Leading Edge Vortex Shedding Research Articles

Lift tailoring on unsteady airfoils with leading-edge vortex shedding using an inverse aerodynamic approach

In this paper, we present a physics-informed approach to tailor the lift profile of an unsteady airfoil through the execution of an appropriate maneuver. In previous research, a low-order aerodynamic model based on the unsteady thin airfoil theory was developed for predicting the flowfield and loads on airfoils undergoing arbitrary motions. The theory was phenomenologically augmented using the concept of leading edge suction parameter (LESP) to incorporate the capability to predict intermittent leading edge vortex (LEV) shedding. The criticality of LESP was used to predict the onset and termination of LEV shedding and thus model the effect of LEVs on the flowfield and loads for a prescribed motion. In the current work, an inverse aerodynamic formulation is developed based on this framework for tackling the inverse problem: to obtain the motion kinematics required for generating a prescribed lift profile for an airfoil operating in the dynamic-stall regime. The LEV-modeling capability of the aerodynamic model enables the motion-design algorithm to take into account the effect of complex phenomena, such as dynamic stall and LEV shedding, which are not taken into account in previous research approaches. Several case studies are presented to demonstrate various scenarios such as lift tracking using pitching and heaving motions, lift cancellation during unsteady motion, and the generation of a given lift profile using two equivalent motions. The kinematic profiles generated by the inverse formulation are also simulated using a high-fidelity unsteady computational fluid dynamics solver to validate the predictions.

Enhancing the Power-Extraction Efficiency of a Flapping Foil by Active Morphing

A computational study of two morphing, power-extracting flapping foils (a NACA 0015 at and a flat plate at ) is conducted by considering three strategies: morphing of the leading edge (LE) or trailing edge (TE) alone, and morphing of both LE and TE simultaneously. The morphing variables are the phase shift and frequency of the edge deformation. All cases take into account the power required to morph the foils. The independently morphing LE/TE edge cases show regions of phase angle and frequency that yield improved efficiency over the rigid baseline of up to 16.8% for the NACA 0015 foil and 22.6% in the flat-plate case. The combined LE and TE cases further increase the efficiency, up to 29.7% for the NACA 0015 foil and 36.2% in the flat-plate case. Three physical mechanisms are identified that lead to efficiency increases in the various cases through the interaction between the morphing foil and shed vortex structure. These are the change in projected area during the plunging stroke, the variation of leading-edge vortex shedding timing during the cycle, and the proximity of the shed vortex structure to the foil during the pitching portion of the stroke.

Integrated Sensing of Camber, Aerodynamic Load, and Vortex Structures over Membrane Wings

Due to the compliant nature of extensible membrane wings, there exists a close relationship between the membrane wing camber and the aerodynamic load. Additionally, the membrane dynamics are often linked to unsteady large-scale flow structures, such as shear layer location or leading-edge vortex shedding. Real-time measurements of the membrane shape, including both mean camber and the frequency content of vibration, provide significant information on the surrounding flowfield. In this work, one method of integrated camber sensing is demonstrated, and the relationships to aerodynamic load and flowfield are shown. Camber is estimated via the capacitance of a dielectric elastomer membrane wing. The relationship between capacitance and camber is defined geometrically. The mean aerodynamic load is shown to be well-captured by applying a simple aeroelastic analysis to the measured camber. Finally, time-resolved membrane kinematics and flowfield measurements are used to illustrate the ties between the dynamic membrane vibration, as measured by capacitance, and the behavior of the shear layer above the wing. Ultimately, this work is a step toward an integrated, closed-loop control method for membrane wings.

