Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight

Aerodynamic forces and power requirements in forward flight in a bumblebee （Bombus terrestris） were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study （the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0-0.66）. The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed （advance ratio 0.66）, i.e. the power curve is Jshaped. Except at the highest flight speed, storing energy elastically can save power up to 20%-30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque （due to the smaller stroke amplitude and stroke frequency used）, the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.

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 6- component 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 aerodynam- ics, 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

Mechanism of unsteady aerodynamic heating with sudden change in surface temperature

The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.

Investigation of Unsteady Aerodynamic Characteristics of a Seagull Wing in Level Flight

Unsteady aerodynamic characteristics of a seagull wing in level flight are investigated using a boundary element method.A new no-penetration boundary condition is imposed on the surface of the wing by considering its deformation.The geometry and kinematics of the seagull wing are reproduced using the functions and data in the previously published literature.The proposed method is validated by comparing the computed results with the published data in the literature.The unsteady aerodynamics characteristics of the seagull wing are investigated by changing flapping frequency and advance ratio.It is found that the peak values of aerodynamic coefficients increase with the flapping frequency.The thrust and drag generations are complicated functions of frequency and wing stroke motions.The lift is inversely proportional to the advance ratio.The effects of several flapping modes on the lift and induced drag(or thrust)generation are also investigated.Among three single modes(flapping, folding and lead & lag),flapping generates the largest lift and can produce thrust alone.For three combined modes,both flapping/folding and flapping/lead & lag can produce lift and thrust larger than the flapping-alone mode can.Folding is shown to increase thrust when combined with flapping,whereas lead & lag has an effect of increasing the lift when also combined with flapping.When three modes are combined together,the bird can obtain the largest lift among the investigated modes.Even though the proposed method is limited to the inviscid flow assumption,it is believed that this method can be used to the design of flapping micro aerial vehicle.

Modeling Technique of the Aircraft Unsteady Aerodynamics Due to the Travelling Gust

The main equations for computing the unsteady aerodynamics of the aircraft undergoing the travelling gust are derived.Research and simulation on a specific example aircraft are performed,the results indicate that the modeling technique of the aircraft unsteady aerodynamics is correct,and it can meet the requirements due to the head⁃on and tail⁃on travelling gusts.

Comparative Study of Machine Learning Modeling for Unsteady Aerodynamics

Modern fighters are designed to fly at high angle of attacks reaching 90 deg as part of their routine maneuvers.These maneuvers generate complex nonlinear and unsteady aerodynamic loading.In this study,different aerodynamic prediction tools are investigated to achieve a model which is highly accurate,less computational,and provides a stable prediction of associated unsteady aerodynamics that results from high angle of attack maneuvers.These prediction tools include Artificial Neural Networks(ANN)model,Adaptive Neuro Fuzzy Logic Inference System(ANFIS),Fourier model,and Polynomial Classifier Networks(PCN).Themain aim of the predictionmodel is to estimate the pitch moment and the normal force data obtained from forced tests of unsteady delta-winged aircrafts performing high angles of attack maneuvers.The investigation includes three delta wing models with 1,1.5,and 2 aspect ratios with four determined variables:change rate in angle of attack(0 to 90 deg),non-dimensional pitch rate(0 to.06),and angle of attack.Following a comprehensive analysis of the proposed identification methods,it was found that the newly proposed model of PCN showed the least error in modeling and prediction results.Based on prediction capabilities,it is seen that polynomial networks modeling outperformed ANFIS and ANN for the present nonlinear problem.

Impact angle constrained fuzzy adaptive fault tolerant IGC method for Ski-to-Turn missiles with unsteady aerodynamics and multiple disturbances

