Flows around two airfoils performing fling and subsequent translation and translation and subsequent clap

The aerodynamic forces and flow structures of two airfoils performing “fling and subsequent translation“ and “translation and subsequent clap“ are studied by numerically solving the Navier-Stokes equations in moving overset grids. These motions are relevant to the flight of very small insects. The Reynolds number, based on the airfoil chord length c and the translation velocity U, is 17. It is shown that: (1) For two airfoils performing fling and subsequent translation, a large lift is generated both in the fling phase and in the early part of the translation phase. During the fling phase,a pair of leading edge vortices of large strength is generated; the generation of the vortex pair in a short period results in a large time rate of change of fluid impulse, which explains the large lift in this period. During the early part of the translation, the two leading edge vortices move with the airfoils;the relative movement of the vortices also results in a large time rate of change of fluid impulse, which explains the large lift in this part of motion. (In the later part of the translation, the vorticity in the vortices is diffused and convected into the wake.) The time averaged lift coefficient is approximately 2.4 times as large as that of a single airfoil performing a similar motion. (2) For two airfoils performing translation and subsequent clap, a large lift is generated in the clap phase. During the clap, a pair of trailing edge vortices of large strength are generated; again, the generation of the vortex pair in a short period (which results in a large time rate of change of fluid impulse) is responsible for the large lift in this period. The time averaged lift coefficient is approximately 1.6 times as large as that of a single airfoil performing a similar motion. (3) When the initial distance between the airfoils (in the case of clap, the final distance between the airfoils) varies from 0.1 to 0.2c, the lift on an airfoil decreases only slightly but the torque decreases greatly. When the distance is about lc， the interference effects between the two airfoils become very small.     

A rotating elliptic airfoil in fluid at rest and in a parallel freestream

This paper reports results of DPIV measurements on a two-dimensional elliptic airfoil rotating about its own axis of symmetry in a fluid at rest and in a parallel freestream. In the former case, we examined three rotating speeds (Re _c,Ω = 400, 1,000 and 2,000), and in the later case, four rotating speeds (Ro _c,Ω = 2.4, 1.2, 0.6 and 0.4), together with two freestream velocities (Re _c,u  = 200 and 1,000) and two starting configurations of the airfoil (i.e., chord parallel to (α ₀ = 0°) or normal (α ₀ = 90°) to the freestream). Results show that a rotating airfoil in a stationary fluid produces two distinct types of vortex structures depending on the Reynolds number. The first type occurs at the lowest Reynolds number (Re _c,Ω = 400), where vortices shed from the two edges or tips of the airfoil dissipated quickly, resulting in the airfoil rotating in a layer of diffused vorticity. The second type occurs at higher Reynolds numbers (i.e., Re _c,Ω = 1,000 and 2,000), where the corresponding vortices rotated together with the airfoil. Due to the vortex suction effect, the torque characteristics are likely to be heavily damped for the first type because of the rapidly subsiding vortex shedding, and more oscillatory for the second type due to persistent presence of tip vortices. In a parallel freestream, increasing the tip-speed ratio (V/U) of the airfoil (i.e., decreasing the Rossby number, Ro _c,Ω) transformed the flow topology from periodic vortex shedding at Ro _c,Ω = 2.4 to the generation of a “hovering vortex” at Ro _c,Ω = 0.6 and 0.4. The presence of the hovering vortex, which has not been reported in literature before, is likely to enhance the lift characteristics of the airfoil. Freestream Reynolds number is found to have minimal effect on the vortex formation and shedding process, although it enhances shear layer instability and produces more small-scale flow structures that affect the dynamics of the hovering vortex. Likewise, initial starting configuration of the airfoil, while affecting the flow transient during the initial phase of rotation, has insignificant effect on the overall flow topology. Unfortunately, technical constraint of our apparatus prevented us from carrying out complimentary force measurements; nevertheless, the results presented herein, which are more extensive than those computed by Lugt and Ohring (1977), will provide useful benchmark data, from which more advanced numerical calculations can be carried out to ascertain the corresponding force characteristics, particularly for those conditions with the presence of hovering vortex.     

