Stabilization control of a hovering model insect:lateral motion

Our previous study shows that the lateral disturbance motion of a model drone fly does not have inherent stability (passive stability),because of the existence of an unstable divergence mode.But drone flies are observed to fly stably.Constantly active control must be applied to stabilize the flight.In this study,we investigate the lateral stabilization control of the model drone fly.The method of computational fluid dynamics is used to compute the lateral control derivatives and the techniques of eigenvalue...     

Stabilization control of a bumblebee in hovering and forward flight

Our previous study shows that the hovering and forward flight of a bumblebee do not have inherent stability （passive stability）. But the bumblebees are observed to fly stably. Stabilization control must have been applied. In this study, we investigate the longitudinal stabilization control of the bumblebee. The method of computational fluid dynamics is used to compute the control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion. Controllability analysis shows that at all flight speeds considered, although inherently unstable, the flight is controllable. By feedbacking the state variables, i.e. vertical and horizontal velocities, pitching rate and pitch angle （which can be measured by the sensory system of the insect）, to produce changes in stroke angle and angle of attack of the wings, the flight can be stabilized, explaining why the bumblebees can fly stably even if they are passively unstable.     

Dynamic flight stability of a model dronefly in vertical flight

The dynamic flight stability of a model dronefly in hovering and upward flight is studied.The method of computational fluid dynamics is used to compute the stability derivatives and the techniques of eigenvalue and eigenvector used to solve the equations of motion.The major finding is as following.Hovering flight of the model dronefly is unstable because of the existence of an unstable longitudinal and an unstable lateral natural mode of motion.Upward flight of the insect is also unstable,and the instability increases as the upward flight speed increases.Inertial force generated by the upward flight velocity coupled with the disturbance in pitching angular velocity is responsible for the enhancement of the instability.     

Lateral dynamic flight stability of hovering insects: theory vs. numerical simulation

In the present paper, the lateral dynamic flight stability properties of two hovering model insects are predicted by an approximate theory based on the averaged model, and computed by numerical simulation that solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theoretical and simulational results provides a test to the validity of the assumptions made in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency (164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency (26 Hz). The following conclusion has been drawn. The theory based on the averaged model works well for the lateral motion of the dronefly. For the hawkmoth, relatively large quantitative differences exist between theory and simulation. This is because the lateral non-dimensional eigenvalues of the hawkmoth are not very small compared with the non-dimensional flapping frequency (the largest lateral non-dimensional eigenvalue is only about 10% smaller than the non-dimensional flapping frequency). Nevertheless, the theory can still correctly predict variational trends of the dynamic properties of the hawkmoth’s lateral motion.     

Dynamic flight stability of hovering model insects: theory versus simulation using equations of motion coupled with Navier–Stokes equations

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical sim- ulation. The theory is based on the averaged model （which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings＇ degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments）; the simulation solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency （164 Hz） and the other is a model hawkmoth which has relatively low wingbeat frequency （26 Hz）. The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low （the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large） compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.     

Dynamic flight stability of a hovering model insect: lateral motion

The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.     

Unsteady aerodynamics modeling for flight dynamics application

In view of engineering application, it is practicable to decompose the aerodynamics into three components: the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms while the third is described using a one-order differential equation and a radial-basis-function (RBF) network. For an aircraft configuration, the mathematical models of 6component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynamics, respectively. The results show that: (1) unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; (2) unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and (3) unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability are analyzed by numerical simulation.     

等热流密度加热垂直下降液膜的研究

利用等热流密度加热条件下降膜流动的三维模型方程进行线性稳定性分析和数值模拟。线性稳定性分析表明，模型方程在小到中等Reynolds数下都适用，并且流向不稳定性增长率随着Reynolds数和Marangoni数增加而增加，展向不稳定性增长率则随着Marangoni数增加而增加，随着Reynolds数增加而减小，流向和展向对扰动波数都存在一个不稳定区间。三维数值模拟表明，在等热流密度加热条件下，液膜在随机扰动的情况下最终会形成带孤立波的三维溪流状结构，液膜与气体的换热也因溪流状结构的出现而加强；在随机扰动的基础上引入占优势地位的展向最不稳定扰动会使得换热增强，液膜会提前破裂；在随机扰动的基础上引入占优势地位的流向最不稳定扰动时，液膜的换热会增强，但不会提前破裂；在随机扰动的基础上同时引入占优势地位的流向和展向最不稳定扰动时，换热会加强且液膜会提前破裂。     

ACTIVE SEPARATION CONTROL FOR THE FLYING-WING UAV USING SYNTHETIC JET

以小展弦比飞翼式无人机为对象,开展了基于零质量射流的主动流动控制数值模拟研究. 比较分析了应用零质量射流前后飞翼式无人机纵向气动特性的改善效果,并通过流场特征的分析探讨了流动控制技术产生气动增益的原因. 研究结果表明在模型中等迎角、大迎角范围,零质量射流技术可以显著增加升力系数,最大幅值达25%,并且拓宽了纵向力矩的线性范围. 机理分析表明,零质量射流扰动通过提高模型绕流场的边界层掺混,增强附面层内外的动量输运,使得附面层有足够的能量克服逆压梯度和黏性损耗,从而达到减缓流动分离甚至使分离流再附的目的.     

