Numerical analysis of active chordwise flexibility on the performance of non-symmetrical flapping airfoils

This paper investigates the effect of active chordwise flexing on the lift, thrust and propulsive efficiency of three types of airfoils. The factors studied are the flexing center location, standard two-sided flexing as well as a type of single-sided flexing. The airfoils are simulated to flap with four configurations, and the effects of flexing under these configurations are investigated. Results show that flexing is not necessarily beneficial for the performance of the airfoils. However, with the correct parameters, efficiency is as high as 0.76 by placing the flexing centre at the trailing edge. The average thrust coefficient is more than twice as high, from 1.63 to 3.57 with flapping and flexing under the right conditions. Moreover, the single-sided flexing also gives an average lift coefficient as high as 4.61 for the S1020 airfoil. The shape of the airfoil does alter the effect of flexing too. Deviating the flexing phase angle away from 90° does not give a significant improvement to the airfoil’s performance. These results greatly enhance the design of a better performing ornithopter wing.     

Design and development considerations for biologically inspired flapping-wing micro air vehicles

In this paper, the decade of numerical and experimental investigations leading to the development of the authors’ unique flapping-wing micro air vehicle is summarized. Early investigations included the study of boundary layer energization by means of a small flapping foil embedded in a flat-plate boundary layer, the reduction of the recirculatory flow region behind a backward-facing step by means of a small flapping foil, and the reduction or suppression of flow separation behind blunt or cusped airfoil trailing edges by flapping a small foil located in the wake flow region. These studies were followed by systematic investigations of the aerodynamic characteristics of single flapping airfoils and airfoil combinations. These unsteady flows were described using flow visualization, laser-Doppler velocimetry in addition to panel and Navier–Stokes computations. It is then shown how this flapping-wing database was used to conceive, design and develop a micro air vehicle which has a fixed wing for lift and two flapping wings for thrust generation. While animal flight is characterized by a coupled force generation, the present design appears to separate lift and thrust. However, in fact, the performance of one surface is closely coupled to the other surfaces.     

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.     

On the Design of Lifting Airfoils with High Critical Mach Number Using Full Potential Theory

 We wish to construct airfoils that have the highest free-stream Mach number for a given set of geometric constraints for which the flow is nowhere supersonic. Nonlifting airfoils that maximize the critical Mach number for a given cross-sectional area are known to possess long sonic segments at their critical speed. To construct lifting airfoils, we proceed under the conjecture that an airfoil with a high value of has the longest possible arc length of sonic velocity over its upper and lower surface. In Kropinski et al. (1995) the lifting problem was tackled in transonic small-disturbance theory. In this paper we numerically construct lifting airfoils with high using the full potential theory and we show that these airfoils have significantly higher than some standard airfoils. We also construct airfoils with higher values of the lift coefficient, by relaxing the speed constraint on the lower surface of the airfoil to have a value less than sonic. Received 13 May 1996 accepted 12 September 1996)     

High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion

High-fidelity numerical simulations with the spectral difference (SD) method are carried out to investigate the unsteady flow over a series of oscillating NACA 4-digit airfoils. Airfoil thickness and kinematics effects on the flapping airfoil propulsion are highlighted. It is confirmed that the aerodynamic performance of airfoils with different thickness can be very different under the same kinematics. Distinct evolutionary patterns of vortical structures are analyzed to unveil the underlying flow physics behind the diverse flow phenomena associated with different airfoil thickness and kinematics and reveal the synthetic effects of airfoil thickness and kinematics on the propulsive performance. Thickness effects at various reduced frequencies and Strouhal numbers for the same chord length based Reynolds number (=1200) are then discussed in detail. It is found that at relatively small Strouhal number (=0.3), for all types of airfoils with the combined pitching and plunging motion (pitch angle 20°, the pitch axis located at one third of chord length from the leading edge, pitch leading plunge by 75°), low reduced frequency (=1) is conducive for both the thrust production and propulsive efficiency. Moreover, relatively thin airfoils (e.g. NACA0006) can generate larger thrust and maintain higher propulsive efficiency than thick airfoils (e.g. NACA0030). However, with the same kinematics but at relatively large Strouhal number (=0.45), it is found that airfoils with different thickness exhibit diverse trend on thrust production and propulsive efficiency, especially at large reduced frequency (=3.5). Results on effects of airfoil thickness based Reynolds numbers indicate that relative thin airfoils show superior propulsion performance in the tested Reynolds number range. The evolution of leading edge vortices and the interaction between the leading and trailing edge vortices play key roles in flapping airfoil propulsive performance.     

