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.     

Experimental study of pitching and plunging airfoils at low Reynolds numbers

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

基于涡量矩理论的绕振荡水翼涡动力学分析

文章采用标准k-ω SST湍流模型和动网格技术, 实现了绕俯仰振荡NACA66水翼非定常流动结构与水动力特性的数值模拟, 并基于有限域涡量矩理论定量表征了局部旋涡结构对水翼动力特性的影响. 研究结果表明: 在水翼升程阶段, 当攻角较小时, 层流向湍流的转捩点由水翼尾缘向前缘移动; 在较大攻角时, 顺时针尾缘涡?TEV在水翼吸力面上生成并向前缘发展, 同时与吸力面上的顺时针前缘涡?LEV融合发展为附着在整个吸力面上的新前缘涡?LEV, 新的?LEV与逆时针尾缘涡+TEV相互作用直至完全脱落, 直接导致了水翼的动力失速, 在回程阶段, 绕振荡水翼的流场结构逐渐由湍流转变为层流. 基于有限域涡量矩理论的定量分析发现, 有限域内附着的?LEV和?TEV提供正升力, 当?LEV发展覆盖整个吸力面时对升力的贡献最大, 占总升力近50%, 而+TEV提供负升力. 同时发现, 有限域内各旋涡内部的不同区域提供的升力有正有负; 而逸出有限域的旋涡内部不同区域提供的升力方向均保持一致, 其中顺时针涡提供正升力, 而逆时针涡提供负升力. 在失速阶段, 域外旋涡整体对升力贡献较小且存在小幅波动, 体现了流动的非定常性.      

Measurement of parallel blade–vortex interaction at low Reynolds numbers

In this study parallel blade–vortex interaction for a Schmidt-propeller configuration has been examined using particle image velocimetry (PIV). This tandem configuration consists of a leading airfoil (forefoil), used to generate a vortical wake of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs) through a pitching or plunging motion, and a trailing airfoil (hindfoil), held fixed with a specified angle of attack and vertical spacing in its wake. The hindfoil incidence (loading) and not the vertical spacing to the incoming vortical wake has been found to dictate the nature of the interaction (inviscid vs. viscous). For cases where the vortex–blade offset is small and the hindfoil is loaded, vortex distortion and vortex-induced separations are observed. By tracking the circulation of the LEV and TEV, it has been found that the vortices are strengthened for the tandem arrangement and in certain cases dissipate quicker in the wake when interacting with the hindfoil. Time-averaged forces obtained using a standard control-volume analysis are then obtained and used to evaluate these vortex-interaction cases. A subsequent analysis of the varying pressure distribution over the suction side of the hindfoil is performed by integrating the Navier–Stokes equations through the velocity field. This allows for a direct comparison of the vortex-induced loading for the various configurations.     

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)     

Parameter dependence of vortex interactions on a two-dimensional plunging plate

The structure and dynamics of the flow field created by a plunging flat-plate airfoil are investigated at a chord Reynolds number of 10,000 while varying plunge amplitude and Strouhal number. Digital particle image velocimetry measurements are used to characterize the shedding patterns and the interactions between the leading- and trailing-edge vortex structures (LEV and TEV), resulting in the development of a wake classification system based on the nature and timing of interactions between the leading- and trailing-edge vortices. The streamwise advancement of the LEV during a plunge cycle and its resulting interaction with the TEV is primarily dependent on reduced frequency; however, for Strouhal numbers above approximately 0.4, significant changes are observed in the formation of vortices shed from the leading and trailing edges, as well as the circulation of the leading-edge vortex. The functional form of the relationship between leading-edge vortex circulation and Strouhal number suggests that the Strouhal number dependence is more specifically a manifestation of the effective angle of attack. Comparison with low-Reynolds-number studies of plunging airfoil aerodynamics reveals a high degree of consistency and suggests applicability of the classification system beyond the range examined in the present work.     

Particle image velocimetry investigation of flow over unsteady airfoil with trailing-edge strip

The flow over a flapped NACA 0012 airfoil, oscillated slightly through the static-stall angle, was investigated by using particle image velocimetry, and was supplemented by surface pressure and dynamic-load measurements. A significant increase in the dynamic lift force and nose-down pitching moment was observed. The most pronounced flow phenomenon was the formation and detachment of an energetic leading-edge vortex compared to the no-flapped airfoil. The details of the underlying physical mechanisms responsible for the various light-stall flow processes were provided via the instantaneous velocity and vorticity fields measurements. In contrast to the Gurney flap, the inverted trailing-edge strip led to an improved negative damping while a reduced lift force. The addition of an inverted strip always led to the appearance of a Karman-type vortex shedding street immediately downstream of the strip over the entire oscillation cycle.     

