Vortex Street Research Articles

Tuning the Actuator Line Method to Properly Modelling Tip Effects in Finite-Length Blades

The Actuator Line Method (ALM) is gaining popularity in wind turbine simulations, as it can better handle some of the challenging operating conditions experienced by modern machines, such as highly turbulent inflows, severe aero-elastic forcing, and complex rotor-to-rotor interactions. However, it still falls behind other medium-fidelity methods such as the Lifting Line Free Vortex Wake (LLFVW) when it comes to resolving tip vortices and their effect on the blade spanwise load profile. The reason for such behavior is still unclear. A recent study suggested that this issue can be solved by reducing the scale of the angle of attack (α) sampling and force insertion towards the tip, without the need of additional corrections. This study builds on these findings to further investigate how the ALM base formulation - in terms of α sampling and force insertion - can be tuned to properly describe tip effects. An in-house ALM tool was employed to simulate a finite, constant-chord, NACA0018 wing, for which high-fidelity blade-resolved CFD (BR-CFD) data are available as benchmark. In the first part of the work, different strategies are outlined, including a novel approach for the de-coupling of the angle of attack sampling step from the force projection one, here called DE-coupled LineAverage (DELA). Their accuracy and sensitivity to ALM numerical settings are assessed at a fixed wing pitch angle of 6°. The analysis is then extended to a wider range of blade pitch angles, benchmarking the new ALM formulation against BR-CFD, ALM with the Dağ and Sørensen correction, and LLFVW in terms of blade loads, tip vortex structure, and computational effort.

On the aeroacoustic simulation and far-field noise modeling of a cylinder turbulent wake at the Reynolds number of 3900

The turbulent wake flows of circular cylinders have been under extensive study due to their strong fluctuating forces and noise levels, yet the relationship between them has rarely been examined. In this study, a high-fidelity numerical simulation is performed for a cylinder wake flow at the Reynolds number of 3900, aimed at far-field noise modeling based on the investigation of noise source characteristics. Despite irregular multi-scale turbulent wake eddies, the primary vortex shedding that resembles the Karman vortex shedding is observed, and the modes extracted by the dynamic mode decomposition technique at the primary shedding frequency and its higher harmonics appear as nearly two-dimensional spanwise structures. A non-permeable Ffowcs Williams and Hawkings (FW-H) approach is used to formulate the far-field noise spectra as the surface integral of unsteady flow samples on the cylinder surface and the volume integral of unsteady stress in the turbulent wake. The former can be modeled as the dipole sound of unsteady lift and drag, and the latter can be modeled as the tonal noise of discrete two-dimensional (i.e., spanwise-averaged) vortex modes. The results show that the vortex sound is extremely weak. Thus, the far-field noise can be modeled almost entirely by the aerodynamic forces, and the quantitative relationship between them is established by the convective FW-H solutions.

Numerical Study on the Hysteresis Effect of Volute Pump with Stay Vanes Based on Vortex Dynamics

Abstract The hysteresis effect of volute pump with stay vanes in the hump zone can aggravate the vibration and jumping of the units, which seriously threatens the unit’s safety and stable operation. The formation mechanism of the hysteresis effect in hump zone is analyzed by carrying out unsteady numerical simulation of the volute pump with stay vanes at medium-low specific speed based on vortex dynamics theory. The results show that hysteresis effect occurs in volute pump, the fluid inertia force in FID is smaller than that in FDD, and the fluid viscous force in FID is larger than that in FDD. The hysteresis effect is not only related to the Karman vortex generated by the flow separation of vane and guide vane, but also closely related to the stall vortex generated in the volute. This work may provide a guide way for the optimal design and stable operation of the volute pump with stay vanes.

