Computation of unsteady viscous flow around a locally flexible airfoil at low Reynolds number

A numerical method for fluid–structure interaction is presented for the analysis of unsteady viscous flow over a locally flexible airfoil. The Navier–Stokes equations are solved by ALE–CBS algorithm, coupling with a structural solver with large deformation. Following the validation of the method, a numerical example for the flight of micro-air vehicles at low Reynolds number is chosen for the computation. The coupling effect of flexible structure with different elastic stiffness on aerodynamic performance is demonstrated. A noticeable camber effect is induced by the deflection of the structure as the elastic stiffness of the structure goes smaller. Moreover, when the vibrating frequencies of the structure with smaller elastic stiffness have a close correlation with the shedding frequencies, the positive impact of the vibration of local flexible surface on the lift of the airfoil is highlighted, which results from the formation of the coherent vortices.     

Computational aerodynamics of low Reynolds number plunging,pitching and flexible wings for MAV applications

Micro air vehicles （MAV＇s） have the potential to revolutionize our sensing and information gathering capabilities in environmental monitoring and homeland security areas. Due to the MAV＇s＇ small size, flight regime, and modes of operation, significant scientific advancement will be needed to create this revolutionary capability. Aerodynamics, structural dynamics, and flight dynamics of natural flyers intersects with some of the richest problems in MAV＇s, inclu- ding massively unsteady three-dimensional separation, transition in boundary layers and shear layers, vortical flows and bluff body flows, unsteady flight environment, aeroelasticity, and nonlinear and adaptive control are just a few examples. A challenge is that the scaling of both fluid dynamics and structural dynamics between smaller natural flyer and practical flying hardware/lab experiment （larger dimension） is fundamentally difficult. In this paper, we offer an overview of the challenges and issues, along with sample results illustrating some of the efforts made from a computational modeling angle.     

Optimal airfoil shapes for low Reynolds number flows

Flow over NACA 0012 airfoil is studied at α = 4^° and 12^° for Re?500. It is seen that the flow is very sensitive to Re. A continuous adjoint based method is formulated and implemented for the design of airfoils at low Reynolds numbers. The airfoil shape is parametrized with a non‐uniform rational B‐splines (NURBS). Optimization studies are carried out using different objective functions namely: (1) minimize drag, (2) maximize lift, (3) maximize lift to drag ratio, (4) minimize drag and maximize lift and (5) minimize drag at constant lift. The effect of Reynolds number and definition of the objective function on the optimization process is investigated. Very interesting shapes are discovered at low Re. It is found that, for the range of Re studied, none of the objective functions considered show a clear preference with respect to the maximum lift that can be achieved. The five objective functions result in fairly diverse geometries. With the addition of an inverse constraint on the volume of the airfoil the range of optimal shapes, produced by different objective functions, is smaller. The non‐monotonic behavior of the objective functions with respect to the design variables is demonstrated. The effect of the number of design parameters on the optimal shapes is studied. As expected, richer design space leads to geometries with better aerodynamic properties. This study demonstrates the need to consider several objective functions to achieve an optimal design when an algorithm that seeks local optima is used. Copyright © 2008 John Wiley & Sons, Ltd.     

Fluid forces on a very low Reynolds number airfoil and their prediction

This paper presents the measurements of mean and fluctuating forces on an NACA0012 airfoil over a large range of angle (α) of attack (0-90°) and low to small chord Reynolds numbers (Re_c), 5.3 × 10³-5.1 × 10⁴, which is of both fundamental and practical importance. The forces, measured using a load cell, display good agreement with the estimate from the LDA-measured cross-flow distributions of velocities in the wake based on the momentum conservation. The dependence of the forces on both α and Re_c is determined and discussed in detail. It has been found that the stall of an airfoil, characterized by a drop in the lift force and a jump in the drag force, occurs at Re_c ? 1.05 × 10⁴ but is absent at Re_c = 5.3 × 10³. A theoretical analysis is developed to predict and explain the observed dependence of the mean lift and drag on α.     

Low Reynolds number aerodynamics of free-to-roll low aspect ratio wings

The aerodynamics of thin, flat-plate wings of various planforms (rectangular, elliptical and Zimmerman) have been studied in free-to-roll experiments in a wind tunnel. Non-zero trim angles at low angles of attack, self-induced roll oscillations with increasing angle of attack and even autorotation in some cases were observed. The rectangular wings with round leading-edge had non-zero trim angles at low incidences due to the asymmetric development of the three-dimensional separation bubble at these low Reynolds numbers. With increasing angle of attack, the bubble increases in length and once reattachment is lost, large amplitude roll oscillations develop. The Strouhal number of the roll oscillations is of the order of 10⁻², which is in the same range as those expected for small aircraft experiencing atmospheric gusts. Velocity measurements revealed that variations in the strength of the vortices drove the rolling motion. At the mean roll angle, because of the time lag in the strength of the vortices, an asymmetric flow is generated, which results in a net rolling moment in the direction of the rolling motion.     

