Quarter Chord Research Articles

Entropy damping and Bulk Viscosity based artificial compressibility methods on dynamically distorting grids

Artificial Compressibility Methods (ACM) rely on an artificial equation that links the pressure and velocity fields to model incompressible flows. These hyperbolic/parabolic equations can rapidly converge to a ‘nearly’ divergence-free flow field in contrast to the methods based on the elliptic pressure Poisson equation. We compare the computational efficacy of two ACMs, namely, the Bulk Viscosity ACM (BVACM) and Entropically Damped Artificial Compressibility (EDAC) recently proposed in the literature. The methods implemented in the in-house high-order finite difference solver, COMPSQUARE, are validated for the test cases of a 2D doubly periodic shear layer (DPSL), a 3D Taylor Green Vortex (TGV), and 2D/3D NACA0012 airfoil pitching about the quarter chord. The efficacy of these methods was also tested on static and dynamic grids using conservative metrics. Although both ACMs yield competitive results, the divergence of the velocity field is found to be more prominent in the highly unsteady regions. BVACM resulted in (a) a superior divergence-free velocity field and (b) 20−38% higher maximum stable time than the EDAC, thereby increasing the computational speed. A higher value of the bulk viscosity coefficient, A, although ensures a stringent divergence-free velocity field, is shown to have minimal effect on the flow statistics and reduce the maximum stable time step. The parabolic–hyperbolic nature of the governing equations and the lack of dual time-stepping in BVACM and EDAC ensures that both these methods are highly scalable on massively parallel architectures. Since the energy equation is no longer required to compute the velocity field, both EDAC and BVACM approaches are found to be 8−10% faster than the weakly compressible Navier–Stokes simulations under the low-Mach number limit.

Wavelet analysis of the flow field around an oscillating airfoil undergoing pure pitching motion at low Reynolds number

This paper investigates the flow field around a NACA (National Advisory Committee for Aeronautics) 0012 airfoil undergoing pure pitching motion using continuous wavelet transform. Wind tunnel experiments were performed with a test-stand that provides a wide range of oscillation frequencies (f = 0–10 Hz). Sinusoidal pure pitching motion was considered with respect to the quarter chord for five reduced frequencies (K = 0.05, 0.1, 0.15, 0.2, and 0.3) at a Reynolds number of Re = 6 × 104. Mean angle of attack and pitch amplitude for all the cases were considered 0° and 6°, respectively. Unsteady surface pressure measurement was conducted, and the lift coefficient was calculated based on the phase-averaged surface pressure coefficient. The unsteady velocity distributions in the airfoil wake have been measured employing a pressure rake. The results indicate that the maximum value of the lift coefficient decreases by increasing the reduced frequency due to the “apparent mass” effects. For K = 0.05, close to the quasi-steady regime, the cl-α loop approximately follows the trend of the static case. Wavelet transform was used as a tool to examine the surface and wake pressure time series. Surface pressure wavelet transform plots indicate the presence of oscillation frequency and its superharmonics. Moreover, surface pressure wavelet analysis shows that the third and higher superharmonic frequencies are sensitive to the airfoil pitch angle during the oscillation cycle. Wavelet transform on wake reveals that the effective wake width gets smaller by increasing the reduced frequency. Furthermore, the trailing edge vortices get weaker by increasing the reduced frequency.

The effect of airfoil elasticity on quasistatic aerodynamics and divergence

Shape-morphing airfoils are of interest due to their benefits for aerodynamic efficiency and commonly involve chordwise elasticity of the airfoil. We aim to examine the influence of chordwise elasticity on the aerodynamic properties and stability in the quasistatic limit. We model a shape-morphing airfoil as two, rear and front, Euler–Bernoulli beams connected to a rigid support at an arbitrary location along its chord. This setup is mounted on a torsion spring and is exposed to a uniform flow. We model aerodynamic forces acting on the wing via thin airfoil theory and obtain the solution of the elastic deflection via regular asymptotic expansions. Then, we substitute this result into the moment balance equation to find the rotation angle. This procedure allows us to examine the influence of chord-wise elasticity on the lift, aerodynamic center, twist angle, and the onset of divergence. We examine these results in terms of the elastic axis location and the dimensionless ratio between aerodynamic moment to bending stiffness. The lift curve slope is smaller than 2π up to the hinge location of about 0.53 chord and is greater than 2π elsewhere. The chord-wise elasticity moves the aerodynamic center forwards and increases the twist angle. In addition, chord-wise elasticity is found to increase the onset of divergence relative to the rigid case. Moreover, unlike the rigid case, divergence also exists for hinges in the front quarter chord. Finally, we present several possible cases of an actuated airfoil validated by numerical simulations.

