Elliptic Airfoil Research Articles

New type of motion trajectory for increasing the power extraction efficiency of flapping wing devices

Flapping wing devices represent a new type of renewable energy extraction technology that has the advantageous characteristics of simple structure, strong adaptability to surroundings, and little impact on the environment. This study numerically investigates the effects of vertical and elliptical airfoil trajectories on the power extraction efficiency of a flapping airfoil device using a transient numerical method based on the overset grid technique. The results are employed to propose a novel reversed-D airfoil trajectory that represents a composite of an elliptical trajectory in the first half of the motion cycle and a standard vertical trajectory in the second half of the motion cycle. The results show that for the elliptical trajectory, when the length of the half-axis in the vertical direction is fixed, the total power harvesting efficiency decreases with the increase of the horizontal half-axis length. In a certain frequency range, the decreased orders of the power extraction ability of the flapping wing are the upstream half-cycle elliptical trajectory, the vertical linear and the downstream half-cycle elliptical trajectory. Based on this understanding, we propose a new type of reversed-D motion trajectory. The power extraction efficiency of flapping wing devices operating in the reversed-D trajectory are investigated using both single and double airfoil designs. The results show that the power extraction efficiency of the single airfoil design moving along the reversed-D trajectory is greater than that obtained for the single airfoil moving along the standard vertical reciprocating trajectory within a specific range of frequency, and the increase is due mainly to an increase in the heave force. The power extraction efficiency of each airfoil in the double airfoil model moving along the reversed-D trajectory is less than that of a single airfoil moving along the vertical trajectory. However, the overall average power extraction efficiency is greater than that of a single airfoil moving along the vertical trajectory, and this increased efficiency is obtained over a larger frequency range than that of a single airfoil moving along the reversed-D trajectory. In addition, the increased efficiency of the double airfoil model is greater in the low frequency region. The proposed reversed-D trajectory facilitates the flexible arrangement of multiple airfoils in a flapping wing design. As such, the proposed reversed-D trajectory provides a promising new methodology for designing flapping wing devices with high power extraction efficiencies.

Lift Generation of an Elliptical Airfoil at a Reynolds Number of 1000

Bumblebees cannot fly! That conclusion is likely to be drawn by scientists who analysed the insect using aerodynamics of stationary wings such as that of a passenger aircraft. Looking at the insect again using a newfound understanding of unsteady aerodynamics; it is clear why bumblebees can fly. Bumblebees utilise mechanisms behind unsteady aerodynamics such as leading-edge vortices (LEVs) formation, wake capture, and rapid end-of-stroke rotation to generate forces that enable the insect to fly. This study focuses on two-dimensional (2D) elliptical airfoil. Earlier works found the aerodynamic characteristics of an elliptical airfoil to differ greatly from a conventional airfoil, and that this airfoil shape could generate the counter-rotating vortices used by insects to generate lift. Therefore, this research aims to study the lift generation of a bumblebee-inspired elliptical airfoil in a normal hovering flight. This study focuses on hovering flight with the insect flies in a nearly stationary position, which explains the importance of lift generation to stay aloft. The motion of the elliptical airfoil is inspired by the flapping kinematics of bumblebees at a typical Reynolds number range of . It is found that the current two-dimensional model is capable of capturing the counter-rotating vortices and correlates the formation of these structures to a high production of lift. These results show that bumblebees utilise these counter-rotating vortices to generate lift enough to fly in hovering flight. This results also indicate that flapping 2D elliptical airfoils can be used to investigate their 3D wing counterparts, which translate to a reduced time and computing costs.

Model order reduction in aerodynamics: Review and applications

The need of the aerospace industry, at national or European level, of faster yet reliable computational fluid dynamics models is the main drive for the application of model reduction techniques. This need is linked to the time cost of high-fidelity models, rendering them inefficient for applications like multi-disciplinary optimization. With the goal of testing and applying model reduction to computational fluid dynamics models applicable to lifting surfaces, a bibliographical research covering reduction of nonlinear, dynamic, or steady models was conducted. This established the prevalence of projection and least mean squares methods, which rely on solutions of the original high-fidelity model and their proper orthogonal decomposition to work. Other complementary techniques such as adaptive sampling, greedy sampling, and hybrid models are also presented and discussed. These projection and least mean squares methods are then tested on simple and documented benchmarks to estimate the error and speed-up of the reduced order models thus generated. Dynamic, steady, nonlinear, and multiparametric problems were reduced, with the simplest version of these methods showing the most promise. These methods were later applied to single parameter problems, namely the lid-driven cavity with incompressible Navier–Stokes equations and varying Reynolds number, and the elliptic airfoil at varying angles of attack for compressible Euler flow. An analysis of the performance of these methods is given at the end of this article, highlighting the computational speed-up obtained with these techniques, and the challenges presented by multiparametric problems and problems showing point singularities in their domain.