Dynamic flight stability of a bumblebee in forward flight

The longitudinal dynamic flight stability of a bumblebee in forward flight is studied. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The primary findings are as the following. The forward flight of the bumblebee is not dynamically stable due to the existence of one （or two） unstable or approximately neutrally stable natural modes of motion. At hovering to medium flight speed [flight speed Ue = （0-3.5）m s^-1; advance ratio J = 0-0.44], the flight is weakly unstable or approximately neutrally stable; at high speed （Ue = 4.5 m s^-1; J = 0.57）, the flight becomes strongly unstable （initial disturbance double its value in only 3.5 wingbeats）.     

高超声速飞行器横侧向失稳非线性分岔分析

针对滑翔式高超声速飞行器大攻角横侧向失稳问题,采用延拓算法和分岔理论,求解并分析了以俯仰舵偏为连续参数的稳态平衡分岔图和以副翼舵偏为连续参数的横侧向机动稳态平衡分岔图,对平衡分支的稳定性和突变点进行了分析,并给出了特征根拓扑结构变化.研究表明,高超声速飞行器存在极限分岔点、Hopf分岔点以及叉型分岔点,且从叉型分岔点延伸出多个平衡分支,引起横侧向的自滚转失稳;从Hopf分岔点延伸出极限环分支,该分支对应较为复杂的极限环运动,其中还包含倍周期分岔、花环分岔、极限环极限点分岔等复杂的分岔现象;在横侧向机动飞行情况下,模型存在横向操作偏离失稳问题,且存在多个不稳定的平衡点.研究结果为实现高超声速飞行器的稳定飞行和控制器的设计提供了极其重要的动力学信息.      

Dynamic flight stability of hovering insects

The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the “rigid body” assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects (hoverfly, cranefly, dronefly and hawkmoth) in hovering flight is studied (the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157 Hz). The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the “rigid body” assumption is tested and how differences in size and wing kinematics influence the applicability of the “rigid body” assumption is investigated. The primary findings are: (1) For insects considered in the present study and those with relatively high wingbeat frequency (hoverfly, drone fly and bumblebee), the “rigid body” assumption is reasonable, and for those with relatively low wingbeat frequency (cranefly and howkmoth), the applicability of the “rigid body” assumption is questionable. (2) The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. (3) Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative M _u (pitching moment produced by unit horizontal speed) as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Z _w (vertical force produced by unit vertical speed) as the primary source of the stable slow subsidence mode. The project supported by the National Natural Science Foundation of China (10232010 and 10472008).     

飞翼布局无人机流动分离控制及机理分析

以小展弦比飞翼式无人机为对象,开展了基于零质量射流的主动流动控制数值模拟研究. 比较分析了应用零质量射流前后飞翼式无人机纵向气动特性的改善效果,并通过流场特征的分析探讨了流动控制技术产生气动增益的原因. 研究结果表明在模型中等迎角、大迎角范围,零质量射流技术可以显著增加升力系数,最大幅值达25%,并且拓宽了纵向力矩的线性范围. 机理分析表明,零质量射流扰动通过提高模型绕流场的边界层掺混,增强附面层内外的动量输运,使得附面层有足够的能量克服逆压梯度和黏性损耗,从而达到减缓流动分离甚至使分离流再附的目的.      

方形截面弹俯仰振荡对滚转特性的影响

飞行器在大气环境中飞行时,经常受阵风等的干扰,引发非指令的自激振荡,威胁飞行安全.通过建立刚体六自由度运动方程和N-S方程的松耦合求解技术,研究强迫俯仰振荡过程对滚转特性的影响.针对背风区涡流形态及横侧向气动特性复杂的方形截面飞行器,数值模拟研究了其不同攻角下的静态滚转气动特性、自由滚转运动特性,以及俯仰振荡时不同振荡速率对滚转气动和运动特性的影响.结果表明,此飞行器在静态时临界攻角约为13°,当攻角小于临界攻角时,滚转方向是静不稳定的,诱发快速滚转运动;当攻角大于临界攻角时,滚转方向是静稳定,其滚转运动是收敛的.研究发现,俯仰振荡一般会降低飞行器滚转方向静稳定或静不稳定的量值,增强滚转方向的动态稳定性.在俯仰振荡的影响下,即使滚转方向是静不稳定的,如果俯仰振荡的频率足够大,飞行器的滚转运动也可能是收敛的.     