Numerical study of particle dispersion in the wake of a static and rotating cylinder at Re = 140 000

In this study, the particle-laden flow in the wake of a static and a rotating cylinder at Reynolds number of 140 000 was investigated using the Reynolds Averaged Navier–Stokes numerical approach. Three turbulence models such as k–ω shear stress transport, Reynolds stress model, and local-correlation transition model (LCTM) were selected to predict the flow topology. Lagrangian approach with one-way coupling was used to track solid spherical particles of different sizes (0.01, 0.1, 2.5, 10, and 50 μm). The study reveals that LCTM is the most accurate to predict the flow topology in both cases. Cylinder's rotation generates different effects on flow structure. It breaks the wake's symmetry and reduces its width, and increases the frequency of vortex shedding and the size of the recirculation zone. Particle transport analysis has revealed that particles' response to the flow depends on their Stokes number and wake flow topology. Particles of 0.01, 0.1, and 2.5 μm distribute in and around vortex cores, while particles of 10 and 50 μm do not penetrate vortex cores. Instead, 10 μm particles accumulate mainly around the periphery of vortices, while 50 μm particles skip the vortex street to the thin shear flow region between vortices to be transported by the mainstream flow. Finally, cylinder rotation reduces the particle spread in the vertical direction and shifts all particle distributions in the cylinder's rotation direction. Analysis of particle dispersion functions showed that cylinder's rotation reduces differences in dispersion extent depending on particle size.

Validation of a BEM correction model for swept blades using experimental data

This study validates a correction model, which extends standard blade element momentum theory to swept blades and, by doing so, enhances wind turbine simulation predictability for these advanced geometries. This correction model addresses limitations in BEM algorithms, accommodating the complexities of swept blades by considering the sweep-induced tip vortex displacement and curved bound vortex self-induction. The validation is based on previously published results from wind tunnel experiments on a horizontal axis wind turbine with straight and swept blades, providing blade-level aerodynamic data for comprehensive numerical comparisons. In both blade configurations (straight and swept), good agreement is found between experimental and numerical results, validating the numerical approach. For the swept blade case, an additional comparison to a BEM algorithm assuming a straight blade and to one accounting for crossflow is drawn, underscoring the former’s inadequacy for swept blades. Comparably minor differences between the fully-corrected and only crossflow-corrected algorithms render the assessment of the proposed BEM correction model’s added benefit uncertain. Using the validated BEM algorithm, the experimental results are corrected for twist deformations of individual blades, enabling a direct comparison of the campaigns with straight and swept blades. Results align with expectations, indicating sweep-induced reductions in axial induction and blade loads in the swept blade section.

On One Tip Vortex Core Circulation Distribution Model in the Near-Field Region of a Wing

On One Tip Vortex Core Circulation Distribution Model in the Near-Field Region of a Wing

Wind tunnel inflow data assimilation in an LES digital twin for improving validation against an experimental wind turbine wake

Wind energy is playing an essential role in the energy transition towards a carbon-neutral system, for which wind turbine wakes are one of the most important aspects. By extracting energy from the flow, the turbine generates power but also decreases the production and increases the loading of downstream wind turbines; and potentially affects nearby structures.To better understand the physical phenomenon, Large Eddy Simulation (LES) offers scale-resolving capabilities and a physical insight into complex turbulence flows. The state of the art in terms of high-fidelity wake simulations consists in combining LES with an Actuator Line Model in order to capture the tip vortices and detailed wake dynamics.This paper focuses on the comparison between such simulation, with experiments in the controlled environment of a wind tunnel, in order to assess the performance and limitations of the model. A large part is dedicated to reproducing a developing flow, with a controlled level of turbulence. The Recycle and Rescale Method is used to provide the mean inflow profile, while a novel approach using controlled volume forces allows to improve the turbulence level of the flow. With the proposed methodology, the mean profile is properly imposed, while the associated turbulence characteristics is improved by roughly 50 %.