Experimental Study on Dynamic Stall of Airfoil in Rotor Reverse Flow Region

The large reverse flow region of the rotor with a high advance ratio is an important factor that affects the performance improvement of helicopters. This paper examines the dynamic stall of the airfoil in the reverse flow region of the rotor to develop a set of dynamic pressure measurement systems for the airfoil in the reverse low region. The pitch oscillation experiment of the NACA0018 airfoil in and out of the rotor reverse flow region has been carried out, and the influence of the airfoil motion parameters on dynamic stalls has been studied. The results show that the airfoil is more likely to stall in the reverse flow region under static conditions and that stall is invariant to the Reynolds number. After a stall occurs, the lift coefficient decreases more slowly with the increase of the angle of attack (about 10% of that in the forward flow state). Under the dynamic environment, in a pitching cycle, the quarter chord moment coefficient of the airfoil alternates between positive and negative frequently during reverse-blowing. The pitching oscillation in the reverse flow region is more sensitive to the changes in airfoil parameters than that under normal flow, and there is a marked difference. The alternating moment of the airfoil in the reverse flow region is significant: the greater the pitching amplitude, the greater the alternating moment. In the reverse-blowing state, with the increase in reduced frequency, the dynamic stall angle of attack increases more significantly.

Shape optimization of airfoil in ground effect based on free-form deformation utilizing sensitivity analysis and surrogate model of artificial neural network

Wings operate in proximity to surfaces for using ground effect to enhance lift-to-drag ratio, but the stability meets challenges. Changing airfoil shape could satisfy the requirement of stability and maximize lift-to-drag ratio, like performing single-objective optimization under a constraint. This research uses free-form deformation technique to adjust the airfoil curve by control points, and reduces the dimension of control variables by sensitivity analysis. Sampling airfoils and corresponding aerodynamics feeds an artificial neural network. Then, the neural network plays as a surrogate to predict fitness value for genetic algorithm execution. It is found that lift-to-drag ratio and static stability height are sensitive to vertical adjustments near the leading edge, one quarter chord point and trailing edge. The trained two-hidden-layer MLP generalizes well. The deformed optimum airfoil with S-shape camber line reduces lift-to-drag ratio to gain adequate static stability. The cause is that the aerodynamic center of pitch and that of altitude are moved upstream together, while the former’s interval is longer than the latter’s. The procedure provides reference for the optimization of airfoil under more states in ground effect zone, and the S-type deformation offers guidance for refinement on wing-in-ground stability.

Aeromechanical Analysis of a Next-Generation Mars Hexacopter Rotor

A three-dimensional (3D) aeromechanical analysis is carried out on the rotor blades of a 20 kg conceptual Mars Hexacopter. The objectives are to understand the aeroelastic behavior of its unique ultrathin low-Reynolds-number and high-Mach-number blades and study the interactions of structures, aerodynamics, and control moments in the Martian atmosphere. Beginning with structural analysis in vacuum, comprehensive analysis is carried out in hover and forward flight using 3D Finite Element Method (FEM), three-dimensional (2D) airfoil tables, and free wake. Natural frequencies of the rotor, elastic response of the blade, control moments at the root, airloads of blade sections, and 3D stresses are studied. Two types of designs are considered: a baseline design with pitch axis at the quarter chord and an unconventional design with the pitch axis moved to the midchord. Unusual nose-up elastic twist is observed on the rotor blades that appears to stem from the trapeze effect that counteracts the flattening effect of the propeller moment. By moving the pitch axis to midchord, the control moment is reduced by 30–40% without any noticeable adverse effect on stability due to the low Lock number. Both designs have maximum stresses well below the material limits, but the midchord design has a more uniform distribution of stress in general and lower levels of shear stress in particular. These and many other unconventional phenomena make Martian aeromechanics unique and ripe with possibilities of innovations tailored to its atmosphere.