Design and Analysis of Rotor/Wing Flap for Canard Rotor/Wing Aircraft

In the present study, a kind of blunt trailing edge airfoil with its flap is designed for the purpose of reducing drags of blunt leading and trailing edge airfoils which are used for rotor/wing of CRW. The aerodynamic characteristics of designed flaps and elliptic airfoil which has the same thickness are numerically investigated based on the Reynolds-averaged Navier–Stokes equations and the SST k-ω two-equation turbulence model. The comparisons of aerodynamic force and moment coefficients show that, the lift characteristic is improved for designed flaps, but the drag will not be reduced if the flap has great bending trailing edge, and small bending trailing edge design is suitable for this kind of flap, and it will reduce the drag and improve the longitudinal stability characteristics.

A Review of Blowing: as an Active Flow Control Strategy

Flow control has significant technological importance as it can manipulate the flow field in a desired way either actively or passively. This wide research area has remained the point of attention for many years as it is applicable to various applications. Blowing as a flow control method, among other methods, is more technically feasible and market ready technique. A brief review from the existing literature on various studies on blowing has been presented along with their outcome. Then, studies were conducted to investigate the performance variation (in terms of lift coefficient, drag coefficient) of different airfoils with respect to various blowing parameters. It was observed that for NACA 0012 airfoil the maximum lift coefficient peaks at a blowing ratio 0.2 and then it decreases whereas the stalling angle increases with rise of blowing ratio. For LA203A both maximum lift coefficient and stalling angle increases with blowing ratio. For thick airfoil, it was found that lift increases with the rise of moment coefficient and blowing ratio and mid chord slots gives better performance at lower angles of attack whereas leading edge slots exhibits better performance at higher angles of attack. In case of thick elliptical airfoil, increase in lift coefficient was noticed with the increase in moment coefficient and blowing ratio but an optimum jet width to chord ratio (0.41) was found beyond which increase in jet width causes drop in lift coefficient. Additionally, it was found that at lower blowing angle thick elliptical airfoil performs better compared to that of higher angles of attack. Study on NACA 0012 and Aerospatiale A proved the fact that lifts increases with rise in blowing ratio at three different jet diameters to chord ratios. This study also found that higher blowing ratio is also advantageous for the turbo machinery in increasing the pressure difference. Lastly, the study on low Re airfoil flow found that increasing blowing ratio has a deleterious effect on aerodynamics performance (in terms of lift and drag coefficient).

Improved Algorithm of Boundary Integral Equation Approximation in 2D Vortex Method for Flow Simulation Around Curvilinear Airfoil

The problem of the accuracy improving is considered for vortex method. The general Galerkin-type approach is considered for the numerical solution of the boundary integral equation. It is shown that the airfoil surface line representation as a polygon consisting of rectilinear panels can lead to incorrect behavior of the numerical solution of the boundary integral equation with respect to unknown vortex sheet intensity, especially in case of considerably different lengths of the neighboring panels. However, in this case, the exact analytical formulae are derived for the coefficients of the linear algebraic system, which approximate the integral equation. The approach is developed which makes it possible to take into account explicitly the curvature of the airfoil surface line. The approximate analytical formulae are derived for the coefficients of the linear system, which are expressed through the integrals of the fractions, which denominators can be equal to zero. Numerical example is considered for the elliptic airfoil in the incident flow at its essentially non-uniform discretization. The suggested algorithm has acceptable numerical complexity, however it permits to obtain rather good numerical results.

On the high-accuracy approach to flow simulation aroundthe airfoils by using vortex method

Some problems connected to vortex methods development for 2D incompressible flow simulation around airfoils are discussed. In the numerical schemes and algorithms which are normally used in the vortex methods, the airfoil is approximated by a polygon consists of rectilinear panels, and the the vortex sheet intensity, which is placed on the airfoil surface line and simulates the airfoil’s influence the flow, is assumed to be piecewise-constant or piecewise-linear function. The most accurate mathematical models and numerical algorithms, based on such approaches, provide the estimation for the order of the error between O(h) and O(h2) for the average vortex sheet intensity over the panels (h is the maximal panel length). In the present research a new approach is developed, where the vortex sheet intensity is assumed to be discontinuous piecewise-linear or piecewise-quadratic function and the curvature of the panels is taken into account. In order to compute the coefficients of the main system of the algebraic equations, the least squares method is used instead of commonly used no-through or no-slip conditions at separate control points or over the panels in the average. It is shown, that the developed approach is much more accurate in comparison with previously known ones: for some test problems (flows around a circular airfoil, an elliptical airfoil and Zhukovsky airfoil) it permits to obtain numerical solution which has error of order O(h4).

