On vortex structures and processes over bluff bodies in impulsive flow

An experimental system that generates and visualizes unsteady motions in air was employed to visualize vortex developments over bluff bodies in impulsive started flow. The study presents photographic sequences of impulsive flow over circular and square cylinders for flow Reynolds number of 200. A comparison of physical and numerical visualization for impulsive flow over a flat plate at 50° angle of attack and for flow Reynolds number of 1,000 is also presented. The visualization examples reveal the details of vortex separation and subsequent developments and may be utilized as a reference to guide and economize computer visualization efforts on unsteady separated flows.Assistant Professor of Aerospace Engineering     

Point vortex model of the unsteady separated flow past a semi-infinite plate with transverse motion

Two-dimensional unsteady separated flow past a semi-infinite plate with transverse motion is considered. The rolling-up of the separated shear-layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A power-law starting flow is assumed along with a power law for the transverse motion. The effects of the motion of the plate on the starting vortex circulation and trajectory are presented. A suitable vortex shedding mechanism is introduced and a class of flows involving several vortices is presented. Finally, some possibilities for actively controlling the production of circulation by moving the plate are discussed.     

Flow structure on a rotating plate

The flow structure on a rotating plate of low aspect ratio is characterized well after the onset of motion, such that transient effects are not significant, and only centripetal and Coriolis accelerations are present. Patterns of vorticity, velocity contours, and streamline topology are determined via quantitative imaging, in order to characterize the leading-edge vortex in relation to the overall flow structure. A stable leading-edge vortex is maintained over effective angles of attack from 30° to 75°, and at each angle of attack, its sectional structure at midspan is relatively insensitive to Reynolds number over the range from 3,600 to 14,500. The streamline topology, vorticity distribution, and circulation of the leading-edge vortex are determined as a function of angle of attack, and related to the velocity field oriented toward, and extending along, the leeward surface of the plate. The structure of the leading-edge vortex is classified into basic regimes along the span of the plate. Images of these regimes are complemented by patterns on crossflow planes, which indicate the influence of root and tip swirl, and spanwise flow along the leeward surface of the plate. Comparison with the equivalent of the purely translating plate, which does not induce the foregoing flow structure, further clarifies the effects of rotation.     

Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins

We investigate experimentally the unsteady, three-dimensional vortex formation of low-aspect-ratio, trapezoidal flat-plate fins undergoing rotation from rest at a 90° angle of attack and Reynolds numbers of O(10³). The objectives are to characterize the unsteady three-dimensional vortex structure, examine vortex saturation, and understand the effects of the root-to-tip flow for different velocity programs. The experiments are conducted in a water tank facility, and the diagnostic tools are dye flow visualization and digital particle image velocimetry. The dye visualizations show that the low-aspect-ratio plate produces symmetric ring-like vortices comprised mainly of tip-edge vorticity. They also indicate the presence of the root-to-tip velocity. For large rotational amplitudes, the primary ring-like vortex sheds and a secondary ring-like vortex is generated while the plate is still in motion, indicating saturation of the leading vortex. The time-varying vortex circulation in the flow symmetry plane provides quantitative evidence of vortex saturation. The phenomenon of saturation is observed for several plate velocity programs. The temporal development of the vortex circulation is often complex, which prevents an objective determination of an exact saturation time. This is the result of an interaction between the developing vortex and the root-to-tip flow, which breaks apart the vortex. However, it is possible to define a range of time during which the vortex reaches saturation. A formation-parameter definition is investigated and is found to reasonably predict the state corresponding to the pinch-off of the initial tip vortex across the velocity programs tested. This event is the lower bound on the saturation time range.     

Evolution of vortex structures in an electromagnetically excited separated flow

Time periodic wall parallel Lorentz forces have been used to excite the separated flow on the suction side of an inclined flat plate. Experiments for a Reynolds number of 10⁴ and an angle of attack of α = 13° are reported. The controlled flow is characterised by a small number of relatively large scale vortices, which are related to the control mechanism. The influence of the main parameters, i.e. the excitation frequency, amplitude and wave form on the suction side flow structures was investigated by analysing time resolved particle image velocimetry (TR-PIV) measurements using continuous wavelet analysis for vortex detection and characterisation. Statistical analysis of the coherent structures of the flow was performed on a large amount of data samples.     

