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.     

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.     

Simulation of incompressible viscous flows around moving objects by a variant of immersed boundary‐lattice Boltzmann method

A variant of immersed boundary‐lattice Boltzmann method (IB‐LBM) is presented in this paper to simulate incompressible viscous flows around moving objects. As compared with the conventional IB‐LBM where the force density is computed explicitly by Hook's law or the direct forcing method and the non‐slip condition is only approximately satisfied, in the present work, the force density term is considered as the velocity correction which is determined by enforcing the non‐slip condition at the boundary. The lift and drag forces on the moving object can be easily calculated via the velocity correction on the boundary points. The capability of the present method for moving objects is well demonstrated through its application to simulate flows around a moving circular cylinder, a rotationally oscillating cylinder, and an elliptic flapping wing. Furthermore, the simulation of flows around a flapping flexible airfoil is carried out to exhibit the ability of the present method for implementing the elastic boundary condition. It was found that under certain conditions, the flapping flexible airfoil can generate larger propulsive force than the flapping rigid airfoil. Copyright © 2009 John Wiley & Sons, Ltd.     

High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion

High-fidelity numerical simulations with the spectral difference (SD) method are carried out to investigate the unsteady flow over a series of oscillating NACA 4-digit airfoils. Airfoil thickness and kinematics effects on the flapping airfoil propulsion are highlighted. It is confirmed that the aerodynamic performance of airfoils with different thickness can be very different under the same kinematics. Distinct evolutionary patterns of vortical structures are analyzed to unveil the underlying flow physics behind the diverse flow phenomena associated with different airfoil thickness and kinematics and reveal the synthetic effects of airfoil thickness and kinematics on the propulsive performance. Thickness effects at various reduced frequencies and Strouhal numbers for the same chord length based Reynolds number (=1200) are then discussed in detail. It is found that at relatively small Strouhal number (=0.3), for all types of airfoils with the combined pitching and plunging motion (pitch angle 20°, the pitch axis located at one third of chord length from the leading edge, pitch leading plunge by 75°), low reduced frequency (=1) is conducive for both the thrust production and propulsive efficiency. Moreover, relatively thin airfoils (e.g. NACA0006) can generate larger thrust and maintain higher propulsive efficiency than thick airfoils (e.g. NACA0030). However, with the same kinematics but at relatively large Strouhal number (=0.45), it is found that airfoils with different thickness exhibit diverse trend on thrust production and propulsive efficiency, especially at large reduced frequency (=3.5). Results on effects of airfoil thickness based Reynolds numbers indicate that relative thin airfoils show superior propulsion performance in the tested Reynolds number range. The evolution of leading edge vortices and the interaction between the leading and trailing edge vortices play key roles in flapping airfoil propulsive performance.     

Numerical investigation of transonic flow over deformable airfoil with plunging motion

In this article, the transonic inviscid flow over a deformable airfoil with plunging motion is studied numerically. A finite volume method based on the Roe scheme developed in a generalized coordinate is used along with an arbitrary Lagrangian-Eulerian method and a dynamic mesh algorithm to track the instantaneous position of the airfoil.The effects of different governing parameters such as the phase angle, the deformation amplitude, the initial angle of attack, the flapping frequency, and the Mach number on the unsteady flow field and aerodynamic coefficients are investigated in detail. The results show that maneuverability of the airfoil under various flow conditions is improved by the deformation. In addition, as the oscillation frequency of the airfoil increases, its aerodynamic performance is significantly improved.     

Bond graph modeling of a typical flapping wing micro-air-vehicle with the elastic articulated wings

In the present research, a new comprehensive model of a flexible articulated flapping wing robot using the bond graph approach is presented. The flapping kinematics of a two-section wing is introduced via the bond graph based approach on a hybrid mechanism providing amplitude and phase characteristics. The aerodynamic quasi-steady approach equipped with stall correlation is utilized according to the reduced flapping frequency and the angle of attack ranges. The local flow velocity and the wing position are calculated in both wing and body coordinates taking into account rotation and translation of the wing different parts. Estimation of the effective angle of attack is performed by calculating the instantaneous torque distribution on both wing sections. Aeroelastic modeling is employed in which the wing structure is assumed as an elastic Euler–Bernoulli beam at the leading edge with three linear torsional modes. In this novel integrated bond graph model, computation of the performance indices including the average lift and thrust, consumed and produced powers by flapping and mechanical efficiency are presented. Due to existence of the numerous geometric and kinematic parameters in articulated flexible flapping wing, such a model is essential for design and optimization. Consequently, an example of a typical parametric study and the results validation are carried out. It is indicated that the sensitivity of the bird performance to relative change in design variables would increase for out of phase flapping, second part stiffness, flapping amplitude, frequency and velocity respectively. It is interesting that by employing the reverse-phase flapping which is possible only via articulated wings, the maximum efficiency could be achieved. In addition, it is shown that adjusting the wing torsional stiffness is a crucial item in design of passive flapping robots. The key advantage of the two-section flapping wing is depicted as the controlling capability of the angle of attack in the outer part of the wing. Finally, the improved version of the bird is being addressed by approximately 15% progress in propulsive efficiency.

