Finite Wing Research Articles

Effect of Aspect Ratio on Finite-Wing Dynamic Stall

The role of aspect ratio on the dynamic stall process of an unswept finite wing is investigated using high-fidelity large-eddy simulations. Three aspect ratios (, 8, and 16) are explored for wings (NACA 0012 cross section) at chord Reynolds number and freestream Mach number . The wings pitch sinusoidally from initial incidence of 4° to a maximum angle of attack of 22° with reduced frequency over one pitching cycle. The three-dimensional unsteady flowfields show similarity among the three wings through laminar separation bubble formation/bursting. The flow topology during dynamic stall exhibits distinctly different evolutions at the higher aspect ratio relative to the lower, baseline aspect ratio. Rather than evolving into a vortex (), the higher-aspect-ratio wings show dramatic three-dimensional deformation of the vortex tube that resembles cellular structures. The vortical structure eventually interacts with the trailing-edge vortex, which contrasts with the lower aspect ratio. Examination of the unsteady loads shows an increase in lift slope, average loads, peak loads, and earlier stall with aspect ratio.

Effect of Fuel Sloshing on the Damping of a Scaled Wing Model—Experimental Testing and Numerical Simulations

Vertical sloshing of liquid-filled tanks has been shown to induce substantial dissipative effects. Building upon these previous results obtained on simpler sloshing systems, a scaled wing prototype is presented here, equipped with a fuel tank that allows the observation of liquid sloshing and quantification of induced dynamic effects. Based on experiments conducted at a 50% filling level for a baffled wing fuel tank model, substantial additional damping effects were demonstrated with liquid inside the tank regardless of the vertical acceleration amplitude. A numerical model based on a finite element wing structural model and a surrogate 1DOF fluid model was explored, with numerical simulations showing good agreement compared to experiments throughout the decaying motion of the system.

Structure and dynamics of a laminar separation bubble near a wing root: towards reconstructing the complete LSB topology on a finite wing

The influence of the wing root junction on the laminar separation bubble forming on the suction surface of a semispan NACA 0018 wing cantilevered from the wind tunnel test section wall is studied using surface flow visualisations, particle image velocimetry and surface pressure measurements at a chord Reynolds number of 125 000 and an angle of attack of 6 $^\circ$ . The test section wall boundary layer upstream of the wing is turbulent, and the spanwise influence of the junction on the separation bubble extends well beyond the test section wall boundary layer thickness. Substantial three-dimensionality is seen in the separation bubble flowfield near the wing root, where earlier transition and a reduction in separation bubble thickness is observed. In contrast with the wing tip, earlier transition and a reduction in separation bubble length occurs near the wing root. Outside of the junction affected region, the separation bubble is similar to separation bubbles forming on two-dimensional geometries, and displays mild spanwise waviness. The transition process away from the end affected regions is characterised by the formation of spanwise roll-up vortices that are shed in a nearly two-dimensional manner across the span. The analysis of the results shows that, near the wing root, the increased level of perturbations leads to earlier vortex roll-up and spanwise flow contributes to more rapid vortex breakdown. The results in the wing root region are complemented by the analysis of data from Toppings and Yarusevych (J. Fluid Mech., vol. 929, 2021, A39) in the wing tip region to provide a more holistic outlook on the laminar separation bubble topology and dynamics on the entire finite wing.

Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers

Linear modal instabilities of flow over untapered wings with aspect ratios$AR=4$and 8, based on the NACA 0015 profile, have been investigated numerically over a range of angles of attack,$\alpha$, and angles of sweep,$\varLambda$, at chord Reynolds numbers$100\le Re\le 400$. Laminar base flows have been generated using direct numerical simulation and selective frequency damping, as appropriate. Several families of unstable three-dimensional linear global (TriGlobal) eigenmodes have been identified and their dependence on geometric parameters has been examined in detail at$Re=400$. The leading global mode A is associated with the peak recirculation in the three-dimensional laminar separation bubble formed on the wing and becomes unstable when recirculation reaches$\textit {O}(10\,\%)$. On unswept wings, this mode peaks in the midspan region of the wake and moves towards the wing tip with increasing$\varLambda$, following the displacement of peak recirculation; its linear amplification leads to wake unsteadiness. Additional amplified modes exist at nearly the same and higher frequencies compared to mode A. The critical$Re$has been identified and it is shown that amplification increases with increasing sweep, up to$\varLambda \approx 10^\circ$. At higher$\varLambda$, all global modes become less amplified and are ultimately stable at$\varLambda =30^\circ$. An increase in amplification of the leading mode with sweep was not observed over the$AR=4$wing, where tip vortex effects were shown to dominate.

