Correlation between vortex structures and unsteady loads for flapping motion in hover

During the past decade, efforts were made to develop a new generation of unmanned aircrafts, qualified as Micro-Air Vehicles. The particularity of these systems resides in their maximum dimension limited to 15 cm, which, in terms of aerodynamics, corresponds to low Reynolds number flows (Re ≈ 10² to 10⁴). At low Reynolds number, the concept of flapping wings seems to be an interesting alternative to the conventional fixed and rotary wings. Despite the fact that this concept may lead to enhanced lift forces and efficiency ratios, it allows hovering coupled with a low-noise generation. Previous studies (Dickinson et al. in Science 284:1954–1960, 1999) revealed that the flow engendered by flapping wings is highly vortical and unsteady, inducing significant temporal variations of the loads experienced by the airfoil. In order to enhance the aerodynamic performance of such flapping wings, it is essential to give further insight into the loads generating mechanisms by correlating the spatial and temporal evolution of the vortical structures together with the time-dependent lift and drag. In this paper, Time Resolved Particle Image Velocimetry is used as a basis to evaluate both unsteady forces and vortical structures generated by an airfoil undergoing complex motion (i.e. asymmetric flapping flight), through the momentum equation approach and a multidimensional wavelet-like vortex parameterization method, respectively. The momentum equation approach relies on the integration of flow variables inside and around a control volume surrounding the airfoil (Noca et al. in J Fluids Struct 11:345–350, 1997; Unal et al. in J Fluids Struct 11:965–971, 1997). Besides the direct link performed between the flow behavior and the force mechanisms, the load characterization is here non-intrusive and specifically convenient for flapping flight studies thanks to its low Reynolds flows’ sensitivity and adaptability to moving bodies. Results are supported by a vortex parameterization which evaluates the circulation of the multiple vortices generated in such complex flows. The temporal evolution of the loads matches the flow behavior and hence reveals the preponderant inertial force component and that due to vortical structures.     

Aerodynamic force and flow structures of two airfoils in flapping motions

Aerodynamic force and flow structures of two airfoils in a tandem configuration in flapping motions are studied, by solving the Navier-Stokes equations in moving overset grids. Three typical phase differences between the fore- and aftairfoil flapping cycles are considered. It is shown that: (1) in the case of no interaction (single airfoil), the time average of the vertical force coefficient over the downstroke is 2.74, which is about 3 times as large as the maximum steady-state lift coefficient of a dragonfly wing; the time average of the horizontal force coefficient is 1.97, which is also large. The reasons for the large force coefficients are the acceleration at the beginning of a stroke, the delayed stall and the “pitching-up” motion near the end of the stroke. (2) In the cases of two-airfoils, the time-variations of the force and moment coefficients on each airfoil are broadly similar to that of the single airfoil in that the vertical force is mainly produced in downstroke and the horizontal force in upstroke, but very large differences exist due to the interaction. (3) For in-phase stroking, the major differences caused by the interaction are that the vertical force on FA in downstroke is increased and the horizontal force on FA in upstroke decreased. As a result, the magnitude of the resultant force is almost unchanged but it inclines less forward. (4) For counter stroking, the major differences are that the vertical force on AA in downstroke and the horizontal force on FA in upstroke are decreased. As a result, the magnitude of the resultant force is decreased by about 20 percent but its direction is almost unchanged. (5) For 90°-phase-difference stroking, the major differences are that the vertical force on AA in downstroke and the horizontal force on FA in upstroke are decreased greatly and the horizontal force on AA in upstroke increased. As a result, the magnitude of the resultant force is decreased by about 28% and it inclines more forward. (6) Among the three cases of phase angles, inphase flapping produces the largest vertical force (also the largest resultant force); the 90°-phase-difference flapping results in the largest horizontal force, but the smallest resultant force.     

Aerodynamic mechanism of forces generated by twisting model-wing in bat flapping flight

The aerodynamic mechanism of the bat wing membrane Mong the lateral border of its body is studied. The twist-morphing that alters the angle of attack （AOA） along the span-wise direction is observed widely during bat flapping flight. An assumption is made that the linearly distributed AOA is along the span-wise direction. The plate with the aspect ratio of 3 is used to model a bat wing. A three-dimensional （3D） unsteady panel method is used to predict the aerodynamic forces generated by the flapping plate with leading edge separation. It is found that, relative to the rigid wing flapping, twisting motion can increase the averaged lift by as much as 25% and produce thrust instead of drag. Furthermore, the aerodynamic forces （lift/drag） generated by a twisting plate-wing are similar to those of a pitching rigid-wing, meaning that the twisting in bat flight has the same function as the supination/pronation motion in insect flight.     