合成射流对失速状态下翼型大分离流动控制的试验研究

为研究低速状态合成射流在抑制翼型气流分离和推迟失速方面的控制机理, 开展了NACA0021 翼型失速特性射流控制的风洞试验研究. 通过系统性的模型测力、翼型瞬态流场粒子图像测速和边界层速度测定的对比试验, 深入探索了合成射流各参数对翼型失速特性控制效果的影响规律. 试验结果表明射流偏角在翼型升力和失速迎角控制方面的效果对射流动量系数较为敏感: 当动量系数较大时, 近切向射流的控制效果更好. 射流动量系数为0.033 时, 偏角30°的射流使得翼型升力系数峰值提高23.56%, 失速迎角增大5°; 而动量系数较小时, 偏角较大的射流能够获得最佳控制效果. 射流动量系数为0.0026 时, 法向射流对翼型最大升力系数控制效果最好(提高9.2%).      

Lift enhancement through flexibility of plunging wings at low Reynolds numbers

In this paper the combined effect of two mechanisms for lift enhancement at low Reynolds numbers are considered, wing oscillations and wing flexibility. The force, deformation and flow fields of rigid and flexible low aspect ratio (AR=3) and high aspect ratio (AR=6) wings oscillating at a fixed post-stall angle of attack of 15° and amplitude of 15% of chord are measured. The force measurements show that flexibility can increase the time-averaged lift coefficient significantly. For low aspect ratio wings the maximum lift coefficient across all Strouhal numbers was C_l=1.38 for the rigid wing as opposed to C_l=2.77 for the flexible wing. Very similar trends were observed for the high aspect ratio wings. This increase is associated with significant deformation of the wing. The root is sinusoidally plunged with small amplitude but this motion is amplified along the span resulting in a larger tip motion but with a phase lag. The amount it is amplified strongly depends on Strouhal number. A Strouhal number of Sr_c=1.5 was selected for detailed flow field measurements due to it being central to the high-lift region of the flexible wings, producing approximately double the lift of the rigid wing. For this Strouhal number the rigid wings exhibit a Leading Edge Vortex (LEV) ring. This is where the clockwise upper-surface LEV pairs with the counter-clockwise lower-surface LEV to form a vortex ring that self-advects upstream and away from the wing's upper surface. Conversely the deformation of the flexible wings inhibits the formation of the LEV ring. Instead a strong upper-surface LEV forms during the downward motion and convects close to the airfoil upper surface thus explaining the significantly higher lift. These measurements demonstrate the significant gains that can be achieved through the combination of unsteady aerodynamics with flexible structures.     

PIV study of flow around unsteady airfoil with dynamic trailing-edge flap deflection

The flow around an oscillating NACA 0015 airfoil with prescheduled trailing-edge flap motion control was investigated by using particle image velocimetry (PIV). Aerodynamic load coefficients, obtained via surface pressure measurements, were also acquired to supplement the PIV results. The results demonstrate that upward flap deflections led to an improved negative peak pitching moment coefficient C _m,peak, mainly as a consequence of the increased suction pressure on the lower surface of the flap. The behavior of the leading-edge vortex (LEV) was largely unaffected. Its strength was, however, reduced slightly compared to that of the uncontrolled airfoil. No trailing-edge vortex was observed. For downward flap deflection, the strength of the LEV was found to be slightly increased. A favorable increase in C _l,max, as a consequence of downward flap-induced positive camber effects, accompanied by a detrimental increase in the nose-down C _m,peak, due to the large pressure increase on the lower surface of the flap, was also observed.     

Unsteady airfoil with a harmonically deflected trailing-edge flap

The effects of a harmonically deflected trailing-edge flap, actuated at different start times and amplitudes but with frequency different from the airfoil motion, on the aerodynamic loads of an oscillating NACA 0015 airfoil were investigated experimentally at Re=2.51×10⁵. Both in-phase and 180° out-of-phase flap deflections, relative to the airfoil motion, were tested. The results show that there was a large change in the hysteretic behavior of the dynamic load loops, and that the formation and detachment of the leading-edge vortex (LEV) were not affected by the flap motion, while the low pressure signature of the vortex was affected by the flap actuation start time. The later the flap actuation the larger the change in the strength of the LEV. The present flap control scheme was also found to be as effective as that achieved by a pulsed ramp flap motion, but with a reduced number of control parameters.     

