Generalized Kutta–Joukowski theorem for multi-vortex and multi-airfoil flow(a lumped vortex model)

For purpose of easy identification of the role of free vortices on the lift and drag and for purpose of fast or engineering evaluation of forces for each individual body,we will extend in this paper the Kutta–Joukowski(KJ) theorem to the case of inviscid flow with multiple free vortices and multiple airfoils. The major simplification used in this paper is that each airfoil is represented by a lumped vortex,which may hold true when the distances between vortices and bodies are large enough. It is found that the Kutta–Joukowski theorem still holds provided that the local freestream velocity and the circulation of the bound vortex are modified by the induced velocity due to the outside vortices and airfoils. We will demonstrate how to use the present result to identify the role of vortices on the forces according to their position,strength and rotation direction. Moreover,we will apply the present results to a two-cylinder example of Crowdy and the Wagner example to demonstrate how to perform fast force approximation for multi-body and multi-vortex problems. The lumped vortex assumption has the advantage of giving such kinds of approximate results which are very easy to use. The lack of accuracy for such a fast evaluation will be compensated by a rigorous extension,with the lumped vortex assumption removed and with vortex production included,in a forthcoming paper.     

Influence of artificial tip perturbation on asymmetric vortices flow over a chined fuselage

An experimental study was conducted with the aim of understanding behavior of asymmetric vortices flow over a chined fuselage.The tests were carried out in a wind tunnel at Reynolds number of 1.87 · 105 under the conditions of high angles of attack and zero angle of sideslip.The results show that leeward vortices flow becomes asymmetric vortices flow when angle of attack increases over 20.The asymmetric vortices flow is asymmetry of two forebody vortices owing to the increase of angle of attack but not asymmetry of vortex breakdown which appears when angle of attack is above 35.Asymmetric vortices flow is sensitive to tip perturbation and is nondeterministic due to randomly distributed natural minute geometrical irregularities on the nose tip within machining tolerance.Deterministic asymmetric vortices flow can be obtained by attaching artificial tip perturbation which can trigger asymmetric vortices flow and decide asymmetric vortices flow pattern.Triggered by artificial tip perturbation, the vortex on the same side with perturbation is in a higher position, and the other vortex on the opposite side is in a lower position.Vortex suction on the lower vortex side is larger, which corresponds to a side force pointing to the lower vortex side.     

Leading-edge flow separation control over an airfoil using a symmetrical dielectric barrier discharge plasma actuator

In order to promote an in-depth understanding of the mechanism of leading-edge flow separation control over an airfoil using a symmetrical Dielectric Barrier Discharge(DBD) plasma actuator excited by a steady-mode excitation, an experimental investigation of an SC(2)-0714 supercritical airfoil with a symmetrical DBD plasma actuator was performed in a closed chamber and a low-speed wind tunnel. The plasma actuator was mounted at the leading edge of the airfoil.Time-resolved Particle Image Velocimetry(PIV) results of the near-wall region in quiescent air suggested that the symmetrical DBD plasma actuator could induce some coherent structures in the separated shear layer, and these structures were linked to a dominant frequency of f0= 39 Hz when the peak-to-peak voltage of the plasma actuator was 9.8 kV. In addition, an analysis of flow structures without and with plasma actuation around the upper side of the airfoil at an angle of attack of18° for a wind speed of 3 m/s(Reynolds number Re = 20000) indicated that the dynamic process of leading-edge flow separation control over an airfoil could be divided into three stages. Initially, this plasma actuator could reinforce the shedding vortices in the separated shear layer. Then, these vortical structures could deflect the separated flow towards the wall by promoting the mixing between the outside flow with a high kinetic energy and the flow near the surface. After that, the plasma actuator induced a series of rolling vortices in the vicinity of the suction side of the airfoil, and these vortical structures could transfer momentum from the leading edge of the airfoil to the separated region, resulting in a reattachment of the separated flow around the airfoil.     