Assessing the effect of turbine size on the coherent structures in the wake using DMD

The aim of this study is to evaluate and quantify the effect of the incoming flow on the coherent structures characterizing the wake of two NREL reference wind turbines with different dimensions: the NREL 5-MW and the NREL 15-MW. The Dynamic Mode Decomposition (DMD) approach has been used to detect dynamically-relevant flow structures. We employ the Sparsity-Promoting version of the DMD (SPDMD) algorithm for ranking the most relevant modes, in order to extract a limited subset of relevant flow features that optimally approximate the original data sequence. The dataset on which the SPDMD is based consists of ordered snapshots obtained by Large Eddy Simulations (LES), where the Actuator Line Method (ALM) simulates the rotor and the Immersed Boundary Method (IBM) models the tower and nacelle. To ensure a realistic comparison, the two turbines are subjected to two turbulent inflows with the same mean Atmospheric Boundary Layer (ABL) obtained through a precursor simulation. The results reveal significant differences in the dependence of the absolute value of the DMD amplitudes on the angular frequency for the two turbines. However, the coherent structures appear to have the same shape for the main modes, although the tip vortex structures have a higher dynamic relevance for the NREL 15-MW turbine. This is due to the larger length scales imposed by the rotor and the lower turbulence intensity at the taller rotor height.

Enhancing Wind Farm Efficiency Through Active Control of the Atmospheric Boundary Layer’s Vertical Entrainment of Momentum

In contemporary wind farm design, the primary focus has traditionally been on reducing wake interference to optimize energy capture from horizontal wind flows. However, with the scaling up of wind farms, their interaction with the Atmospheric Boundary Layer (ABL) evolves, making vertical entrainment the main mechanism for the exchange of momentum and energy. This study introduces a methodical approach to augment the efficiency of large-scale offshore wind farms by actively controlling this vertical entrainment of momentum within the ABL. The strategy involves the precise engineering of advection fluxes to alter wind flow dynamics, utilizing turbines as effective vortex generators, toward a process of ”regenerative wind farming.” This setup aims to create a vorticity and vertical flux system akin to those observed in highly unstable ABLs. Expanding upon previous studies that focused on single Vertical Axis Wind Turbines (VAWTs), our research explores the implementation of multi-rotor systems equipped with lift-generating wings. These systems are designed to exert forces perpendicular to the prevailing wind direction, thus creating trailing vortices and directing the flow orthogonally for improved vertical advection. This research is part of a comprehensive investigative framework that combines experiments and multifidelity simulations. The current study extends those findings to wind farm simulations, aiming to assess the impact of ABL control on a full wind farm scale. The first part of the work validates an established analytical wind farm performance model against real wind farm data for thirty-one wind farms in the North Sea and Baltic Sea. The results confirm the predicted trend of decreased performance with increased wind farm size and density. The model is used to calculate the performance of a wind farm for varying regimes of vertical entrainment due to the creation of large-scale circulatory systems. The results are compared against 3D vortex simulations of the full wind farm in ”regenerative wind farming” mode. Our results demonstrate a notable improvement in wind speeds at the turbine hub height and the potential to double the feasible density of wind farms without compromising efficiency compared to traditional setups. These findings suggest a promising pathway towards a more sustainable and profitable future in wind energy, achieved through the strategic manipulation of ABL momentum, regenerating the energy in the wind farm.

Wind tunnel investigations of an individual pitch control strategy for wind farm power optimization

Abstract. This article presents the results of an experimental wind tunnel study which investigates a new control strategy named Helix. The Helix control employs individual pitch control for sinusoidally varying yaw and tilt moments to induce an additional rotational component in the wake, aiming to enhance wake mixing. The experiments are conducted in a closed-loop wind tunnel under low-turbulence conditions to emphasize wake effects. Highly sensorized model wind turbines with control capabilities similar to full-scale machines are employed in a two-turbine setup to assess wake recovery potential and explore loads on both upstream and downstream turbines. In a single-turbine study, detailed wake measurements are carried out using a fast-response five-hole pressure probe. The results demonstrate a significant improvement in energy content within the wake, with distinct peaks for clockwise and counterclockwise movements at Strouhal numbers of approximately 0.47. Both upstream and downstream turbine dynamic equivalent loads increase when applying the Helix control. The time-averaged wake flow streamwise velocity and rms value reveal a faster wake recovery for actuated cases in comparison to the baseline. Phase-locked results with azimuthal position display a leapfrogging behavior in the baseline case in contrast to the actuated cases, where distorted shedding structures in the longitudinal direction are observed due to a changed thrust coefficient and an accompanying lateral vortex shedding location. Additionally, phase-locked results with the additional frequency reveal a tip vortex meandering, which enhances faster wake recovery. Comparing the Helix cases with clockwise and counterclockwise rotations, the latter exhibits slightly higher gains and faster wake recovery. This difference is attributed to Helix' additional rotational component acting in either the same or the opposite direction as the wake rotation. Overall, both Helix cases exhibit significantly faster wake recovery compared to the baseline, indicating the potential of this technique for improved wind farm control.

