An experimental study of a bio-inspired corrugated airfoil for micro air vehicle applications

An experimental study was conducted to investigate the aerodynamic characteristics of a bio-inspired corrugated airfoil compared with a smooth-surfaced airfoil and a flat plate at the chord Reynolds number of Re _C  = 58,000–125,000 to explore the potential applications of such bio-inspired corrugated airfoils for micro air vehicle designs. In addition to measuring the aerodynamic lift and drag forces acting on the tested airfoils, a digital particle image velocimetry system was used to conduct detailed flowfield measurements to quantify the transient behavior of vortex and turbulent flow structures around the airfoils. The measurement result revealed clearly that the corrugated airfoil has better performance over the smooth-surfaced airfoil and the flat plate in providing higher lift and preventing large-scale flow separation and airfoil stall at low Reynolds numbers (Re _C  < 100,000). While aerodynamic performance of the smooth-surfaced airfoil and the flat plate would vary considerably with the changing of the chord Reynolds numbers, the aerodynamic performance of the corrugated airfoil was found to be almost insensitive to the Reynolds numbers. The detailed flow field measurements were correlated with the aerodynamic force measurement data to elucidate underlying physics to improve our understanding about how and why the corrugation feature found in dragonfly wings holds aerodynamic advantages for low Reynolds number flight applications.     

An investigation into the effects of unsteady parameters on the aerodynamics of a low Reynolds number pitching airfoil

The growing applications of low Reynolds number (LRN) operating vehicles impose the need for accurate LRN flow solutions. These applications usually involve complex unsteady phenomena, which depend on the kinematics of the vehicle such as pitching, plunging, and flapping of a wing. The objective of the present study is to address the issues related to LRN aerodynamics of a harmonically pitching NACA0012 airfoil. To this end, the influence of unsteady parameters, namely, amplitude of oscillation, d, reduced frequency, k, and Reynolds number, Re, on the aerodynamic performance of the model is investigated. Computational fluid dynamics (CFD) is utilized to solve Navier–Stokes (N–S) equations discretized based on the Finite Volume Method (FVM). The resulting instantaneous lift coefficients are compared with analytical data from Theodorsen’s method. The simulation results reveal that d, k, and Re are of great importance in the aerodynamic performance of the system, as they affect the maximum lift coefficients, hysteresis loops, strength, and number of the generated vortices within the harmonic motion, and the extent of the so-called figure-of-eight phenomenon region. Thus, achieving the optimum lift coefficients demands a careful selection of these parameters.     

Correlation between vortex structures and unsteady loads for flapping motion in hover

During the past decade, efforts were made to develop a new generation of unmanned aircrafts, qualified as Micro-Air Vehicles. The particularity of these systems resides in their maximum dimension limited to 15 cm, which, in terms of aerodynamics, corresponds to low Reynolds number flows (Re ≈ 10² to 10⁴). At low Reynolds number, the concept of flapping wings seems to be an interesting alternative to the conventional fixed and rotary wings. Despite the fact that this concept may lead to enhanced lift forces and efficiency ratios, it allows hovering coupled with a low-noise generation. Previous studies (Dickinson et al. in Science 284:1954–1960, 1999) revealed that the flow engendered by flapping wings is highly vortical and unsteady, inducing significant temporal variations of the loads experienced by the airfoil. In order to enhance the aerodynamic performance of such flapping wings, it is essential to give further insight into the loads generating mechanisms by correlating the spatial and temporal evolution of the vortical structures together with the time-dependent lift and drag. In this paper, Time Resolved Particle Image Velocimetry is used as a basis to evaluate both unsteady forces and vortical structures generated by an airfoil undergoing complex motion (i.e. asymmetric flapping flight), through the momentum equation approach and a multidimensional wavelet-like vortex parameterization method, respectively. The momentum equation approach relies on the integration of flow variables inside and around a control volume surrounding the airfoil (Noca et al. in J Fluids Struct 11:345–350, 1997; Unal et al. in J Fluids Struct 11:965–971, 1997). Besides the direct link performed between the flow behavior and the force mechanisms, the load characterization is here non-intrusive and specifically convenient for flapping flight studies thanks to its low Reynolds flows’ sensitivity and adaptability to moving bodies. Results are supported by a vortex parameterization which evaluates the circulation of the multiple vortices generated in such complex flows. The temporal evolution of the loads matches the flow behavior and hence reveals the preponderant inertial force component and that due to vortical structures.     