A method to carry out shape optimization with a large number of design variables

A new method for shape optimization with relatively large number of design variables is proposed. It is well known that gradient‐based methods converge to a local optimum. As a result, utilization of a richer design space does not necessarily lead to a better design. This is demonstrated via the design of an airfoil for maximum lift for Re = 1000 and α = 4° flow. The airfoil is represented by fourth‐order non‐uniform rational B‐splines, and the control points are used as design variables. Starting with a NACA0012 airfoil, it is found that the optimal airfoil obtained with 13 control points has far superior aerodynamic performance than the ones obtained with 39 and 61 control points. For effective utilization of a richer design space, it is proposed that the number of design variables be increased gradually. The method is demonstrated by designing high lift airfoils for Re = 1000 and 1 × 10⁴. The objective function is the maximization of the time‐averaged lift coefficient for α = 4°. The optimization cycle with 27 control points is initiated with the optimal airfoil obtained with 13 control points. The process is continued with gradual increase in the number of design variables. Beyond a certain number of control points, the optimization leads to a spontaneous appearance of corrugations on the upper surface of the airfoil. The corrugations are responsible for the generation of small vortices that add to the suction on the upper surface of the airfoil and lead to enhanced lift. A stabilized finite element method is used to solve the unsteady flow and adjoint equations. Copyright © 2012 John Wiley & Sons, Ltd.     

A new direct design method for the medium thickness wind turbine airfoil

The newly developed integral function of airfoil profiles based on Trajkovski conformal transform theory could be used to optimize the profiles for the thin thickness airfoil. However, it is hard to adjust the coefficients of the integral function for the medium thickness airfoil. B-spline curve has an advantage of local adjustment, which makes it to effectively control the airfoil profiles at the trailing edge. Therefore, a new direct design method for the medium thickness wind turbine airfoil based on airfoil integral expression and B-spline curve is presented in this paper. An optimal mathematical model of an airfoil is built. Two new airfoils with similar thickness, based on the new designed method and the original integral method, are designed. According to the comparative analysis, the CQU-A25 airfoil designed based on the new method exhibits better results than that of the CQU-I25 airfoil which is designed based on the original method. It is demonstrated that the new method is feasible to design wind turbine airfoils. Meanwhile, the comparison of the aerodynamic performance for the CQU-A25 airfoil and for the DU91-W2-250 airfoil is studied. Results show that the maximum lift coefficient and the maximum lift/drag ratio of the CQU-A25 airfoil are higher than the ones of DU91-W2-250 airfoil in the same condition. This new airfoil design method would make it possible to design other airfoils with different thicknesses.     

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.      

Numerical evaluation of the aerodynamic influence of the helicopter composite blade trailing edge tabs

In classical composite helicopter rotor blade production, a small flat tab must be formed along the entire trailing edge, in order to enable proper merging of the upper and the lower surface plies during manufacturing. By this, the original airfoil shape is altered. Such fixed tabs have been added in a range of possible angular positions to several existing asymmetrical helicopter airfoils, and their capability to change the moment coefficient about the aerodynamic center of the airfoils was initially analyzed. Although usual tabs are proportionally small, angular domains in which they do not remarkably change the required nearly zero aerodynamic moment, were quantified as very narrow. In the next stage, an algorithm has been defined and implemented: (a) for the determination of optimum angular tab positions for several asymmetrical airfoils, that satisfy the moment requirement (for such airfoils optimum tab direction cannot be known in advance), and (b) for the reduction of the influence of eventual inherent numerical errors of applied software to a minimum. The accuracy of this algorithm has been verified on a symmetrical airfoil, for which the optimum tab position is readily known. In the next step, the tab influence on other aerodynamic airfoil characteristics, and the influence on flight performance of a light helicopter from an on-going project, has been analyzed. Several possible tab design concepts were defined, and some characteristic aspects of their implementation were considered. At the level of preliminary helicopter performance calculations, the influence of the two general outcomes of the tab designs were analyzed, one that preserves initial relative airfoil thickness, and another which leads to its reduction. In the first case, the influence of the slight increase of drag coefficient was taken into account, while in the second one, the decrease of drag coefficient, accompanied with necessary additional strengthening and added blade mass was considered. In both cases applied modifications proved to have moderate direct influence on helicopter flight performance, compared with a hypothetic case that the original airfoil without tab could have been used instead. General conclusions have imposed the need for very careful approach in tab design for asymmetrical airfoils, which must be primarily focused on the tab’s potential remarkable influence on the aerodynamic moment.     

Numerical analysis of the s1020 airfoils in tandem under different flapping configurations

The objective of this project is to improve the performance of the efficiency, thrust and lift of flapping wings in tandem arrangement. This research investigates the effect of the arrangement of the airfoils in tandem on the performance of the airfoils by varying the phase difference and distance between the airfoils. Three flapping configurations from an earlier phase of a research which gives high efficiency, thrust and lift are used in the tandem simulation. It is found all the different flapping configurations show improvement in the efficiency, thrust or lift when the distance between the two airfoils and the phase angle between the heaving positions of the two airfoils are optimal. The average thrust coefficient of the tandem arrangement managed to attain more than twice that of the single one （4.84 vs. 2.05）. On the other hand, the average lift coefficient of the tandem arrangement also increased to 4.59, as compared to the original single airfoil value of 3.04. All these results obtained will aid in the design of a better ornithopter with tandem wing arrangement.     

