficients ( CT ) over which the skewed wake effect is dominant. The regressed models are selected based on an optimal trade-off between accuracy and complexity, with complexity constrained to remain comparable with Branlard's yaw engineering model. The selected models are subsequently verified using three unseen cases that span different operating conditions and wind turbine models. Verification is performed through a series of evaluations, including generalization performance tests, implementation within the BEM framework to assess their aerodynamic performances, and quantitative errors and loading analyses. The results demonstrate that the proposed models improve both the amplitude accuracy and azimuthal phase of induced velocities compared with the existing models of Coleman and Branlard, enabling it to accurately capture the phase of the peak aerodynamic forces across each annulus and to predict the nonrestoring yaw moment occurring in the inboard region of the turbine, which other models fail to reproduce.

The present study extends the idea of the vertical-axis wind turbine (VAWT) “vortex generator mode” for wake recovery on a wind farm scale, working towards the concept of “regenerative wind farming”, where upstream turbines entrain vertical momentum for those downstream. An experimental wind tunnel demonstration of the regenerative wind farming concept for an array of nine H-type VAWTs arranged in a 3×3 grid layout is performed. Volumetric particle tracking velocimetry measures the wake within the simulated wind farm while using two vortex generator modes achieved through a fixed blade pitch. The results demonstrate the strong dependence of the wake topology of a VAWT on the streamwise vorticity system, which can be effectively modified by pitching the blades and subsequently changing the load distribution of the different quadrants of a VAWT. An increase in momentum entrainment in the wake is observed for both vortex generator modes of operation, highlighting the potential of achieving regenerative wind farming. The derived available power within the farm increases by factors of 6.4 and 2.1 for the pitch-in and pitch-out cases compared to the baseline case, respectively, considering potential rotors directly in line with those upwind.

Wake losses are a significant source of inefficiency in wind farm arrays, hindering the development of high-energy-density wind farms offshore. Studies have demonstrated the potential of vertical-axis wind turbines (VAWTs) to achieve high-energy-density configurations, due to their increased rate of wake recovery compared with their horizontal-axis counterparts. Recent works have demonstrated a wake control technique for VAWTs that utilizes blade pitch to accelerate the wake recovery, hereinafter referred to as the “vortex-generator” method. The present work is an experimental investigation of the wake topology using this control technique for the novel X-Rotor VAWT. The time-averaged wake topology of the X-Rotor has been measured by stereoscopic particle-image velocimetry at three fixed-pitch conditions of the top blades, namely pitch-in, pitch-out, and a baseline case with no pitch applied. The results demonstrate the wake recovery mechanism linked to the streamwise vorticity system of the rotor and the mechanisms that lead to a streamwise momentum recovery, where the pitched-in case injects high-momentum flow from above the rotor while ejecting the wake from the sides. In contrast, the pitched-out case operates in a mirrored fashion, with high-momentum flow injected into the wake from the sides while low-momentum flow is ejected out axially above the rotor. These modes of operation demonstrate a significant increase in the available power for hypothetical downstream turbines, reaching as high as a factor of 2.2 two rotor diameters downstream compared with the baseline case. The pitched-in case exhibits a higher rate of momentum recovery in the wake, compared with the pitch-out configuration.

The aerodynamics of the multi-rotor system with lifting-devices (MRSL), an innovative concept of wind energy harvesting machine, is preliminary investigated using Large Eddy Simulation (LES) with actuator techniques. In the current setup, turbulent inflow conditions are considered, but inflow wind shear is excluded. Consistent with previous studies, the results demonstrate faster wake recovery of the MRSL compared to its conventional counterpart, namely the wind turbine system without the lifting-devices. Additionally, a set of high-fidelity simulations further reveals that the enhanced wake recovery is robust under both laminar and turbulent inflow conditions, remaining largely unaffected by variations in the ambient turbulence level. The present work provides proof-of-concept evidence that the effectiveness of MRSLs is not significantly hindered by ambient turbulence, motivating future research to evaluate their performance within a realistic atmospheric boundary layer.