Flow field characteristics study of a flapping airfoil using computational fluid dynamics

The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with complex nonlinear vortex shedding and viscous phenomena. The respective fluid dynamics of such a flow is investigated here through Computational Fluid Dynamics (CFD) based on the Finite Volume Method (FVM). The governing equations are the unsteady, incompressible two-dimensional Navier-Stokes (N-S) equations. The airfoil is a thin ellipsoidal geometry performing a modified figure-of-eight-like flapping pattern. The flow field and vortical patterns around the airfoil are examined in detail, and the effects of several unsteady flow and system parameters on the flow characteristics are explored. The investigated parameters are the amplitude of pitching oscillations, phase angle between pitching and plunging motions, mean angle of attack, Reynolds number (Re), Strouhal number (St) based on the translational amplitudes of oscillations, and the pitching axis location (x/c). It is shown that these parameters change the instantaneous force coefficients quantitatively and qualitatively. It is also observed that the strength, interaction, and convection of the vortical structures surrounding the airfoil are significantly affected by the variations of these parameters.     

Dynamic stall behavior from unsteady force measurements

A direct force measurement technique employing piezoelectric load cells is used to experimentally investigate a two-dimensional airfoil (NACA 0012) undergoing dynamic stall. The load cells are installed at each end of the airfoil and give the force response in two directions in the plane normal to the airfoil axis during oscillations. Experiments are carried out at a Reynolds number based on the airfoil chord equal to 7.7×10⁴, and at four reduced frequencies, k=0.005, 0.01, 0.02, and 0.04. Phase-averaged lift of the airfoil undergoing dynamic stall is presented. It is observed that hysteresis loops of the lift occur both when the airfoil is pitched to exceed its static stall limit and when it is still within its static stall limit, and they grow in size with increasing k at the same pitching mean angle of attack and pitching amplitude. Both the lift and the drag induced by the pitching motion are further analyzed using the methods of higher order correlation analysis and continuous wavelet transforms to undercover their nonlinear and nonstationary features, in addition to classical FFT-based spectral analysis. The results are quantitatively illustrated by an energy partition analysis. It is found that the unsteady lift and drag show opposite trends when the airfoil undergoes transition from the pre-stall regime to the full-stall regime. The degree of nonlinearity of the lift increases, and the lift show a nonstationary feature in the light-stall regime, while the nonlinearity of the drag decreases, and the drag shows nonstationary feature in both the light-stall and the full-stall regimes. Furthermore, the lift and the drag have significant nonlinear interactions as shown by the correlation analysis in the light-stall regime.     

Power extraction efficiency improvement of a fully-activated flapping foil: With the help of an auxiliary rotating foil

The power extraction efficiency improvement of a fully-activated flapping foil with the help of an auxiliary rotating foil is numerically examined in this work. A NACA0015 airfoil is placed in a two-dimensional laminar flow and synchronously performs the imposed pitching and plunging motions. An auxiliary smaller foil, which rotates about its center, is arranged below the flapping foil. As a consequence, the vortex interaction between the flapping foil and the rotating foil occurs. At a Reynolds number of 1100 and the position of the pitching axis at one-third chord, the effects of the distance between the flapping foil and the auxiliary foil, the phase difference between the rotating motion and the flapping motion as well as the frequency of flapping motion on the power extraction performance are systematically investigated. It is found that compared to the single flapping foil, the efficiency of power extraction for the flapping foil with an auxiliary device can be improved. Based on the numerical analysis, it is indicated that the enhanced plunging contribution, which is caused by the increased lift force owing to the vortex interaction, directly helps the efficiency improvement.     