An impact angle constrained fuzzy adaptive fault tolerant integrated guidance and control method for Ski-to-Turn(STT)missiles subject to unsteady aerodynamics and multiple disturbances is proposed.Unsteady aerodynamics appears when flight vehicles are in a transonic state or confronted with unstable airflow.Meanwhile,actuator failures and multisource model uncertainties are introduced.However,the boundaries of these multisource uncertainties are assumed unknown.The target is assumed to execute high maneuver movement which is unknown to the missile.Furthermore,impact angle constraint puts forward higher requirements for the interception accuracy of the integrated guidance and control(IGC)method.The impact angle constraint and the precise interception are established as the object of the IGC method.Then,the boundaries of the lumped disturbances are estimated,and several fuzzy logic systems are introduced to compensate the unknown nonlinearities and uncertainties.Next,a series of adaptive laws are developed so that the undesirable effects arising from unsteady aerodynamics,actuator failures and unknown uncertainties could be suppressed.Consequently,an impact angle constrained fuzzy adaptive fault tolerant IGC method with three loops is constructed and a perfect hit-to-kill interception with specified impact angle can be implemented.Eventually,the numerical simulations are conducted to verify the effectiveness and superiority of the proposed method.

Numerical study of the influence of dome shape on the unsteady aerodynamic performance of a high-speed train's pantograph subjected to crosswind

This study aims to investigate the unsteady aerodynamic performance of a high-speed train’s pantograph with respect to two different dome shapes and without dome under a20°yaw angle using a delayed detached eddy simulation method.Further,the influence of the dome shape on the simulation results is determined.The accuracy of the numerical method was validated by comparing a few of the numerical results with the wind tunnel test results,and high consistency was observed.An analysis of aerodynamic forces and flow structures around the pantograph was performed.The dome had significant influence on velocity field distribution surrounding the pantograph,particularly in the wake of flow region.Compared with the case where the dome was absent,vortex intensity around the pantograph increased after installing the dome.The existence of the bathtub-type dome resulted in greater flow field disturbance and vortex strength than the baffle-type dome.Moreover,the dome considerably affected time-averaged aerodynamic coefficients and their fluctuations,especially the bathtub-type dome.Additionally,the power spectral density of the unsteady aerodynamic coefficient of each pantograph component exhibited significant peaks and typical broadband distribution characteristics.

Unsteady aerodynamic modeling at high angles of attack using support vector machines

Abstract Accurate aerodynamic models are the basis of flight simulation and control law design. Mathematically modeling unsteady aerodynamics at high angles of attack bears great difficulties in model structure determination and parameter estimation due to little understanding of the flow mechanism. Support vector machines （SVMs） based on statistical learning theory provide a novel tool for nonlinear system modeling. The work presented here examines the feasibility of applying SVMs to high angle.-of-attack unsteady aerodynamic modeling field. Mainly, after a review of SVMs, several issues associated with unsteady aerodynamic modeling by use of SVMs are discussed in detail, such as sele, ction of input variables, selection of output variables and determination of SVM parameters. The least squares SVM （LS-SVM） models are set up from certain dynamic wind tunnel test data of a delta wing and an aircraft configuration, and then used to predict the aerodynamic responses in other tests. The predictions are in good agreement with the test data, which indicates the satisfving learning and generalization performance of LS-SVMs.

Panel/full-span free-wake coupled method for unsteady aerodynamics of helicopter rotor blade

A full-span free-wake method is coupled with an unsteady panel method to accurately predict the unsteady aerodynamics of helicopter rotor blades in hover and forward flight. The unsteady potential-based panel method is used to consider aerodynamics of finite thickness multi-bladed rotors, and the full-span free-wake method is applied to simulating dynamics of rotor wake. These methods are tightly coupled through trailing-edge Kutta condition and by converting doublet-wake panels to full-span vortex filaments. A velocity-field integration technique is also adopted to overcome singularity problem during the interaction between the rotor wake and blades. Helicopter rotors including Caradonna–Tung, UH-60A, and AH-1G rotors, are simulated in hover and forward flight to validate the accuracy of this approach. The predicted aerodynamic loads of rotor blades agree well with available measured data and computational fluid dynamics （CFD） results, and the unsteady dynamics of rotor wake is also well simulated. Compared to CFD, the present method obtains accurate results more efficiently and is suitable to rotorcraft aeroelastic analysis.

