Forward flight of a model butterfly: Simulation by equations of motion coupled with the Navier-Stokes equations

The forward flight of a model butterfly was studied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body oscillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the upstroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small negative horizontal force, whilst in the upstroke, the body angle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizontal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-massspecific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.     

A flow control mechanism in wing flapping with stroke asymmetry during insect forward flight

A theoretical modeling approach as well as an unsteady analytical method is used to study aerodynamic characteristics of wing flapping with asymmetric stroke-cycles in connection with an oblique stroke plane during insect forward flight. It is revealed that the aerodynamic asymmetry between the downstroke and the upstroke due to stroke-asymmetrical flapping is a key to understand the flow physics of generation and modulation of the lift and the thrust. Predicted results for examples of given kinematics validate more specifically some viewpoints that the wing lift is more easily produced when the forward speed is higher and the thrust is harder, and the lift and the thrust are generated mainly during downstroke and upstroke, respectively. The effects of three controlling parameters, i.e. the angles of tilted stroke plane, the different downstroke duration ratios, and the different angles of attack in both down- and up-stroke, are further discussed. It is found that larger oblique angles of stroke planes generate larger thrust but smaller lift; larger downstroke duration ratios lead to larger thrust, while making little change in lift and input aerodynamic power; and again, a small increase of the angle of attack in downstroke or upstroke may cause remarkable changes in aerodynamic performance in the relevant stroke.The project supported by the National Natural Science Foundation of China (10072066, 90305009) and the Chinese Academy of Sciences (KJCX-SW-L04, KJCX2-SW-L2)The English text was polished by Ron Marshall.     

N-S方程数值研究翼型对微型扑翼气动特性的影响

首先基于嵌套网格发展了一套适用于三维扑翼研究的非定常雷诺平均Navier-Stokes(RANS)方程数值模拟方法.为了解决微型扑翼在低马赫数下的收敛问题,使用了预处理方法,湍流模型为BL模型.在该方法的基础上,保持状态参数和扑翼表面形状一定的情况下,分别研究了一系列不同厚度、不同弯度的翼型对于微型扑翼气动特性的影响....     

Efficiency of an auto-propelled flapping airfoil

The present study deals with an investigation of the flow aerodynamic characteristics and the propulsive velocity of a system equipped with a nature inspired propulsion system. In particular, the study is aimed at studying the effect of the flapping frequency on the flow behavior. We consider a NACA0014 airfoil undergoing a vertical sinusoidal flapping motion. In contrast to nearly all previous studies in the literature, the present work does not impose any velocity on the inlet flow. During each iteration the outer flow velocity is computed after having determined the forces exerted on the airfoil. Forward motion may only be produced by flapping motion of the airfoil. This is more consistent with the physical phenomenon. The non-stationary viscous flow around the flapping airfoil is simulated using Ansys-Fluent 12.0.7. The airfoil movement is achieved using the deformable mesh technique and an in-house developed User Define Function (UDF). Our results show the influence of flapping frequency and amplitude on both the airfoil velocity and the propulsive efficiency. The resulting motion is contrasts to the applied forces. In the present study, the frequency ranges from 0.1 to 20 Hz while the airfoil amplitude values considered are: 10%, 17.5%, 25% and 40%.     

Aerodynamics and mechanisms of elementary morphing models for flapping wing in forward flight of bat

Large active wing deformation is a significant way to generate high aerodynamic forces required in bat's flapping flight. Besides the twisting, elementary morphing models of a bat wing are proposed, including wing-bending in the spanwise direction, wing-cambering in the chordwise direction, and wing area-changing. A plate of aspect ratio 3 is used to model a bat wing, and a three-dimensional unsteady panel method is used to predict the aerodynamic forces. It is found that the cambering model has great positive influence on the lift, followed by the area-changing model and then the bending model. Further study indicates that the vortex control is a main mechanism to produce high aerodynamic forces. The mechanisms of aerodynamic force enhancement are asymmetry of the cambered wing and amplification effects of wing area-changing and wing bending. Lift and thrust are generated mainly during downstroke, and they are almost negligible during upstroke by the integrated morphing model-wing.     

