Generalized Kutta–Joukowski theorem for multi-vortex and multi-airfoil flow with vortex production——A general model

By using a special momentum approach and with the help of interchange between singularity velocity and induced flow velocity, we derive in a physical way explicit force formulas for twodimensional inviscid flow involving multiple bound and free vortices, multiple airfoils, and vortex production. These force formulas hold individually for each airfoil thus allowing for force decomposition, and the contributions to forces from singularities(such as bound and image vortices,sources, and doublets) and bodies out of an airfoil are related to their induced velocities at the locations of singularities inside this airfoil. The force contribution due to vortex production is related to the vortex production rate and the distance between each pair of vortices in production, thus frameindependent. The formulas are validated against a number of standard problems. These force formulas, which generalize the classic Kutta–Joukowski theorem(for a single bound vortex) and the recent generalized Lagally theorem(for problems without a bound vortex and vortex production) to more general cases, can be used to identify or understand the roles of outside vortices and bodies on the forces of the actual body, optimize arrangement of outside vortices and bodies for force enhancement or reduction, and derive analytical force formulas once the flow field is given or known.     

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.     

A new non-linear vortex lattice method:Applications to wing aerodynamic optimizations

This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM) approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.     

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.     

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.     

Transient aeroelastic responses and flutter analysis of a variable-span wing during the morphing process

To investigate the transient aeroelastic responses and flutter characteristics of a variablespan wing during the morphing process,a novel frst-order state-space aeroelastic model is proposed.The time-varying structural model of the morphing wing is established based on the Euler-Bernoulli beam theory with time-dependent boundary conditions.A nondimensionalization method is used to translate the time-dependent boundary conditions to be time-independent.The time-domain aerodynamic forces are calculated by the reduced-order unsteady vortex lattice method.The morphing parameters,i.e.,wing span length and morphing speed,are of particular interest for understanding the fundamental aeroelastic behavior of variable-span wings.A test case is proposed and numerical results indicate that the flutter characteristics are sensitive to both of the two morphing parameters.It could be noticed that the aeroelastic characteristics during the wing extracting process are more serious than those during the extending process at the same morphing speed by transient aeroelastic response analysis.In addition,a faster morphing process can get better aeroelastic performance while the mechanism comlexity will arise.     

An experimental investigation on static directiona 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 instability 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 windward 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 yawing 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.     

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     

Numerical Investigation of the Effects of Wind Tunnel Model Vibrations on the Measured Aerodynamic Properties of Airfoils and Wings

This paper presents a numerical prediction of the unsteady flow field around oscillating airfoils at high angles of attack by solving unsteady Reynolds-averaged Navier-Stokes equations with SST turbulence model in order to simulate the effects of wind tunnel model vibrations on the aerodynamic properties of airfoils,especially high-aspect-ratio wings in a wind tunnel.The effects of the phase lagging between different modes of oscillations,i.e.,the airfoil plunging oscillation mode,the pitching oscillation mode,and the forward-backward oscillation mode,are also studied.It is shown that the vibrations (oscillations) of airfoils can cause the unsteady shedding of large-size separated vortex to precede the stationary stall incidence,hence lead to a stall onset at some earlier (lower) incidence than that in the steady sense.The different phase lagging has different effect on the flow field.When the pitching oscillation mode has small phase lagging behind the plunging oscillation mode,the effect of vibrations is large.Besides,if the amplitude of the oscillations is large enough,and the different modes of vibrations match or combine appropriately,the unsteady stall may occur 2° earlier in angle of attack than the case where airfoils keep stationary.     

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.     

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。     

平面自由剪切层三维离散涡丝的数值模拟

本文用离散涡丝方法对平面自由剪切层进行数值模拟，给出了初始展向涡丝的随空间发展所形成的成对反转流向涡以及涡卷起和涡丝合并的图案，分析了流向涡产生的根源。得到了剪切层的速度剖面，给出了不同速度差与对流速度比之下涡丝的演变特点。     

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.     

脱体涡流型翼面非定常气动力计算方法

本文研究了细长三角翼在脱体涡流型时变攻角所产生的非定常气动力的机理,并采用了一种时间历程的,考虑翼面前、后缘涡面随局部气流拖出并由时间发展逐步形成的数值方法,称之为涡面生成法,计算结果表明该方法是稳定和有效的。     

涡轮叶片尾缘凹坑/凸起结构气膜冷却特性研究

为探究吸力面凹坑和凸起结构对涡轮叶片尾缘气膜冷却特性的影响,在吹风比M=1.1时(雷诺数Re=2.5×10~5),采用数值模拟方法,通过在叶片尾缘吸力面上加入凹坑或凸起,对涡轮叶片尾缘的冷却性能和流动机理进行了详细分析。结果表明:与原始结构相比,叶片尾缘凹坑和凸起结构提高了劈缝出口下游远距离端X/H6 (H为劈缝宽度,为4.8mm)区域气膜冷却效率,对下游的X/H6区域气膜冷却效率影响较小;三种叶片尾缘结构,沿着流向方向会产生由二维展向涡到发卡涡,再到流向涡的变化过程,凹坑和凸起结构通过抑制流体的扰动,改变流体流动情况,提高了劈缝出口下游远距离端气膜冷却效率。     

具有轴向流的可压缩非定常旋涡流

本文研究埋定常轴对称自由旋涡流动结构的可压缩效应，探索旋涡的密度变化，粘性扩散和热传导的耦合作用机制。在回顾了前人某些典型结果之后，首次给邮了具有轴向拉伸率的可压缩非定常轴对称自由旋涡在高Ｒｅ数和小Ｍ数下的近似解析解。     

二维振荡机翼跨声速非定常绕流的变域变分有限元解

本文首先对文献（１－３）提出的二维振荡机翼含激波跨声速非定常绕流的变分原理进行了改造，使之能适用于时间推进法；构造了三维时空的可变节点有限元来捕获自由尾涡面，而跨声流中的激波采用人工密度法捕获。在远场边界上使用简化的无反射条件和新型非定常Ｋｕｔｔａ条件。用本文方法求解了作俯爷振荡的ＮＡＣＡ６４Ａ０１０翼型的跨声速绕流，计算结果令人满意。本文方法可以推广到三维机翼及二维和三维叶栅的同类气动力问题上去     

飞机尾流的快速建模方法

尾流的强度主要由飞机的飞机重量、飞行速度和机翼形状所决定和仿真尾流的保守被动模型可很好的描述尾流系统中水蒸汽、位温等保守被动量的运动演化规律,但这种参数仿真时间长、对计算机要求高,不能实时预测任一机型所产生的尾流的状态分布特性.为此提出了一种尾流的快速建模方法,很好的解决了以往尾流实时仿真时的缺点,为飞机飞行过程中实时预测前机尾流的影响区域提供理论依据,从而减少尾流事故的发生.