褶皱幅度对仿生翼型滑翔气动特性的影响

蜻蜓翅膀具有独特的褶皱状形貌．研究者们致力于利用仿生学原理,设计在低雷诺数条件下具有更优气动性能的褶皱翼型．本文采用计算流体力学方法,求解二维不可压Navier-Stokes方程组,探讨了四种翼型（平板翼型、流线翼型、小幅度褶皱翼型和大幅度褶皱翼型）的气动表现．在低雷诺数条件下得到以下结果：(1) 较小幅度的褶皱结构有利于增加升力和减小阻力．(2) 雷诺数变化时褶皱翼型的升力系数呈非线性变化;在特定雷诺数区间,幅度相近的褶皱翼型会发生相对气动优势的转变．(3) 褶皱结构内的回流区通过减小粘性阻力,使得翼型总阻力下降．(4) 翼型前缘的极小区域会产生脉冲高升力,对升力表现产生较大影响．这些结果表明,调整褶皱幅度是实现褶皱翼型气动优化的有效方案．     

An experimental study of the effects of pitch-pivot-point location on the propulsion performance of a pitching airfoil

An experimental investigation was conducted to characterize the evolution of the unsteady vortex structures in the wake of a pitching airfoil with the pitch-pivot-point moving from 0.16C to 0.52C (C is the chord length of the airfoil). The experimental study was conducted in a low-speed wind tunnel with a symmetric NACA0012 airfoil model in pitching motion under different pitching kinematics (i.e., reduced frequency k=3.8–13.2). A high-resolution particle image velocimetry (PIV) system was used to conduct detailed flow field measurements to quantify the characteristics of the wake flow and the resultant propulsion performance of the pitching airfoil. Besides conducting “free-run” PIV measurements to determine the ensemble-averaged velocity distributions in the wake flow, “phase-locked” PIV measurements were also performed to elucidate further details about the behavior of the unsteady vortex structures. Both the vorticity–moment theorem and the integral momentum theorem were used to evaluate the effects of the pitch-pivot-point location on the propulsion performance of the pitching airfoil. It was found that the pitch-pivot-point would affect the evolution of the unsteady wake vortices and resultant propulsion performance of the pitching airfoil greatly. Moving the pitch-pivot-point of the pitching airfoil can be considered as adding a plunging motion to the original pitching motion. With the pitch-pivot-point moving forward (or backward), the added plunging motion would make the airfoil trailing edge moving in the same (or opposite) direction as of the original pitching motion, which resulted in the generated wake vortices and resultant thrust enhanced (or weakened) by the added plunging motion.     

Experimental investigation of the effect of chordwise flexibility on the aerodynamics of flapping wings in hovering flight

Ornithopters or mechanical birds produce aerodynamic lift and thrust through the flapping motion of their wings. Here, we use an experimental apparatus to investigate the effects of a wing's twisting stiffness on the generated thrust force and the power required at different flapping frequencies. A flapping wing system and an experimental set-up were designed to measure the unsteady aerodynamic and inertial forces, power usage and angular speed of the flapping wing motion. A data acquisition system was set-up to record important data with the appropriate sampling frequency. The aerodynamic performance of the vehicle under hovering (i.e., no wind) conditions was investigated. The lift and thrust that were produced were measured for different flapping frequencies and for various wings with different chordwise flexibilities. The results show the manner in which the elastic deformation and inertial flapping forces affect the dynamical behavior of the wing. It is shown that the generalization of the actuator disk theory is, at most, only valid for rigid wings, and for flexible wings, the power P varies by a power of about 1.0  of the thrust T. This aerodynamic information can also be used as benchmark data for unsteady flow solvers.     

Reynolds number, thickness and camber effects on flapping airfoil propulsion

The effect of varying airfoil thickness and camber on plunging and combined pitching and plunging airfoil propulsion at Reynolds number Re=200, 2000, 20 000 and 2×10⁶ was studied by numerical simulations for fully laminar and fully turbulent flow regimes. The thickness study was performed on 2-D NACA symmetric airfoils with 6-50% thick sections undergoing pure plunging motion at reduced frequency k=2 and amplitudes h=0.25 and 0.5, and for combined pitching and plunging motion at k=2, h=0.5, phase ?=90°, pitch angle θ_o=15° and 30° and the pitch axis was located at 1/3 of chord from leading edge. At Re=200 for motions where positive thrust is generated, thin airfoils outperform thick airfoils. At higher Re significant gains could be achieved both in thrust generation and propulsive efficiency by using a thicker airfoil section for plunging and combined motion with low pitch amplitude. The camber study was performed on 2-D NACA airfoils with varying camber locations undergoing pure plunging motion at k=2, h=0.5 and Re=20 000. Little variation in thrust performance was found with camber. The underlying physics behind the alteration in propulsive performance between low and high Reynolds numbers has been explored by comparing viscous Navier-Stokes and inviscid panel method results. The role of leading edge vortices was found to be key to the observed performance variation.     