Time-resolved wake structure and kinematics of bat flight

We present synchronized time-resolved measurements of the wing kinematics and wake velocities for a medium sized bat, Cynopterus brachyotis, flying at low-medium speed in a closed-return wind tunnel. Measurements of the motion of the body and wing joints, as well as the resultant wake velocities in the Trefftz plane are recorded at 200 Hz (approximately 28–31 measurements per wing beat). Circulation profiles are found to be quite repeatable although variations in the flight profile are visible in the wake vortex structures. The circulation has almost constant strength over the middle half of the wing beat (defined according the vertical motion of the wrist, beginning with the downstroke). A strong streamwise vortex is observed to be shed from the wingtip, growing in strength during the downstroke, and persisting during much of the upstroke. At relatively low flight speeds (4.3 m/s), a closed vortex structure behind the bat is postulated.     

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.     

前后双扑翼水平距离及相位差对其气动性能的影响

通过在动态网格上求解Navier-Stokes方程,对前后双扑翼的非定常粘性流场进行了数值模拟和气动干扰分析,考察了前后翼不同水平距离和不同相位差对其气动力和气动效率的影响。结果表明,扑动前翼和静止后翼间的气动干扰在各种不同水平距离下都有利于气动特性的改善,但气动干扰的作用随着前后翼水平距离的增大而减弱;前后双翼扑动的相位差是影响气动性能的重要参数,两翼间的气动干扰是否有利则与相位差和水平距离有直接联系。     

Structural Analysis of a Dragonfly Wing

Dragonfly wings are highly corrugated, which increases the stiffness and strength of the wing significantly, and results in a lightweight structure with good aerodynamic performance. How insect wings carry aerodynamic and inertial loads, and how the resonant frequency of the flapping wings is tuned for carrying these loads, is however not fully understood. To study this we made a three-dimensional scan of a dragonfly (Sympetrum vulgatum) fore- and hindwing with a micro-CT scanner. The scans contain the complete venation pattern including thickness variations throughout both wings. We subsequently approximated the forewing architecture with an efficient three-dimensional beam and shell model. We then determined the wing’s natural vibration modes and the wing deformation resulting from analytical estimates of 8 load cases containing aerodynamic and inertial loads (using the finite element solver Abaqus). Based on our computations we find that the inertial loads are 1.5 to 3 times higher than aerodynamic pressure loads. We further find that wing deformation is smaller during the downstroke than during the upstroke, due to structural asymmetry. The natural vibration mode analysis revealed that the structural natural frequency of a dragonfly wing in vacuum is 154 Hz, which is approximately 4.8 times higher than the natural flapping frequency of dragonflies in hovering flight (32.3 Hz). This insight in the structural properties of dragonfly wings could inspire the design of more effective wings for insect-sized flapping micro air vehicles: The passive shape of aeroelastically tailored wings inspired by dragonflies can in principle be designed more precisely compared to sail like wings —which can make the dragonfly-like wings more aerodynamically effective.     

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.     

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.

     

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.     

An unconventional mechanism of lift production during the downstroke in a hovering bird (<Emphasis Type="Italic">Zosterops japonicus</Emphasis>)

An unconventional mechanism of ventral clap is exploited by hovering passerines to produce lift. Quantitative visualization of the wake flow, analysis of kinematics and evaluation of the transient lift force was conducted to dissect the biomechanical role of the ventral clap in the asymmetrical hovering flight of passerines. The ventral clap can first abate and then augment lift production during the downstroke; the net effect of the ventral clap on lift production is, however, positive because the extent of lift augmentation is greater than the extent of lift abatement. Moreover, the ventral clap is inferred to compensate for the zero lift production of the upstroke because the clapping wings induce a substantial elevation of the lift force at the end of the downstroke. Overall, our observations shed light on the aerodynamic function of the ventral clap and offer biomechanical insight into how a bird hovers without kinematically mimicking hovering hummingbirds.     