Leading-edge Suction Behavior of Unsteady Airfoils in Forward And Reverse Flows

To model unsteady airfoil aerodynamics in forward and reverse flows in a simple and robust manner requires a strong understanding of the complex flow dynamics and their relation to first-order concepts. The current work explores the relation between the leading-edge suction force, represented nondimensionally by the leading-edge suction parameter (LESP), and the flow physics of forward and reverse dynamic stall as a function of freestream Reynolds number, airfoil thickness, and motion kinematics for the NACA 0012, 0015, and 0018 airfoils using computational tools. The relation between the LESP and critical events associated with leading-edge vortex (LEV) shedding was found to be independent of flow direction barring the signature to identify LEV initiation. Leading-edge suction was observed to continue to increase after LEV initiation in reverse flow and could be attributed to the combined effect of a weak LEV and strong trailing-edge vortice. While LESP, forces, and moments were found to be moderately dependent on airfoil thickness and strongly dependent on the Reynolds number in forward flow conditions and the critical LESP, in addition, was weakly dependent on motion kinematics, the aerodynamics were observed to be largely independent of said parameters in reverse flow. This allows for a single critical LESP value to be used for symmetric airfoils to indicate LEV initiation when the blunt edge is experiencing reversed flow, a finding which serves to largely reduce the empirical dependencies while modeling unsteady reverse dynamic stall in low-order methods.

Oscillating-Foil Turbine Performance Improvement by the Addition of Double Gurney Flaps and Kinematics Optimization

Refinement of the performance of a fully constrained oscillating-foil turbine is carried out via the addition of passive double Gurney flaps. Flaps ranging from hGF=0.005c to 0.075c are added at the trailing edge of the NACA 0015 blade of turbines operating in high-efficiency regimes without leading-edge vortex shedding (LEVS). Performance improvements are determined using 2D numerical simulations with an unsteady Reynolds-averaged Navier–Stokes (URANS) approach. Based on a recent study of the double Gurney flaps on stationary foils, instantaneous power-extraction coefficients are analyzed and modifications of the foil’s kinematics are tested in order to fully benefit from the Gurney flaps’ performance improvements. Modifications to the pivot point location of the foil, to the pitch-heave phase, and to the pitching amplitude of the turbine are considered. Improvements are found for all turbine cases studied, including some of the previously optimal cases reported in the literature. The double Gurney flaps, being a simple and passive device, offer great practical application potential. They represent an efficient refinement to already robust and high-performance oscillating-foil turbines operating without the perceived benefit of leading-edge vortex shedding, an essential characteristic for actual, finite-span applications.

Numerical study on the energy extraction performance by flapping foils in a density stratified flow

An energy extractor based on fully-activated flapping foils operating in a density stratified flow is studied numerically. The effect of stratification strength characterizing as the internal Froude number on the energy extraction performance is first investigated by fixing a typical set of parameters. The hydrodynamic characteristics of flapping foils with different kinematics in the stratified regime are then examined by varying the pitching amplitude. Our results suggest that the stratification effect decreases the energy harvesting efficiency owing to resulting poor synchronization between forces and flapping motion. Within the considered parametric space, the minimum energy extraction performance is identified at the Froude number around Fr=2, giving rise to an attached boundary layer without the favorable flow separation and leading edge vortex shedding. Nevertheless, a sudden increase of extracted power is observed when the stratification level is enhanced to Fr=1, which is attributed to the distinct flow structures generated by the induced internal waves. For the varying kinematics, the Froude number corresponding to the minimum performance is found to increase as the pitching amplitude becomes higher. It is indicated that the induced internal waves tend to dominate the flow patterns at a highly strong stratification, whereas the kinematics of flapping foils still play a crucial role in determining the vortex dynamics for the moderate and weak stratification strength.

Global instability and mode selection in flow fields around rectangular prisms

Large-eddy simulations of the unsteady flows around rectangular prisms with chord-to-depth ratios (B/D) ranging from 3 to 12 are carried out at a Reynolds number of 1000. A particular focus of the study is the physical mechanisms governing the global instability of the flow. The coherent structures and velocity spectra reveal that large-scale leading-edge vortices (L vortices) are formed by the coalescence of Kelvin–Helmholtz rollers. Based on dynamic mode decomposition, the interactions between the L vortex and the trailing-edge vortex (T vortex) at different B/D values are revealed. It is found that the phase difference between the L and T vortices is the critical factor promoting a stepwise increase in the Strouhal number with increasing B/D. According to the phase analysis, there are two types of pressure feedback-loop mechanisms maintaining the self-sustained oscillations. When B/D = 4–5, the feedback loop covers the separation region, and the global instability is controlled by the impinging shear-layer instability. When B/D = 3 and 6–12, the feedback loop covers the entire chord, and the global instability is controlled by the impinging leading-edge vortex shedding instability. Self-sustained oscillations of the shear layer still exist after a splitter plate is placed in the near wake, indicating that the T vortex shedding is not essential in triggering the global instability. Nevertheless, with the participation of the T vortex, the primary instability mode may be reselected due to the upper and lower limits of the shedding frequency imposed by the T vortex.