Study of wake characteristics behind an oscillating NACA 0012 airfoil in deep dynamic stall regime

PurposeThis study aims to investigate the wake behind an oscillating airfoil at a various angle of incidence and Reynolds number in a deep dynamic stall condition.Design/methodology/approachNACA 0012 airfoil is allowed to undergo harmonic pitching motion about the quarter chord axis at Reynolds numbers of 0.5 * 105, 1.17 * 105, 1.7 * 105 and 2.12 * 105, and the reduced frequency of 0.1. The experiments are conducted at a set of mean and amplitude angle of attack that covered the angle of incidence from −5° to 25°. The wake rake is placed at a distance of one chord from the trailing edge of the airfoil.FindingsThe hysteresis of the flow during the upstroke and the downstroke motion are captured. The huge growth in the velocity defect and the wake thickness beyond the angle of attack of 15° explicate the appearance of the strong unsteady effects on the wake. The results also show that at the reduced frequency of 0.1, the wake structure is of drag producing type due to the momentum deficit.Originality/valueStreamwise velocity profile and the turbulent intensity profiles are presented to show the effects of Reynolds number and angle of incidence on the wake behind the oscillating airfoil at the reduced frequency of 0.1, and in the intermediate range of Reynolds number is the novelty of the study.

Investigation of Wing, Fuselage and Tail Design Parameters in Boeing and Airbus Aircraft

The study aims to examine the wing, fuselage and tail design parameters of Airbus and Boeing aircraft and to reveal the design criteria for the sizing of large commercial jets. Tin the study, the design and sizing data of 11 Airbus models and 14 Boeing models were compiled. The number of abreast seats, maximum seats, fuselage length, fuselage width, fineness ratio, tail section length, cockpit length and cargo compartment length are the main parameters studied about the fuselage design. Wing area, wingspan, aspect ratio, mean aerodynamic chord (MAC), taper ratio, dihedral angle, quarter chord sweep angle, and winglet lengths are the main parameters studied about the wing design. The area, span, aspect ratio, taper ratio, and quarter chord sweep angle of vertical and horizontal tail are the main parameters studied about the tail design. As a result of the study, exceptional designs and average design criteria for Airbus and Boeing aircraft have been revealed with the help of charts presented. In addition, the obtained linear correlations reveal that the MAC has about 0.14 times the wingspan and about 1.168 times the average chord length.

Experimental investigation of shock-buffet criteria on a pitching airfoil

An experimental investigation of the shock-buffet phenomenon subject to unsteady pitching supercritical airfoil around its quarter chord has been conducted in a transonic wind tunnel. The model was equipped with pressure taps connected to the fast response pressure-transducers. Measurements were conducted at different free-stream Mach number from 0.61 to 0.76. The principle goal of this investigation was to experimentally discuss the shock-buffet criterion over a SC(2)-0410 supercritical pitching related to the hysteresis loops of total drag and trailing edge pressure, the behaviour of the shock wave foot location, the pressure distribution over the upper surface, and by implementing the wavelet analysis of the normal force. To ensure capturing the buffet phenomenon by utilizing these criteria, a pressure port has been drilled exactly at the trailing edge of the airfoil where its output was used to detect the buffet phenomenon for different conditions. Visual representation of the flow using the shadow graph flow visualization technique for different test cases is further used to illustrate the unsteady shock wave motion. A comparative analysis of experimental measurements shows that the conducted criteria confirm each other when the buffet phenomenon occurs at the position of the oscillating cycle.

INFLUENCE OF SURFACE ROUGHNESS ON THE DYNAMIC STALL OF A ROTARY WING SECTION IN SUBSONIC FLOW

Wear involves the losses of some material from the surface and leads to the surface roughness. In the present work, the influence of surface roughness on the dynamic stall of a rotary wing section in subsonic flow has been investigated with different degree of surface roughness. The airfoil surface roughness was estimated using arithmetic mean roughness value (ISO-4287/1). For this purpose an indicial response method for unsteady, two dimensional flow is used to calculating the unsteady lift and pitching moment of NACA 0012 airfoil undergoing a pitching oscillation in the deep dynamic stall regime. Using the ANSYS-5.8 software as a source for the preliminary static data that required by the indicial method. The investigation is done through a number of test cases with different mean angles of attack, amplitude and reduced frequencies for airfoil oscillating around its quarter chord axis. The results include the time dependent behaviour and hysteresis loops of the lift and pitching moment for the airfoil with different degree of surface roughness. For rough airfoil an aerodynamic characteristic showed a reduction in the lift coefficient, separation point moved forward to the leading edge, the boundary layer reattachment take place at smaller angle of attack, the stall angle decrease and the pitching moment coefficient decrease as compared with smoother airfoil. So the periodic test must be done and re-coating the rotary wing if the surface roughness increased.