一种可用于机翼优化设计中的气动噪声预测模型

发展了一种可用于翼型/机翼外形设计中的气动噪声快速预测方法。相较于传统的半经验噪声预测方法,该方法以两方程非线性k-ε湍流模型模化雷诺应力的雷诺平均方程为背景,考虑了升力系数、三维流动效应以及机翼几何参数等因素对后缘噪声的影响。而相对于直接数值模拟或声类比拟方法,该方法虽不能准确预测噪声强度,但其计算量小,能给出不同翼型/机翼的相对总声压级,以及总声压级随升力系数的变化情况,易于应用于翼型/机翼气动外形优化设计中。通过计算分析二维NACA0012翼型几何参数或来流状态的改变所带来的气动噪声差异,与ANOPP软件及Brooks等计算结果进行对比,验证了该模型的可靠性。最后,计算分析二维、三维翼型/机翼气动噪声,凸显该方法在翼型/机翼气动外形优化设计中的应用价值。     

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.     

平板大攻角绕流升力和阻力系数的计算

二维平板或二维对称薄翼型大攻角绕流升力和阻力系数与攻角之间存在的函数关系一般用数据表格的形式给出。本文根据垂直平板绕流阻力实验数据和对称薄翼型全攻角绕流实验数据,分析得到了平板大攻角绕流总压力及其升力分量和阻力分量系数的近似计算公式。结果表明：平板总压力系数约等于攻角正弦值的2倍;总压力的阻力分量系数约等于攻角正弦值平方的2倍;升力分量系数约为攻角2倍的正弦值。计算结果与两组试验数据具有较好的一致性。     

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.     

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.     

Bifurcations of transonic flow past simple airfoils with elliptic and wedge-shaped noses

A turbulent transonic flow past two symmetric airfoils with flat midparts is studied numerically. Using the Reynolds-averaged Navier-Stokes equations, we analyze the flow past a 9% thick airfoil with an elliptic nose. A range of the free-stream Mach number M_∞, in which flow bifurcations occur, is determined. Values of M_∞ that give rise to significant changes in the lift coefficient with variations of the angle of attack are specified. Flow bifurcations are also revealed for a thin double wedge, i.e., a sort of a hexagon.     

Designing wing airfoils with active flow controls

A method of designing wing airfoils in separationless flow with suction of a portion of the external flow and reactive jet injection from the rear of the body (the total pressure and the density in the jet are different from those in the freestream) within the framework of the ideal incompressible fluid model is proposed. It is shown that this method of active flow control makes it possible considerably to increase the airfoil lift as compared with the same airfoil with no suction or injection. Examples of the design of such airfoils in separationless flow are presented. The reliability of the results obtained is confirmed by a numerical experiment using the Fluent program.     

N-S方程数值研究翼型对微型扑翼气动特性的影响

首先基于嵌套网格发展了一套适用于三维扑翼研究的非定常雷诺平均Navier-Stokes(RANS)方程数值模拟方法.为了解决微型扑翼在低马赫数下的收敛问题,使用了预处理方法,湍流模型为BL模型.在该方法的基础上,保持状态参数和扑翼表面形状一定的情况下,分别研究了一系列不同厚度、不同弯度的翼型对于微型扑翼气动特性的影响....     

Effect of one-sided unsteady energy supply on aerodynamic characteristics of airfoils in a transonic flow

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of one-sided pulsed-periodic energy supply is studied. Based on the numerical solution of two-dimensional unsteady gas-dynamic equations, the change in the flow structure in the vicinity of a symmetric airfoil at different angles of attack and the aerodynamic characteristics of the airfoil as functions of the amount of energy supplied asymmetrically (with respect to the airfoil) are determined. The results obtained are compared with the data calculated for the flow past the airfoil at different angles of attack without energy supply. It is found that a given lift force can be obtained with the use of energy supply at a much better lift-to-drag ratio of the airfoil, as compared to the case of the flow past the airfoil at an angle of attack. The moment characteristics of the airfoil are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 82–87, November–December, 2008.     

Effect of asymmetric pulsed periodic energy supply on aerodynamic characteristics of airfoils

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of local pulsed periodic energy supply is considered. The numerical solution of two-dimensional unsteady equations of gas dynamics allowed determining the changes in the flow structure near a symmetric airfoil and its aerodynamic characteristics depending on the magnitude of energy in the case of its asymmetric (with respect to the airfoil) supply. The results obtained are compared with the calculated data for the flow around the airfoil at different angles of attack without energy supply. With the use of energy supply, a prescribed lift force can be obtained with a substantially lower wave drag of the airfoil, as compared with the flow around the airfoil at an angle of attack. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 70–76, November–December, 2007.