Mechanisms of Morphing Wall Flow Control by Traveling Waves over an Airfoil

The main two mechanisms of morphing wall flow control are direct injection of momentum in the streamwise direction and indirect momentum transfer via triggering instabilities. Traveling waves have been shown to perform better than standing waves, probably because they can use both mechanisms. However, the relative importance of the two mechanisms is not known. To differentiate between the mechanisms, a range of parameters (frequency, amplitude, and starting location) at stall (15 deg angle of attack) and poststall (20 deg angle of attack) is tested using wall-resolved large-eddy simulations with a sharp-interface curvilinear immersed boundary method at a low Reynolds number of over a NACA0018 airfoil. The results of the simulations demonstrate that the flow is reattached within a range of nondimensional frequencies, actuation amplitudes, and starting locations of oscillation at the stall and poststall angles of attack. Significant lift enhancement and drag reduction are also observed within these ranges. The nondimensional frequency range at which the flow is reattached is found to be similar to the dominant nondimensional frequencies of leading-edge vortex shedding of the unactuated airfoil. These indicate that the indirect transfer of momentum is the dominant mechanism because direct injection of momentum increases with the increase of amplitude and frequency; that is, separation should reduce as they increase. Nevertheless, direct injection of momentum improves the performance relative to pure excitations of standing waves when instabilities are triggered.

An investigation of tidal turbine performance and loads under various turbulence conditions using Blade Element Momentum theory and high-frequency field data acquired in two prospective tidal energy sites in Australia

Potential tidal energy sites are characterized by strong currents and high levels of shear, which is the main source of turbulent kinetic energy production. Enhanced turbulence levels are known to intensify fatigue loads acting on turbine blades, possibly causing premature device failure. Blade Element Momentum (BEM) numerical models allow for the investigation of device performance and loadings prior to device deployment and support turbine design optimization at low computational expenses. High-frequency novel Acoustic Doppler Current Profiler (AD2CP) data from two tidally energetic sites in Australia are used to feed a BEM model optimized to incorporate unsteady flow corrections. Power, thrust and bending moments coefficients as well as separation points are estimated to describe the performance of a turbine under various turbulence intensities and integral length scales. Results reveal that standard deviations were more sensitive than mean coefficients and turbulence intensities had a greater impact on performance coefficients than integral length scales. Periodic oscillations of separation points at two stations suggest the presence of weak dynamic stall but also that leading-edge vortex shedding is constrained to the blade roots. These findings highlight the need of assessing turbulence in tidal energy sites and support design improvements which can endure unsteady conditions.

Interaction of quasi-two-dimensional vortical gusts with airfoils, unswept and swept wings

A nearly two-dimensional vortex of small core size has been produced by the transient plunging motion of an upstream airfoil and it interacted with the downstream wings. Depending on the offset distance of the vortex and wing angle of attack, the incident vortex filament deforms, diffuses, and loses coherence, while inducing leading-edge vortex formation and shedding from the wing. No significant spanwise flow develops in the incident vortices during the interaction. The interaction with the swept wing at each spanwise plane appears to be unaffected by the other spanwise planes. The counter-clockwise vortex induces a positive lift peak as it approaches the wing, which can be predicted by the potential flow assumption. The peak lift force is proportional to the circulation of the incident vortex and has its maximum near the zero-offset distance. The minimum lift coefficient is reached after the vortex has just passed and caused flow separation on the lower surface. The maximum lift coefficients for the finite unswept and swept wings can be estimated by making a correction for the aspect ratio and using the independence principle. The only exception is observed for the swept wing at a post-stall angle of attack for which the leading-edge vortex shedding becomes parallel to the leading-edge and increases the peak lift force.Graphical abstract

Aerodynamic correlation and flow pattern of high-rise building with side ratio of 3:1 under twisted wind profile: A computational study