On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings

Insect wings are subjected to fluid, inertia and gravitational forces during flapping flight. Owing to their limited rigidity, they bent under the influence of these forces. Numerical study by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007) showed that a flexible wing is able to generate almost as much lift as a rigid wing during flapping. In this paper, we take a closer look at the relationship between wing flexibility (or stiffness) and aerodynamic force generation in flapping hovering flight. The experimental study was conducted in two stages. The first stage consisted of detailed force measurement and flow visualization of a rigid hawkmoth-like wing undergoing hovering hawkmoth flapping motion and simple harmonic flapping motion, with the aim of establishing a benchmark database for the second stage, which involved hawkmoth-like wing of different flexibility performing the same flapping motions. Hawkmoth motion was conducted at Re = 7,254 and reduced frequency of 0.26, while simple harmonic flapping motion at Re = 7,800 and 11,700, and reduced frequency of 0.25. Results show that aerodynamic force generation on the rigid wing is governed primarily by the combined effect of wing acceleration and leading edge vortex generated on the upper surface of the wing, while the remnants of the wake vortices generated from the previous stroke play only a minor role. Our results from the flexible wing study, while generally supportive of the finding by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007), also reveal the existence of a critical stiffness constant, below which lift coefficient deteriorates significantly. This finding suggests that although using flexible wing in micro air vehicle application may be beneficial in term of lightweight, too much flexibility can lead to deterioration in flapping performance in terms of aerodynamic force generation. The results further show that wings with stiffness constant above the critical value can deliver mean lift coefficient almost the same as a rigid wing when executing hawkmoth motion, but lower than the rigid wing when performing a simple harmonic motion. In all cases studied (7,800 ≤ Re ≤ 11,700), the Reynolds number does not alter the force generation significantly.     

Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing

This paper is motivated by the works of Dickinson et al. (Science 284:1954–1960, 1999) and Sun and Tang (J Exp Biol 205:55–70, 2002) which provided two different perspectives on the influence of wing–wake interaction (or wake capture) on lift generation during flapping motion. Dickinson et al. (Science 284:1954–1960, 1999) hypothesize that wake capture is responsible for the additional lift generated at the early phase of each stroke, while Sun and Tang (J Exp Biol 205:55–70, 2002) believe otherwise. Here, we take a more fundamental approach to study the effect of wing–wake interaction on the aerodynamic force generation by carrying out simultaneous force and flow field measurements on a two-dimensional wing subjected to two different types of motion. In one of the motions, the wing at a fixed angle of attack was made to follow a motion profile described by “acceleration-constant velocity-deceleration”. Here, the wing was first linearly accelerated from rest to a predetermined maximum velocity and remains at that speed for set duration before linearly decelerating to a stop. The acceleration and deceleration phase each accounted for only 10% of the stroke, and the stroke covered a total distance of three chord lengths. In another motion, the wing was subjected to the same above-mentioned movement, but in a back and forth manner over twenty strokes. Results show that there are two possible outcomes of wing–wake interaction. The first outcome occurs when the wing encounters a pair of counter-rotating wake vortices on the reverse stroke, and the induced velocity of these vortices impinges directly on the windward side of the wing, resulting in a higher oncoming flow to the wing, which translates into a higher lift. Another outcome is when the wing encounters one vortex on the reverse stroke, and the close proximity of this vortex to the windward surface of the wing, coupled with the vortex suction effect (caused by low pressure region at the center of the vortex), causes the net force on the wing to decrease momentarily. These results suggest that wing–wake interaction does not always lead to lift enhancement, and it can also cause lift reduction. As to which outcome prevails depend very much on the flapping motion and the timing of the reverse stroke.     

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.     