Effect of flexure on aerodynamic propulsive efficiency of flapping flexible airfoil

The aim of present study is to investigate the effect of chord-wise flexure amplitude on unsteady aerodynamic characteristics for a flapping airfoil with various combinations of Reynolds number and reduced frequency. Unsteady, viscous flows over a single flexible airfoil in plunge motion are computed using conformal hybrid meshes. The dynamic mesh technique is applied to illustrate the deformation modes of the flexible flapping airfoil. In order to investigate the influence of the flexure amplitude on the aerodynamic performance of the flapping airfoil, the present study considers eight different flexure amplitudes (a₀) ranging from 0 to 0.7 in intervals of 0.1 under conditions of Re=10⁴, reduced frequency k=2, and dimensionless plunge amplitude h₀=0.4. The computed unsteady flow fields clearly reveal the formation and evolution of a pair of leading edge vortices along the body of the flexible airfoil as it undergoes plunge motion. Thrust-indicative wake structures are generated when the flexure amplitude of the airfoil is less than 0.5 of the chord length. An enhancement in the propulsive efficiency is observed for a flapping airfoil with flexure amplitude of 0.3 of the chord length. This study also calculates the propulsive efficiency and thrust under various Reynolds numbers and reduced frequency conditions. The results indicate that the propulsive efficiency has a strong correlation with the reduced frequency. It is found that the flow conditions which yield the highest propulsive efficiency correspond to Strouhal number St of 0.255.     

Numerical investigations into the asymmetric effects on the aerodynamic response of a pitching airfoil

The effects of asymmetric sinusoidal motion on pitching airfoil aerodynamics were studied by numerical simulations for 2-D flow around a NACA0012 airfoil at Re=1.35×10⁵. Various unsteady parameters (amplitude of oscillation, d; reduced frequency, k) were applied to investigate the effect of asymmetry parameter S on the instantaneous force coefficients and flow patterns. The results reveal that S has a noticeable effect on the aerodynamic performance, as it affects the instantaneous force coefficient, maximum lift and drag coefficient, hysteresis loops and the flow structures.     

Experimental study of pitching and plunging airfoils at low Reynolds numbers

Measurements of the unsteady flow structure and force time history of pitching and plunging SD7003 and flat plate airfoils at low Reynolds numbers are presented. The airfoils were pitched and plunged in the effective angle of attack range of 2.4°–13.6° (shallow-stall kinematics) and ?6° to 22° (deep-stall kinematics). The shallow-stall kinematics results for the SD7003 airfoil show attached flow and laminar-to-turbulent transition at low effective angle of attack during the down stroke motion, while the flat plate model exhibits leading edge separation. Strong Re-number effects were found for the SD7003 airfoil which produced approximately 25 % increase in the peak lift coefficient at Re = 10,000 compared to higher Re flows. The flat plate airfoil showed reduced Re effects due to leading edge separation at the sharper leading edge, and the measured peak lift coefficient was higher than that predicted by unsteady potential flow theory. The deep-stall kinematics resulted in leading edge separation that led to formation of a large leading edge vortex (LEV) and a small trailing edge vortex (TEV) for both airfoils. The measured peak lift coefficient was significantly higher (~50 %) than that for the shallow-stall kinematics. The effect of airfoil shape on lift force was greater than the Re effect. Turbulence statistics were measured as a function of phase using ensemble averages. The results show anisotropic turbulence for the LEV and isotropic turbulence for the TEV. Comparison of unsteady potential flow theory with the experimental data showed better agreement by using the quasi-steady approximation, or setting C(k) = 1 in Theodorsen theory, for leading edge–separated flows.     