This study numerically investigates twisted-wind effect on aerodynamic correlation and flow pattern of high-rise building with 3:1 side ratio. Spatial-temporal correlation of aerodynamic forces and flow filed under conventional wind profile (CWP) and twisted wind profile (TWP) are comprehensively compared. Proper orthogonal decomposition (POD) is further employed to extract wake flow pattern and mode correlation. The results show that twisted-wind effect on building with long afterbody is unique. Specifically, compared with CWP, TWP augments mean wind loads in three perpendicular directions (e.g., CMx under TWP30 is increased by 60.56% compared to CWP). The original two vortex structures (i.e., leading-edge vortex shedding (LEVS) and trailing-edge vortex shedding (TEVS)) appearing in CWP transit to relatively weaker alternate-edge vortex shedding (AEVS) in TWP, thus, the fluctuating lateral base moment and torsional force are reduced by 30.60% and 28.24% respectively under TWP30 compared to CWP. Correlation of wind load components and correlation of layer force are significantly magnified because TWP intensifies vertical moment exchange and force coupling effect, this possibly results in stronger wind-induced responses. POD analysis reveals essential mechanism of twisted-wind effect and shows that flow pattern (i.e., energy proportion, dominant frequency, mode shape and mode correlation) is largely changed by TWP.

Influence of inter-foil spacing on energy extraction of tandem oscillating hydrofoils

The tandem configuration of two hydrofoils is an effective way to improve the power of the energy-extraction system. In such a configuration, the inter-foil spacing between two hydrofoils is one of the important configuration parameters. The effect of the inter-foil spacing on the energy-extraction power is investigated by the STAR CCM + based on an overset mesh. First, a fixed motion phase shift between two foils of −180° is proposed with adjustment of the inter-foil spacing. Then, the global phase shift is established; for keeping it constant, the motion phase shift is correspondingly changed with adjustment of the inter-foil spacing. Based on the systematical studies of the energy-extraction power of the tandem foils with spacing, it is found that in the tandem foils system, the energy extraction of the upstream foil is changed tiny. With increasing the spacing between two foils, the energy-extraction power of the downstream foil shows a very obvious periodic fluctuation when the motion phase shift is constant. Due to the loss of wake velocity, the global phase using the freestream velocity causes errors in describing the downstream foil-vortex interaction, so the wake phase model using the average wake velocity is a better choice. For the small effective angle of attack hydrofoils with only shear layer vortices, the wake energy does not change with distance, so the maximum efficiency of tandem foils with different inter-foil spacings is almost the same. But when the leading edge vortex shedding occurs, the energy extraction of the tandem foils is significantly affected by the inter-foil spacing due to the change of the wake energy.

Leading-edge-vortex tailoring on unsteady airfoils using an inverse aerodynamic approach

In this paper, we present an approach to obtain a desired leading-edge vortex (LEV) shedding pattern from unsteady airfoils through the execution of suitable motion kinematics. Previous research revealed that LEV shedding is associated with the leading-edge suction parameter (LESP) exceeding a maximum threshold. A low-order method called LESP-modulated discrete vortex method (LDVM) was also developed to predict the onset and termination of LEV shedding from an airfoil undergoing prescribed motion kinematics. In the current work, we present an inverse-aerodynamic formulation based on the LDVM to generate the appropriate motion kinematics to achieve a prescribed LESP variation, and thus, the desired LEV shedding characteristics from the airfoil. The algorithm identifies the kinematic state of the airfoil required to attain the target LESP value through an iterative procedure performed inside the LDVM simulation at each time step. Several case studies are presented to demonstrate design scenarios such as tailoring the duration and intensity of LEV shedding, inducing LEV shedding from the chosen surface of the airfoil, promoting or suppressing LEV shedding during an unsteady motion on demand, and achieving similar LEV shedding patterns using different maneuvers. The kinematic profiles generated by the low-order formulation are also simulated using a high-fidelity unsteady Reynolds-averaged Navier–Stokes method to confirm the accuracy of the low-order model.

Instability modes of the flows around a streamlined box girder

The instability modes of the flows around a streamlined box girder at a Reynolds number of 40,000 are studied based on the large-eddy simulation and dynamic mode decomposition techniques. In particular, the mechanism behind the streamwise vortex shedding, which may trigger the vortex-induced vibrations (VIV) of the structures, is explored based on the spanwise-averaged velocity fields. The streamwise vortex shedding mode is found to be a coupling of the impinging leading-edge vortex shedding and the trailing-edge vortex shedding, although the leading-edge vortices may be masked by inherent turbulent fluctuations in the three-dimensional flows. Two dominant streamwise vortex shedding modes coexist in the flow, and the frequency of each mode is closely related to the leading-edge vortex number on the side faces of the deck. A very-low-frequency fluctuating mode is identified based on the three-dimensional velocity fields. This low-frequency mode is related to the periodic enlargement and shrinkage of the main separation bubble and can significantly modulate the streamwise vortex shedding modes in amplitude.