Control of Dynamic Stall on Swept Finite Wings

A low-amplitude high-frequency flow control strategy for mitigation of transient tip stall is demonstrated for the case of a finite swept wing using high-fidelity wall-resolved large-eddy simulations. A wing of aspect ratio and NACA 0012 section is considered at freestream Mach number and chord Reynolds number . The wing undergoes an oscillatory pitching motion with reduced frequency and angle of attack between and 22 deg, resulting in deep dynamic tip stall for the uncontrolled case. Spanwise uniform low-amplitude pulsed forcing is imparted through a zero-net mass flow blowing/suction slot located on the wing lower surface near the leading edge using both moderate and high frequencies, and 50, respectively. The imposed small fluctuations are amplified through the natural receptivity of the laminar separation bubble (LSB) and, in the case of the highest frequency, completely inhibit its bursting along the wing, which precludes outboard flow separation and subsequent dynamic tip stall. The lower-frequency forcing cannot overcome eventual bursting of the LSB near the wingtip; however, the resulting separation is localized to the tip region unlike the full outboard unloading of the uncontrolled case. Conditioning of the leading-edge flow through targeted manipulation of the LSB and its inherent dynamics maintained or enhanced the effectively attached flow throughout the pitching cycle, resulting in significant reductions in the cycle-averaged drag and in the force and moment excursions.

Flutter of a finite rectangular Wing’D mill in pitch and heave

Exact solutions of flutter are explored for a mode suitable for an oscillating 2D hydrofoil version of the summarised FlutterWing windpump which radically surpasses the old rotary fanpump. The imaginary part G of the 1D Theodorsen wake lift factor T rises singularly from the steady to allow 1D pure pitch flutter around the leading edge at low frequency. But its logarithmic infinite negative pitch damping by the shed vorticity is capped by the log of the 2D span. The downwash of an oscillating trailing (tip) vortex is reduced by a function of the reduced frequency based on spanwise distance. Its lag damps pitch and further raises the pitch unstable aspect ratio A to above 36. All binary pitch & heave neutral flutter frequency contours in (inertia, imbalance) space still pass through a nexus of the same total pitch inertia and imbalance as the corrected virtual mass concentrated at ¾ chord, a very high total in water. The internal bound windwise vortex from ¼ chord to trailing edge reduces as A−2 the 1D lift slope at all frequencies. It expands the 1D T = ½ double root of high frequency elliptical contours kissing the low frequency limit line at the nexus to make them dip below the line to the right of the nexus as hyperbolae with the nexal ray as left asymptote. Thus low A discovers a new wedge of high frequency binary flutter with real mass moments less than the virtual, as in water.

Finite wing effects on the energy harvesting from stall-induced oscillations

The modeling of aeroelastic harvesters usually employs methods for two-dimensional aerodynamics. Such convenient practice reflects the lack in the literature of efficient tools with low computational cost to assess unsteady and nonlinear aerodynamics loads accounting for three-dimensional wing effects. In this sense, the present work aims to fulfill this gap by developing a nonlinear unsteady lifting line to investigate finite wing effects on the power generation from stall-induced oscillations. The aerodynamic model links the Beddoes–Leishman dynamic stall method to a linear unsteady lifting line. The optimization of energy harvesters from stall-induced pitching oscillations is revisited considering the three-dimensional aerodynamic model. Results reveal that the three-dimensional harvester’s dynamic behavior may differ from the two-dimensional case, and the harvested power reduction is observed.