Aerodynamic forces and flow fields of a two-dimensional hovering wing

This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (α _A) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping are found to be more sensitive to changes in α _A than in Re. In fact, a subtle change in α _A may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient around α _A = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at α _A = 30° and a neutral wake structure at α _A = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering motion only, the unique force characteristics observed here, particularly their strong dependence on α _A, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics to help them to stay aloft and maneuver. An erratum to this article can be found at     

Design and development considerations for biologically inspired flapping-wing micro air vehicles

In this paper, the decade of numerical and experimental investigations leading to the development of the authors’ unique flapping-wing micro air vehicle is summarized. Early investigations included the study of boundary layer energization by means of a small flapping foil embedded in a flat-plate boundary layer, the reduction of the recirculatory flow region behind a backward-facing step by means of a small flapping foil, and the reduction or suppression of flow separation behind blunt or cusped airfoil trailing edges by flapping a small foil located in the wake flow region. These studies were followed by systematic investigations of the aerodynamic characteristics of single flapping airfoils and airfoil combinations. These unsteady flows were described using flow visualization, laser-Doppler velocimetry in addition to panel and Navier–Stokes computations. It is then shown how this flapping-wing database was used to conceive, design and develop a micro air vehicle which has a fixed wing for lift and two flapping wings for thrust generation. While animal flight is characterized by a coupled force generation, the present design appears to separate lift and thrust. However, in fact, the performance of one surface is closely coupled to the other surfaces.     

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.     

Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight

Aerodynamic forces and power requirements in forward flight in a bumblebee (Bombus terrestris) were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study (the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0–0.66). The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed (advance ratio 0.66), i.e. the power curve is J-shaped. Except at the highest flight speed, storing energy elastically can save power up to 20%–30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque (due to the smaller stroke amplitude and stroke frequency used), the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.The project supported by the National Natural Science Foundation of China (10232010) and the National Aeronautic Science fund of China (03A51049)The English text was polished by Xing Zhang.     

一种扑翼运动的模型实验及流场测量方法

俯旋、下拍、仰旋、上挥是一般昆虫运动的四个典型运动过程 ,本文通过研制三维和二维扑翼流场模拟装置以及相应的运动控制系统 ,实现了对昆虫扑翼飞行的上述过程的模拟。在测量方面 ,流场信息主要是通过自研制的 2D -DPIV(二维粒子速度成像仪 )来获得。该系统装备了高分辨率的高速CCD摄像机能够较为精细地动态量化流场 ,3维和 2维流场的动态流动显示以及量化测量都是通过它来实现。初步实验结果表明 ,模拟装置能成功地刻画昆虫翼的典型运动特征 ,2D -DPIV系统也能捕捉和反映强非定常特性的流场。本文还显示了实验中发现的一些有趣的现象 ,这些现象将作为我们进一步研究的重点     

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.     

The influence of the wake of a flapping wing on the production of aerodynamic forces

The effect of the wake of previous strokes on the aerodynamic forces of a flapping model insect wing is studied using the method of computational fluid dynamics. The wake effect is isolated by comparing the forces and flows of the starting stroke (when the wake has not developed) with those of a later stroke (when the wake has developed). The following has been shown. (1) The wake effect may increase or decrease the lift and drag at the beginning of a half-stroke (downstroke or upstroke), depending on the wing kinematics at stroke reversal. The reason for this is that at the beginning of the half-stroke, the wing ``impinges' on the spanwise vorticity generated by the wing during stroke reversal and the distribution of the vorticity is sensitive to the wing kinematics at stroke reversal. (2) The wake effect decreases the lift and increases the drag in the rest part of the half-stroke. This is because the wing moves in a downwash field induced by previous half-stroke's starting vortex, tip vortices and attached leading edge vortex (these vortices form a downwash producing vortex ring). (3) The wake effect decreases the mean lift by 6%–18% (depending on wing kinematics at stroke reversal) and slightly increases the mean drag. Therefore, it is detrimental to the aerodynamic performance of the flapping wing. The project supported by the National Natural Science Foundation of China (10232010) and the National Aeronautic Science Fund of China(03A51049) The English text was polished by Xing Zhang