Extraction of aerodynamic damping and prediction of vortex-induced vibration of bridge deck using CFD simulation of forced vibration

This study presents computational fluid dynamics (CFD) simulation of forced vibration of a bridge deck for extraction of amplitude-dependent aerodynamic damping in the vicinity of vortex lock-in region. The coordinate system fixed on the oscillating body is used to bypass the requirement of mesh updating. The three-dimensional flow around the vibrating deck is assumed to be homogeneous in spanwise direction and simulated using the efficient high-order spectral element/Fourier method. The aerodynamic damping is extracted from the simulated lift and then used to estimate the steady-state vortex-induced vibration (VIV) amplitude for given wind velocity and structural parameters. A good match of VIV amplitudes between simulations and wind tunnel tests validates the accuracy of simulation. The VIV mechanisms are discussed from the vortex shedding modes, distributions of dynamic pressure and energy transfer from flow to bridge deck. The leading-edge vortex shedding rather than Karman vortex shedding is identified to be responsible for the VIV. The hysteresis of VIV is observed which is related to the mode change of impinging leading-edge vortex and leading-edge vortex shedding. Finally, a novel forced vibration technique with a varying amplitude is proposed that permits extraction of aerodynamic damping by a single CFD run with improved efficiency.

Energy extraction of oscillating foil with an active deflecting trailing-edge flap

The method of oscillating-foil energy extraction can be used to extract kinetic energy from the surrounding flow by a combined pitching and heaving motion of the foil. In order to improve the efficiency of energy extraction, a slotted foil with an active deflecting trailing-edge flap—inspired by the structure of the tail edge of bird wings—is designed. In this study, the unsteady Reynolds-averaged Navier–Stokes equation is solved to investigate the energy extraction performance of an oscillating foil at a Reynolds number of 5.0 × 105. In the numerical simulation, the dynamic overset mesh technology is used in order to ensure the accuracy and convergence of numerical solution. The effect of the deflecting motion of trailing-edge flaps on the efficiency of energy extraction is studied at a range of oscillating frequencies. In addition, the flow control mechanisms of slots on the oscillating foil are revealed by comparing the flow fields of the slotted foil and the NACA0015 foil. The result shows that active deflecting trailing-edge flaps can improve the efficiency of energy extraction over a wide range of oscillation frequencies. The active deflection of trailing-edge flaps increases the energy extraction efficiency of oscillating foils by 21.1% relative to conventional foils under a specific operating condition of oscillating frequency f* = 0.18. A detailed analysis of the flow fields indicates that the slot on the foil can suppress flow separation, while it has a negative effect on the attachment of leading-edge vortices. The deflecting trailing-edge flap enhances the heaving force. Therefore, the energy output and the efficiency of the oscillating foil are enhanced especially at the operating conditions of the oscillating foil without leading-edge vortex shedding.

Usefulness of Inviscid Linear Unsteady Lifting-Line Theory for Viscous Large-Amplitude Problems

Unsteady lifting-line theory (ULLT) is a low-order method capable of modeling interacting unsteady and finite wing effects at low computational cost. Most formulations of the method assume inviscid flow and small amplitudes. Although these assumptions might be suitable for small-amplitude aeroelastic problems at high Reynolds numbers, modern engineering applications increasingly involve lower Reynolds numbers, large-amplitude kinematics, and vortex structures that lead to aerodynamic nonlinearities. This paper establishes that ULLT still provides a useful solution for low-Reynolds-number, large-amplitude kinematics problems, by comparing ULLT results against those of experimentally validated computational fluid dynamics simulations at . Three-dimensional effects stabilize leading-edge vortex (LEV) structures, resulting in a good prediction of whole wing force coefficients by ULLT. Although the inviscid spanwise force distributions are accurate for small-amplitude kinematics, the ULLT cannot model three-dimensional vortical structures, and thus it cannot correctly predict the force distribution due to the LEV. It can, however, predict the shedding of LEVs to a limited extent via the leading-edge suction parameter criterion. This can then be used as an indicator of the usefulness of the force distribution results.