激波在平板上诱导的旋涡强度的测量

运动激波通过两个等攻角平板后诱导出两个同向旋转的旋涡，这两个旋涡在随当地气流向下游运动的同时，绕涡核连线中心旋转。本文通过测量涡对的转动角度速度，获得了每个旋涡的强度。实验结果表明，由此测得的旋涡强度不同用于小攻角平板起动涡公式计算了起动涡强度。     

Kutta–Joukowsky theorem in viscous and unsteady flow

Nominally two-dimensional air flow over a thin flat plate at low Reynolds number is investigated. The primary objective is to experimentally determine with good accuracy the small magnitude lift force, generated by the plate at various angles of attack, by means of application of the Kutta–Joukowsky theorem where circulation is obtained from the line integral of velocity around the flat plate using non-invasive laser doppler velocimeter. Specific focus is on assessing applicability of the Kutta–Joukowsky theorem, originally theorized for inviscid and steady flow, in the post-stall region. At high angles of attack, due to severe flow separation from both the edges of the flat plate and occurrence of periodic vortex shedding, wake flow is found to be highly viscous, turbulent and unsteady. Nevertheless, the results show a remarkably good agreement with previous investigations in both the linear range and the non-linear range of the lift curve without any correction applied to the data. The line integral of velocity along the rectangular loop enclosing the flat plate shows that the vertical components, albeit smaller in magnitude, possess the same sign and hence are additive in contribution to the circulation, whereas the horizontal components possess opposite signs and hence are subtractive in their contribution to the circulation. The paper presents some interesting and hitherto undisclosed features of flow field around the flat plate.     

The flexibility effect of a plate according to various angles of attack in a free-stream

This paper presents a computational fluid–structure interaction analysis for a flexible plate in a free-stream to investigate the effects of flexibility and angle of attack on force generation. A Lattice Boltzmann Method with an immersed boundary technique using a direct forcing scheme model of the fluid is coupled to a finite element model with rectangular bending elements. We investigated the effects of various angles of attack of a flexible plate fixed at one of the end edges in a free-stream at a Reynolds number of 5000, which represents the wing flapping condition of insects and small birds in nature. The lift of the flexible plate is maintained at the large angle of attack, whereas the rigid plate shows the largest lift at angles of attack around 30–40° and then drastic reductions in the lift at the large angle of attack. If we consider the efficiency as the lift divided by the drag, the flexible plate shows better efficiency at angles of attack greater than 30° compared to the rigid plate. The better performance of the flexible plate at large angles of attack comes from the deformation of the plate, which produces an interaction between the trailing edge vortex and the short edge vortex. The horseshoe-shaped vortex produced by a large vortex interaction at the trailing edge side has an important role in increasing the lift, and the small projection area due to the deformation reduces the drag. Furthermore, we investigate the role of flexibility on the lift and the drag force of the rectangular plate in a free-stream as the Reynolds number increases. Whenever a large vortex interaction at the trailing edge side is shown, the efficiency of the rectangular plate is improved. Especially, the flexible plate shows better efficiency as the Reynolds number increases regardless of the angle of attack.     

高机动飞行器非指令运动及其控制的研究进展

高机动飞行器往往都是通过大攻角飞行来实现高机动科目的, 在发展高机动飞行器的过程中, 其非指令运动是伴随着大攻角飞行而常常出现的运动形态. 为此, 应在飞行器设计的早期阶段, 充分研究所设计布局的大攻角流动性态及其相应的非指令运动的形态;揭示这类运动形态的主控流动;在此基础上形成和发展流动控制新技术, 以达到抑制非指令运动的目的. 由于大攻角前体非对称涡往往与非指令运动密切相关, 为此本文首先指出前体非对称涡流动对头部微扰动十分敏感, 以致长期以来让人们误认为这类流动具有不确定性. 研究表明, 通过设置人工微扰动可使前体非对称涡流动具有可重复性, 并揭示该流动随扰动周向角变化的响应、演化规律. 通过利用大、小后掠翼两类翼身组合体的典型布局形式, 研究它们所呈现的摇滚运动形态, 揭示其摇滚运动的不同主控流动机理, 在此基础上分别发展了抑制小、大后掠翼身组合体摇滚运动的流动控制技术: 快速旋转头部扰动和适当设置扰动位使翼、身的两对非对称涡处于反相. 在抑制非指令运动的研究中, 深入理解和揭示头部微扰动对非对称涡流动的响应、演化机理是至关重要的, 应予以特别关注.     

