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.     

Dynamic stall behavior from unsteady force measurements

A direct force measurement technique employing piezoelectric load cells is used to experimentally investigate a two-dimensional airfoil (NACA 0012) undergoing dynamic stall. The load cells are installed at each end of the airfoil and give the force response in two directions in the plane normal to the airfoil axis during oscillations. Experiments are carried out at a Reynolds number based on the airfoil chord equal to 7.7×10⁴, and at four reduced frequencies, k=0.005, 0.01, 0.02, and 0.04. Phase-averaged lift of the airfoil undergoing dynamic stall is presented. It is observed that hysteresis loops of the lift occur both when the airfoil is pitched to exceed its static stall limit and when it is still within its static stall limit, and they grow in size with increasing k at the same pitching mean angle of attack and pitching amplitude. Both the lift and the drag induced by the pitching motion are further analyzed using the methods of higher order correlation analysis and continuous wavelet transforms to undercover their nonlinear and nonstationary features, in addition to classical FFT-based spectral analysis. The results are quantitatively illustrated by an energy partition analysis. It is found that the unsteady lift and drag show opposite trends when the airfoil undergoes transition from the pre-stall regime to the full-stall regime. The degree of nonlinearity of the lift increases, and the lift show a nonstationary feature in the light-stall regime, while the nonlinearity of the drag decreases, and the drag shows nonstationary feature in both the light-stall and the full-stall regimes. Furthermore, the lift and the drag have significant nonlinear interactions as shown by the correlation analysis in the light-stall regime.     

Prediction of high frequency gust response with airfoil thickness effects

The unsteady lift forces that act on an airfoil in turbulent flow are an undesirable source of vibration and noise in many industrial applications. Methods to predict these forces have traditionally treated the airfoil as a flat plate. At higher frequencies, where the relevant turbulent length scales are comparable to the airfoil thickness, the flat plate approximation becomes invalid and results in overprediction of the unsteady force spectrum. This work provides an improved methodology for the prediction of the unsteady lift forces that accounts for the thickness of the airfoil. An analytical model was developed to calculate the response of the airfoil to high frequency gusts. The approach is based on a time-domain calculation with a sharp-edged gust and accounts for the distortion of the gust by the mean flow around the airfoil leading edge. The unsteady lift is calculated from a weighted integration of the gust vorticity, which makes the model relatively straightforward to implement and verify. For routine design calculations of turbulence-induced forces, a closed-form gust response thickness correction factor was developed for NACA 65 series airfoils.     

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.      

An investigation into the effects of unsteady parameters on the aerodynamics of a low Reynolds number pitching airfoil

The growing applications of low Reynolds number (LRN) operating vehicles impose the need for accurate LRN flow solutions. These applications usually involve complex unsteady phenomena, which depend on the kinematics of the vehicle such as pitching, plunging, and flapping of a wing. The objective of the present study is to address the issues related to LRN aerodynamics of a harmonically pitching NACA0012 airfoil. To this end, the influence of unsteady parameters, namely, amplitude of oscillation, d, reduced frequency, k, and Reynolds number, Re, on the aerodynamic performance of the model is investigated. Computational fluid dynamics (CFD) is utilized to solve Navier–Stokes (N–S) equations discretized based on the Finite Volume Method (FVM). The resulting instantaneous lift coefficients are compared with analytical data from Theodorsen’s method. The simulation results reveal that d, k, and Re are of great importance in the aerodynamic performance of the system, as they affect the maximum lift coefficients, hysteresis loops, strength, and number of the generated vortices within the harmonic motion, and the extent of the so-called figure-of-eight phenomenon region. Thus, achieving the optimum lift coefficients demands a careful selection of these parameters.     

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.     

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。     

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。     

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.     

Input-output reduced-order modeling of unsteady flow over an airfoil at a high angle of attack based on dynamic mode decomposition with control

Due to the damage caused by stall flutter, the investigation and modeling of the flow over a wind turbine airfoil at high angles of attack are essential. Dynamic mode decomposition (DMD) and dynamic mode decomposition with control (DMDc) are used to analyze unsteady flow and identify the intrinsic dynamics. The DMDc algorithm is found to have an identification problem when the spatial dimension of the training data is larger than the number of snapshots. IDMDc, a variant algorithm based on reduced dimension data, is introduced to identify the precise intrinsic dynamics. DMD, DMDc and IDMDc are all used to decompose the data for unsteady flow over the S809 airfoil that are obtained by numerical simulations. The DMD results show that the dominant feature of a static airfoil is the adjacent shedding vortices in the wake. For an oscillating airfoil, the DMDc results may fail to consider the effect of the input and have an identification problem. IDMDc can alleviate this problem. The dominant IDMDc modes show that the intrinsic flow for the oscillating case is similar to the unsteady flow over the static airfoil. Moreover, the input–output model identified by IDMDc can give better predictions for different oscillating cases than the identified DMDc model.     

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.      

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.     