Simulating tip effects in vertical-axis wind turbines with the actuator line method

Simulation of the complex, unsteady aerodynamics characterizing Darrieus rotors requires computational tools with a fidelity higher than the ubiquitous Blade Element Momentum (BEM) theory. Among them, the Actuator Line Method (ALM) stands out in terms of accuracy and computational cost. This approach, however, still fails to resolve the vortex-like structures shed at the blade ends, overestimating turbine performance at the higher rotational speeds. Moving from this background, in this study a comprehensive investigation on the ALM’s capability to simulate tip effects and their impact on rotor performance is carried out. To this end, the ALM tool developed by the authors in the ANSYS® FLUENT® environment (v. 20.2) and specifically tailored to the simulation of vertical-axis machines was employed. Both a steady finite wing and a fictitious one-blade Darrieus H-rotor, for which high-fidelity blade-resolved CFD data are available as benchmark, were considered as test cases. ALM simulations were first performed without any correction for different cell sizes and force projection radii, so that the limits of the original approach could be assessed. Then, two different sub-models were applied: the classical semi-empirical Glauert correction and a new methodology based on the Lifting Line Theory (LLT), which was recently proposed by Dağ and Sørensen (DS). The latter was here adapted to vertical-axis machines. Eventually, the blade spanwise load profiles coming from the three approaches were assessed and compared, proving the superior performance of the DS model.

Pitch/Plunge Equivalence for Dynamic Stall of Unswept Finite Wings

Pitch/plunge equivalence for deep dynamic stall of a straight finite wing is considered by employing large-eddy simulations. The flowfields are computed with a well-established time-implicit high-fidelity large-eddy simulation approach. The wing has a moderate aspect ratio of and a NACA 0012 section incorporating a rounded tip. The flow parameters are a freestream Mach number of and chord Reynolds numbers of . Pure pitching and equivalent plunging maneuvers are considered with a reduced frequency of and minimum and maximum effective angles of attack of 4 and 22 deg, respectively. The pitch and plunge dynamic stall cases are compared in detail in terms of the unsteady three-dimensional flow structure, surface pressure, and loading. Differences in the lift and moment coefficient are shown to be correctable, employing a steady thin-airfoil theory for a cambered airfoil that accounts for the rotation-induced apparent camber present in the pitching case. This pitch/plunge equivalence is extendable to the dynamic stall of a swept wing, as demonstrated in another paper by the authors [“Pitch–Plunge Equivalence for Dynamic Stall of Swept Finite Wings,” AIAA Journal (submitted for publication)].

Pitch/Plunge Equivalence for Dynamic Stall of Swept Finite Wings

A high-fidelity numerical study is undertaken to expand the notion of pitch/plunge equivalence to finite, swept wings undergoing deep-dynamic stall and builds upon the analysis of straight wings in another paper by the authors [“Pitch/Plunge Equivalence for Dynamic Stall of Unswept Finite Wings,” AIAA Journal (submitted for publication)]. The wing has an aspect ratio of with a NACA 0012 section, a rounded tip, and a sweep angle of ; it operates at a Reynolds number of and a Mach number of . Equivalent pure-pitch and pure-plunge motions at two different reduced frequencies are considered to assess pitch-induced apparent camber on the wing and its effects on the three-dimensional flow structure, surface topology, and aerodynamic loading. Regardless of the motion type or rate, the wing undergoes dynamic tip stall that is initiated through the outboard separation of a dynamic stall vortex as it lifts off the surface and forms into an arch vortex before ejecting into the wake. The pitching cases exhibit an advanced development and evolution in time of these features that are observed as variable amplifications of the aerodynamic loading, which is due predominantly to an apparent camber effect. Corrections to the total and sectional lift and moment coefficients are explored by extending steady thin-airfoil theory to pitching swept wings. Remarkably, the corrected plunge-equivalent histories provide a full collapse of the force and moment responses between the pitching and plunging cases, despite the delayed behavior of the flow structure. This equivalence and the similar process of dynamic stall should facilitate the comparison of experiments and/or simulations employing different motion types, even for finite-aspect-ratio and swept wings.