Unstable unsteady aerodynamic modeling based on least squares support vector machines with general excitation

Common,unsteady aerodynamic modeling methods usually use wind tunnel test data from forced vibration tests to predict stable hysteresis loop.However,these methods ignore the initial unstable process of entering the hysteresis loop that exists in the actual maneuvering process of the aircraft.Here,an excitation input suitable for nonlinear system identification is introduced to model unsteady aerodynamic forces with any motion in the amplitude and frequency ranges based on the Least Squares Support Vector Machines(LS-SVMs).In the selection of the input form,avoiding the use of reduced frequency as a parameter makes the model more universal.After model training is completed,the method is applied to predict the lift coefficient,drag coefficient and pitching moment coefficient of the RAE2822 airfoil,in sine and sweep motions under the conditions of plunging and pitching at Mach number 0.8.The predicted results of the initial unstable process and the final stable process are in close agreement with the Computational Fluid Dynamics(CFD)data,demonstrating the feasibility of the model for nonlinear unsteady aerodynamics modeling and the effectiveness of the input design approach.

Effects of unsteady deformation of flapping wing on its aerodynamic forces

Effects of unsteady deformation of a＇flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations on a dynamically deforming grid. Aerodynamic forces on the flapping wing are not much affected by considerable twist, but affected by camber deformation. The effect of combined camber and twist deformation is similar to that of camber deformation. With a deformation of 6% camber and 20% twist （typical values observed for wings of many insects）, lift is increased by 10% - 20% and lift-to-drag ratio by around 10% compared with the case of a rigid fiat-plate wing. As a result, the deformation can increase the maximum lift coefficient of an insect, and reduce its power requirement for flight. For example, for a hovering bumblebee with dynamically deforming wings （6% camber and 20% twist）, aerodynamic power required is reduced by about 16% compared with the case of rigid wings.

A SIMPLIFIED THEORY FOR UNSTEADY AERODYNAMIC FORCES ACTING ON AN AIRFOIL FLYING ABOVE SEA-WAVES

A simplified theoretical method based on the quasi-steady wing theory wasproposed to study the unsteady aerodynamic forces acting on an airfoil flying in non-uniform flow.Comparison between the theoretical results and the numerical results based on nonlinear theory wasmade. It shows that the simplified theory is a good approximation for the investigation of theaerodynamic characteristics of an airfoil flying above sea-waves. From on the simplified theory itis also found that an airfoil can get thrust from a wave-disturbed airflow and thus the total dragis reduced. And the relationship among the thrust, the flying altitude, the flying speed and thewave parameters was worked out and discussed.

Numerical Study of the Unsteady Aerodynamics of Freely Falling Plates

The aerodynamics of freely falling objects is one of the most interesting flow mechanics problems.In a recent study,Andersen,Pesavento,and Wang[J.Fluid Mech.,vol.541,pp.65-90(2005)]presented the quantitative comparison between the experimental measurement and numerical computation.The rich dynamical behavior,such as fluttering and tumbling motion,was analyzed.However,obvious discrepancies between the experimental measurement and numerical simulations still exist.In the current study,a similar numerical computation will be conducted using a newly developed unified coordinate gas-kinetic method[J.Comput.Phys,vol.222,pp.155-175(2007)].In order to clarify some early conclusions,both elliptic and rectangular falling plates will be studied.Under the experimental condition,the numerical solution shows that the averaged translational velocity for both rectangular and elliptical plates are almost identical during the tumbling motion.However,the plate rotation depends strongly on the shape of the plates.In this study,the details of fluid forces and torques on the plates and plates movement trajectories will be presented and compared with the experimental measurements.

Optimum Duty Cycle of Unsteady Plasma Aerodynamic Actuation for NACA0015 Airfoil Stall Separation Control

Unsteady dielectric barrier discharge（DBD） plasma aerodynamic actuation technology is employed to suppress airfoil stall separation and the technical parameters are explored with wind tunnel experiments on an NACA0015 airfoil by measuring the surface pressure distribution of the airfoil.The performance of the DBD aerodynamic actuation for airfoil stall separation suppression is evaluated under DBD voltages from 2000 V to 4000 V and the duty cycles varied in the range of 0.1 to 1.0.It is found that higher lift coefficients and lower threshold voltages are achieved under the unsteady DBD aerodynamic actuation with the duty cycles less than 0.5as compared to that of the steady plasma actuation at the same free-stream speeds and attack angles,indicating a better flow control performance.By comparing the lift coefficients and the threshold voltages,an optimum duty cycle is determined as 0.25 by which the maximum lift coefficient and the minimum threshold voltage are obtained at the same free-stream speed and attack angle.The non-uniform DBD discharge with stronger discharge in the positive half cycle due to electrons deposition on the dielectric slabs and the suppression of opposite momentum transfer due to the intermittent discharge with cutoff of the negative half cycle are responsible for the observed optimum duty cycle.