地面涡研究

 The formation mechanism and the flow characteristics of the ground vortices as well as the method of eliminating ground vortices are studied in this paper. It is noted that, when air is sucked into an aircraft engine, on the ground a momentum moment is exerted on a point sink flow by a lateral wind or a reversed jet from the tail pipe, resulting in the formation of eddy stream known as ground vortices. Through an analysis of numerous experimental data it is found that the ground vortices are composed of two vortices instead of a single and concentrated free vortex.The tangitial velocity distribution curves of the ground vortex can be expressed as two independent functions: one is a directly proportional function located at the core, and the other is an inversely proportional function around the outer surrounding. The pressure distribution is also composed of two parabolic functions.In addition, a method of eliminating the ground vortices is presented, and it is of important engineering significance to eliminate the ground vortices.     

NUMERICAL SIMULATION OF UNSTEADY FLOW AROUND A CIRCULAR CYLINDER AT HIGH REYNOLDS NUMBERS

A Lagrangian-Eulerian hybrid scheme to solve unsteady N-S equation in two-dimensional incompressible fluid at high Reynolds numbers is presented in this paper. A random walk is imposed to simulate the viscous diffusion, the vortex-in-cell method is used to obtain the convection velocity, and nascent vortices are created on a cylinder to satisfy the zero-slip condition. The impulsively started flow around a circular cylinder and the separation induced by a pair of incident vortices symmetrically approaching a circular cylinder have been successfully simulated by the hybrid scheme. The impulsively started flow from rest has been computed at Reynolds numbers 3000 and 9500. Comparisons are made with those results of finite-difference method, vortex method and flow visualization. Agreement is good. The particular attention has been paid to the evolutions of flow pattern. A topological analysis has been proposed in the region of the near wake. The bulge, isolated secondary vortex, a pair of secondary vortices     

Computations of unsteady transonic flow over airfoil at low Reynolds number

Transonic flow over a thin airfoil at low Reynolds number was studied numerically by directly solving two-dimensional full Navier-Stokes equations through 5th order weighted essentially non-oscillatory(WENO) scheme without using any turbulence model.A series of distinguished unsteady phenomena for a thin 2-D transonic airfoil flow were presented.Due to continuous adverse pressure gradient in the subsonic flow downstream of the sonic line, the unsteady separated boundary layer with main vortex and secondary vortex was developed at the rear of the airfoil.At the trailing edge,the vortex-shedding was characterized by periodical connection of the main vortex and secondary vortex on the other side of the airfoil.The unsteady separation and vortex-shedding occurred with the same period.On the airfoil surface,the average pulse pressure related to the unsteady supersonic region was obviously smaller than that related to the vortex-shedding at the trailing edge.With the attack angle increasing from 0° to 2°, the frequency of vortex-shedding decreases about 4.2%.At last, the turbulence intensity and many second-order statistics in the wake region were investigated.      

Experimental study of flow field distribution over a generic cranked double delta wing

The flow fields over a generic cranked double delta wing were investigated. Pressure and velocity distributions were obtained using a Pitot tube and a hot wire anemometer. Two different leading edge shapes, namely ‘‘sharp" and ‘‘round", were applied to the wing. The wing had two sweep angles of 55° and 30°. The experiments were conducted in a closed circuit wind tunnel at velocity 20 m/s and angles of attack of 5°–20° with the step of 5°. The Reynolds number of the model was about 2 ×10~5 according to the root chord. A dual vortex structure was formed above the wing surface. A pressure drop occurred at the vortex core and the root mean square of the measured velocity increased at the core of the vortices, reflecting the instability of the flow in that region. The magnitude of power spectral density increased strongly in spanwise direction and had the maximum value at the vortex core. By increasing the angle of attack, the pressure drop increased and the vortices became wider; the vortices moved inboard along the wing, and away from the surface; the flow separation was initiated from the outer portion of the wing and developed to its inner part. The vortices of the wing of the sharp leading edge were stronger than those of the round one.     