Wind turbine blades in standstill or parked conditions often experience large angles of attack (AoA), where vortex-induced vibrations (VIV) may occur that increase the risk of structural damage. To better understand the VIV of airfoils at high AoA from an aerodynamic perspective, we conducted experimental investigations into the vortex dynamics of a surging airfoil at a 90∘ incidence undergoing forced vibrations. Experiments were conducted at two reduced frequencies (k) to demonstrate the lock-in effect, where the vortex shedding frequency aligns with the motion frequency. Results indicate distinct vortex shedding behaviors: at higher k value of 0.38, downstream wake vortices form when the airfoil is moving upwind, while upstream vortices emerge during the downwind motion, interacting with the downstream vortices and leading to an outward flow. At lower k value of 0.19, the wake remains directed to the downwind side, regardless of the airfoil’s motion direction. Lock-in is evident in both cases, with one vortex pair shed per cycle at lower k and two pairs at higher k. Furthermore, the study examines the influence of vortex dynamics on unsteady aerodynamic loads. The results show that drag peaks when the airfoil moves upwind near the center position of its trajectory; at higher k, negative drag occurs as the airfoil moves downwind near the center, driven by the interactions among convection, turbulent momentum, pressure, and viscous forces. A reduced-order load estimation model for a flat plate is applied to the experimental data, showing good agreement during the upwind motion of the airfoil, which is the design condition for the original flat plate model. However, during the downwind motion, as the flow condition does not match the original flat plate design condition, the circulatory part of the model is modified to account for the presence of two pairs of vortices in the flow field, yielding improved agreement with the drag values determined from the measured flow field. The findings highlight distinct flow patterns and vortex interactions for the two motion cases, offering insights into their impact on aerodynamic loads.

Within the framework of the European Union Horizon 2020 project HOMER (Holistic Optical Metrology for Aero-Elastic Research), data assimilation (DA) algorithms for dense flow field reconstructions developed by different research teams, hereafter referred to as the participants, were comparatively assessed. The assessment is performed using a synthetic database that reproduces the turbulent flow in the wake of a cylinder in ground effect, placed at the distance of one diameter from a lower wall. Downstream of the cylinder, this wall continues either in the form of a flat steady wall, or of a flexible panel undergoing periodic oscillations; these two situations correspond to two different test cases, the latter being introduced to extend the evaluation to fluid–structure interaction problems. The input data for the data assimilation algorithms were datasets containing the particle locations and their trajectories identification numbers, at increasing tracer concentrations from 0.04 to 1.4 particles/mm³ (equivalent image density values between 0.005 and 0.16 particles per pixel, ppp). The outputs of the DA algorithms considered for the assessment were the three components of the velocity, the nine components of the velocity gradient tensor and the static pressure, defined in the flow field on a Cartesian grid, as well as the static pressure on the wall surface, and its position in the deformable wall case. The results were analysed in terms of errors of the output quantities with respect to the ground-truth values and their distributions. Additionally, the performances of the different DA algorithms were compared with that of a standard linear interpolation approach. The velocity errors were found in the range between 3 and 11% of the bulk velocity; furthermore, the use of the DA algorithms enabled an increase of the measurement spatial resolution by a factor between 3 and 4. The errors of the velocity gradients were of the order of 10–15% of the peak vorticity magnitude. Accurate pressure reconstruction was achieved in the flow field, whereas the evaluation of the surface pressure revealed more challenging. As expected, lower errors were obtained for increasing seeding concentration. The difference of accuracy among the results of the different data assimilation algorithms was noticeable especially for the pressure field and the compliance with governing equations of fluid motion, and in particular mass conservation. The analysis of the flexible panel test case showed that the panel position could be reconstructed with micrometric accuracy, rather independently of the data assimilation algorithm and the seeding concentration. The accurate evaluation of the static pressure field and of the surface pressure proved to be a challenge, with typical errors between 3 and 20% of the free-stream dynamic pressure.

