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.     

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.     

Unsteady response of airfoils due to small-scale pitching motion with considerations for foil thickness and wake motion

Unsteady pressures, forces, and pitching moments generated by foils experiencing vibratory motion in an incompressible, attached flow configuration are studied within this work. Specifically, two-dimensional, unsteady potential flow and unsteady Reynolds-Averaged Navier–Stokes calculations are performed on various Joukowski foils undergoing sinusoidal, variable amplitude, small-scale pitching motion at a chord-based Reynolds number of 10${}^6$ over a range of reduced frequencies between 0.01–100. These calculated results from both approaches are compared directly to predictions from implementing the Theodorsen model, which treats foils as infinitely thin, flat plates that shed a planar sheet of vorticity. The effects of relaxing these seemingly strict conditions are explored, and the particular terms which control the unsteady responses are identified and discussed. For increasing pitch amplitudes and reduced frequencies the shed wake is seen to become quite non-planar and to form coherent vortex structures. Despite this wake behavior, the normalized airfoil responses at the disturbance reduced frequency are seen to be largely unaffected. However, non-negligible responses are generated across a wide range of other frequencies. Potential flow calculations for symmetric Joukowski foils show that there is marginal effect of foil thickness at reduced frequencies less than one. For higher reduced frequency conditions however, the unsteady lift response is seen to experience both an amplification of level and a phase shift relative to the Theodorsen model. A specific augmenting expression is developed for this behavior through analysis within the potential flow framework.     

Buffeting in transonic flow prediction using time‐dependent turbulence model

In transonic flow conditions, the shock wave/turbulent boundary layer interaction and flow separations on wing upper surface induce flow instabilities, ‘buffet’, and then the buffeting (structure vibrations). This phenomenon can greatly influence the aerodynamic performance. These flow excitations are self‐sustained and lead to a surface effort due to pressure fluctuations. They can produce enough energy to excite the structure. The objective of the present work is to predict this unsteady phenomenon correctly by using unsteady Navier–Stokes‐averaged equations with a time‐dependent turbulence model based on the suitable (k–ε) turbulent eddy viscosity model. The model used is based on the turbulent viscosity concept where the turbulent viscosity coefficient (Cμ) is related to local deformation and rotation rates. To validate this model, flow over a flat plate at Mach number of 0.6 is first computed, then the flow around a NACA0012 airfoil. The comparison with the analytical and experimental results shows a good agreement. The ONERA OAT15A transonic airfoil was chosen to describe buffeting phenomena. Numerical simulations are done by using a Navier–Stokes SUPG (streamline upwind Petrov–Galerkin) finite‐element solver. Computational results show the ability of the present model to predict physical phenomena of the flow oscillations. The unsteady shock wave/boundary layer interaction is described. Copyright © 2005 John Wiley & Sons, Ltd.     

Leading edge vortex formation and detachment on a flat plate undergoing simultaneous pitching and plunging motion: Experimental and computational study

This study focuses on the formation and detachment of a leading edge vortex (LEV) appearing on an airfoil when its effective angle of attack is dynamically changed, inducing additional forces and moments on the airfoil. Experimental measurements of the time-resolved velocity field using Particle Image Velocimetry (PIV) are complemented by a computational study using an URANS (Unsteady Reynolds-Averaged Navier–Stokes) framework. In this framework a transition-sensitive Reynolds-stress model of turbulence, proposed by Maduta et al. (2018), which combines the near-wall Reynolds-Stress model by Jakirlic and Maduta (2015) and a phenomenological transition model governing the pre-turbulent kinetic energy by Walters and Cokljat (2008), is employed. Combined pitching and plunging kinematics of the investigated flat plate airfoil enable the effective inflow angle to be arbitrarily prescribed. A qualitative assessment of flow fields and a quantitative comparison of LEV characteristics in terms of its center position and circulation as well as an investigation of the mechanism causing the vortex to stop accumulating circulation revealed close agreement between the experimental and simulation results. Further considerations of the lift contribution from the pressure and suction side of the airfoil to the overall lift indicates that the qualitative lift evolution is reproduced even if the pressure side contribution is neglected. This reveals important characteristics of such airfoil dynamics, which can be exploited in future experimental studies, where direct aerodynamic force and moment measurements are greatly inhibited by dominating inertial forces.     