Comparative Analysis of the Characteristics of the Vortex Wake behind a Flapping Wing Performing Oscillations of Different Types

The wake characteristics of a custom-designed airfoil performing pitching oscillations, heaving oscillations, and a combination of pitch and heave oscillations are compared in this study. The influence of flapping parameters are investigated at a constant Reynolds number Re\(_{c} = 2640\) and is presented for the Strouhal numbers based on the oscillation amplitude, St_A, varying in the \(0.1 \leqslant {\text{S}}{{{\text{t}}}_{A}} \leqslant 0.4\) range. The generation of vorticity above and below the airfoil depends on the airfoil’s initial direction of motion and remains the same for all types of flapping oscillations investigated. The evolution of the leading-edge and trailing-edge vortices is presented. The heaving oscillations of the airfoil are found to have a greater influence on the characteristics of the leading edge vortex. The wake behind the combined pitch-heave oscillations appears to be governed by pitching oscillations below \({\text{S}}{{{\text{t}}}_{A}} = 0.24\), whereas it is driven by heaving oscillations above \({\text{S}}{{{\text{t}}}_{A}} = 0.24\). The force computations indicate that the mere existence of the reverse von Kármán street is not sufficient to develop the thrust on the airfoil. The periodic component of velocity fluctuations significantly influences the wake characteristics. The anisotropic stress field developed around the airfoil due to the periodic fluctuations of the velocity is presented. The coherent structures developed in the wake are identified using the proper orthogonal decomposition and a qualitative comparison of the structures for different flapping oscillations is presented. The energy transfer from the flapping airfoil to the fluid for different flapping oscillations is highest for heaving oscillations followed by combined pitch-heave oscillations and pitching oscillations.

     

The aerodynamics of a cylinder submerged in the wake of another

Flow-induced fluctuating lift (C_Lf) and drag (C_Df) forces and Strouhal numbers (St) of a cylinder submerged in the wake of another cylinder are investigated experimentally for Reynolds number (Re)=9.7×10³–6.5×10⁴. The spacing ratio L^⁎ (=L/D) between the cylinders is varied from 1.1 to 4.5, where L is the spacing between the cylinders and D is the cylinder diameter. The results show that C_Lf, C_Df and St are highly sensitive to Re due to change in the inherent nature of the flow structure. How the flow structure is dependent on Re and L^⁎ is presented in a flow structure map. Zdravkovich and Pridden (1977) observed a ‘kink’ in time-mean drag distribution at L^⁎≈2.5 for Re>3.1×10⁴, but not for Re≤3.1×10⁴. The physics is provided here behind the presence and absence of the ‘kink’ that was left unexplained since then.     

Aerodynamics of intermittent bounds in flying birds

Flap-bounding is a common flight style in small birds in which flapping phases alternate with flexed-wing bounds. Body lift is predicted to be essential to making this flight style an aerodynamically attractive flight strategy. To elucidate the contributions of the body and tail to lift and drag during the flexed-wing bound phase, we used particle image velocimetry (PIV) and measured properties of the wake of zebra finch (Taeniopygia guttata, N = 5), flying at 6–10 m s⁻¹ in a variable speed wind tunnel as well as flow around taxidermically prepared specimens (N = 4) mounted on a sting instrumented with force transducers. For the specimens, we varied air velocity from 2 to 12 m s⁻¹ and body angle from −15° to 50°. The wake of bounding birds and mounted specimens consisted of a pair of counter-rotating vortices shed into the wake from the tail, with induced downwash in the sagittal plane and upwash in parasagittal planes lateral to the bird. This wake structure was present even when the tail was entirely removed. We observed good agreement between force measures derived from PIV and force transducers over the range of body angles typically used by zebra finch during forward flight. Body lift:drag (L:D) ratios averaged 1.4 in live birds and varied between 1 and 1.5 in specimens at body angles from 10° to 30°. Peak (L:D) ratio was the same in live birds and specimens (1.5) and was exhibited in specimens at body angles of 15° or 20°, consistent with the lower end of body angles utilized during bounds. Increasing flight velocity in live birds caused a decrease in C _L and C _D from maximum values of 1.19 and 0.95 during flight at 6 m s⁻¹ to minimum values of 0.70 and 0.54 during flight at 10 m s⁻¹. Consistent with delta-wing theory as applied to birds with a graduated-tail shape, trimming the tail to 0 and 50% of normal length reduced L:D ratios and extending tail length to 150% of normal increased L:D ratio. As downward induced velocity is present in the sagittal plane during upstroke of flapping flight, we hypothesize that body lift is produced during flapping phases. Future efforts to model the mechanics of intermittent flight should take into account that flap-bounding birds may support up to 20% of their weight even with their wings fully flexed.     