Effects of wing locations on wing rock induced by forebody vortices

Previous studies have shown that asymmetric vortex wakes over slender bodies exhibit a multi-vortex structure with an alternate arrangement along a body axis at high angle of attack. In this investigation, the effects of wing locations along a body axis on wing rock induced by forebody vortices was studied experimentally at a subcritical Reynolds number based on a body diameter. An artificial perturbation was added onto the nose tip to fix the orientations of forebody vortices. Par-ticle image velocimetry was used to identify flow patterns of forebody vortices in static situations, and time histories of wing rock were obtained using a free-to-roll rig. The results show that the wing locations can affect significantly the motion patterns of wing rock owing to the variation of multi-vortex patterns of forebody vortices. As the wing locations make the forebody vortices a two-vortex pattern, the wing body exhibits regularly divergence and fixed-point motion with azimuthal varia-tions of the tip perturbation. If a three-vortex pattern exists over the wing, however, the wing-rock patterns depend on the impact of the highest vortex and newborn vortex. As the three vortices together influence the wing flow, wing-rock patterns exhibit regularly fixed-points and limit-cycled oscillations. With the wing moving backwards, the newborn vortex becomes stronger, and wing-rock patterns become fixed-points, chaotic oscillations, and limit-cycled oscillations. With fur-ther backward movement of wings, the vortices are far away from the upper surface of wings, and the motions exhibit divergence, limit-cycled oscillations and fixed-points. For the rearmost location of the wing, the wing body exhibits stochastic oscillations and fixed-points.     

Numerical study of separation on the trailing edge of a symmetrical airfoil at a low Reynolds number

This study focuses on the trailing-edge separation of a symmetrical airfoil at a low Rey-nolds number. Finite volume method is adopted to solve the unsteady Reynolds-averaged Navier-Stokes (RANS) equation. Flow of the symmetrical airfoil SD8020 at a low Reynolds number has been simulated. Laminar separation bubble in the flow field of the airfoil is observed and process of unsteady bubble burst and vortex shedding from airfoil surfaces is investigated. The time-dependent lift coefficient is characteristic of periodic fluctuations and the lift curve varies nonlinearly with the attack of angle. Laminar separation occurs on both surfaces of airfoil at small angles of attack. With the increase of angle of attack, laminar separation occurs and then reattaches near the trailing edge on the upper surface of airfoil, which forms laminar separation bubble. When the attack of angle reaches certain value, the laminar separation bubble is unstable and produces two kinds of large scale vortex, i.e. primary vortex and secondary vortex. The periodic processes that include secondary vortex production, motion of secondary vortex and vortex shedding cause fluctuation of the lift coefficient. The periodic time varies with attack of angle. The secondary vortex is relatively stronger than the primary vortex, which means its influence is relatively stronger than the primary vortex.     

An experimental investigation on static directional stability

A generic aircraft usually loses its static directional stability at moderate angle of attack (typically 20–30?). In this research, wind tunnel studies were performed using an aircraft model with moderate swept wing and a conventional vertical tail. The purpose of this study was to investigate flow mechanisms responsible for static directional stability. Measurements of force, surface pressure and spatial flow field were carried out for angles of attack from 0? to 46? and sideslip angles from ?8? to 8?. Results of the wind tunnel experiments show that the vertical tail is the main contributor to static directional stability, while the fuselage is the main contributor to static directional instabil-ity of the model. In the sideslip attitude for moderate angles of attack, the fuselage vortex and the wing vortex merged together and changed asymmetrically as angle of attack increased on the wind-ward side and leeward side of the vertical tail. The separated asymmetrical vortex flow around the vertical tail is the main reason for reduction in the static directional stability. Compared with the wing vortices, the fuselage vortices are more concentrated and closer to the vertical tail, so the yaw-ing moment of vertical tail is more unstable than that when the wings are absent. On the other hand, the attached asymmetrical flow over the fuselage in sideslip leads to the static directional instability of the fuselage being exacerbated. It is mainly due to the predominant model contour blockage effect on the windward side flow over the model in sideslip, which is strongly affected by angle of attack.     