     

Wake structure and aerodynamic characteristics of an auto-propelled pitching airfoil

In the present study, we investigate the wake configuration as well as the flow aerodynamic and propulsive characteristics of a system equipped with a nature-inspired propulsion system. The study focuses on the effect of a set of pitching frequency and amplitude values on the flow behavior for a symmetric foil performing pitching sinusoidal rolling oscillations. The viscous, non-stationary flow around the pitching foil is simulated using ANSYS FLUENT 13. The foil movement is reproduced using the dynamic mesh technique and an in-house developed UDF (User Define Function). Our results show the influence of the pitching frequency and the amplitude on the wake. We provide the mechanisms relating the system behavior to the applied forces. The frequency varies from 1 to 400 Hz and the considered amplitudes are 18%, 24%, 30%, 37%, 53%, 82% and 114% of the foil chord.     

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.

     

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, 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.     

剪切流作用下层合梁非线性振动特性研究

针对剪切流中层合梁的大变形非线性振动问题, 采用高阶剪切变形锯齿理论和冯·卡门应变描述层合梁的变形模式和几何非线性效应, 构建了大变形层合梁非线性振动有限元数值模型; 采用基于任意拉格朗日?欧拉方法的有限体积法求解不可压缩黏性流体纳维-斯托克斯方程, 结合层合梁和流体的耦合界面条件建立了剪切流作用下层合梁流固耦合非线性动力学数值模型, 采用分区并行强耦合方法对层合梁的流致非线性振动响应进行了迭代计算. 研究了不同速度分布的剪切流作用下单层梁和多层复合材料梁的振动响应特性, 并验证了本文数值建模方法的有效性. 结果表明: 剪切流作用下单层梁的振动特性与均匀流作用下的情况不同, 梁的运动轨迹受剪切流影响向下偏斜, 随着速度分布系数增加, 尾部流场中的涡结构发生改变; 刚度比对剪切流作用下层合梁的振动特性有显著影响, 随着刚度比的增加, 层合梁振动的振幅增大, 主导频率下降, 运动轨迹由‘8’字形逐渐变得不对称; 发现了不同厚度比和铺层角度情况下, 层合梁存在定点稳定模式、周期极限环振动模式和非周期振动模式三种不同的振动模式, 改变层合梁铺层角度可实现层合梁周期极限环振动模式向非周期振动模式转变.      

二维扩压叶栅非定常分离流控制途径探索

二维扩压叶栅非定常黏性数值模拟结果表明,在一定攻角范围内,叶片前缘点附近的周期性吹吸气激励能有效控制混乱的非定常分离流．详细研究了非定常激励频率、幅值、位置对流场的影响．满足一定条件的非定常激励能够使流动由无序变为有序,时均气动性能提高。     

Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil

Flying and marine animals often use flapping wings or tails to generate thrust. In this paper, we will use the simplest flapping model with a sinusoidal pitching motion over a range of frequency and amplitude to investigate the mechanism of thrust generation. Previous work focuses on the Karman vortex street and the reversed Karman vortex street but the transition between two states remains unknown. The present numerical simulation provides a complete scenario of flow patterns from the Karman vortex street to reversed Karman vortex street via aligned vortices and the ultimate state is the deflected Karman vortex street, as the parameters of flapping motions change. The results are in agreement with the previous experiment. We make further discussion on the relationship of the observed states with drag and thrust coefficients and explore the mechanism of enhanced thrust generation using flapping motions.     

Flow-structure interactions of two parallel inverted flags with small separation distances in a water tunnel

In this study, the dynamics and flow fields of two parallel inverted flags are investigated using particle image velocimetry technology. The separation distance between two flags is less than two times the length of the flag, and the length ratio of these two flags is considered in the investigation. The results show that for the dynamic behaviours of two identical flags with a larger separation distance, the anti-phase and in-phase modes occur successively in the periodic oscillation as the flow velocity increases. The anti-phase and in-phase oscillations occur according to the formation position of the low-pressure and recirculation areas at different flow velocities. Moreover, a novel coupled flapping mode is observed at smaller separation distances: the contact anti-phase flapping mode, in which one flag oscillates with a large symmetric amplitude, and the other flag oscillates with a single-side large amplitude. As the separation distance further decreases, the in-phase mode appears for a larger range of flow velocity values, to avoid contact for the largest possible amplitude oscillation. Finally, as the length ratio decreases to 0.75, the oscillation frequency of the shorter flag becomes twice that of the longer flag, causing the in-phase and anti-phase oscillations to occur simultaneously in one cycle (i.e., the multi-phase flapping state). Interestingly, the two flags oscillate out of phase in the flapping apart process to avoid contact at a higher flow velocity. In general, the lower amplitude of the longer flag and two contact flags relative to that of an isolated flag clearly indicates the importance of two equal-length and non-contact flags for energy harvesting.     

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.     