Hovering Helicopter Rotors Modeling Using the Actuator Line Method

An implementation of the actuator line method (ALM) is applied to a hovering helicopter rotor. This method, which is widely used for wind turbine simulations, replaces the rotor blades by momentum source terms in the unsteady Reynolds-averaged Navier–Stokes equations. The removal of the blade mesh significantly reduces the computational mesh size, thus lowering the computational cost. The ALM is presented along with some improvements, notably the choice and treatment of the projection kernel. A parameter sweep is performed showcasing the importance of proper selection of the Gaussian smearing coefficient for accurate rotor performance predictions with a value of scaled around a quarter chord in size. With this value, a new set of simulations on a refined mesh is performed and analyzed covering global rotor performance coefficients, sectional blade loading, tip vortex characteristics in terms of positions, circulation, and core radius. The ALM is benchmarked against an equivalent blade resolved case on the well-known S-76 rotor. Results confirm the appropriateness of the ALM model for a hovering rotor for main flow features and performance metrics, although there was a small loss of accuracy on the tip blade loading in the presence of a blade–vortex interaction. Finally, computational performances indicate an elapsed-time speed-up between 3 and 4× in addition to a greater parallel efficiency in favor of the ALM.

Numerical study of the propulsive performance of two-dimensional pitching foils at very high frequencies: scaling laws and turbulence effects

PurposeThis paper aims to analyze the propulsive performance of small-amplitude pitching foils at very high frequencies with double objectives: to find out scaling laws for the time-averaged thrust and propulsive efficiency at very high frequencies; and to characterize the Strouhal number above which the effect of turbulence on the mean values cannot be neglected.Design/methodology/approachThe thrust force and propulsive efficiency of a pitching NACA0012 foil at high reduced frequencies (k) and a Reynolds number Re = 16 000 are analyzed using accurate numerical simulations, both assuming laminar flow and using a transition turbulence model. The time-averaged results are validated with available experimental data for k up to about 12 (Strouhal number, St, up to 0.6). This study also compares the present numerical results with the predictions of theoretical models and existing numerical results. For a foil pitching about its quarter chord with amplitude α0 = 8o, the reduced frequency is varied here up to k = 30 (St up to 2), much higher than in any previous numerical or experimental work.FindingsFor this pitch amplitude, turbulence effects are found negligible for St ≲ 0.8, and affecting less than 10% to the time-averaged thrust coefficient for larger St Linear potential theory fails for very large k, even for the small pitch amplitude considered, particularly for the power coefficient, and therefore for the propulsive efficiency. It is found that St2 for large St, in agreement with recent models, and the propulsive efficiency decays as 1/k, in disagreement with the linear potential theory.Originality/valuePitching foils are increasingly studied as efficient propellers and energy harvesting devices. Their performance at very high reduced frequencies has not been sufficiently analyzed before. The authors provide accurate numerical simulations to discern when turbulence is relevant for the computation of the time-averaged thrust and efficiency and how their scaling with the reduced frequency is affected in relation to the laminar-flow predictions. This is relevant because some small-amplitude theoretical models predict high propulsive efficiency of pitching foils at very high frequencies over certain ranges of the structural parameters, and only very accurate numerical simulations may decide on these predictions.

Preliminary design of bionic flapping wing vehicle

This paper deals with the preliminary design of bionic flapping wing vehicle. The design is driven by its requirement and objective namely the maximum weight should be less than 0.5 kg with 1.5 m wingspan. In the conceptual design, the wing planform, wing structures and system of flapping mechanism will be considered to find the initial configuration and then continued the sizing of the flapping vehicle. The analysis of designed flapping vehicle is increasingly complex due to firstly the generation of time-dependent aerodynamic forces and moments from unsteady flow around the flapping wing, secondly, flexible wing structure which generates higher thrust may cause a structure failure and thirdly, a flapping mechanism system generating differential flapping motion for the vehicle maneuver. The aerodynamic analysis for given flapping motion model is carried out using Computational Fluid Dynamics method based the solution of unsteady Reynold Averaged Navier-Stokes equations and the structure analysis is conducted with the input of aerodynamic loads using Finite Element method to find critical stresses that may cause a structure failure. As a solution of differential flapping two controlled servos are used. The architecture of electrical system is made to analysis of the distribution of data signal and power. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The selection of system components is performed by considering weight constraint. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The wing platform has elliptical shape with airfoil maximum camber of 6% chord at a quarter chord. The outer body and wing are made of foam laminated by glass fibre with the foam density of 0.045 g/cm3. The horizontal tail is made of mylar film with density of 1.38 g/cm3 and its area of 168.3 cm2. As simulated results, the amount of total lift is 4.18 Newton generated at 6 Hz flapping frequency.