Experimental study of three-dimensional vortex structures in translating and rotating plates

Motivated by the unsteady force generation of flying animals, vortex formation and vorticity transport processes around small aspect-ratio translating and rotating plates with a high angle of attack are investigated. Defocusing Digital Particle Image Velocimetry was employed to explore the structure and dynamics of the vortex generated by the plates. For both translating and rotating cases, we observe the presence of a spanwise flow over the plate and the consequent effect of vorticity transport due to the tilting of the leading-edge vortex. While the spanwise flow is confined inside the leading-edge vortex for the translating case, it is widely present over the plate and the wake region of the rotating case. The distribution of the spanwise flow is a prominent distinction between the vortex structures of these two cases. As the Reynolds number decreases, due to the increase in viscosity, the leading-edge and tip vortices tend to spread inside the area swept by the rotating plate. The different vorticity distributions of the low and high Reynolds number cases are consistent with the difference in measured lift forces, which is confirmed using the vorticity moment theory.     

Self-similar problem of separated ideal-fluid flow over an expanding plate

The research carried out in [1–8] is developed by considering the self-similar problem of the unsteady separated flow over a plate expanding from a point with the constant velocity D of a plane-parallel stream of ideal fluid with velocity V_∞. At infinity the flow is uniform, steady and normal to the surface of the plate. A wide range of values of the parameter α=V_∞/D is investigated. On the value of α there depends, in particular, the direction of shedding of the vortex sheets (VS) which, in accordance with the Joukowsky-Chaplygin condition, occur in separated flow over a plate. A comparison is made with the results obtained when the sheets are replaced by vortex filaments (VF). In accordance with [9] the choice of the intensity of the VF ensures, like the introduction of VS, the finiteness of the flow velocity at the edges of the plate. Within the framework of the unsteady analogy and the law of plane sections the problem of the flow over a delta wing at an angle of attack reduces to the unsteady flow over an expanding plate investigated. In addition to [3, 9], this question was also examined in [10–15]. In [11–15] and in [3] the analysis is based on VS and in [9, 10] on VF. Special attention is paid to the topology of the flow, in particular, to the structure of the so-called conical streamlines and their points of convergence and divergence (this was done in [3] for a special, nonlinear law of expansion of the plate and a variable free-stream velocity). The results obtained for the models with VS and VF are compared over a broad range of values of α, not only with respect to the integral characteristics, as in [12], but also with respect to the flow patterns. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 62–69, September–October, 1988.     

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.     

Flow structure and heat transfer of impingement jet

This paper presents the characteristics of flow behavior and thermal fields of both free and impingement jets issued from circular orifice nozzle at Re = 9,700. The flow behavior of a single round jet and impingement jet were observed by smoke flow visualization recorded by a high speed video camera with 5,000 frames per second. Heat transfer coefficient on the impingement surface was calculated varying the Reynolds number and the separation distance between nozzle exit and plate. Time-series analysis was applied to the visualization image to get the information of time variation of flow behavior. Probability distribution of vortex scale induced by the jet at discrete positions was investigated. Experimental results show that the potential core is not a continuous phenomenon with time and the frequency of vortex ring formation have similar features regardless of whether the impingement plate was set on or not, furthermore the time-series analysis with flow visualization images makes clear the detailed flow behavior.     

Application of a vortex lattice numerical model in the calculation of inviscid incompressible flow around delta wings

The flow over a flat plate delta wing at incidence and in sideslip is studied using vortex lattice models based on streamwise penelling. For the attached flow problem the effect of sideslip is simulated by modifying the standard vortex lattice model for zero sideslip by aligning the trailing vortices aft of the wing along the resultant flow direction. For the separated flow problem a non-linear vortex lattice model is developed for both zero and non-zero sideslip angles in which the shape and position of the leading edge separation vortices are calculated by an iterative procedure starting from an assumed initial shape. The theoretical values are compared with available theoretical and experimental results.     