Kutta–Joukowsky theorem in viscous and unsteady flow

Nominally two-dimensional air flow over a thin flat plate at low Reynolds number is investigated. The primary objective is to experimentally determine with good accuracy the small magnitude lift force, generated by the plate at various angles of attack, by means of application of the Kutta–Joukowsky theorem where circulation is obtained from the line integral of velocity around the flat plate using non-invasive laser doppler velocimeter. Specific focus is on assessing applicability of the Kutta–Joukowsky theorem, originally theorized for inviscid and steady flow, in the post-stall region. At high angles of attack, due to severe flow separation from both the edges of the flat plate and occurrence of periodic vortex shedding, wake flow is found to be highly viscous, turbulent and unsteady. Nevertheless, the results show a remarkably good agreement with previous investigations in both the linear range and the non-linear range of the lift curve without any correction applied to the data. The line integral of velocity along the rectangular loop enclosing the flat plate shows that the vertical components, albeit smaller in magnitude, possess the same sign and hence are additive in contribution to the circulation, whereas the horizontal components possess opposite signs and hence are subtractive in their contribution to the circulation. The paper presents some interesting and hitherto undisclosed features of flow field around the flat plate.     

弯度翼型大迎角时分离涡流场的多平衡态现象

基于kω的SST两方程湍流模型,在时间域求解雷诺平均Navier-Stokes方程,模拟弯度翼型大迎角时的分离流动。通过给翼型施加一定形式的扰动,重点关注了翼型弯度对大迎角分离涡流场平衡态转移的影响。研究结果表明:与相同厚度20%以上的对称翼型相比,2%弯度的翼型出现分离涡流场平衡态转移的起始迎角变小2°左右,迎角区间变宽约1°;在厚度相对较小的NACA2416翼型上也发现上述分离涡平衡态转移现象。由此说明翼型弯度在一定程度上促使了分离涡平衡态的转移。     

UNSTEADY LIFT AND SOUND PRODUCED BY AN AIRFOIL IN A TURBULENT BOUNDARY LAYER

An analysis is made of the unsteady lift exerted on a stationary rigid body immersed in an incompressible, plane-wall turbulent boundary layer. The lift is expressed as a surface integral over the body involving theupwash velocity induced by the “free” vorticity Ω (found by taking explicit account of the interaction of the body with the flow and excluding the bound vorticity) and a harmonic function X₂that depends only on the shape of the body. The upwash velocity is the free-field velocity given in terms of Ω by the Biot–Savart formula, augmented by the velocity field of a conventional distribution of image vortices in the wall. The function X₂can be interpreted as the velocity potential of flow past the body, produced by motion of the wall at unit speed towards the body. Detailed predictions are made of the lift on a slender airfoil placed in the outer region of the boundary-layer. When the airfoil chord is large compared to the boundary-layer thickness, vortex shedding into the wake causes the magnitude of the net upwash velocity near the trailing edge to be small. The main contributions to the surface integral are then from the nose region, where the upwash velocity may be estimated independently of the fluctuations near the trailing edge. Analytical results for a thin plate airfoil of chord 2a at distance h from the wall show that the lift increases as a/h increases; it is ultimately independent of a and scales with the ratio of h to the hydrodynamic wavelength. Application is made to determine the sound generated by the airfoil in a weakly compressible boundary layer flow over a finite elastic plate.     

Experimental analysis of passive bio-inspired covert feathers for stall and post-stall performance enhancement

Technologies inspired by the functioning and behavior of biological beings are commonly developed for aircraft flight. Among the bio-inspired approaches that have grown in interest, particularly for unmanned aerial vehicle flight, is based on the behavior of bird’s cover feathers under higher angles of attack. The covert feathers, when activated by separated flows, promote lift increment that helps in certain maneuvers. This work investigates the benefit in the stall and post-stall performance of employing bio-inspired covert feathers devices attached to an airfoil’s upper surface. To fill the gaps in the recent technical literature, experimental analysis of an SD7003 airfoil was executed in a wind tunnel with the application of bio-inspired covert feathers of different shapes and tapes in three chordwise positions. The bio-inspired devices were conceived to resemble the feathers’ lightness and discrete-distribution along with the wing model. Experiments were carried out measuring the aerodynamic forces and moment at Reynolds number around 170,000 for static and dynamic ramp-up and hold pitching motion. It has been confirmed that the use of bio-inspired covert feathers brought benefits to the stall and post-stall behavior of the airfoil. The maximum lift has increased, and the transition from attached to stalled flow around the airfoil tends to be smoother when the devices were used. Four shapes for the bio-inspired devices and three positions in chordwise direction were considered. The best performance among the case was encountered for a jagged bio-inspired device taped at a quarter-chord position. Indeed, the most forward position for all the devices resulted in higher maximum lift and increment to the respective angle of attack. Ramp-up and hold wind tunnel tests also confirmed the best performance of jagged bio-inspired devices nearer the leading edge. The aerodynamic response to the pitching motion showed that the stall and post-stall regime occur much smoother, indicating that the approach presents good potential for dynamic stall or gust response passive control.