Implementation and validation of a strongly coupled numerical model of a fully passive flapping foil turbine

This paper presents the implementation and validation of a strongly coupled numerical model of a fully passive flapping foil turbine operating at a high Reynolds number. Thanks to a strong fluid–solid coupling strategy, the well known added-mass instability is mitigated while simulating a lightweight flapping foil. The numerical results are first validated in the case of a fixed foil undergoing static stall. The model is then validated with respect to numerical results available in the literature for a heavy flapping foil turbine. Finally, the numerical results of the strongly coupled model are compared to experimental data of a lightweight turbine prototype tested in a confined channel. The numerical results have shown to be in good agreement with the experimental measurements. Indeed, the kinematics and harvesting performances of the turbine prototype have been accurately reproduced by the numerical simulations. Besides, the leading edge vortex shedding observed in the experiments has also been precisely reproduced by the numerical results. The strongly coupled model implemented and validated in the present paper constitutes a useful tool for expanding the parameter space in the search for an optimised design of the fully passive flapping foil turbine.

Fluid–structure interaction of a flexible membrane wing at a fixed angle of attack

Fluid–structure interaction of a flexible membrane wing was investigated experimentally at a fixed angle of attack (α = 14°). The Reynolds numbers (Re) based on the chord length of the membrane wing were 6 × 104, 6.6 × 104, and 8 × 104, respectively, which belong to low Reynolds numbers. Membrane deformations and the global flow fields around the membrane wing were measured synchronously with two-dimensional time-resolved particle image velocimetry. The membrane performs strongly periodic standing-wave vibration modes while interacting with the surrounding flow. Although the flow fields and membrane vibrations are coupled in all Re cases, it is newly discovered that, at Re = 6 × 104, the dominant frequency of the flow is around 9.1 Hz (Strouhal number St = 0.15) instead of the dominant membrane vibration frequency of 35.1 Hz (first-order vibration mode, St = 0.56). By tracking the Lagrangian coherent structures over the membrane, it is revealed that the vortical structures at Re = 6 × 104 are affected by the flow from both the leading- and trailing-edges. The frequency of 35.1 Hz in the power spectrum of flow is attributed to the successive shedding of leading-edge vortices coupled with membrane vibration, while the dominant frequency of flow field (9.1 Hz) is resulted from the interaction of strong trailing-edge reverse flow and the leading-edge separated flow, and the mechanism is explored. For higher Re cases (Re = 6.6 × 104 and 8 × 104), the membrane presents second- and third-order vibration modes separately. The dominant frequencies of the flow structure and membrane vibration are consistent, and the periodic shedding of leading-edge vortices is the main flow characteristic in both Re cases.

Coupled framework for limit-cycle oscillations modeling based on leading-edge vortex shedding

Current trends in the aircraft industry involve higher aspect-ratio wings made of lighter materials. These trends seek to reduce fuel emissions and increase flight efficiency by reducing drag to lift ratio and overall weight, respectively, of the aircraft. This results in reduced structural stiffness and coupling between the aeroelastic modes and flight dynamics. The flutter phenomenon is of particular interest for aeroelastic studies, and modeling post-flutter limit-cycle oscillations (LCO) is a challenging problem.Several studies have been developed to allow fast simulations of the highly non-linear aerodynamic situations, with leading-edge vortex modulation been a proved solution for modeling some forms of LCOs in airfoils. This article proposes a framework based on the 3D expansion of this method using strip theory and coupling with modal structural model for simulations of aerodynamic based non-linear phenomenon. A cantilevered flat plate is used for testing and validating the framework against wind-tunnel experiments and the industry standard approach. The results show that the proposed model is able to capture the main behavior of the LCO observed in the experiments and is directly comparable with the current approaches used at the industry. The framework allows for scalability and is also fast enough to provide time-based results in under two days for a desktop simulation, reducing the need of expensive cluster computations. Finally, since it is completely physics-based it allows for the engineer to get insights on the aerodynamic flow at a fraction of the cost of more detailed CFD models.