Trailing vortex at drifting ship hull: a numerical study on wandering and turbulence

ABSTRACT Trailing vortices are commonly associated with so-called contrails in the sky. These show instability phenomena which manifest in transverse motions and sudden thickness changes. Aircraft aerodynamics considers this so-called far field whereas for naval hydrodynamics the near-field is of dominating interest. For the latter, vortices are intensively investigated at the propeller, but they emerge also at manoeuvring ship hulls or blunt stern shapes. And this is studied within the current paper: the major trailing vortex next to the KVLCC2 hull at large drift incidence. Numerical simulations with the SST-based IDDES model are conducted with OpenFOAM. The target is to reveal details of the vortex centre flow like the evolution of turbulence and the characteristics and consequences of vortex wandering. The results reveal a low-frequency broadband wandering motion next to a broad turbulent inertial subrange and that about two thirds of resolved TKE can be attributed to wandering.

Studies on the Evolution of Fatigue Strength of Aluminium Wires for Overhead Line Conductors.

Traditional ACSR overhead wires, which consist of a high-strength steel core and several layers of aluminium wires, are currently the most popular overhead line conductor (OHL) design globally. Operating conditions, particularly operating under varying stresses from Karman vortices, lead to the fatigue cracking of wires of the outer layer, followed by wires of the inner layers. Karman vortices are formed by the detachment of a laminar wind stream flowing around the conductor, which causes vibrations in the conductor called wind or aeolian oscillations. Aluminium wires are manufactured using standard batch material drawing technology. Although the fatigue strength of such wires is not standardised, there are various criteria for evaluating this characteristic, as well as established limits on the number of cycles needed to break the first wires of the outer layer. Fatigue strength also strongly depends on the geometric structure of the wire and its operating conditions. The article analyses the influence of the mechanical condition of aluminium wires used in ACSR cables on their fatigue strength. We then present results from aluminium wire fatigue tests conducted on a specially constructed test rig. In addition, fatigue cracks were interpreted using scanning microscopy.

Effect of pressure pores size on hydrodynamic and hydroacoustic marine propeller performances under cavitating case

The numerical work presented in the paper investigates the effect of pressure pores on hydrodynamic and hydroacoustic performances. This research aims to reduce cavitation area and underwater noise by mitigating the tip vortex cavitation. Compared to the few studies devoted to the pressure pores technique, several configurations based on the E779A marine propeller have been tested by considering different azimuthal and radial step values, a wider pore region concentrated at the top of the blade, and several pore diameter values. In addition, a numerical simulation was started to verify the effectiveness of the theoretical models in detecting the effect of pressure pores on the acoustic propagation generated by the propellers tested. The numerical approaches combining cavitating flow and noise propagation are performed using a hybrid method, which solves the Ffowcs Williams-Hawkings (FW–H) equation. A validation of the numerical simulation is carried out for cavitating and non-cavitating cases. Open water performances, cavitation area, sound pressure levels, and thrust distributions are analysed for two cavitation numbers. σ= 1,763 and σ= 1,029. The obtained results reveal that the cavitation area decreases as the pressure pore radius increases, but a slight reduction in propulsive efficiency accompanies this. Particularly for the pores radius of 0,00264D, propeller efficiency loss doesn't exceed 2,6 % and 4,05 % for the two cavitation numbers investigated. Nevertheless, this configuration showed better acoustic performances with a diminution of 10 dB in overall sound pressure level compared to the propeller without pressure pores.