Asymmetric motion of a two-dimensional symmetric flapping model

A two-dimensional symmetric flapping model is studied in terms of the bifurcation using discrete vortex method. This model consists of two wings attached together at a hinge, and the flapping motion of the wings is symmetric with respect to the horizontal line. The center of mass of this model can move according to the hydrodynamic force generated by an interaction of the wing and vortices separated from boundary layer. The bifurcation parameter is a time scale of the dissipation, which is simplified to contrast the transition of the type of the motion. Bifurcation diagram shows that steady motion of zero-mean velocity (with symmetric flapping) is unstable in a parameter region, and that there is another region where two types of a steady stable flapping motion coexist. We illustrate these types of the motion.     

Limit cycle oscillation suppression controller design and stability analysis of the periodically time-varying flapping flight dynamics in hover

Nonlinear Dynamics - The periodically time-varying forces make the equilibrium state of Beihawk, an X-shaped flapping-wing aircraft, to be a periodic limit cycle oscillation. However, traditional...     

Mixing characteristics of a film-exciting flapping jet

We have recently discovered a new type of self-excited flapping jets due to a flexible film whose leading edge is fixed at the nozzle exit [Exp Ther Fluid Sci, 106, 226-233]. This paper is to report the experimental investigation on mixing characteristics of the jet induced by a rectangular FEP film. Hot wire anemometry and flow visualization are used to examine the flapping jet flow versus the non-flapping counterpart. Experiments are conducted under the following conditions: i.e., L/D = 1.0 (fixed), W/D = 0.03 ~ 1.0 (varying) and Re = 10000 ~ 45000 (varying); where W and L are the film's width and length, D is the nozzle-exit diameter, and Re is the Reynolds number defined by Re U_oD/ν with U_o and ν being the jet-exit velocity and fluid viscosity.It is found that the jet-flapping frequency f_F varies with W in a complex fashion while it grows roughly linearly with increasing U_o for W/D ≥ 0.5. The flapping Strouhal number St_F f_FD/U_o ranges in 0.13 ≤ St_F ≤ 0.23 for Re = 15,000 ~ 45,000. These Strouhal numbers are substantially lower than that (≈ 0.45 ~ 0.7) for the primary vortex generation in the free jet, but one to two orders of magnitude higher than those from the conventional self-exciting fluidic devices. In general, the flapping jet decays and spreads more rapidly than does the free jet. As W increases, the decaying and spreading rates both grow. Of significance, the centerline evolutions of Taylor and Kolmogorov scales versus the integral scale are examined to characterize the small scales of turbulence against the large-scale motion.     

Wing characteristics and flapping behavior of flying insects

This paper is concerned with the flapping characteristics and the structure dynamics of insect wings. The flapping behavior of some insects is studied using a threedimensional motion analysis system. The experimental system is composed of two high-speed video cameras, a motion grabber, and a personal computer. The three-dimensional representation of insect flapping can be gained by the system. The extrinsic skeleton vibration produced by insect flapping is examined with the optical displacement detector system. The structural properties of some insect wings are also studied by a three-dimensional, optical shape measurement system. Some functional principles underlying insect wing design are revealed by the measurements of surface roughness and flapping analysis.     

VISCOELASTIC CONSTITUTIVE MODEL RELATED TO DEFORMATION OF INSECT WING UNDER LOADING IN FLAPPING MOTION

Flexible insect wings deform passively under the periodic loading during napping flight. The wing flexibility is considered as one of the specific mechanisms on improving insect flight performance. The constitutive relation of the insect wing material plays a key role on the wing deformation, but has not been clearly understood yet. A viscoelastic constitutive relation model was established based on the stress relaxation experiment of a dragonfly wing (in vitro). This model was examined by the finite element analysis of the dynamic deformation response for a model insect wing under the action of the periodical inertial force in flapping. It is revealed that the viscoelastic constitutive relation is rational to characterize the biomaterial property of insect wings in contrast to the elastic one. The amplitude and form of the passive viscoelastic deformation of the wing is evidently dependent on the viscous parameters in the constitutive relation.     