Recording onto a single-frame multiple exposures of the tracer particles has the potential to simplify the hardware needed for 3D PTV measurements, especially when dealing with high-speed flows. The analysis of such recordings, however, is challenged by the unknown time tag of each particle exposure, alongside their unknown organization into physical trajectories (trajectory tag). Using a sequence of two or more illumination pulses with a constant time separation leads to the well-known directional ambiguity problem, whereby it is not possible to distinguish the direction of motion of the tracer particles. Instead, an irregular and asymmetric sequence of time separation for the illumination pulses allows recognizing the time tag of the unique sequence of positions in the image, composing the trace. A criterion is formulated here that recognizes unambiguously the trace pattern, based upon the principle of kinematic similarity. A combinatorial algorithm is proposed whereby a signal-to-noise ratio is introduced for every candidate trace. The approach is combined with an additional criterion that favors trace regularity (minimum velocity fluctuations). The algorithm is illustrated making use of particle motion examples. Furthermore, it is assessed using 3D experimental data produced with time-resolved analysis (single-frame, single-exposure) using the Shake-the-Box method. Traces with a three-pulse sequence yield a detection rate of 85%. The latter declines with the number of pulses. Conversely, the error rate rapidly vanishes with the samples number, which confirms the reliability of trace detection criterion when more pulses are comprised in the sequence.

The airfoil DU91-W2-150 was investigated in the Low Speed Low Turbulence Tunnel at the Delft University of Technology to study unsteady aerodynamics. This experimental study tested the airfoil under a wide range of angles of attack (AoA) from 0° to 310° at three Reynolds numbers ((Formula presented.)) from (Formula presented.) to (Formula presented.). Pressure on the airfoil surface was measured and particle image velocimetry (PIV) measurements were conducted to capture the flow field in the wake. By examining the force coefficient and comparing the wake contours, it shows that an upwind concave surface provides a higher load compared to a convex surface upwind case, highlighting the critical role of surface shape in aerodynamics. When comparing separation at specific locations along the chord for all three (Formula presented.) values, it is observed that as (Formula presented.) increases, separation tends to occur at lower AoA, both for positive stall and negative stall. The examination of the aerodynamic force variation indicates that, during reverse flow, fluctuations are more pronounced compared to forward flow. This is owing to separation occurring at the aerodynamic leading edge (geometric trailing edge) in reverse flow. In terms of vortex shedding frequency, the study found a nearly constant normalized Strouhal number ((Formula presented.)) of 0.16 across various (Formula presented.) and AoA values in fully separated regions, indicating a consistent pattern under these conditions. However, a slight increase in (Formula presented.), between 0.16 and 0.20, was observed for AoA values exceeding 180°, possibly due to the convex curvature of the airfoil in the upwind direction. In conclusion, this research not only corroborates previous findings for small AoA values but also adds new data on the aerodynamic behavior of the DU91-W2-150 airfoil under large AoA values, offering various perspectives on the effects of surface curvature, (Formula presented.), and flow conditions on key aerodynamic parameters.

Accurate modelling of wind turbine wakes is critical for optimizing wind farm performance, but the complexity of wake interactions poses significant challenges. This study presents a two-phase blind test campaign, part of the Horizon Europe TWEET-IE project, designed to benchmark numerical models and investigate wake control strategies using wind tunnel experiments. Conducted with tandem wind turbine models at the Technical University of Munich and the National Technical University of Athens, the tests include inflow, load, power, and wake velocity measurements under controlled conditions. Phase I serves as an open-data benchmarking exercise for a baseline scenario without wake control, while Phase II introduces active individual blade pitch control to the upstream turbine, challenging participants to simulate advanced wake dynamics. This paper reviews Phase I results and details the experimental framework for Phase II, providing a foundation for advancing wake modelling and control in wind energy research.