横摆振荡翼型动态气动掠效应试验研究

大型风力机设计对获取翼型更加全面、准确的动态载荷提出更高要求, 研究翼型横摆振荡动态气动特性具有重要意义. 借助"电子凸轮"技术和动态数据同步采集手段, 针对翼型动态“掠效应”首次开展了横摆振荡风洞试验研究, 研究表明: 横摆振荡翼型的气动曲线存在明显迟滞效应, 吸力面压力周期性波动是主要诱因, 且随着振荡频率、初始迎角和振幅的增大, 气动迟滞特性均增强; 升力和压差阻力随横摆角变化的迟滞回线呈"W"形, 俯仰力矩迟滞回线呈"M"形, 升力差量迟滞回线呈"$\infty$"形; 负行程下翼型气动力相对于正行程下的更高, 且负行程下翼型气动力随振荡频率的增大而略有增大, 正行程下则明显减小; 升力系数功率谱密度分布在振荡频率倍频处的能量集中的幅值随着振荡频率增大有增大趋势; 吸力面1.2%和40%弦长处压力的滞回特性较强, 是由于翼面剪切层涡和动态分离涡周期性发展、运动、破裂和重建; 振幅为$10^{\circ}$时, 升力迟滞曲线呈"$^{\wedge}$"形, 振幅为$30^{\circ}$ 时, 升力迟滞曲线呈"$^{\wedge\wedge\wedge}$"形.      

Impulse generated during unsteady maneuvering of swimming fish

The relationship between the maneuvering kinematics of a Giant Danio (Danio aequipinnatus) and the resulting vortical wake is investigated for a rapid, ‘C’-start maneuver using fully time-resolved (500 Hz) particle image velocimetry (PIV). PIV illuminates the two distinct vortices formed during the turn. The fish body rotation is facilitated by the initial, or “maneuvering” vortex formation, and the final fish velocity is augmented by the strength of the second, “propulsive” vortex. Results confirm that the axisymmetric vortex ring model is reasonable to use in calculating the hydrodynamic impulse acting on the fish. The total linear momentum change of the fish from its initial swimming trajectory to its final swimming trajectory is balanced by the vector sum of the impulses of both vortex rings. The timing of vortex formation is uniquely synchronized with the fish motion, and the choreography of the maneuver is addressed in the context of the resulting hydrodynamic forces.     

Time resolved PIV analysis of flow over a NACA 0015 airfoil with Gurney flap

A NACA 0015 airfoil with and without a Gurney flap was studied in a wind tunnel with Re _c = 2.0 × 10⁵ in order to examine the evolving flow structure of the wake through time-resolved PIV and to correlate this structure with time-averaged measurements of the lift coefficient. The Gurney flap, a tab of small length (1–4% of the airfoil chord) that protrudes perpendicular to the chord at the trailing edge, yields a significant and relatively constant lift increment through the linear range of the C _L versus α curve. Two distinct vortex shedding modes were found to exist and interact in the wake downstream of flapped airfoils. The dominant mode resembles a Kàrmàn vortex street shedding behind an asymmetric bluff body. The second mode, which was caused by the intermittent shedding of fluid recirculating in the cavity upstream of the flap, becomes more coherent with increasing angle of attack. For a 4% Gurney flap at α = 8°, the first and second modes corresponded with Strouhal numbers based on flap height of 0.18 and 0.13. Comparison of flow around ‘filled’ and ‘open’ flap configurations suggested that the second shedding mode was responsible for a significant portion of the overall lift increment.     

Large aerodynamic forces on a sweeping wing at low Reynolds number

The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically. After an initial start from rest, the wing is made to execute an azimuthal rotation (sweeping) at a large angle of attack and constant angular velocity. The Reynolds number (Re) considered in the present note is 480 (Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root). During the constant-speed sweeping motion, the stall is absent and large and approximately constant lift and drag coefficients can be maintained. The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows. Soon after the initial start, a vortex ring, which consists of the leading-edge vortex (LEV), the starting vortex, and the two wing-tip vortices, is formed in the wake of the wing. During the subsequent motion of the wing, a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength. This prevents the LEV from shedding. As a result, the size of the vortex ring increases approximately linearly with time, resulting in an approximately constant time rate of the first moment of vorticity, or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wingspan. The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force. The project supported by the National Natural Science Foundation of China (10232010)     