Accuracy of Küchemann’s prediction for the locus of aerodynamic centres on swept wings compared to an inviscid panel method

AbstractThe locus of aerodynamic centres of a finite wing is the collection of all spanwise section aerodynamic centres, and depends on aspect ratio, wing sweep and planform shape. This locus is of great importance in the positioning of vortex elements in lifting-line theory. Traditionally, these vortex elements are placed along the quarter-chord of a wing, leading to inaccurate predictions of aerodynamic coefficients for swept wings due to the discontinuity in the line of vorticity at the wing root. An analytical solution was presented by Küchemann in 1956 to determine the locus of aerodynamic centres as a function of sweep. While experimental studies have been performed to visualise this locus, no large amount of data is available to fully evaluate the accuracy of Küchemann’s analytical solution. In the present study, a numerical approach is taken using a high-order panel method for inviscid, incompressible flow to calculate the locus of aerodynamic centres for elliptic wings over a wide range of sweep angles, aspect ratios and profile thicknesses. An inviscid panel method is chosen over full CFD solutions because of their ability to isolate the inviscid phenomena. Küchemann’s prediction is compared to this numerical data. The root mean square error is calculated for each wing in a broad design space to determine the accuracy of Küchemann’s theory. It is shown to be remarkably accurate over the range of cases studied, with the root mean square error staying below 4% for all wings with aft sweep and aspect ratios higher than $R_A=5$ . The actual difference between Küchemann’s prediction and numerical data is lower than that for the majority of the span for many of the wing designs considered, with the RMS error being skewed by the results at the tip. Results demonstrate that Küchemann’s analytical equations can be used as an accurate approximation for the locus of aerodynamic centres and could be used in modern numerical lifting-line algorithms*.

On Trapeze Wing Aerodynamics Calculations Based on Improved Vortex Lattice Method

This paper presents, aerodynamics coefficients calculation (Lifting & drag coefficients, pressure central location) of Trapeze wing shape configurations for different aspect ratios (ARs) values by using improved vortex lattice method (VLM), compared with finite-wing and slender body theories. The planar wing was divided into N panels of the size: 6X6 with trapezoid shape panels. As expected, for high ARs the VLM solution for the lifting coefficient is coincided with the finite wing theory whereas for small ARs (<1) it is coincided with the slender body theory (~1). Afterwards, we obtained that the calculated VLM induced drag becomes closer to the finitewing theory as the AR value is increased.

Effect of Winglets on Wing Tip Vortices

Abstract Wing tip vortices are generated at finite wing tips. On the one side the wing tip vortices are essential for the generation of lift, but on the other side they also generate induced drag. Winglets are devices that reduce the induced drag without reducing substantially the lift of the wing. The reduction of induced drag is of the order of a few percent, but in long range travels this can save substantial fuel. Two wings were investigated, one without winglets and one with winglets. Both wings had NACA 4412 airfoil sections, including the section of the winglet. The chord of the winglet was half of the chord of the wing.

Enhanced Prediction of Three-Dimensional Finite Iced Wing Separated Flow Near Stall

Icing on three-dimensional wings causes severe flow separation near stall. Standard improved delayed detached eddy simulation (IDDES) is unable to correctly predict the separating reattaching flow due to its inability to accurately resolve the Kelvin-Helmholtz instability. In this study, a shear layer adapted subgrid length scale is applied to enhance the IDDES prediction of the flow around a finite NACA (National Advisory Committee for Aeronautics) 0012 wing with leading edge horn ice. It is found that applying the new length scale contributes to a more accurate prediction of the separated shear layer (SSL). The reattachment occurs earlier as one moves towards either end of the wing due to the downwash effect of the wing tip vortex or the influence of end-wall flow. Consequently, the computed surface pressure distributions agree well with the experimental measurements. In contrast, standard IDDES severely elongates surface pressure plateaus. For instantaneous flow, the new length scale helps correctly resolve the rollup and subsequent pairing of vortical structures due to its small values in the initial SSL. The computed Strouhal numbers of vortical motions are approximately 0.2 in the initial SSL based on the vorticity thickness and 0.1 around the reattachment based on the separation bubble length. Both frequencies increase when moving towards the wing tip due to the downwash effect of the tip vortex. In comparison, the excessive eddy viscosity levels from the standard IDDES severely delay the rollup of spanwise structures and give rise to "overcoherent" structures.

Applying Frequency-Domain Unsteady Lifting-Line Theory to Time-Domain Problems

Frequency-domain unsteady lifting-line theory is better developed than its time-domain counterpart. To take advantage of this, this paper proposes a method to transform time-domain kinematics to the frequency domain, perform a convolution, and then return the results back to the time domain. This paper demonstrates how well-developed frequency-domain methods can be easily applied to time-domain problems, enabling prediction of forces and moments on finite wings undergoing arbitrary kinematics. Results are presented for rectangular wings of various aspect ratios, undergoing pitch and heave kinematics. Computational fluid dynamics is used to test the effectiveness of the method in the Euler and low-Reynolds-number () regimes. Overall, the proposed method provides fast and reasonably accurate predictions of lift and moment coefficients, particularly in comparison to strip theory, which is commonly used for problems involving arbitrary kinematics.