Numerical simulations of wind farms consisting of innovative wind energy harvesting systems are conducted. The novel wind harvesting system is designed to generate strong lift (vertical force) with lifting-devices. It is demonstrated that the tip-vortices generated by these lifting-devices can substantially enhance wake recovery rates by altering the vertical entrainment process. Specifically, the wake recovery of the novel systems is based on vertical advection processes instead of turbulent mixing. Additionally, the novel wind energy harvesting systems are hypothesized to be feasible without requiring significant technological advancements, as they could be implemented as Multi-Rotor Systems with Lifting-devices (MRSLs), where the lifting-devices consist of large airfoil structures. Wind farms with these novel wind harvesting systems, namely MRSLs, are termed regenerative wind farm, inspired by the concept that the upstream MRSLs actively entrain energy for the downstream ones. With the concept of regenerative wind farming, much higher wind farm capacity factors are anticipated. Specifically, the results indicate that the wind farm efficiencies can be nearly doubled by replacing traditional wind turbines with MRSLs under the tested conditions, and this disruptive advancement can potentially lead to a profound reduction in the cost of future renewable energy.

Measuring the velocity field around a complex object by volumetric PIV is hindered by shadow formation (illumination) as well as camera occlusion (imaging). These have been recently dealt with by multiplying illumination and imaging directions (redundancy) and by the integration of ray-tracing techniques to include the effect of visual blockage caused by the object (object-aware particle reconstruction, Wieneke & Rockstroh, 2024). The problem of light reflections blinding regions of the images has not been afforded yet. The latter pertains to interactions between illumination and imaging through the object surface and it poses additional challenges to ghost particle formation, particle detection and tracking in general. This study proposes a method to effectively detect such regions, and measures to modify the particle triangulation algorithm.
The viability of this novel reflection-aware Lagragian particle tracking (RA-LPT) approach is examined by application to two experiments of varying complexity. The first case is the flow around a stationary wall-mounted cube as imaged with a redundant number of cameras. The second experiment tackles an elite runner sprinting across the measurement region obtained with the Ring-of-Fire technique. A considerable reduction of ghost particles (false positives) is attained, while the formation of voids (false negatives) is also minimized. The overall result of the method maximizes the measurement region around and in proximity of the object of interest.

A method is proposed to obtain full-domain spatial modes based on proper orthogonal decomposition (POD) of particle image velocimetry (PIV) measurements taken at different (overlapping) spatial locations. This situation occurs when large domains are covered by multiple non-simultaneous measurements and yet the large-scale flow field organization is to be captured. The proposed methodology leverages the definition of POD spatial modes as eigenvectors of the spatial correlation matrix, where local measurements, even when not obtained simultaneously, provide each a portion of the latter, which is then analyzed to synthesize the full-domain spatial modes. The measurement domain coverage is found to require regions overlapping by 50–75% to yield a smooth distribution of the modes. The procedure identifies structures twice as large as each measurement patch. The technique, referred to as Patch POD, is applied to planar PIV data of a submerged jet flow where the effect of patching is simulated by splitting the original PIV data. Patch POD is then extended to 3D robotic measurement around a wall-mounted cube. The results show that the patching technique enables global modal analysis over a domain covered with a multitude of non-simultaneous measurements.

Particle-laden turbulent flows occur in various natural and industrial processes, highlighting the need for a comprehensive understanding of the interaction between the dispersed phase and the carrier flow. This study investigates the fluid dynamics of a simplified car side-view mirror model, experimentally analyzed using the particle tracking velocimetry technique in the laboratories of Delft University of Technology. Experimental measurements are used to validate a computational fluid dynamics model developed in the OpenFOAM environment. The overall objective of the research is to establish a benchmark for validating Eulerian–Lagrangian numerical models in terms of both flow dynamics and particle trajectories. In this study, the validation is limited to the Eulerian fields; validation of the discrete-phase modeling will be addressed in future work.