A new bionic MAV＇s flapping motion based on fruit fly hovering at low Reynolds number

On the basis of the studies on the high unsteady aerodynamic mechanisms of the fruit fly hovering the aerodynamic advantages and disadvantages of the fruit fly flapping motion were analyzed. A new bionic flapping motion was proposed to weaken the disadvantages and maintain the advantages, it may be used in the designing and manufacturing of the micro air vehicles (MAV’s). The translation of the new bionic flapping motion is the same as that of fruit fly flapping motion. However, the rotation of the new bionic flapping motion is different. It is not a pitching-up rotation as the fruit fly flapping motion, but a pitching-down rotation at the beginning and the end of a stroke. The numerical method of 3rd-order Roe scheme developed by Rogers was used to study these questions. The correctness of the numerical method and the computational program was justified by comparing the present CFD results of the fruit fly flapping motion in three modes, i.e., the advanced mode, the symmetrical mode and the delayed mode, with Dickinson’s experimental results. They agreed with each other very well. Subsequently, the aerodynamic characteristics of the new bionic flapping motion in three modes were also numerically simulated, and were compared with those of the fruit fly flapping. The conclusions could be drawn that the high unsteady lift mechanism of the fruit fly hovering is also effectively utilized by this new bionic flapping. Compared with the fruit fly flapping, the unsteady drag of the new flapping decreases very much and the ratio of lift to drag increases greatly. And the great discrepancies among the mean lifts of three flapping modes of the fruit fly hovering are effectively smoothed in the new flapping. On the other hand, this new bionic flapping motion should be realized more easily. Finally, it must be pointed out that the above conclusions were just drawn for the hovering flapping motion. And the aerodynamic characteristics of the new bionic flapping motion in forward flight are going to be studied in the next step. The project supported by the National Natural Science Foundation of China (10232010, 10032060, 90605005).     

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     

顺桨风力机塔叶干涉翼型非稳气动力时频特性

由于风力机叶片与塔筒流场相互干涉,实际气动力与理想情况存在较大差异,这种干涉作用造成的气动力差异给叶片与塔筒结构可靠性带来不可忽视的影响.以翼型DU91-W2-250为研究对象,采用瞬态数值分析与本征正交分解方法,考虑叶片和塔筒流场相互干涉作用,分析顺桨工况翼型非稳气动力时频特性及其影响规律,量化不同雷诺数下塔叶相对位置及几何参数对气动力均值、波动幅度和频率的影响程度,通过流场模态能量分布形态分析,揭示流场干涉对气动力的影响机制.结果表明,翼型气动中心至塔筒几何中心的垂直距离、水平距离以及塔筒直径相对于翼型弦长的无量纲参数y*,x*和D*对气动力均有不同程度影响,其中y*对升阻力系数均值影响最大,对频率无明显影响,y*绝对值越大,C_l均值越接近单翼型C_l值,y*绝对值越小升阻力系数波动幅度越大,y*从-12增大到12,升力系数均值最小值为-0.48,最大值为1.16;x*减小和D*增大,反向阻力均值增大,波动幅度增大,波动频率略有下降,当x*小于临界值5时,带塔翼型阻力均值反向;在计算范围内,带塔翼型升力系数均值相对于单翼型升力系数最大偏差为...     