Unsteady Aerodynamic Characteristics of Pitching Flat Plates at Low Reynolds Numbers

A computational study is conducted on thin flat plates to simulate flows of Reynolds numbers at to provide understanding and guidance for micro air vehicles and other low-Reynolds-number airfoil designs. A synergistic effort between experiments and validated and computational fluid dynamics (CFD) tools were used as part of this study. The CFD tool used in this study is an established Reynolds-averaged Navier–Stokes (RANS) solver with a Spalart–Allmaras turbulence model and a correlation-based laminar–turbulent boundary-layer transition model. The computational method was validated against experimental data for flat plates under steady and unsteady kinematic conditions. The objective of the study was to understand unsteady characteristics of a thin flat plate undergoing harmonic pitching (no plunging) around the quarter chord under incompressible flow conditions. Pitching amplitudes were limited to 10 deg to ensure there was no effect of dynamic stall. The focus of this study is to characterize unsteady aerodynamics based on reduced frequency, which was varied between 0.005, 0.05, and 0.5. The unsteady condition of 0.05 was compared against experiments, 2-D RANS, and 3-D hybrid RANS/large-eddy simulation formulations. It was observed that the lift characteristics were reasonably well predicted by the CFD tools when compared to experimental observations. At a reduced frequency of , the pitching motion causes an apparent stabilization of vortices resulting in higher oscillatory lift amplitude than the static value. The 3-D RANS better predicted the pitching-moment characteristics compared to the 2-D RANS, attributed to the breakdown of the leading-edge vortex. It was observed that, although thinner flat-plate airfoils have a higher maximum lift coefficient compared to the thicker NACA 0012, they also produce higher instantaneous pitching moment.

Vortex moment map for unsteady incompressible viscous flows

In this paper, a vortex moment map (VMM) method is proposed to predict the pitching moment on a body from the vorticity field. VMM is designed to identify the moment contribution of each given vortex in the flow field. Implementing this VMM approach in starting flows of a NACA0012 airfoil, it is found that, due to the rolling up of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs), the unsteady nose-down moment about the quarter chord is higher than the steady-state value. The time variation of the unsteady moment is closely related to the LEVs and TEVs near the body and the VMM gives an intuitive understanding of how each part of the vorticity field contributes to the pitching moment on the body.

On the multiscale oscillations of a hinged plate under stratified coherent motions

Wind tunnel experiments are conducted to characterize and quantify the unsteady motions of a rigid plate under stratified turbulence containing spatially-varied, energetic vortices. The structure was able to oscillate around a vertical axis located at a quarter chord length from the leading edge. Vertically-oriented, von-Kármán vortices that varied in frequency and strength along the vertical span of the plate were imposed on the incoming flow using a variety of tapered cylinders. Telemetry and hotwire anemometry were used to characterize the motions of the plate, and wake at selected locations. Results show that the plate oscillations is dominated by two distinct modes. One of them, fp, corresponds to the mean flow-induced oscillation frequency; whereas the other, fv, is determined by the distribution of the vortex shedding cells from the non-uniform cylinders. These frequencies exhibited distinct trends with the distance from the cylinders, and the distribution of the incoming coherent motions, which were determined by the tapered ratio of the cylinders, Rt. In particular, fvincreased proportionally with Rt, whereas fp was inversely proportional with Rt in the near wake. These characteristic frequencies were constant in the far field with values dependent on Rt.

A modified Leishman–Beddoes model for airfoil sections undergoing dynamic stall at low Reynolds numbers

A modified Leishman–Beddoes (Leishman and Beddoes, 1989) model is proposed to predict the aerodynamic load responses of airfoils undergoing dynamic stall at low Reynolds, low Mach numbers and low to very high equivalent reduced pitch rates. The modifications include using Wagner function aerodynamics for the attached flow model, defining and using a time-varying reduced pitch rate, equating the time delays applied to the normal force, the separation point location and the vortex shedding and using Sheng and Galbraith’s dynamic stall onset criteria (Sheng et al., 2006).The steady and unsteady force and pitching moment measurements of three airfoils with distinct stall mechanisms (a flat plate, a NACA0012, and a NACA0018) are used to demonstrate the validity of this new model. Dynamic tests consist of oscillating the airfoils in pitch around the quarter chord with a mean angle A0=10∘ and with different prescribed reduced frequencies from k=0.015, to k=0.16, and amplitudes from, A=5° to 20°, at Reynolds numbers of the order of Re≃1.8×104. The resulting equivalent reduced pitch rates range from r′=0.001 to 0.06. The computations of the values of the different model parameters are demonstrated and it is observed that the values of the time delay parameters change continuously and smoothly with time instead of jumping discontinuously at discrete time instances as proposed by Leishman and Beddoes (1989).It is shown that the modified Leishman–Beddoes model is in good agreement with experiments for low to moderate equivalent reduced pitch rates (r′≤0.04). It also significantly improves the dynamic load prediction in this range of pitch rates, in comparison to the original Leishman–Beddoes model. Nevertheless, as for the original model, the modified model presented here becomes inaccurate at the highest equivalent reduced pitch rates of r′>0.05.