Detached eddy simulation of hydrokinetic turbine wake in shallow water depths

Detached eddy simulations (DES) have been performed for flow over a solitary hydrokinetic turbine for two different tip-speed ratios λ = 3.64 and 6.15 and three different tip-clearances (δ = 0.1D, 0.2D, and 0.35D) to elucidate the effect of air-water interface on the turbine performance and wake recovery in shallow water conditions. The power predictions show good agreement with experimental data for λ = 3.64, but a large 12% error for λ = 6.15. The interface introduced unsteadiness in the power predictions, which increased with λ. The interface did not affect the mean power predictions for lower λ significantly, but reduced power for higher λ. The two-phase simulations for λ = 6.15 showed significant improvement in wake deficit and near-wake TKE prediction compared to the single-phase simulations. The improved predictions were identified because the interface causes early tip vortex entanglement and TKE burst. The DES predictions also show turbulence anisotropy maps consistent with the experimental data. Analysis reveals that turbulence is one-dimensional, dominated by streamwise fluctuations behind the blade tip region; two-dimensional, dominated by transverse and spanwise fluctuations in the TKE burst region; and approaches three-dimensional isotropy in the fully developed wake region. Detailed analysis of the vortical structures and wake characteristics reveals that the interface significantly affects the vortex advection, breakdown, and wake evolution. In particular, they enhance the wake deficit, which slows down the advection of the tip vortex filaments, causing an early vortex entanglement. The tip vortices show interaction with vortices generated underneath the interface, but these interactions seem localized. The tip vortex breakdown was identified due to instabilities generated during vortex entanglement and interaction with interface vortices for λ = 6.15 case, and because of tip and root vortex interaction for λ = 3.64. Although the two-phase simulations are encouraging compared to the single-phase case, TKE is still underpredicted in the near-wake region, possibly because of turbulence or rotating interface modeling issues. Two-phase simulations also predict significantly higher swirl, which needs further investigation.

Flow Structure Control Using Plasma Actuators

In the last few years, achieving precise control over flow structures has become increasingly crucial in aeronautics, space engineering, and wind turbine optimization. This study simulated the effects of dielectric barrier discharge on undisturbed air for flow structure control by means of plasma actuators. The analysis involved examining the flowfield, potential distribution, charge density, and components of the velocity vector within the computational domain based on numerical simulation results. The investigation revealed that the maximum flow velocity, accelerated by the plasma actuator, reached 4.5 m/s with a corresponding flow opening angle of 11.3°. The study also explored the impact of dielectric barrier discharge on the flow around a cylinder with a plasma actuator in on/off states. The physical characteristics of the flow around a circular cylinder were identified for both switched-off and switched-on plasma actuators. Notably, the study demonstrated the efficacy of reducing the cylinder’s drag factor by suppressing the Karman vortex street through the operation of four plasma actuators based on dielectric barrier discharge. The obtained results exhibited good agreement with experimental data. The developed approach demonstrated high computational efficiency. Activation of the plasma actuators significantly reduced the drag factor for the cylinder from 1.2 to 0.1.

Effects of an Owl Airfoil on the Aeroacoustics of a Small Wind Turbine

Aerodynamic noise emitted by small wind turbines is a concern due to their proximity to urban environments. Broadband airfoil self-noise has been found to be the major source, and several studies have discussed techniques to reduce airfoil leading-edge and trailing-edge noises. Reduction mechanisms inspired by owl wings and their airfoil sections were found to be most effective. However, their effect/s on the tip vortex noise remain underexplored. Therefore, this paper investigates the effects of implementing an owl airfoil design on the tip vortex noise generated by the National Renewable Energy Laboratory (NREL) Phase VI wind turbine to gain an understanding of the relationship, if any, between airfoil design and the tip vortex noise mechanism. Numerical prediction of aeroacoustics is employed using the Ansys Fluent Broadband Noise Sources function for airfoil self-noise radiation. Detailed comparisons and evaluations of the generated acoustic power levels (APLs) for two distinguished inlet velocities were made with no loss in torque. Although the owl airfoil design increased the maximum generated APL by the baseline model from 105 dB to 110 dB at the lower inlet velocity, it significantly reduced the surface area generating the noise, and reduced the maximum APL generated by the baseline model by 4 dB as the inlet velocity increased. The ability of the owl airfoil to mitigate the velocity effects along the span of the blade was found to be its main noise reduction mechanism.