基于涡流发生器的翼型失速流动控制及雷诺数效应影响研究

针对所设计的三角形涡流发生器开展用于翼型失速流动控制的风洞实验研究,重点讨论涡流发生器几何参数、方向角、安装位置及实验雷诺数等因素对翼型失速流动控制的影响。实验结果表明:涡流发生器作用下,在干净翼失速迎角后能够形成一个升力几乎不随迎角变化的相对稳定的高升力状态,抑制了失速流动的发生,与此同时阻力大幅下降;本文所设计的涡流发生器方向角过大时会削弱翼型失速流动控制的效果;同一涡流发生器作用下雷诺数过大其失速流动控制效果会急剧恶化,第一种涡流发生器控制翼型失速的雷诺数有效范围略宽于第二种涡流发生器。     

翼型大攻角状态下表面吸气驻涡增升的数值模拟实验

用数值模拟方法给出了翼型大攻角状态表面吸气后绕翼型流动的某些新现象并对流场的特性进行了机理性研究,其中包括吸气对翼型背风面分离涡的驻涡增升作用;吸气孔位置对流场的影响;不同吸气强度以及间歇式吸气的增升效应。数值模拟的出发方程为N-S方程,差分格式为Beam-Warming格式。数值实验表明:(1)吸气可有效地提高翼型大攻角状态下的升力;(2)在一定吸气强度下吸气可使翼型背风面上涡的非定常脱落现象消失从而起到驻涡作用;(3)吸气孔位置在翼面的中部附近增升效果较好;(4)在一定范围内吸气强度越强其升力越高;(5)间歇式吸气也可提高平均升力,但引起升力的波动。     

Aeroelastic interactions and trajectory selection of vortex gusts impinging upon Joukowski airfoils

The dynamically-coupled interactions of vortex gusts encountering a symmetric Joukowski airfoil on linear elastic supports is formulated analytically and evaluated numerically using a time-dependent conformal mapping. The Brown and Michael framework models the unsteady shedding of vorticity from the airfoil into the wake, and the aeroelastic motion of the airfoil is analyzed using quasi-steady, apparent mass, and fully-unsteady aerodynamic models. Special attention is paid to the influences of the strength of the incident vortex and the airfoil natural frequency on the initial upstream placement of a vortex gust that achieves direct impingement. These results are weakly sensitive to the initial vortex position in the limits of either large or small structural natural frequency, and the initial vertical vortex position to achieve impingement changes monotonically with the vortex strength. A comparison of the numerical model with available experimental vortex gust measurements over stationary airfoils highlights the appropriate use of the point-vortex model for inviscid vortex–airfoil interaction problems without significant vortex strength decay, which occurs for predominantly viscous interactions of close vortex–airfoil encounters.     

对称翼型低雷诺数小攻角升力系数非线性现象研究

采用Rogers发展的三阶Roe格式,求解非定常不可压N-S方程,时间方向为二阶精度双时间步方法, 数值模拟了对称翼型SD8020低雷诺数(Re=40000,100000)条件下,流场层流分离涡结构和升力系数随攻角的变化．同试验比较证明了数值模拟的正确性．通过对数值模拟时均化流场结果的详细分析,发现对称翼型在小雷诺数0°攻角附近出现的层流分离泡,其内部结构和演化规律都不同于经典层流分离泡模型,从而提出了一种后缘层流分离泡模型．并应用该模型对对称翼型小攻角低雷诺数流场特性以及升力系数非线性效应的形成机理进行了研究和解释．     

基于三路舵机驱动的扑翼飞行模型气动特性研究

扑动而形成非定常气动现象是扑翼飞行过程中产生高升力的主要原因。本文以Ellington实验的鹰蛾翅膀为原形,设计扑翼实验及数值计算模型。通过压差传感器对翅膀模型上翼面固定位置进行测压,分析前缘涡的产生及脱落情况(考虑动压效应)。测量上下翼面固定位置处的压差,揭示扑翼飞行中产生高升力的主要原因。利用烟风洞观察扑翼模型周围流场结构及特殊涡产生变化情况。另外,根据Ellington提供的升力关系式估算了扑翼模型在一个周期内的平均升力。最后,基于三维欧拉方程对扑翼飞行气动特性进行数值模拟,计算结果与实验吻合良好。     