Reynolds Number Scaling of the Propulsive Performance of a Pitching Airfoil

Simulations of symmetrical NACA airfoils pitching about their quarter chord point are presented to investigate the scaling of their performance metrics, especially their dependence on Reynolds number. Variations in the Reynolds number (), pitch amplitude (), and thickness ratio () consistently show that the scaling for thrust, power, and efficiency derived in a recent study of heaving and pitching teardrop airfoils applies unchanged for the present case. The empirically determined coefficients in these scaling relationships are found to depend on the square root of Reynolds number, suggesting laminar flow scaling. The thrust and power are relatively insensitive to Reynolds numbers greater than about 16,000, but the efficiency continues to show a significant Reynolds number influence because it is strongly influenced by the drag on the airfoil.

Numerical investigation of the effect of airfoil thickness on onset of dynamic stall

Effect of airfoil thickness on onset of dynamic stall is investigated using large eddy simulations at chord-based Reynolds number of 200 000. Four symmetric NACA airfoils of thickness-to-chord ratios of 9 %, 12 %, 15 % and 18 % are studied. The three-dimensional Navier–Stokes solver, FDL3DI is used with a sixth-order compact finite difference scheme for spatial discretization, second-order implicit time integration and discriminating filters to remove unresolved wavenumbers. A constant-rate pitch-up manoeuver is studied with the pitching axis located at the airfoil quarter chord. Simulations are performed in two steps. In the first step, the airfoil is kept static at a prescribed angle of attack ($=4^{\circ }$). In the second step, a ramp function is used to smoothly increase the pitch rate from zero to the selected value and then the pitch rate is held constant until the angle of attack goes past the lift-stall point. The solver is verified against experiments for flow over a static NACA 0012 airfoil. Static simulation results of all airfoil geometries are also compared against XFOIL predictions with a generally favourable agreement. FDL3DI predicts two-stage transition for thin airfoils (9 % and 12 %), which is not observed in the XFOIL results. The dynamic simulations show that the onset of dynamic stall is marked by the bursting of the laminar separation bubble (LSB) in all the cases. However, for the thickest airfoil tested, the reverse flow region spreads over most of the airfoil and reaches the LSB location immediately before the LSB bursts and dynamic stall begins, suggesting that the stall could be triggered by the separated turbulent boundary layer. The results suggest that the boundary between different classifications of dynamic stall, particularly leading edge stall versus trailing edge stall, is blurred. The dynamic-stall onset mechanism changes gradually from one to the other with a gradual change in some parameters, in this case, airfoil thickness.

The Effect of Damping Coefficient, Spring Coefficient, and Mass Ratio on the Power Extraction Performance of a Semiactive Flapping Wing

The effect of varying damping coefficient C∗, spring coefficient K∗, and mass ratio M∗ on the semiactive flapping wing power extraction performance was numerically studied in this paper. A numerical code based on Finite Volume method to solve the two-dimensional Navier-Stokes equations and coupled with Finite Center Difference method to solve the passive plunging motion equation is developed. At a Reynolds number of 3400 and the pitching axis at quarter chord from the leading edge of the wing, the power extraction performance of the semiactive flapping wing with different damping coefficient, spring coefficient, and mass ratio is systematically investigated. The optimal set of spring coefficient is found at a value of 1.00. However, the variation of mass ratio M∗ cannot increase the maximum mean power coefficient and power efficiency, but it can influence the value of damping coefficient C∗ at which the wing achieves the maximum mean power coefficient and power efficiency. Moreover, insensitivity of the mean power coefficient and power efficiency to the variation of damping coefficient C∗ is observed for the wing with smaller mass ratio, which indicates the wing with smaller M∗ has better working stability.