椭圆形控制环量翼型气动力的计算

本文用边界层理论与计及分离尾迹影响的位流理论相结合的方法计算控制环量翼型的绕流,用离散涡模型模拟分离尾迹的影响。由上、下翼面分离点处引入离散涡。只是翼型附近尾迹中的离散涡可以自由移动。离翼型较远的离散涡假设为按来流速度移动。忽略射流出口上游的边界层对射流的影响。这些简化使本文的方法十分有效。与实验比较表明,本文的方法能较准确地计算出翼型的分离点位置和分离点前的压强分布。计算出的升力系数与射流动量系数的关系与实验相符很好。     

翼型近尾迹流动的PIV研究—运动学特性

利用在线式PIV系统(ParticleImageVelocimetry),在低速风洞中对NACA0012翼型在雷诺数2.39×105,0°和4°攻角下的近尾迹流动进行了实验研究。实验结果表明,在较高的雷诺数下翼型近尾迹流动是一种以旋涡的运动学和动力学特性为主导的湍流剪切流。在测量范围内,翼型的尾缘处是近尾迹涡街的形成区;尾缘后0.5倍弦长的区域存在类似于卡门涡街的有序结构,是旋涡发展区域,旋涡具有较好的稳定性;距翼型尾缘0.5倍弦长至1倍弦长的区域,是翼型近尾迹流动由有序走向无序区域,旋涡开始破裂。翼型表面边界层对翼型近尾迹湍流剪切流的演化有重要影响。实验结果还给出了近尾迹流动的平均速度、湍流强度和剪切应变变化率,以及速度脉动量的二阶关联量u'u',u'v'和v'v' 的分布。      

翼型—扰流片的分离气动特性计算

本文介绍了用涡面元法模拟带扰流片的翼型低速无粘分离绕流。在翼型和扰流片的面元上分布线性变化涡。在扰流片后的上下分离流线的面元上分布等强度的涡。上分离流线始自扰流片的梢部，下分离流线自翼型的后缘引出。分离所泡由两离散涡结尾。气泡内总压为常值，它与涡强大小一同求解。分离气泡的形状在迭代求解过程中确定。压强分布和升力系数的计算值与现存文献的数值结果和实验数据是一致的。     

Experimental and numerical investigation of threedimensional vortex structures of a pitching airfoil at a transitional Reynolds number

This research examines the vortex behaviors and aerodynamic forces in dynamic stall phenomena at a transitional Reynolds number(Re = 90000) using experimental and numerical approaches.Periodic sinusoidal pitching motion at two different reduced frequencies is used to achieve the dynamic stall of a NACA 0012 airfoil.Several leading edge vortices form and detach in the dynamic stall stage.The flow then quickly transitions to a full separation zone in the stall stage when the angle of attack starts to decrease.There is discrepancy between the phaseaveraged and instantaneous flow field in that the small flow structures increased with angle of attack, which is a characteristic of the flow field at the transitional Reynolds number.The interaction between the streamwise vortices in the three-dimensional numerical results and the leading edge vortex are the main contribution to the turbulent flow.In addition, the leading edge vortex that supplies vortex lift is more stable at higher reduced frequency, which decreases the lift fluctuation in the dynamic stall stage.The leading edge vortex at higher reduced frequency is strong enough to stabilize the flow, even when the airfoil is in the down-stroke phase.     

Aerodynamic periodicity of transient aerodynamic forces of flexible plunging airfoils

For flapping micro-air vehicles, periodical aerodynamics in every plunging period is always desired in the design of aircraft controlling system. During the periodic plunges of rigid airfoil, either periodical or non-periodical aerodynamic forces can be generated. Real airfoils are usually flexible so that the effect of flexibility on unsteady characteristics of aerodynamic periodicity should be considered. In this study, a fluid structure interaction analysis is employed to systematically investigate the aerodynamic periodicity of a periodically plunging flexible airfoil. The influences of several dimensionless kinematic and structural parameters on aerodynamic periodicity are investigated. The results show that the aerodynamic periodicity of plunging flexible airfoil qualitatively resembles that of rigid airfoil as the mechanisms contributing to aerodynamic periodicity are kept for airfoil with various flexibilities. However, aerodynamic periodicity at small plunging amplitude and high Reynolds number can be improved as airfoil becomes medium flexible but worsened as airfoil is very flexible. The reason is that the deformation of the airfoil changes the strength and structure of the nearby vortices, thereby leading to weak vortex–vortex and vortex–airfoil interactions. The extent of improvement in aerodynamic periodicity is also found significantly influenced by incoming velocity.     