Experimental study of wings undergoing active root flapping and pitching

This paper presents the results of experiments carried out on mechanical wings undergoing active root flapping and pitching in the wind tunnel. The objective of the work is to investigate the effect of the pitch angle oscillations and wing profile on the aerodynamic forces generated by the wings. The experiments were repeated for a different reduced frequency, airspeed, flapping and pitching kinematics, geometric angle of attack and wing sections (one symmetric and two cambered airfoils). A specially designed mechanical flapper was used, modelled on large migrating birds. It is shown that, under pitch leading conditions, good thrust generation can be obtained at a wide range of Strouhal numbers if the pitch angle oscillation is adjusted accordingly. Consequently, high thrust was measured at both the lowest and highest tested Strouhal numbers. Furthermore, the work demonstrates that the aerodynamic forces can be sensitive to the Reynolds number, depending on the camber of the wings. Under pitch lagging conditions, where the effective angle of attack amplitude is highest, the symmetric wing was affected by the Reynolds number, generating less thrust at the lowest tested Reynolds value. In contrast, under pure flapping conditions, where the effective angle of attack amplitude was lower but still significant, it was the cambered wings that demonstrated Reynolds sensitivity.     

Investigation of steady plasma actuation effect on aerodynamic coefficients of oscillating airfoil at low Reynolds number

In this work, numerical study of two dimensional laminar incompressible flow around an oscillating NACA0012 airfoil is proceeded using the open source code Open FOAM. Oscillatory motion types including pitching and flapping are considered. Reynolds number for these motions is assumed to be 12000 and effects of these motions and also different unsteady parameters such as amplitude and reduced frequency on aerodynamic coefficients are studied. For flow control on airfoil, dielectric barrier discharge plasma actuator is used in two different positions on airfoil and its effect is compared for the two types of considered oscillating motions. It is observed that in pitching motion, imposing plasma leads to an improvement in aerodynamic coefficients, but it does not have any positive effect on flapping motion.Also, for the amplitudes and frequencies investigated in this paper, the trailing edge plasma had a more desirable effect than other positions.     

Thrust augmentation of flapping airfoils in low Reynolds number flow using a flexible membrane

The unsteady aerodynamic thrust and aeroelastic response of a two-dimensional membrane airfoil under prescribed harmonic motion are investigated computationally with a high-order Navier–Stokes solver coupled to a nonlinear membrane structural model. The effects of membrane prestress and elasticity are examined parametrically for selected plunge and pitch–plunge motions at a chord-based Reynolds number of 2500. The importance of inertial membrane loads resulting from the prescribed flapping is also assessed for pure plunging motions. This study compares the period-averaged aerodynamic loads of flexible versus rigid membrane airfoils and highlights the vortex structures and salient fluid–membrane interactions that enable more efficient flapping thrust production in low Reynolds number flows.     

Aerodynamics of laminar separation flutter at a transitional Reynolds number

Experimental observations of self-sustained pitch oscillations of a NACA 0012 airfoil at transitional Reynolds numbers were recently reported. The aeroelastic limit cycle oscillations, herein labelled as laminar separation flutter, occur in the range 5.0×10⁴≤Re_c≤1.3×10⁵. They are well behaved, have a small amplitude and oscillate about θ=0°. It has been speculated that laminar separation leading to the formation of a laminar separation bubble, occurring at these Reynolds numbers, plays an essential role in these oscillations. This paper focuses on the Re_c=7.7×10⁴ case, with the elastic axis located at 18.6% chord. Considering that the experimental rig acts as a dynamic balance, the aerodynamic moment is derived and is empirically modelled as a generalized Duffing–van-der-Pol nonlinearity. As expected, it behaves nonlinearly with pitch displacement and rate. It also indicates a dynamically unstable equilibrium point, i.e. negative aerodynamic damping. In addition, large eddy simulations of the flow around the airfoil undergoing prescribed simple harmonic motion, using the same amplitude and frequency as the aeroelastic oscillations, are performed. The comparison between the experiment and simulations is conclusive. Both approaches show that the work done by the airflow on the airfoil is positive and both have the same magnitude. The large eddy simulation (LES) computations indicate that at θ=0°, the pitching motion induces a lag in the separation point on both surfaces of the airfoil resulting in negative pitching moment when pitching down, and positive moment when pitching up, thus feeding the LCO.