Dynamics of co-rotating vortices in a flow around a bio-inspired corrugated airfoil

Bio-inspired corrugated airfoils show favourable aerodynamic characteristics such as high coefficient of lift and delayed stall at low Reynolds numbers. Two-dimensional (2D) direct numerical simulation has been performed here on a corrugated airfoil at various angles of attack (0°, +5°, -5°) and Reynolds number of 280 to 6700. The objective is to analyse the pressure variation inside the corrugations and correlate it to the vortex movement across the corrugations and the overall aerodynamic characteristics of the corrugated airfoil. The flow characteristics have been examined based on the local Strouhal numbers in the corrugations of the airfoil. It is observed that the pressure variation in each corrugation is the result of vortex merging and separation in the corrugation which plays a major role in changing the flow characteristics. The Strouhal number of the flow is dictated by the most dominant local Strouhal number. The numerical results are further compared with experimental results obtained using particle image velocimetry, and the two set of results are found to match well. These results are significant because they elucidate the effect of corrugation, angle of attack, and Reynolds number on flow over a corrugated airfoil.     

EXPERIMENTAL INVESTIGATION ON LIFT INCREMENT OF A PLASMA CIRCULATION CONTROL AIRFOIL

利用等离子体激励器发展了新型的环量增升技术,并对二维NACA0012翼型绕流实施控制。由于NACA0012翼型为尖后缘构型,环量增升装置由2个非对称型介质阻挡放电等离子体激励器构成。一个等离子体激励器贴附于翼型吸力面靠近后缘处,其诱导的壁面射流沿来流方向指向下游;另一个等离子体激励器贴附于翼型压力面靠近后缘处,其诱导的壁面射流与来流方向相反指向上游。在风洞中通过时间解析二维PIV系统对翼型绕流流场进行了测量,基于翼型弦长的雷诺数Re=20 000。结果表明在等离子体激励器的控制下,翼型压力面靠近后缘处可以形成一个定常回流区,从而起到虚拟气动外形的作用,因此翼型吸力面的流场得到加速,压力面的流场得到减速,使得翼型压力面的吸力以及压力面的压力都得到增加,进而增加了翼型的环量。风洞天平测力实验进一步验证了该环量增升技术的有效性。在整个攻角范围内,施加控制的翼型的升力系数相比没有控制的工况有明显的提高。     

On the high-frequency response of unsteady lift and circulation: A dynamical systems perspective

In this paper, we consider the unsteady aerodynamics of a two-dimensional airfoil as a dynamical system whose input is the angle of attack (or airfoil motion) and output is the lift force. Based on this view, we discuss the evolution of lift and circulation from a purely dynamical perspective through step response, frequency response, transfer function, etc. In particular, we point to the relation between the high-frequency gain of the transfer function and the physics of the development of lift and circulation. Based on this view, we show that the circulatory lift dynamics is different from the circulation dynamics. That is, we show that the circulatory lift is not lift due to circulation. In fact, we show that the circulatory–non-circulatory classification is arbitrary. By comparing the steady and unsteady thin airfoil theory, we show that the circulatory lift possesses some acceleration (added-mass) effects. Finally, we perform simulations of Navier–Stokes equations to show that a non-circulatory maneuver in the absence of a free stream induces viscous circulation over the airfoil.     

基于相交不稳定性的尾流自消散机翼实验研究

飞机尾流是复杂的流动现象,相关控制的研究常采用简化模型,抓住主要矛盾进行尾流不稳定性的学术探索. 采用结构化矩形机翼模型,通过添加扰流片来模拟襟翼的一种作动方式,引入一对与主翼涡反向的小涡,以期诱发尾涡的瑞利-路德维希相交不稳定性. 改变模型在水槽中的拖曳速度以及机翼攻角,采用粒子图像速度场仪定量研究单主翼尾涡发展特性以及双涡相互作用特性. 研究表明,未添加扰流片时,尾涡环量在45 个翼展内相对于初始环量衰减了10%;而添加了扰流片的实验中,在较好的实验参数组合情况下,主翼尾涡环量较初始环量降低35%~45%. 结果表明添加适当扰流片产生的反向小涡能诱发与主翼尾涡的相交不稳定性,在尾流涡系中引入自消散机制,加速机翼尾涡的消散过程,达到提早消弱尾涡的目的.