Aerodynamic characteristics of airfoils with energy supply

The possibility of controlling the aerodynamic characteristics of airfoils with the help of one-sided pulsed-periodic energy supply is studied. The change in the flow structure near the airfoil and its aerodynamic characteristics are determined as functions of the magnitude of energy supply and of the energy-supply location by means of the numerical solution of two-dimensional unsteady equations of gas dynamics. It is demonstrated that external energy supply can substantially improve the aerodynamic characteristics of airfoils with a high lift-to-drag ratio. The moment characteristics of the airfoil are found.     

Flow field characteristics study of a flapping airfoil using computational fluid dynamics

The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with complex nonlinear vortex shedding and viscous phenomena. The respective fluid dynamics of such a flow is investigated here through Computational Fluid Dynamics (CFD) based on the Finite Volume Method (FVM). The governing equations are the unsteady, incompressible two-dimensional Navier-Stokes (N-S) equations. The airfoil is a thin ellipsoidal geometry performing a modified figure-of-eight-like flapping pattern. The flow field and vortical patterns around the airfoil are examined in detail, and the effects of several unsteady flow and system parameters on the flow characteristics are explored. The investigated parameters are the amplitude of pitching oscillations, phase angle between pitching and plunging motions, mean angle of attack, Reynolds number (Re), Strouhal number (St) based on the translational amplitudes of oscillations, and the pitching axis location (x/c). It is shown that these parameters change the instantaneous force coefficients quantitatively and qualitatively. It is also observed that the strength, interaction, and convection of the vortical structures surrounding the airfoil are significantly affected by the variations of these parameters.     

Aerodynamic characteristics of a delta wing in hypersonic flow

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 66–69, March–April, 1994.     

局部粗糙机翼表面气动特性影响研究

采用柱型粗糙元,以尖劈和机翼外形为基础,利用CFD数值模拟方法,研究机翼表面局部粗糙区域对其周围气动特性的影响。研究相同粗糙元高度下,粗糙元位于尖劈表面不同位置时局部边界层和气动特性的变化情况;基于流动分区理论,采用空气动力学理论分析与数值模拟结合的方法,分析F16机翼可接受的局部粗糙元高度;根据分析结果,在改进平板外形基础上,验证不同粗糙元高度对改进目标块区域气动特性的影响程度,并给出流经局部粗糙区域的流体发展状况。为了验证数值结果的准确性,采用S-A与SST湍流模型进行对比求解。本文工作对复杂大气环境引起的飞行器局部粗糙表面区域气动特性变化的研究具有指导意义。     

基于FlowStar软件的栅格舵气动特性模拟

栅格舵是由外部边框和内部若干薄栅格组成的一种新型气动力面和控制面。由于其具有尺寸小、重量轻和易折叠等结构特点,以及升力特性好、铰链力矩小和压心位置随马赫数变化小等良好的气动性能,越来越受到重视和广泛应用。但是,由于栅格舵是特殊的蜂窝结构,常规的结构网格生成困难,并且栅格壁之间存在严重的波系干扰,流场结构复杂,给数值模拟带来了挑战。本文针对栅格舵流场结构复杂、网格生成和数值模拟难度大的难题,采用国家数值风洞工程(NNW)项目团队自主开发的非结构混合网格流场软件FlowStar,对栅格舵气动特性开展了数值模拟研究。首先,通过十字栅格舵全弹标模外形,验证了数值模拟方法的可靠性。然后,通过研究栅格不同形状对栅格舵气动特性的影响规律,给出了栅格舵设计时尽量采用气动性能较高和结构强度较好的菱形栅格,以及尽可能少用或不用正三角形栅格的指导建议。最后,开展了类Space X迎风面局部弧形栅格舵气动特性模拟研究,结果表明,弧形后掠可以有效降低阻力,提高升阻比;攻角为0°时,与平直栅格舵相比,弧形后掠栅格舵在亚跨声速阶段,阻力降低约8%,马赫数大于2时,阻力降低约15%。本文研究可为栅格舵的设计提供参考和...