Structure and dynamics of a laminar separation bubble near a wingtip

The three-dimensional flow topology of a laminar separation bubble forming on the suction surface of a semispan wing with an aspect ratio of $2.5$ and NACA 0018 airfoil section is characterised experimentally using surface pressure measurements and particle image velocimetry at a chord Reynolds number of $125\ 000$ . In the inboard region of the wing, the separation bubble is essentially two-dimensional, and the transition process in the separated shear layer leads to periodic vortex shedding, which dominates the bubble dynamics, similar to two-dimensional separation bubbles. However, progressive spanwise changes in the mean structure and vortex dynamics occur near the wingtip, leading to an open separation and eventual suppression of the bubble. In the immediate proximity of the wingtip, the boundary layer remains attached, no vortex shedding occurs and the flow remains laminar, terminating separation bubble formation. Despite variations in the mean separation bubble topology and vortex dynamics along the span, the fundamental shedding characteristics remain nearly invariant across the portion of the wing where vortex shedding occurs, and the flow appears to lock onto a common instability mode across the span, leading to minimal changes in the mean bubble characteristics despite notable changes in the effective angle of attack along the span. A comparison with available surface flow visualisations from previous studies indicates that the observed changes to the mean bubble footprint along the span of the wing are similar across different geometries and flow characteristics, suggesting similarities in the three-dimensional bubble topology and dynamics on finite wings.

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.

Experimental Investigation of the Flow Characteristics and Noise Generation at the Wing–Wall Junction

AbstractThis paper is concerned with the flow characteristics and noise generation at the finite wing–wall junction. To characterize junction flow noise, acoustic measurements were taken in the aco...

Experimental investigation on stall flutter over a vertically mounted rigid finite wing

As stall flutter has relevant engineering implications, such as in blades of wind turbine and HALE (highaltitude long-endurance aircraft). This work presents the experimental investigation of rigid wing setup in a closed-circuit wind tunnel having 2.1 m × 1.5 m test section. The experimental campaign reached stable and symmetrical LCO within the freestream range from 9 m/s up to 14 m/s (1.69 × 105 < Re < 2.63 × 105 ). Two techniques were used for position tracking: one mechatronic and one image-based. The latter used ‘shakethe-box’ method applied to a body, which has proven a successful approach as a non-intrusive tool.

Experimental Flow Field Investigation of the Bio-Inspired Corrugated Wing for MAV Applications

This is an experimental flow field study of a bio-inspired corrugated finite wing from the dragonfly intended to assess the flow behavior over the wing and compare it with a wing of the same geometry with filled corrugation, at low Reynolds numbers 46000 and 67000. The work purpose is to explore the potential application of such types of wings for Micro Air Vehicles (MAVs) or micro sized Unmanned Air Vehicles (UAVs). Two types of wings are taken into account: first wing was a bio-inspired corrugated wing which was obtained from the mid span of the dragonfly, and the second wing was the same geometry with filled corrugation. Both wings were fabricated by using 3-D printing machine. The tufts were glued at three different locations i.e. at center, 30%, and 60% of the semi-span towards the right side of the wing at the trailing edge. The boundary layers were measured by using boundary layer rakes inside the open-end low speed wing tunnel with varied angles of attack. The results of the tuft flow visualization showed that the flow pattern at different span locations was different at different angles of attack and different wing velocities (Reynolds number). The fluctuations of the two different wings at the same angle of attack and Reynolds number were found different. Also, the directions of the flow for both wings were found to be different at different span locations. The boundary layer measurement results for both wings were found to be different at the same angles of attack and Reynolds numbers. The flow pattern also showed that the wing’s upper as well as lower surface behaved differently on the same wing under the same measurement conditions. The results showed that the corrugated wing outperformed the conventional wing at low Reynolds number and the stall angle of the corrugated wing was more than the conventional wing.