Influence of heat transfer on the aerodynamic performance of a plunging and pitching NACA0012 airfoil at low Reynolds numbers

The unsteady low Reynolds number aerodynamics phenomena around flapping wings are addressed in several investigations. Elsewhere, airfoils at higher Mach numbers and Reynolds numbers have been treated quite comprehensively in the literature. It is duly noted that the influence of heat transfer phenomena on the aerodynamic performance of flapping wings configurations is not well studied. The objective of the present study is to investigate the effect of heat transfer upon the aerodynamic performance of a pitching and plunging NACA0012 airfoil in the low Reynolds number flow regime with particular emphasis upon the airfoil's lift and drag coefficients. The compressible Navier–Stokes equations are solved using a finite volume method. To consider the variation of fluid properties with temperature, the values of dynamic viscosity and thermal diffusivity are evaluated with Sutherland's formula and the Eucken model, respectively. Instantaneous and mean lift and drag coefficients are calculated for several temperature differences between the airfoil surface and freestream within the range 0–100 K. Simulations are performed for a prescribed airfoil motion schedule and flow parameters. It is learnt that the aerodynamic performance in terms of the lift C_L and drag C_D behavior is strongly dependent upon the heat transfer rate from the airfoil to the flow field. In the plunging case, the mean value of C_D tends to increase, whereas the amplitude of C_L tends to decrease with increasing temperature difference. In the pitching case, on the other hand, the mean value and the amplitude of both C_D and C_L decrease. A spectral analysis of C_D and C_L in the pitching case shows that the amplitudes of both C_D and C_L decrease with increasing surface temperature, whereas the harmonic frequencies are not affected.     

Qualitative features of high lift hovering dynamics and inertial manifolds

Hovering aerodynamics, such as that practiced by dragonflys, hummingbirds, and certain other small insects, utilizes special patterns of vorticity to generate high lift flows. Such lift as we measure it computationally on the airfoil surface is in good agreement with downstream thrust measured in the physical laboratory. In this paper we examine the qualitative signatures of this dynamical system. A connection to the theory of inertial manifolds, more specifically the instance of time-dependent slow manifolds, is initiated. Additional interest attaches to the fact that in our compact computational domain, the forcing is on the boundary. Because of its highly oscillatory nature, in this dynamics one proceeds rapidly up the bifurcation ladder at relatively low Reynolds numbers. Thus, aside from its intrinsic interest, the hover model provides an attractive vehicle for a better understanding of dynamical system attractor dynamics and inertial manifold theory.The authors appreciate grants of NAS computational resources at the NASA Ames Research Laboratories with the support of the NASA Lewis Research Laboratory.     

High-lift airfoil trailing edge separation control using a single dielectric barrier discharge plasma actuator

Control of flow separation from the deflected flap of a high-lift airfoil up to Reynolds numbers of 240,000 (15 m/s) is explored using a single dielectric barrier discharge (DBD) plasma actuator near the flap shoulder. Results show that the plasma discharge can increase or reduce the size of the time-averaged separated region over the flap depending on the frequency of actuation. High-frequency actuation, referred to here as quasi-steady forcing, slightly delays separation while lengthening and flattening the separated region without drastically increasing the measured lift. The actuator is found to be most effective for increasing lift when operated in an unsteady fashion at the natural oscillation frequency of the trailing edge flow field. Results indicate that the primary control mechanism in this configuration is an enhancement of the natural vortex shedding that promotes further momentum transfer between the freestream and separated region. Based on these results, different modulation waveforms for creating unsteady DBD plasma-induced flows are investigated in an effort to improve control authority. Subsequent measurements show that modulation using duty cycles of 50–70% generates stronger velocity perturbations than sinusoidal modulation in quiescent conditions at the expense of an increased power requirement. Investigation of these modulation waveforms for trailing edge separation control similarly shows that additional increases in lift can be obtained. The dependence of these results on the actuator carrier and modulation frequencies is discussed in detail.     

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.     

A study on the mechanism of high-lift generation by an airfoil in unsteady motion at low reynolds number

The aerodynamic force and flow structure of NACA 0012 airfoil performing an unsteady motion at low Reynolds number (Re=100) are calculated by solving Navier-Stokes equations. The motion consists of three parts: the first translation, rotation and the second translation in the direction opposite to the first. The rotation and the second translation in this motion are expected to represent the rotation and translation of the wing-section of a hovering insect. The flow structure is used in combination with the theory of vorticity dynamics to explain the generation of unsteady aerodynamic force in the motion. During the rotation, due to the creation of strong vortices in short time, large aerodynamic force is produced and the force is almost normal to the airfoil chord. During the second translation, large lift coefficient can be maintained for certain time period and , the lift coefficient averaged over four chord lengths of travel, is larger than 2 (the corresponding steady-state lift coefficient is only 0.9). The large lift coefficient is due to two effects. The first is the delayed shedding of the stall vortex. The second is that the vortices created during the airfoil rotation and in the near wake left by previous translation form a short “vortex street” in front of the airfoil and the “vortex street” induces a “wind”; against this “wind” the airfoil translates, increasing its relative speed. The above results provide insights to the understanding of the mechanism of high-lift generation by a hovering insect. The project supported by the National Natural Science Foundation of China (19725210)     

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。     

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.