Exploration of the rotational power consumption of a rigid flapping wing

The development of Micro Air Vehicles with flapping wings is inspired from the observation and study of natural flyers such as insects and birds. This article explores the rotational power consumption of a flapping wing using a mechanical flapper at Re ≃ 4,500. This mechanical flapper is simplified to a 2D translation and a rotation in a water tank. Moreover, the wing kinematics are reduced to a linear translation and a rotation for the purpose of our study. We introduce the notion of non-ideal flapper and associated non-ideal rotational power. Such non-ideal devices are defined as consuming power for adding and removing mechanical power to and from the flow, respectively. First, we use a traditional symmetrical wing kinematic which is a simplified kinematic inspired from natural flyers. The lift coefficient of this flapping is about C _L ≃ 1.5. This symmetrical wing kinematic is chosen as a reference. Further, wing kinematics with asymmetric rotations are then compared with this one. These new kinematics are built using a differential velocity defined according to the translational kinematics, a time lag and a distance, r _kp. The analogy of this distance is discussed as a key point to follow along the chord. First, the wing kinematics are varied keeping a similar shape for the profiles of the angular velocity. It is shown that when compared to the reference wing kinematic, a 10% reduction in the rotational power is obtained whilst the lift is reduced by 9%. Second, we release the limitation to a similar shape for the profiles of the angular velocity leading to a novel shape for the angular velocity profile named here as “double bump” profile. With these new wing kinematics, we show that a 60% reduction in the non-ideal rotational power can be achieved whilst the lift coefficient is only reduced by 1.7%. Such “double bump kinematics” could then be of interest to increase the endurance of Micro Air Vehicles.     

Dynamic wind loads and wake characteristics of a wind turbine model in an atmospheric boundary layer wind

An experimental study was conducted to characterize the dynamic wind loads and evolution of the unsteady vortex and turbulent flow structures in the near wake of a horizontal axis wind turbine model placed in an atmospheric boundary layer wind tunnel. In addition to measuring dynamic wind loads (i.e., aerodynamic forces and bending moments) acting on the wind turbine model by using a high-sensitive force-moment sensor unit, a high-resolution digital particle image velocimetry (PIV) system was used to achieve flow field measurements to quantify the characteristics of the turbulent vortex flow in the near wake of the wind turbine model. Besides conducting “free-run” PIV measurements to determine the ensemble-averaged statistics of the flow quantities such as mean velocity, Reynolds stress, and turbulence kinetic energy (TKE) distributions in the wake flow, “phase-locked” PIV measurements were also performed to elucidate further details about evolution of the unsteady vortex structures in the wake flow in relation to the position of the rotating turbine blades. The effects of the tip-speed-ratio of the wind turbine model on the dynamic wind loads and wake flow characteristics were quantified in the terms of the variations of the aerodynamic thrust and bending moment coefficients of the wind turbine model, the evolution of the helical tip vortices and the unsteady vortices shedding from the blade roots and turbine nacelle, the deceleration of the incoming airflows after passing the rotation disk of the turbine blades, the TKE and Reynolds stress distributions in the near wake of the wind turbine model. The detailed flow field measurements were correlated with the dynamic wind load measurements to elucidate underlying physics in order to gain further insight into the characteristics of the dynamic wind loads and turbulent vortex flows in the wakes of wind turbines for the optimal design of the wind turbines operating in atmospheric boundary layer winds.     

钝后缘风力机翼型的环量控制研究

钝后缘风力机翼型具有结构强度高、对表面污染不敏感等优点,但其较大的阻力系数使得翼型的整体气动特性不够理想. 利用环量控制方法对钝后缘风力机翼型进行了流动控制,以改善钝后缘风力机翼型的气动特性,减弱尾迹区脱体涡强度. 通过对钝后缘风力机翼型环量控制方法进行相关的数值模拟,对比研究了环量控制方法的增升减阻效果, 研究了环量控制下翼型升阻力特性随射流动量系数的变化规律,并对不同射流动量系数下环量控制方法的气动品质因子和控制效率进行了分析. 研究结果表明:环量控制方法能够大幅提升钝后缘风力机翼型的升力系数,同时有效地降低翼型的阻力系数; 翼型的升力系数随射流动量系数的增大而增大,表现出很明显的分离控制阶段和超环量控制阶段的变化规律; 射流能耗的功率系数随射流动量系数的增大而增大,且增长速率逐渐增大;实施环量控制方法后叶片的输出功率同样随射流动量系数增大而增大,但增长速率逐渐降低. 总体来说,环量控制方法可以有效地改善钝后缘风力机翼型的气动特性以及功率输出特性,在大型风力机流动控制中具有很好的应用前景.      