Asymmetric vortex shedding flow past an inclined flat plate at high incidence

This paper reports an experimental investigation of the vortex shedding wake behind a long flat plate inclined at a small angle of attack to a main flow stream. Detailed velocity fields are obtained with particle-image velocimetry (PIV) at successive phases in a vortex shedding cycle at three angles of attack, α=20°, 25° and 30°, at a Reynolds number Re≈5,300. Coherent patterns and dynamics of the vortices in the wake are revealed by the phase-averaged PIV vectors and derived turbulent properties. A vortex street pattern comprising a train of leading edge vortices alternating with a train of trailing edge vortices is found in the wake. The trailing edge vortex is shed directly from the sharp trailing edge while there are evidences that the formation and shedding of the leading edge vortex involve a more complicated mechanism. The leading edge vortex seems to be shed into the wake from an axial location near the trailing edge. After shedding, the vortices are convected downstream in the wake with a convection speed roughly equal to 0.8 the free-stream velocity. On reaching the same axial location, the trailing edge vortex, as compared to the leading edge vortex, is found to possess a higher peak vorticity level at its centre and induce more intense fluid circulation and Reynolds stresses production around it. It is found that the results at the three angles of attack can be collapsed into similar trends by using the projected plate width as the characteristic length of the flow.     

动失速型非定常分离涡结构的控制

本文对动失速型非定常分离涡结构的控制方法，在低速风洞中应用相平均测压技术进行了实验研究。在二元平板模型中部安装一作俯仰振荡的扰流板产生动失速型分离涡，在其上游安装另一用作控制的小扰流板。实验结果表明，应用前置的振荡小扰流板可影响并改变动失速分离涡的强度和对流特性。在最有利的控制相位下，涡吸力峰可降低４８％，涡对流时间可以推迟０．１９周期。对于间歇式振荡扰流板，采用相位提前控制方式比相位滞后控制方式更有效。     

均匀、振荡及组合流绕平板流动的尾迹研究

本文利用离散涡模型及改进的新生涡产生机制对三种不同来流绕平板的近尾迹进行数值研究。计算讨论了定常流中平板绕流流动的总体特性和近尾迹流场;对于简谐振荡来流,相应于K_c=2.0、4.0 和10.0 分别得到两种不同的尾迹形态。给出了小 K_c 数平板尾迹涡配对、运动的新模式而相应的阻力、惯性力系数计算比以前涡模拟结果更接近于 U 型管实验结果。对于流向组合来流本文模拟了涡锁定及其动力特性并于实验相符,给出了流向扰动对平板绕流流动的影响。     

Scaling of flow separation on a pitching low aspect ratio plate

We use two different dye injection approaches, in two different water tunnels, to visualize the formation and subsequent evolution of leading-edge vortices and related separated structures, for a pitching low aspect ratio plate. The motion is a smoothed linear pitch ramp from 0° to 40° incidence, brief hold, and return to 0°, executed at reduced pitch rates ranging from 0.1 to 0.35 and about various pivot locations. All cases evince a leading edge vortex with pronounced axial flow, which leads to formation of large-scale, three-dimensional flow structures, culminating in a large vortical structure centered at the wing symmetry plane. Pitch is also compared to plunge, where the plunge-induced angle of attack is taken as the geometric pitch incidence angle, ignoring pitch-rate effects. At successively increasing values of convective time C/U, the three-dimensional patterns of the flow structure are remarkably similar for the pitching and plunging motions. The similarity of these patterns persists, though they are shifted in time, for variation of either the location of the pitching axis or the dimensionless pitch rate.     

数值研究平板方舵激波-湍流边界层干扰

数值研究了平板方舵激波-湍流边界层干扰流场。模拟出了分离激波与弓型激波砬撞后形成的“λ”激波结构;消晰地显示了分离区中的旋涡结构,发现流场中会出现二次分离涡,并从理论上分析了流场对称面涡心形态与非定常的关系,得到了涡心为不稳定螺旋点或出现极限环是非定常流动特征的新结论。     

Improving vortex models via optimal control theory

Low-order inviscid point vortex models have demonstrated success in capturing the qualitative behavior of aerodynamic forces resulting from unsteady lifting surface maneuvers. However, the quantitative agreement is often lacking for separated flows as a result of the ambiguity in the edge conditions in this fundamentally unsteady process. In this work, we develop a model reduction framework in which such models can be systematically improved with empirical results. We consider the low-order impulse matching vortex model in which, in its original form, Kutta conditions are applied at both edges to determine the strengths of single point vortices shed from each edge. Here, we relax the Kutta condition imposed at the plate׳s edges and instead seek the time rate of change of the vortex strengths that minimize the discrepancy between the model-predicted and high-fidelity simulation force histories, while the vortex positions adhere to the dynamics of the low-order model. A constrained minimization problem is constructed within an optimal control framework and solved by means of variational principles. The optimization approach is demonstrated on several unsteady wing maneuvers, including pitch-up and impulsive translation at a fixed angle of attack. Additionally, a stitching technique is introduced for extending the time interval over which the model is optimized.