     

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。     

局部弹性翼型非定常分离的动力学特性

对在低雷诺数下局部弹性翼型绕流中, 局部弹性导致的自激振动所产生的复杂非定常流动分离现象和描述方法进行了分析. 采用ALE-CBS方法数值模拟了具有可动边界的绕流流场问题, 同时采用Galerkin方法求解局部弹性结构的控制方程. 着重研究了翼型的局部弹性对流动分离和翼型性能的影响, 并分别从Eulerian和Lagrangian的角度分析了局部弹性结构导致的不同非定常分离现象, 其中Lagrangian角度可以方便地揭示出局部弹性翼型大幅度提高升力的机理和流动中的能量迁移. 结果表明翼型的局部弹性对非定常分离和分离泡的演化过程有着明显的影响, 可以使得流体质点由主流获取动量实现再附, 并且在一定的攻角下可以将固定分离转变为移动分离, 从而明显地提高了翼型的升力.      

Heaving motions of a ram wing translating above water

Some high-speed marine vehicles utilize wings operating in the air but in close proximity to the water. At small clearances under the wings, and with augmentation of the incident airflow by front air-based propulsors, water surface deformations can influence the aerodynamic characteristics of such lifting surfaces. A dynamic model is developed in this paper for unsteady forces on a two-dimensional ram wing. The current model is based on the extreme-ground-effect theory for airflow and a linearized potential flow theory for water surface deformations. Parametric results are presented for aerodynamic characteristics of a flat plate, including a static lift coefficient, sensitivity on height, and added mass and damping coefficients in heaving motions. Variable parameters include relative speed, airflow augmentation, and frequency and amplitude of heaving oscillations. The developed method can be applied for more general dynamic modeling of high-speed air-supported marine craft.     

Two-dimensional incompressible unsteady airfoil theory—An overview

Two-dimensional unsteady airfoil theory has a history that dates back at least 75 years. Closed-form solutions have been obtained for airfoil loads due to step response (either to a pitch input or to a gust), due to airfoil oscillations in the frequency domain, and due to generalized airfoil motions in the Laplace domain. It has also been shown that the response of airloads to airfoil motions can be formulated in state space in terms of ordinary differential equations that approximate the airfoil and flow field response. The more recent of these models are hierarchical in that the states represent inflow shape functions that form a convergent series in a Ritz–Galerkin sense. A comparison of the various approaches with each other and with alternative computational approaches yields insight into both the methodologies and the solutions.     

An unsteady airfoil theory applied to pitching motions validated against experiment and computation

An inviscid theoretical method that is applicable to non-periodic motions and that accounts for large amplitudes and non-planar wakes (large-angle unsteady thin airfoil theory) is developed. A pitch-up, hold, pitch-down motion for a flat plate at Reynolds number 10,000 is studied using this theoretical method and also using computational (immersed boundary method) and experimental (water tunnel) methods. Results from theory are compared against those from computation and experiment which are also compared with each other. The variation of circulatory and apparent-mass loads as a function of pivot location for this motion is examined. The flow phenomena leading up to leading-edge vortex shedding and the limit of validity of the inviscid theory in the face of vortex-dominated flows are investigated. Also, the effect of pitch amplitude on leading-edge vortex shedding is examined, and two distinctly different vortex-dominated flows are studied using dye flow visualizations from experiment and vorticity plots from computation.     