Aerodynamic techniques to mitigate the 3D loss in the power coefficient of vertical axis wind turbines

The three-dimensional tip loss effect is a critical phenomenon affecting the performance of vertical-axis wind turbines. The vortices on the blades become more complex with the turbine rotation, most notable at the tips, leading to three-dimensional aerodynamic losses and decreasing the turbine power coefficient. Therefore, mitigating the aerodynamic losses at the tips could improve the technological development of these devices. However, the numerical methods to analyze the tip vortices in VAWTs have a high computational cost, and experimental data to verify them is limited. In this study, three passive flow control techniques that mitigate the three-dimensional effects of a vertical axis wind turbine Darrieus H-type have been investigated experimentally in a wind tunnel to quantify their impact on the power coefficient and validate the theoretical results found in the literature. The tested passive flow control aerodynamic designs of the blade tips consist of leading-edge serration, anhedral, and endplate techniques. The results of this work include the experimental power coefficient curves as a function of the tip speed ratio for a two-blade VAWT model without any modification and with the three passive control techniques. The experimental process characterizes the VAWT techniques in a range of Tip Speed Ratios between 0.37 and 3.1. Our results indicate that the leading-edge serration, anhedral, and endplate techniques effectively mitigate the three-dimensional losses, increasing the power coefficient by 7.1%, 14.3%, and 25%, respectively, compared to the reference model. The endplate model exhibited the best Cp improvement. However, it could cause the highest bending on the blade tips of the three tested techniques.

Effect of combined surge and pitch motion on the aerodynamic performance of floating offshore wind turbine

Floating offshore wind turbines (FOWTs) can encounter variations in the phase difference and amplitude of combined surge-pitch platform motion. The phase difference between surge and pitch movement can result in the superposition or cancellation of wind turbine motion, potentially leading to significant changes in its aerodynamic characteristics. Herein, a wind turbine model was developed using the computational fluid dynamics (CFD) method to investigate the aerodynamic performance of the wind turbine. The findings revealed significant variations in the aerodynamics characteristics of the wind turbine when subjected to surge and pitch motions. When the rotor moves forward with a large relative velocity, dynamic stall can be triggered and induce the violent fluctuation of aerodynamic load. Moreover, vortex ring state (VRS) may occur when the wind turbine moves backward, leading to the recirculation of tip and root vortices and possibly causing negative thrust and torque. The trend of the drag force acting on the tower exhibits an almost complete opposition to that of the rotor thrust with the change of phase difference in the combined surge-pitch motion. It is also noted that the tower lift fluctuates asymmetrically, and as the platform motion amplitude increases, the tower lift gradually increases towards one side.

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.

Aerodynamic and acoustic study of a small scale lightly loaded hovering rotor using large eddy simulation

The aerodynamics and acoustics of a small-scale lightly loaded hovering rotor operating at low Reynolds number is investigated using high-fidelity numerical simulation. A canonical geometry is considered, which allows for different flow topologies typical of transitional flows to develop along the span. Specifically, regions with laminar attached flow, trailing edge laminar separation with prominently 2D structures, and successive laminar separation, transition and reattachment with prominently 3D structures are identified. Furthermore, the lightly loaded configuration is conducive to significant blade-wake interaction, that in turn affects the dynamics of the boundary layer. The acoustic footprint of these phenomena is analyzed by correlating pressure fluctuations in the flow to those at the blade surface. It is found that the radiated noise is characterized by tonal peaks at the blade passing frequency and harmonics, and by a broadband hump at higher frequencies, consistent with experimental observations. The broadband hump exhibits distinct peaks that are found to originate from the separated shear layers on both pressure and suction sides. In particular, two noise generation mechanisms arising at two different frequencies in the broadband hump are identified. One is due to the interaction between an instability transported in the tip vortex of one blade and the leading edge of the following blade, and another one is found to rely on the interaction between an instability transported in the tip vortex and in the wake of one blade scattered by the trailing edge of the following blade.