The influence of free-stream disturbances on low Reynolds number airfoil experiments

The results of an investigation of the influence of free stream disturbances on the lift and drag performance of the Lissaman 7769 airfoil are presented. The wind tunnel disturbance environment is described using hot-wire anemometer and sound pressure level measurements. The disturbance level is increased by the addition of a ‘turbulence screen’ upstream of the test section and/or the addition of a flow restrictor downstream of the test section. For the Lissaman airfoil it was found that the problems associated with obtaining accurate wind tunnel data at low chord Reynolds numbers (i.e., below 200,000) are compounded by the extreme sensitivity of the boundary layers to the free stream disturbance environment. The effect of free stream disturbances varies with magnitude, frequency content, and source of the disturbance.     

Numerical investigations into the asymmetric effects on the aerodynamic response of a pitching airfoil

The effects of asymmetric sinusoidal motion on pitching airfoil aerodynamics were studied by numerical simulations for 2-D flow around a NACA0012 airfoil at Re=1.35×10⁵. Various unsteady parameters (amplitude of oscillation, d; reduced frequency, k) were applied to investigate the effect of asymmetry parameter S on the instantaneous force coefficients and flow patterns. The results reveal that S has a noticeable effect on the aerodynamic performance, as it affects the instantaneous force coefficient, maximum lift and drag coefficient, hysteresis loops and the flow structures.     

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.     

Reynolds number, thickness and camber effects on flapping airfoil propulsion

The effect of varying airfoil thickness and camber on plunging and combined pitching and plunging airfoil propulsion at Reynolds number Re=200, 2000, 20 000 and 2×10⁶ was studied by numerical simulations for fully laminar and fully turbulent flow regimes. The thickness study was performed on 2-D NACA symmetric airfoils with 6-50% thick sections undergoing pure plunging motion at reduced frequency k=2 and amplitudes h=0.25 and 0.5, and for combined pitching and plunging motion at k=2, h=0.5, phase ?=90°, pitch angle θ_o=15° and 30° and the pitch axis was located at 1/3 of chord from leading edge. At Re=200 for motions where positive thrust is generated, thin airfoils outperform thick airfoils. At higher Re significant gains could be achieved both in thrust generation and propulsive efficiency by using a thicker airfoil section for plunging and combined motion with low pitch amplitude. The camber study was performed on 2-D NACA airfoils with varying camber locations undergoing pure plunging motion at k=2, h=0.5 and Re=20 000. Little variation in thrust performance was found with camber. The underlying physics behind the alteration in propulsive performance between low and high Reynolds numbers has been explored by comparing viscous Navier-Stokes and inviscid panel method results. The role of leading edge vortices was found to be key to the observed performance variation.     

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.     

随机湍流工况低雷诺数风力机翼型优化研究

为改善小型风力机随机湍流工况适应性,以NACA0012翼型为研究对象,采用非嵌入式概率配置点法,获得随机湍流工况下小型风力机叶片翼型运行攻角分布规律;在气动优化中耦合层流分离预测,基于Transition SST模型、拉丁超立方试验设计、Kriging模型和带精英策略非支配排序遗传算法NSGA-II进行高湍流低雷诺数风力机翼型气动优化。结果表明,优化翼型叶片平均风能捕获效率分别提高3.01%和4.76%,标准差分别降低4.76%和14.93%,优化翼型湍流适应性增强。该方法将翼型设计与湍流风况相匹配,为湍流工况低雷诺数翼型及小型风力机设计提供参考。     

Turbulence modelling of the flow past a pitching NACA0012 airfoil at and Reynolds numbers

This paper provides a study of the NACA0012 dynamic stall at Reynolds numbers 10⁵ and 10⁶ by means of two- and three-dimensional numerical simulations. The turbulence effect on the dynamic stall is studied by statistical modelling. The results are compared with experiments concerning each test case. Standard URANS turbulence modelling have shown a quite dissipative character that attenuates the instabilities and the vortex structures related to the dynamic stall. The URANS approach Organised Eddy Simulation (OES) has shown an improved behaviour at the high Reynolds number range. Emphasis is given to the physical analysis of the three-dimensional dynamic stall structure, for which there exist few numerical results in the literature, as far as the Reynolds number range is concerned. This study has shown that the downstroke phases of the pitching motion are subjected to strong three-dimensional turbulence effects along the span, whereas the flow is practically two-dimensional during the upstroke motion.     