Stability of aneurysm solutions in a fluid-filled elastic membrane tube

When a hyperelastic membrane tube is inflatedby an internal pressure, a localized bulge will form when thepressure reaches a critical value. As inflation continues thebulge will grow until it reaches a maximum size after whichit will then propagate in both directions to form a hat-likeprofile. The stability of such bulging solutions has recentlybeen studied by neglecting the inertia of the inflating fluidand it was shown that such bulging solutions are unstableunder pressure control. In this paper we extend this recentstudy by assuming that the inflation is by an inviscid fluidwhose inertia we take into account in the stability analysis.This reflects more closely the situation of aneurysm forma-tion in human arteries which motivates the current series ofstudies. It is shown that fluid inertia would significantly re-duce the growth rate of the unstable mode and thus it has astrong stabilizing effect.     

一种平行曲柄连杆扑翼机构的设计、优化与实现

提出了一种来自于昆虫结构启发的平 行曲柄连杆的扑翼机构. 该机构依靠两组平行布置的曲 柄连杆和连杆间的翼面控制机构实现, 既能够保证扑翼运动左右翼面的对称性, 又能够实现挥拍 攻角的调节和控制, 采用MATLAB的非线性优化工具对该扑翼机构进行了运动参数的 优化, 并设计制作了大比例的实物扑翼模型进行测力分析. 结果验证了这种扑 翼机构能够给出非定常高升力.     

On the unsteady motion and stability of a heaving airfoil in ground effect

This study explores the fluid mechanics and force generation capabilities of an inverted heaving airfoil placed close to a moving ground using a URANS solver with the Spalart-Allmaras turbulence model. By varying the mean ground clearance and motion frequency of the airfoil, it was possible to construct a frequency-height diagram of the various forces acting on the airfoil. The ground was found to enhance the downforce and reduce the drag with respect to freestream. The unsteady motion induces hysteresis in the forces’ behaviour. At moderate ground clearance, the hysteresis increases with frequency and the airfoil loses energy to the flow, resulting in a stabilizing motion. By analogy with a pitching motion, the airfoil stalls in close proximity to the ground. At low frequencies, the motion is unstable and could lead to stall flutter. A stall flutter analysis was undertaken. At higher frequencies, inviscid effects overcome the large separation and the motion becomes stable. Forced trailing edge vortex shedding appears at high frequencies. The shedding mechanism seems to be independent of ground proximity. However, the wake is altered at low heights as a result of an interaction between the vortices and the ground.     

平流层飞艇动力学与控制研究进展

本文简要介绍了飞艇的发展沿革和研究现状. 通过同传统的航空器、航天器、潜艇和低空飞艇进行比较, 阐述了平流层飞艇的飞行原理. 从基本运动模型和复杂受力情况的角度, 系统地讨论了飞艇动力学研究进展, 包括空气动力学研究、静力分析、热力学分析、柔性体动力学及流固耦合研究. 然后综述了飞艇控制方法研究进展, 包括小扰动线性化控制、输入输出反馈线性化控制、基于Lyapunov 非线性稳定性的控制及其他控制方法. 最后展望了在平流层飞艇动力学与控制领域需要从6 个方面加强研究.      

An analytical control law of length rate for tethered satellite system

Based on the nonlinear dynamic equations of a tethered satellite system with three-dimensional attitude motion, an analytical tether length rate control law for deployment is derived from the equilibrium positions of the system and the scheme of the value range of the expected in-plane pitch angle. The proposed control law can guarantee that the tensional force acting on the end of the tether remains positive. The oscillation of the out-of-plane roll motion in conjunction with the in-plane pitch motion is effectively suppressed during deployment control. The analytical control law is still applicable, even if the system runs on a Keplerian elliptical orbit with a large eccentricity. The local stability of the non-autonomous system during deployment control is analyzed using the Floquet theory, and the global behavior is numerically verified using simple cell mapping. The numerical simulations in the paper demonstrate the proposed analytical control law.     

Stabilizing effect of diffusion in enhanced oil recovery and three-layer Hele-Shaw flows with viscosity gradient

In the presence of diffusion, stability of three-layer Hele-Shaw flows which models enhanced oil recovery processes by polymer flooding is studied for the case of variable viscosity in the middle layer. This leads to the coupling of the momentum equation and the species advection-diffusion equation the hydrodynamic stability study of which is presented in this paper. Linear stability analysis of a potentially unstable three-layer rectilinear Hele-Shaw flow is used to examine the effects of species diffusion on the stability of the flow. Using a weak formulation of the disturbance equations, upper bounds on the growth rate of individual disturbances and on the maximal growth rate over all possible disturbances are found. Analytically, it is shown that a short-wave disturbance if unstable can be stabilized by mild diffusion of species, where as an unstable long-wave disturbance can always be stabilized by strong diffusion of species. Thus, an otherwise unstable three-layer Hele-Shaw flow can be completely stabilized by a large enough diffusion, i.e., by increasing enough the magnitude of the species diffusion coefficient. The magnitude of this diffusion coefficient required to completely stabilize the flow will depend on the magnitude of interfacial viscosity jumps and the viscosity gradient of the basic viscous profile of the middle layer.