摆线桨非定常动态失速的三维效应

对摆线桨三维全尺寸模型进行了非定常数值模拟。验证了两种嵌套网格方法的可靠性与适用性,针对二维/三维情况下摆线桨非定常涡流动特性及诱导分离特性开展了数值分析,重点研究了展向气动力随方位角的分布与全局流场的诱导速度分布,并分析了尾迹捕捉精度与涡量耗散特征。结果表明:受摆线桨切向速度、展向诱导速度等三维效应影响,两种计算结果的瞬态气动力极值差值达到44%。三维动态失速涡的产生、脱落与再附明显弱于二维翼型情况,这对于摆线桨非定常气动特性有较大影响。      

电磁控制涡激振荡的实验研究

利用电介质溶液中圆柱体侧表面附近分布的电磁场产生电磁力可有效改变流体边界层及尾涡结构。本文以减振为目标,对电磁力控制涡激振荡进行了实验研究。实验在转动水槽中进行,通过吊杆将装有电磁激活板的圆柱插在槽内液体中。吊杆上的应变片用于测试圆柱的升力,注入适当的染料用来显示流场。结果表明：对称电磁力作用下,脱体涡被抑制,从而使升力的振荡受到有效抑制,进而抑制圆柱的振动,双排方向相反的涡变为单排正负交错的涡。当电磁力足够大时,圆柱的振荡被完全消除,流场达到定常。     

翼型近尾迹流动的PIV研究—动力学机制

利用在线式互相关PIV(ParticleImageVelocimetry)系统,在低速风洞中对NACA0012翼型在雷诺数2.39×105,0°和4°攻角下的近尾迹流动进行了详细测量。实验结果表明,翼型近尾迹存在有序的涡街结构,涡街在尾缘处形成后,在向下游的迁移中,会经历一个发展壮大、失稳破碎的演化过程,流动从有序走向无序。翼型的近尾迹是一种以旋涡的运动学特性和动力学机制为主导的流动现象。本文着重探讨了翼型尾缘处的涡街形成机理,尾迹内的流动机制,以及近尾迹的流动稳定性。      

Separation control on NACA23012 using synthetic jet

A numerical study of separation control has been made to investigate aerodynamic characteristics of NACA23012 airfoil with synthetic jets. Computed results demonstrated that stall characteristics and control surface performance could be substantially improved by resizing separation vortices. The maximum lift was obtained when the separation point coincides with the synthetic jet location and the non-dimensional frequency is about 1. In addition, separation control effect was proportional to the peak velocity of the synthetic jet. It was observed that the actual flow control mechanism and flow structure is fundamentally different depending on the range of synthetic jet frequency. For low frequency range, small vortices due to synthetic jet penetrated to the large leading edge separation vortex, and as a result, the size of the leading edge vortex was remarkably reduced. For high frequency range, however, small vortex did not grow up enough to penetrate into the leading edge separation vortex. Instead, synthetic jet firmly attached the local flow and influenced the circulation of the virtual airfoil shape which is the combined shape of the main airfoil with the separation vortex. As a way to reduce the jet peak velocity, performance of a multi-array synthetic jet was investigated. Moreover, a high frequency multi-location synthetic jet was exploited to efficiently eliminate the unstable flow structure which was observed in low frequency range. Finally, by changing the phase angle in multi-location synthetic jets, highly controlled flow characteristics could be obtained with multi-array/multi-location synthetic jets. This shows efficiency of the current approach in separation control using synthetic jet.