振动翼型和襟翼的绕流特性研究

用数值模拟手段详细地研究了振动翼型和襟翼的绕流问题,数值模拟的出发方程为Euler和N-S方程,格式为Bcam-Warming格式的改进型。数值实验主要针对流场的二大特性进行的,即振动对激波的影响和振动对分离的抑制作用,结果表明:(1)随翼型或襟翼的振动激波强度和位置也相应地变化但这一变化滞后于攻角的变化;(2)振幅加大激波强度的变化和激波运动范围也加大;(3)振动频率越高对激波的影响反而较低频时要小;(4)流动条件的不同可使升力回线的走向发生变化;(5)振动对分离有明显的抑制作用。     

CFD结合降阶模型预测阵风响应

传统的阵风响应主要在频域内进行分析,气动载荷基于线性方法计算,不能考虑黏性和跨声速流动影响. 飞机设计需考虑不同频率和不同形状阵风的响应,基于CFD的阵风响应预测由于计算工况太多,工作量巨大. 本文发展了一种CFD结合非定常气动力ARMA(autoregressive-moving-averagemodel)降阶模型的阵风响应分析方法,CFD只要针对给定频率和形状的一种阵风响应进行计算,对获得的气动力时间历程运用线性最小二乘法参数辨识ARMA降阶模型的系数,则对任意频率和形状的阵风,代入降阶模型即可确定该阵风的响应,大大提高了计算效率. 为效验发展的方法,先计算NACA0012翼型在低马赫数0.11的阵风响应,通过对比CFD、ARMA降阶模型及早期发展的不可压阵风响应预测方法的结果,验证了方法的有效性. 再对比CFD、ARMA在跨声速马赫数0.8的阵风响应预测结果,证实所发展的方法对跨声速阵风响应预测亦是有效的.      

Exploration of plasma-based control for low-Reynolds number airfoil/gust interaction

Large-eddy simulation (LES) is employed to investigate the use of plasma-based actuation for the control of a vortical gust interacting with a wing section at a low Reynolds number. Flow about the SD7003 airfoil section at 4° angle of attack and a chord-based Reynolds number of 60,000 is considered in the simulation, which typifies micro air vehicle (MAV) applications. Solutions are obtained to the Navier–Stokes equations that were augmented by source terms used to represent body forces imparted by the plasma actuator on the fluid. A simple phenomenological model provided these body forces resulting from the electric field generated by the plasma. The numerical method is based upon a high-fidelity time-implicit scheme and an implicit LES approach which are used to obtain solutions on a locally refined overset mesh system. A Taylor-like vortex model is employed to represent a gust impinging upon the wing surface, which causes a substantial disruption to the undisturbed flow. It is shown that the fundamental impact of the gust on unsteady aerodynamic forces is due to an inviscid process, corresponding to variation in the effective angle of attack, which is not easily overcome. Plasma control is utilised to mitigate adverse effects of the interaction and improve aerodynamic performance. Physical characteristics of the interaction are described, and several aspects of the control strategy are explored. Among these are uniform and non-uniform spanwise variations of the control configuration, co-flow and counter-flow orientations of the directed force, pulsed and continuous operations of the actuator and strength of the plasma field. Results of the control situations are compared with regard to their effect upon aerodynamic forces. It was found that disturbances to the moment coefficient produced by the gust can be greatly reduced, which may be significant for stability and handling of MAV operations.     

FLOW STRUCTURE IN THE TURBULENT BOUNDARY LAYER OVER DIRECTIONAL RIBLETS SURFACES

本文采用时间解析的二维粒子图像测速技术,对零压力梯度光滑以及汇聚和发散沟槽表面平板湍流边界层统计特性和流动结构进行了研究.结果表明在垂直于汇聚和发散沟槽表面的对称平面内,相对于光滑壁面,发散沟槽壁面使当地边界层厚度、壁面摩擦阻力、湍流脉动、雷诺应力等明显减小;而汇聚沟槽壁面对湍流边界层特性和流动结构的影响正好相反,汇聚沟槽使壁面流体有远离壁面向上运动的趋势,因而导致边界层厚度增加了约43%;同时,在汇聚沟槽表面情况下流向大尺度相干结构更容易形成,这对减阻是不利的.此外,顺向涡数量在湍流边界层的对数区均存在一个极大值,发散沟槽表面所对应的极大值位置更靠近沟槽壁面,而在汇聚沟槽表面则有远离壁面的趋势,由顺向涡诱导产生的较强的喷射和扫掠运动会在湍流边界层中产生较强的剪切作用,顺向涡数量的减少是发散沟槽壁面当地摩擦阻力降低的主要原因.