The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings

The effects of corrugation and wing planform （shape and aspect ratio） on the aerodynamic force production of model insect wings in sweeping （rotating after an initial start） motion at Reynolds number 200 and 3500 at angle of attack 40℃ are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio （AR） of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing （forewing）, hawkmoth and dragon- fly （forewing）, respectively （AR of these wings varies greatly, from 2.84 to 5.45）. The following facts are shown. （1） The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex （LEV）. （2） The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r2 （the radius of the second ：moment of wing area） is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. （3） The effects of AR are remarkably small： whenAR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients.

The influence of the wake of a flapping wing on the production of aerodynamic forces

The effect of the wake of previous strokes on the aerodynamic forces of a flapping model insect wing is studied using the method of computational fluid dynamics. The wake effect is isolated by comparing the forces and flows of the starting stroke （when the wake has not developed） with those of a later stroke （when the wake has developed）. The following has been shown. （1） The wake effect may increase or decrease the lift and drag at the beginning of a half-stroke （downstroke or upstroke）, depending on the wing kinematics at stroke reversal. The reason for this is that at the beginning of the half-stroke, the wing “impinges” on the spanwise vorticity generated by the wing during stroke reversal and the distribution of the vorticity is sensitive to the wing kinematics at stroke reversal. （2） The wake effect decreases the lift and increases the drag in the rest part of the half-stroke. This is because the wing moves in a downwash field induced by previous half-stroke＇s starting vortex, tip vortices and attached leading edge vortex （these vortices form a downwash producing vortex ring）. （3） The wake effect decreases the mean lift by 6%-18% （depending on wing kinematics at stroke reversal） and slightly increases the mean drag. Therefore, it is detrimental to the aerodynamic performance of the flapping wing.

Aerodynamics and mechanisms of elementary morphing models for flapping wing in forward flight of bat

Large active wing deformation is a significant way to generate high aerodynamic forces required in bat＇s flapping flight. Besides the twisting, elementary morphing models of a bat wing are proposed, including wing-bending in the spanwise direction,wing-cambering in the chordwise direction, and wing area-changing. A plate of aspect ratio 3 is used to model a bat wing, and a three-dimensional unsteady panel method is used to predict the aerodynamic forces. It is found that the cambering model has great positive influence on the lift, followed by the area-changing model and then the bending model. Further study indicates that the vortex control is a main mechanism to produce high aerodynamic forces. The mechanisms of aerodynamic force enhancement are asymmetry of the cambered wing and amplification effects of wing area-changing and wing bending. Lift and thrust are generated mainly during downstroke, and they are almost negligible during upstroke by the integrated morphing model-wing.

CFD Based Determination of Dynamic Stability Derivatives in Yaw for a Bird

Dynamic yaw stability derivatives of a gull bird are determined using Computational Fluid Dynamics（CFD） method. Two kinds of motions are applied for calculating the dynamic yaw stability derivatives CNr and CNβ. The first one relates to a lateral translation and, separately, to a yaw rotation. The second one consists of a combined translational and rotational motion. To determine dynamic yaw stability derivatives, the simulation of an unsteady flow with a bird model showing a harmonic motion is performed. The flow solution for each time step is obtained by solving unsteady Euler equations based on a finite volume approach for a small reduced frequency. Then, an evaluation of unsteady forces and moments for one cycle is conducted using harmonic Fourier analysis. The results of the dynamic yaw stability derivatives for both simulations of the model show a good agreement.

Enclosure enhancement of flight performance

We use a potential flow solver to investigate the aerodynamic aspects of flapping flights in enclosed spaces. The enclosure effects are simulated by the method of images. Our study complements previous aerodynamic analyses which considered only the near-ground flight. The present results show that flying in the proximity of an enclosure affects the aerodynamic performance of flapping wings in terms of lift and thrust generation and power consumption. It leads to higher flight efficiency and more than 5% increase of the generation of lift and thrust.