低雷诺数下柔性翼型气动性能分析

基于流固耦合方法对吸力面5% 至95% 弦长处为三段柔性结构的NACA0012 翼型绕流进行了数值模拟,研究了不同弹性模量下柔性翼型的气动性能和结构响应. 结果表明：在大攻角下,翼面变形影响着翼型表面的非定常流场,起到延缓失速和提高升力的作用;失速后柔性翼的升力系数下降得较为缓慢,且柔性越大,升力系数下降得越平缓;适当减小弹性模量能够提高翼型的气动性能,然而弹性模量过小反而不利于翼型气动性能的提升,并且翼面会产生大幅度的振动.     

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.     

Effect of vortex shedding in unsteady aerodynamic forces for a low Reynolds number stationary wing at low angle of attack

This study elucidates the relation between wake vortex shedding and aerodynamic force fluctuations for a low Reynolds number wing from time resolved particle image velocimetry (TR-PIV) experimental measurements. The results reveal a periodic lift and drag variation within the shedding cycle and resolve the frequencies of those fluctuations from a proper orthogonal decomposition (POD) and power spectral density (PSD) analysis. To show the effect of vortex shedding on the body force fluctuations, the evolution of instantaneous aerodynamic forces is compared to the pressure field of the fluid flow and to the vortical structures in the wake of the airfoil. A six step model describing the vortex-force relation is proposed. It shows that changes in lift such as maximum lift and minimum lift are associated with the detachment of a vortex. It also shows that the minimum or local minimum drag value is obtained at the onset formation of a vortex on the airfoil wake. Similarly, the maximum or local maximum drag is obtained at the onset formation of the saddle on the airfoil wake. The model further explains the asymmetry observed in the unsteady drag force evolution. The model can be used to optimize flow control and fluid-structure interaction applications.     

可变形儒可夫斯基翼型亚音速非定常气动力的研究

对于翼面变形速度远小于来流速度情况下的儒可夫斯翼型亚音速绕流问题,通过仿射变换将可压缩流动转换成不可压缩流动,将解析解和离散涡方法相结合计算变形机翼的不可压缩流动速度场,再利用逆变换得到变形机翼的亚音速流动速度场,进而分析非定常气动力特性,建立变形机翼的准定常升力系数和非定常附加升力系数在可压缩和不可压缩两种状态下的简单近似对应关系。计算结果显示变形机翼的非定常气动升力近似等于准定常计算结果叠加上虚拟质量力导致的非定常附加升力,该非定常附加升力随翼型变形速率呈线性关系,由机翼当前时刻飞行姿态、翼型及其变形速率确定,与具体变形历史过程无关。低来流马赫数时虚拟质量力导致的非定常效应显著,高亚音速流动时准定常升力起主导作用。同时还分析了不同马赫数下机翼往复变形过程中升力的变化特性,指出尽管高亚音速变形机翼的气动升力近似等于准定常气动升力,但不能忽视非定常附加升力的影响,非定常附加升力将导致完成往复变形需要外界输入正比于Ma∞/[(1-Ma2∞)]的功。     

Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil

A laminar separation bubble occurs on the suction side of the SD7003 airfoil at an angle of attack α =  4–8° and a low Reynolds number less than 100,000, which brings about a significant adverse aerodynamic effect. The spatial and temporal structure of the laminar separation bubble was studied using the scanning PIV method at α =  4° and Re = 60,000 and 20,000. Of particular interest are the dynamic vortex behavior in transition process and the subsequent vortex evolution in the turbulent boundary layer. The flow was continuously sampled in a stack of parallel illuminated planes from two orthogonal views with a frequency of hundreds Hz, and PIV cross-correlation was performed to obtain the 2D velocity field in each plane. Results of both the single-sliced and the volumetric presentations of the laminar separation bubble reveal vortex shedding in transition near the reattachment region at Re = 60,000. In a relatively long distance vortices characterized by paired wall-normal vorticity packets retain their identities in the reattached turbulent boundary layer, though vortices interact through tearing, stretching and tilting. Compared with the restricted LSB at Re = 60,000, the flow at Re = 20,000 presents an earlier separation and a significantly increased reversed flow region followed by “huge” vortical structures.