Analysis of non-symmetrical flapping airfoils

Simulations have been done to assess the lift, thrust and propulsive efficiency of different types of non-symmetrical airfoils under different flapping configurations. The variables involved are reduced frequency, Strouhal number, pitch amplitude and phase angle. In order to analyze the variables more efficiently, the design of experiments using the response surface methodology is applied. Results show that both the variables and shape of the airfoil have a profound effect on the lift, thrust, and efficiency. By using non- symmetrical airfoils, average lift coefficient as high as 2.23 can be obtained. The average thrust coefficient and efficiency also reach high values of 2.53 and 0.61, respectively. The lift production is highly dependent on the airfoil＇s shape while thrust production is influenced more heavily by the variables. Efficiency falls somewhere in between. Two-factor interac- tions are found to exist among the variables. This shows that it is not sufficient to analyze each variable individually. Vorticity diagrams are analyzed to explain the results obtained. Overall, the S1020 airfoil is able to provide relatively good efficiency and at the same time generate high thrust and lift force. These results aid in the design of a better ornithopter＇s wing.     

Numerical analysis on the propulsive performance and vortex shedding of fish‐like travelling wavy plate

Numerical analysis is carried out to investigate viscous flow over a travelling wavy plate undergoing lateral motion in the form of a streamwise travelling wave, which is similar to the backbone undulation of swimming fish. The two‐dimensional incompressible Navier–Stokes equations are solved using the finite element technique with the deforming‐spatial‐domain/stabilized space–time formulation. The objective of this study is to elucidate hydrodynamic features of flow structure and vortex shedding near the travelling wavy plate and to get into physical insights to the understanding of fish‐like swimming mechanisms in terms of drag reduction and optimal propulsive performance. The effects of some typical parameters, including the phase speed, amplitude, and relative wavelength of travelling wavy plate, on the flow structures, the forces, and the power consumption required for the propulsive motion of the plate are analysed. These results predicted by the present numerical analysis are well consistent with the available data obtained for the wave‐like swimming motion of live fish in nature. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Effects of camber angle on aerodynamic performance of flapping-wing micro air vehicle

This study investigates the unsteady aerodynamic characteristics of the cambered wings of a flapping-wing micro air vehicle (FW-MAV) in hover. A three-dimensional fluid–structure interaction solver is developed for a realistic modeling of large-deforming wing structure and geometry. Cross-validation is conducted against the experimental results obtained also in the present study to establish more accurate analyses of cambered wings. An investigation is carried out on the unsteady vortex structures around the wings caused by the passive twisting motion. A parametric study is then conducted to evaluate the aerodynamic performance with respect to the camber angle at three different flapping frequencies including normal operating conditions. The camber angles producing the largest thrust and highest propulsive efficiency are estimated at each flapping frequency, and their effects on aerodynamic performance are analyzed in terms of the stroke phase. The timing and magnitude of the passive twisting motion, which are dependent on the camber angle at the operating frequency, greatly affects the unsteady vortex structure. Consequently, the camber angle designed at the operating frequency plays a key role in enhancing the aerodynamic performance of FW-MAVs.     

Frequency lock-in during nonlinear vibration of an airfoil coupled with van der Pol Oscillator

The frequency lock-in during the nonlinear vibration of a turbomachinery blade is modeled using a spring-mounted airfoil coupled with a van der Pol Oscillator (VDP) oscillator. The proposed reduced-order model uses the nonlinear VDP oscillator to represent the oscillatory nature of wake dynamics caused by the vortex shedding. The damping term in the VDP oscillator is assumed to be nonlinear. The coupled equations governing the pitch and plunge motion of an airfoil are used to approximate the vibration of a turbomachinery blade. Springs having cubic-order nonlinearity for their stiffnesses are used to mount the airfoil. The unsteady lift acting on the blade is modeled using a self-excited nonlinear wake oscillator. The model for wake dynamics takes into account the influence of blade inertia. The nonlinear coupled three degrees of freedom (dof) aeroelastic system is studied for instability resulting in the frequency lock-in phenomenon. The equations are transformed into non-dimensional form, and then the frequencies of the coupled system are plotted to demonstrate the frequency lock-in. Further, the method of multiple scales is used to derive modulation equations which represent the amplitude and phase of the oscillation. The results obtained using the method of multiple scales are compared with direct numerical solutions to verify the present modeling method. The steady-state amplitudes of the response are plotted against the detuning parameter, which represents the frequency response curve. Further, the sensitivity of non-dimensional parameters such as coupling coefficients, mass ratio, reduced velocity, static unbalance, structural damping coefficient and the ratio of uncoupled pitch and plunge natural frequencies on the frequency response is investigated. The study revealed that parameters such as mass ratio, reduced velocity, structural damping coefficient, and coupling coefficients have a stronger influence in suppressing the amplitude of vibration. Meanwhile, parameters such as the frequency ratio, static unbalance, reduced velocity, and mass ratio significantly affect the range of frequency in which the lock-in phenomenon happens. Further, linear perturbation analysis is done to understand the qualitative effect of the system parameters such as coupling coefficients, mass ratio, frequency ratio, and static unbalance on the range of lock-in.