This study presents the experimental validation of regenerative wind farms (RGWFs), a novel wind farm concept designed to enhance overall wind farm performance. RGWFs employ multi-rotor systems with lifting devices (MRSLs), an innovative wind energy harvester engineered to stimulate strong vertical energy entrainment, thereby accelerating wake recovery. In the experiments, MRSLs are scaled for wind tunnel testing, with their rotors modeled using porous disks and their lifting devices represented by wings. The tested RGWFs comprise up to 3 × 3 MRSLs. Flow quantities within RGWFs and aerodynamic loads on MRSLs are measured using volumetric particle tracking velocimetry and strain gauges. Compared to conventional wind farms, flow analysis indicates that vertical energy entrainment is significantly enhanced in RGWFs, as evidenced by a more than 200 % increase in thrust on the second-row MRSLs and so on. These experimental results, which are in line with the previous numerical predictions, highlight the promising potential of RGWFs.

This study experimentally investigates the dynamic stall of a pitching NACA 643418 airfoil under reverse flow conditions, whereby the geometric trailing edge is located upstream of the geometric leading edge. The investigation focuses on the correlation between surface pressure, aerodynamic forces, and the evolution of the dynamic stall vortex (DSV) and the aerodynamic trailing edge vortex (TEV). A range of mean angles of attack from 5° to 25°, pitching amplitudes from 5° to 15°, and reduced frequencies between 0.05 and 0.21 were tested on an airfoil using a combination of particle image velocimetry (PIV) and surface pressure measurements. The results reveal a distinct dynamic stall mechanism in reverse flow conditions: multiple flow separations occur during both the upstroke and downstroke periods, yet the DSV maintains partial attachment. While the outer layer of the DSV sheds into the flow, its inner core remains anchored and is subsequently reinforced by shear layer feeding. This sustained vorticity injection leads to periodic DSV re-growth, which manifests in the force hysteresis loop as multiple distinct peak regions. In addition, it is also found that the largest difference between conventional and reverse flow dynamic stall lies in the initial stage of the DSV development. For reverse flow dynamic stall cases, the initial flow separation near the leading edge causes a gradual decrease in the pressure coefficient. However, for conventional dynamic stall cases, the laminar separation bubbles that occur before the DSV cause the maximum suction on the airfoil surface. Furthermore, by comparing the dominant modes from Proper Orthogonal Decomposition (POD) analysis, it is found that the type of flow regime depends mainly on the mean angle of attack within the tested range of pitching amplitudes and frequencies. In particular, the dominant vortex determines the flow dynamics. At low mean angles of 5° and 10°, the most energetic flow features are associated with DSV dynamics. At a mean angle of 15°, both DSV and TEV dynamics contribute. At higher mean angles of 20° and 25°, the flow is dominated more by TEV dynamics. Despite these mean-angle-dependent variations in modal dominance, all dominant POD modes share a consistent physical interpretation where they capture the growth or decay of DSV and TEV structures.

Abstract: This paper presents the first full-scale particle image velocimetry (PIV) measurements to analyze the flow field of a car under real driving conditions. The Ring of Fire (RoF) measurement concept, introduced by Terra et al. (Exp Fluids 58:83, 2017. https://doi.org/10.1007/s00348-017-2331-0), is adapted to automotive demands to validate CFD simulations for further improvements of vehicle aerodynamics. The experiment consists of a tunnel setup, where neutrally buoyant helium-filled soap bubbles are used as flow tracers and are illuminated by two high-speed lasers. Four high-speed cameras captured the particles motion in two separate Stereo-PIV configurations with fields of view of 1.3 × 0.6 m² and 2.8 × 2.2 m². Data for a Volkswagen up!, while driving on a test track at a constant speed of 33.33 m/s, was acquired for the wake and the side mirror region and processed with standard multi-pass PIV algorithms, in order to quantify the flow field and estimate limits of the described measurement principle for on-road car aerodynamics. The resulting ensemble averaged velocity fields are compared with CFD simulations, showing agreement for the here considered cases within 7.0–9.7%, based on the root-mean-square error between the experimental and the numerical results. Furthermore, drag calculation from the obtained velocity fields based on moment conservation is performed and the percent difference to wind tunnel measurements reaches values below 3.0%.