Computational Investigation of Aerodynamic Characteristics for Elliptic UAVs’ Wing

Unmanned Aerial Vehicles, UAVs, gained an important role in modern military and civilian applications. Developments in UAVs technology improve its performance and maneuverability with acceptable cost. Elliptic airfoil had been widely used in the development of Rotor/Wing subsonic aircraft. The present work aims to investigate the effect of various elliptic airfoil parameters, such as Reynolds number, angle of attack and airfoil thickness, on aerodynamic behavior using two-dimensional computational study. The computational results were validated by experimental results. Angles of attack was evaluated from 0° to 18° in order to analyze aerodynamic characteristics up to stall condition, while Reynolds number was evaluated at values of 1×10⁵, 3×105, 2×106, and 8×106, to cover the range of rotary and fixed wing flight conditions. Thickness ratio was ranged from 5% to 25% to include the UAVs airfoil thicknesses so that choice best thickness gets max lift to drag ratio. In addition, the thicknesses location was evaluated for a range of 30% to 70% to get suitable location gets max left to drag ratio. The ANSYS-Fluent software was used with Spalart-Allmaras turbulence model, and found that the maximum lift to drag ratio which improve the UAV capability in this study is at Re=2×106, angle of attack at 8°, max thickness ratio of (0.1chord) located at (0.3chord).

Bifurcations and route to chaos for flow over an oscillating airfoil

Using immersed boundary methods, we perform numerical simulations for flow over an elliptical airfoil oscillating at a reduced frequency of 6.283 over a range of Strouhal number with Reynolds number 500. We quantify the response of this nonlinear system through time-histories of aerodynamic lift and thrust force coefficients, their Fourier spectra, phase maps, Poincáre sections, and higher-order spectral analysis. When the oscillation amplitude increases, this nonlinear system undergoes bifurcations, thus eventually achieving chaotic solutions. The aerodynamic response moves quasi-periodically through to chaos. We also relate these behavioral changes in the response of the system to the wake transitions. We also present cross-bispectrum between the lift and thrust coefficients, and auto-trispectrum for the lift coefficient to study cubic coupling among various frequency components. We find the strongest quadratic and cubic coupling between the excitation frequency components. We also observe the cubic coupling among various frequency components responsible for generating new harmonics in the spectra of the lift force at higher Strouhal numbers.

High Reynolds Viscous Flow Simulation Past the Elliptical Airfoil by Random Vortex Blob

In this paper, numerical simulation for a two-dimensional viscous and incompressible flow past the elliptical airfoil is presented by Random Vortex Blob (RVB). RVB is a numerical technique to solve the incompressible, two-dimensional and unsteady Navier-Stocks equations by converting them to rotational non-primitive formulations. In this method, the velocity vector at a certain point can be calculated without considering any grid around it, so the RVB method can be treated as a meshless method. Accordingly, the turbulent flow past a cylinder as well as an elliptical airfoil is investigated. In both cases, the obtained mean time velocities are compared with available numerical and experimental results where an acceptable agreement is observed. Having known the velocity field, by employing momentum balance, the drag and lift coefficients caused by flow past the elliptical airfoil with different diameter ratios and Re=105 are calculated and compared with experimental data where a good consistency is achieved.

Lift improvements using duty-cycled plasma actuation at low Reynolds numbers

An experimental study on active flow control over an elliptic airfoil is performed using an alternating-current dielectric-barrier-discharge (AC-DBD) plasma actuator combined with the duty-cycled technique. This study aims to eliminate or decrease the nonlinearities of the lift curves within a range of small angles of attack at low Reynolds numbers. The results of plasma actuator characterization in the quiescent air show that the duty-cycled plasma actuation can generate periodic sustained vortices with strengthened vorticity and streamwise momentum in comparison of steady-on mode. The wind tunnel test results show that the baseline airfoil exhibits the clearer nonlinear behavior at small AOA for lower Reynolds numbers. With duty-cycled plasma actuation, a rigidly linear proportional control of the lift that varies with the AOA is achieved with the reduced frequency f+=1. The surface oil-flow measurement shows the plasma actuator can delay the separation and result in an enhanced lift when the laminar boundary layer separation occurs without reattachment. When the long laminar separation bubble appears in the trailing edge region, the plasma actuator can eliminate the bubble. In this case, the extra lift supplied by the bubble is eliminated, leading to a reduced airfoil lift. The linear proportional control of the lift can be achieved by the appropriate enhanced and reduced lift changes which can be supplied by the duty-cycled plasma actuation.