飞行器纵向俯仰气动特性计算研究

应用有限体积方法求解三维可压缩雷诺平均N-S方程,计算了巡航导弹外形飞行器作小振幅俯仰运动时的动态绕流流场和空气动力特性,开展了导弹绕不同转轴、以不同频率和在不同迎角范围内进行俯仰运动的非定常气动力迟滞特性研究。计算结果表明,当导弹作快速俯仰运动时,在上仰和下俯过程中的同一迎角瞬间,绕导弹流场流动明显不同,表现出明显的非定常迟滞特性。导弹的非定常气动力迟滞特性随俯仰运动频率的增大明显增强,且气动力迟滞曲线随着俯仰轴位置的变化而变化。在同一减缩频率下,导弹在不同迎角范围内作周期俯仰运动时,相同的运动相位角所对应的升力系数对迎角的导数是一致的,而不同减缩频率下升力系数对迎角的导数随运动相位角变化曲线明显不同。     

An experimental study of the effects of pitch-pivot-point location on the propulsion performance of a pitching airfoil

An experimental investigation was conducted to characterize the evolution of the unsteady vortex structures in the wake of a pitching airfoil with the pitch-pivot-point moving from 0.16C to 0.52C (C is the chord length of the airfoil). The experimental study was conducted in a low-speed wind tunnel with a symmetric NACA0012 airfoil model in pitching motion under different pitching kinematics (i.e., reduced frequency k=3.8–13.2). A high-resolution particle image velocimetry (PIV) system was used to conduct detailed flow field measurements to quantify the characteristics of the wake flow and the resultant propulsion performance of the pitching airfoil. Besides conducting “free-run” PIV measurements to determine the ensemble-averaged velocity distributions in the wake flow, “phase-locked” PIV measurements were also performed to elucidate further details about the behavior of the unsteady vortex structures. Both the vorticity–moment theorem and the integral momentum theorem were used to evaluate the effects of the pitch-pivot-point location on the propulsion performance of the pitching airfoil. It was found that the pitch-pivot-point would affect the evolution of the unsteady wake vortices and resultant propulsion performance of the pitching airfoil greatly. Moving the pitch-pivot-point of the pitching airfoil can be considered as adding a plunging motion to the original pitching motion. With the pitch-pivot-point moving forward (or backward), the added plunging motion would make the airfoil trailing edge moving in the same (or opposite) direction as of the original pitching motion, which resulted in the generated wake vortices and resultant thrust enhanced (or weakened) by the added plunging motion.     

A numerical investigation into the effects of Reynolds number on the flow mechanism induced by a tubercled leading edge

Leading-edge modifications based on designs inspired by the protrusions on the pectoral flippers of the humpback whale (tubercles) have been the subject of research for the past decade primarily due to their flow control potential in ameliorating stall characteristics. Previous studies have demonstrated that, in the transitional flow regime, full-span wings with tubercled leading edges outperform unmodified wings at high attack angles. The flow mechanism associated with such enhanced loading traits is, however, still being investigated. Also, the performance of full-span tubercled wings in the turbulent regime is largely unexplored. The present study aims to investigate Reynolds number effects on the flow mechanism induced by a full-span tubercled wing with the NACA-0021 cross-sectional profile in the transitional and near-turbulent regimes using computational fluid dynamics. The analysis of the flow field suggests that, with the exception of a few different flow features, the same underlying flow mechanism, involving the presence of transverse and streamwise vorticity, is at play in both cases. With regard to lift-generation characteristics, the numerical simulation results indicate that in contrast to the transitional flow regime, where the unmodified NACA-0021 undergoes a sudden loss of lift, in the turbulent regime, the baseline foil experiences gradual stall and produces more lift than the tubercled foil. This observation highlights the importance of considerations regarding the Reynolds number effects and the stall characteristics of the baseline foil, in the industrial applications of tubercled lifting bodies.     

Investigation of steady plasma actuation effect on aerodynamic coefficients of oscillating airfoil at low Reynolds number

In this work, numerical study of two dimensional laminar incompressible flow around an oscillating NACA0012 airfoil is proceeded using the open source code Open FOAM. Oscillatory motion types including pitching and flapping are considered. Reynolds number for these motions is assumed to be 12000 and effects of these motions and also different unsteady parameters such as amplitude and reduced frequency on aerodynamic coefficients are studied. For flow control on airfoil, dielectric barrier discharge plasma actuator is used in two different positions on airfoil and its effect is compared for the two types of considered oscillating motions. It is observed that in pitching motion, imposing plasma leads to an improvement in aerodynamic coefficients, but it does not have any positive effect on flapping motion.Also, for the amplitudes and frequencies investigated in this paper, the trailing edge plasma had a more desirable effect than other positions.     

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)     

低雷诺数流理论

最近,严宗毅教授编著的《低雷诺数流理论》已由北京大学出版社出版（2002年）.本书是适合于从事缓慢或小尺度黏性流动研究和有关工程技术人员参考的一本不可多得的专著,也是供高等院校有关专业研究生和高年级学生学习的一本优秀教材. 近30年来,为适应环境、生物、化学工程广泛应用