Image based three-dimensional (3D) particle tracking is currently the most widely used technique for volumetric velocity measurements. Inspecting the flow-field around an object is however, hampered by the latter, obstructing the view across it. In this study, the problem of measurement limitations due to the above is addressed. The present work builds upon the recent proposal from Wieneke and Rockstroh (2024 Meas. Sci. Technol. 35 055303), whereby the information of the occluded lines of sight can be incorporated into the particle tracking algorithm. The approach, however, necessitates methods that accurately evaluate the shape and position of the object within the measurement domain. Methods of object marking and the following 3D registration of a digital object model (CAD) are discussed. For the latter, the iterative closest point registration algorithm is adopted. The accuracy of object registration is evaluated by means of experiments, where marking approaches that include physical and optically projected markers are discussed and compared. Three objects with growing level of geometrical complexity are considered: a cube, a truncated wing and a scaled model of a sport cyclist. The registered CAD representations of the physical objects are included in aerodynamic experiments, and the flow field is measured by means of large-scale particle tracking using helium filled soap bubbles. Results indicate that object registration enables a correct reconstruction of flow tracers within regions otherwise affected by domain clipping as a consequence of obstructed camera lines-of-sight. Finally, the combined visualization of the object and the surrounding flow pattern offers means of insightful data inspection and interpretation, along with posing a basis for particle image velocimetry data assimilation at the fluid-solid interface.

Unsteady inlet flow distortion can influence the stability and performance of any propulsion system, in particular for more novel, short and slim intakes of future aero-engine configurations. As such, the requirement for measurement methods able to provide high spatial resolution data is important to aid the understanding of these flow fields. This work presents flow field characterisations at a crossflow plane within a short aeroengine intake using stereoscopic particle image velocimetry (SPIV). A series of tests were conducted across a range of crosswind and high angle of attack conditions for a representative short and slim aspirated intake configuration at two operating points in terms of mass flow rate. The velocity maps were measured at a crossflow plane within the intake at an axial position L/D = 0.058 from where a fan is expected to be installed. The diameter of the measurement plane was 250 mm, and the final spatial resolution of the velocity fields had a vector pitch of 1.5 mm which is at least two orders of magnitude richer than conventional pressure-based distortion measurements. The work demonstrates the ability to perform robust non-intrusive flow measurements within modern intake systems in an industrial wind tunnel environment across a wide range of operating conditions; hence, it is suggested that SPIV can potentially become part of standard industrial testing. The results provide rich datasets that can notably improve our understanding of unsteady distortions and influence the design of novel, closely coupled engine-intake systems.

Recording multiple exposures of the tracer particles onto a single digital image has the potential to simplify the hardware needed for 3D PTV measurements. A sequence with equal time intervals leads to the well-known directional ambiguity problem. Instead, a sequence with irregular time-intervals (two or more) allows resolving the ambiguity. Two fundamental criteria are introduced that determine whether a set of particle samples corresponds to a physical trace for a given neighborhood: the kinematic similarity criterion imposes similarity (i.e. proportionality) between the length travelled by the particle and time elapsed. Additionally, the trace regularity criterion favors sets with minimum fluctuations of the velocity vector. A numerical algorithm, based on combinatorial analysis is presented, whereby all possible sets are scrutinized and the set of particles yielding the minimum disparity from the above criteria corresponds to the physical trace. The algorithm is demonstrated using 3D experimental data and results are benchmarked against the state-of-the-art time-resolved analysis Shakethe-Box (single-frame, single-exposure).