Enhanced thrust performance of a two dimensional elliptic airfoil at high flapping frequency in a forward flight

This study is motivated by our earlier investigation Lua et al. (2016) which shows that a two-dimensional elliptic airfoil undergoing sinusoidal flapping motion experiences thrust deterioration when the flapping frequency exceeds a certain critical value (or critical Strouhal number, Stcr). To alleviate this unfavorable thrust generation condition, we propose two novel effective angle of attack profiles, namely smooth trapezoid (STEA) profile and elliptic trapezoid (ETEA) profile. These profiles are designed to ensure that the airfoil still experiences the same effective angle of attack amplitude as the sinusoidal flapping while concurrently reducing the detrimental effect of high rotation rate. The effectiveness of these two proposed profiles is confirmed by our numerical and experimental studies. In particular, our results show that at low to moderate flapping frequency, thrust generation is almost invariant to the type of angle of attack profiles applied, but at high flapping frequency (St>Stcr), the proposed profiles produce higher thrust than the sinusoidal flapping. The thrust augmentation can be attributed to the suppression of the adverse low pressure region in the vicinity of the airfoil, which is a consequence of the reduced rotation rate. Of the two proposed profiles, the ETEA with its steep acceleration phase produces a higher time-average thrust than the STEA near the stroke reversal. Also, in line with our previous finding, thrust augmentation for both STEA and ETEA is a function of the base length of the trapezoid, with a broader one producing a better thrust performance.

Improvement of effectiveness of EMHD flow separation control

The present numerical study shows that the effectiveness of flow separation control using Electro-Magneto-Hydro-Dynamic (EMHD) method can be improved by choosing the dimensions of the actuator based on the Reynolds number and the shape of the model studied. The width of the electrode/magnet for most effective flow separation control should be approximately 2.5 times the boundary layer thickness, which in turn is dependent on the Reynolds number. The length of the EMHD actuator for most effective flow separation control can be the shortest based on manufacturing constraints as well as on the possibility of shifting of separation point. The application of Lorentz force inside the boundary layer near the separation point provides the most effective flow separation control. The studies are done for flow over a cylinder in low Reynolds number regime (Reynolds number = 200) and for flow over an elliptical airfoil in high Reynolds number regime (Reynolds number = 1.6 × 105).

Effect of Gurney Flaps on an Elliptical Airfoil

A low-speed wind tunnel investigation is presented characterizing the impact of Gurney flaps on an elliptical airfoil. The chordwise attachment location and height of the flaps were varied, as was the Reynolds number. The results showed strong nonlinearities in the lift curve which were present for all tested geometries. Flap effectiveness was seen to diminish as the flap was moved closer to the trailing edge stemming from flap submersion in separated flow. For the tested cases, the measured lift coefficients showed a weak Re dependency. The upper airfoil surface was shown to carry approximately 80% of the total lift load. The top surface caused a pitching moment reversal associated with nonlinearity in the lift curve.

On the acoustics of a circulation control airfoil

A two-dimensional elliptical circulation control airfoil model is studied in the Florida State Aeroacoustic Tunnel. Far-field acoustics are obtained via a 55 microphone phased array. Single microphone spectra are also obtained, and it is shown that background noise is significant. In order to circumvent this problem, beamforming is employed. The primary sources of background noise are from the tunnel collector and jet/sidewall interaction. The deconvolution approach to mapping acoustic sources (DAMAS) is employed to remove the effects of the array point spread function. Spectra are acquired by integrating the DAMAS result over the source region. The resulting DAMAS spectral levels are significantly below single microphone levels. Although the DAMAS levels are reduced from those of a single microphone or delay and sum beamforming (DAS), they are still above those of a NACA 0012, estimated using NAFNoise, at the same geometric and free-stream conditions. A scaling analysis is performed on the processed array data. With a constant free-stream velocity and a varying jet velocity the data scale as jet Mach number to the 6th power. If the momentum coefficient is held constant and the free-stream velocity is varied the data scale as free-stream Mach number to the 7th power.

On the thrust performance of a flapping two-dimensional elliptic airfoil in a forward flight

In this paper, results of numerical and experimental studies are presented for a flapping two-dimensional (2D)elliptic airfoil in a forward flight condition at a Reynolds number of 5000.The study is motivated by the experiment of Read et al. (2003), which shows that the thrust coefficient of a 2D NACA0012 airfoil deteriorated at high flapping frequency (or Strouhal number) when the induced effective angle of attack profile ceases to be a simple harmonic function in time. As to why non-simple-harmonic profile of effective angle of attack is detrimental to thrust generation is not fully understood. The paper is an attempt to address this issue by examining the flow mechanism, including near field flow structures and the associated transient aerodynamic forces and pressure field, responsible for the observed behavior. Our results show that thrust suppression can be attributed to an adverse suction effect due to high rotation rate of the airfoil and the presence of an attached leading edge vortex generated in the previous stroke. The results further show that the condition for best efficiency need not necessary coincides with the condition of best thrust performance; this observation has been made in past studies of flapping flight.

Reynolds Number Effects on Rotor Blade Sections in Reverse Flow

The retreating blade of a high-advance-ratio rotor encounters a wide range of Reynolds numbers when passing through the reverse flow region. The present work was aimed at providing an improved understanding of Reynolds number effects in both forward and reverse flow. Time-averaged sectional airloads and surface oil flow visualizations were obtained experimentally for four airfoil cross sections at Reynolds numbers between and . Two airfoils with a sharp geometric trailing edge (a NACA 0012 and a NACA 0024) and two airfoils with a blunt geometric trailing edge (a 24% thick elliptical airfoil and a 26% thick cambered ellipse airfoil) were tested. This work shows that the airloads for a NACA 0012 in reverse flow are insensitive to Reynolds number due to early flow separation, because it acts as a “thin” airfoil due to the sharp aerodynamic leading edge. The airloads of thicker airfoils were found to be more sensitive to Reynolds number. In reverse flow, the NACA 0024 exhibits a decrease in the magnitude of the airloads with increasing Reynolds number for . The lift curve of an elliptical airfoil becomes more linear with increasing Reynolds number. The character of the lift curve for the cambered ellipse airfoil changes drastically for in both forward and reverse flow. These results provide insight for the design of high-speed helicopter rotor blades by examining the sensitivity of airloads to the range of Reynolds numbers encountered in the reverse flow region.

Thrust Enhancement on a Two Dimensional Elliptic Airfoil in a Forward Flight

Thrust Enhancement on a Two Dimensional Elliptic Airfoil in a Forward Flight

Lift Build-Up on Circulation Control Airfoils

Circulation control airfoils modify the lift by changing the jet momentum (injected tangent to a blunt trailing edge), whereas conventional sharp trailing-edge airfoils control their lift primarily by changing the angle of attack. For a step input in the angle of attack, the lift develops with a certain indicial time lag, which for sharp trailing-edge airfoils may be represented by Wagner’s function. This paper explores the similarities between Wagner’s lift build-up function and lift build-up over elliptical circulation control airfoils using numerical simulations for a 15% thickness-to-chord ratio elliptic circulation control airfoil. Following a thorough validation, the lift response to a step change in jet momentum is simulated using time-accurate flow simulations. The results highlight an excellent correlation between the time lags of the Wagner function and the circulation control airfoil lift response to the corresponding step input, suggesting that the Wagner function may lend itself for representing circulation control lift dynamics. Additional transient behaviors are also compared, and similarities as well as ranges of applicability are discussed.

Vortex flow structures and interactions for the optimum thrust efficiency of a heaving airfoil at different mean angles of attack

The thrust efficiency of a two-dimensional heaving airfoil is studied computationally for a low Reynolds number using a vortex force decomposition. The auxiliary potentials that separate the total vortex force into lift and drag (or thrust) are obtained analytically by using an elliptic airfoil. With these auxiliary potentials, the added-mass components of the lift and drag (or thrust) coefficients are also obtained analytically for any heaving motion of the airfoil and for any value of the mean angle of attack α. The contributions of the leading- and trailing-edge vortices to the thrust during their down- and up-stroke evolutions are computed quantitatively with this formulation for different dimensionless frequencies and heave amplitudes (Stc and Sta) and for several values of α. Very different types of flows, periodic, quasi-periodic, and chaotic described as Stc, Sta, and α, are varied. The optimum values of these parameters for maximum thrust efficiency are obtained and explained in terms of the interactions between the vortices and the forces exerted by them on the airfoil. As in previous numerical and experimental studies on flapping flight at low Reynolds numbers, the optimum thrust efficiency is reached for intermediate frequencies (Stc slightly smaller than one) and a heave amplitude corresponding to an advance ratio close to unity. The optimal mean angle of attack found is zero. The corresponding flow is periodic, but it becomes chaotic and with smaller average thrust efficiency as |α| becomes slightly different from zero.