Flight dynamics in forward flights of cabbage white butterfly

Comparative study between a discrete vortex method and an immersed boundary–lattice Boltzmann method in 2D flapping flight analysis

It is well known that aircraft undergoing high angle of attack excursions (e.g., the Cobra maneuver) may experience asymmetric forebody vortex shedding under certain conditions. The detachment of these vortices from the forebody is similar to that observed from von Karman vortex shedding from cylinders. A series of experiments, where a von Karman vortex street wake was made to impinge upon a 70-degree delta wing, was conducted at Wichita State University. The aim is to better understand the mixing mechanism that occurs at these high angle of attack flight regimes in a less Reynolds number sensitive environment. A von Karman wake having a frequency similar to the forebody shedding process is used. As the von Karman vortex filaments are entrained by the shear layer, they appear to wrap themselves around the core. There is a temporal correlation to the burst location of the delta wing’s leading-edge vortices, indicating modulation of the burst location. Additionally, the core becomes distorted. It has been found that the vortex burst location is moved forward towards the apex when subjected to the von Karman wake. Nomenclature c Wing root chord d Cylinder diameter FOV Field of View LE Leading Edge Rec Chord Reynolds number, U∞c/ν ReD Diameter Reynolds number, U∞d/ν s Coordinate along root chord U∞ Freestream Velocity x Coordinate along horizontal direction α Angle of attack (deg) Introduction Delta wings have evolved over the years and are now used primarily in the form of leading edge extensions on many fighter aircraft. As these aircraft become more and more maneuverable, the understanding of the physics of time-dependent unsteady flows is becoming more important. In particular, if accurate computational models of these maneuvers are to be developed, it is necessary to understand the mechanisms involved in features such as vortex bursting and mixing on the lee side of the delta wing. This is true of maneuvers such as the Cobra and other “hyper-agile” maneuvers. To understand the situation, it is important to briefly discuss some of the experimental findings in the areas of vortex bursting behavior, the Cobra maneuver physics, and forebody shedding. On the Impingement of a von Karman Vortex Street on a Delta Wing Ismael Heron and Roy Y. Myose Department of Aerospace Engineering Wichita State University, Wichita KS 67260-0044 It is well documented that delta wings at a fixed angle of attack generate lift by separating a shear layer of air (or fluid, such as water) at the leading edge, and this shear layer forms two strong counter-rotating vortices on either side of the wing. These leadingedge (LE) vortices undergo small fluctuations in space, but remain relatively fixed over the suction side of the delta wing, and are critical to the generation of lift, as they produce a large suction peak on the surface. Two much smaller vortices, the secondary vortices, are also formed, as seen in Figure 1. In other words, LE vortices are the result of a balance between vorticity being generated at the leading edge, and the ability of the flow field to convect said vorticity along the vortex core. The LE vortices are not stable, and at some point their coherent structure will undergo a dramatic change, expanding around the core, slowing down axially, and either forming a bubble or a spiral, with the spiral form being more predominant at Reynolds numbers of interest to delta wing designers. This change, called vortex burst or breakdown, is dependent on the aspect ratio of the wing, angle of attack, pressure gradients, yaw angle, and swirl angle of the vortex, among others. The exact reason for this bursting is not known, but research has focused on two general areas. (a) The flows upstream and downstream of the vortex burst are two separate and very different flows, and the vortex burst is a necessary feature, similar to a hydraulic jump. (b) The core of the LE vortex serves as a mechanical waveguide for longitudinal waves; these waves either coalesce, or they become critical, thereby triggering the burst. Regardless of the burst triggering mechanism, the effect of the vortex burst is to reduce the lift generated by the delta wing. If the delta wing is pitched to a given angle of attack (α) and then maintained at that angle until the transient flow features die down, it is said to be tested under “static” conditions. As this 22nd Applied Aerodynamics Conference and Exhibit 16 19 August 2004, Providence, Rhode Island AIAA 2004-4731 Copyright © 20 * Graduate Research Assistant, Student Member AIAA. † Associate Professor, Associate Fellow AIAA. Copyright ©2004 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.

An experimental study of the breakdown of leading-edge vortices on diamond, cropped, delta, and double delta wings during dynamic pitching

The aim of the present work is to provide an insight into the aerodynamic performances of the beetle during take-off which had been estimated in previous investigations. We employed a scaled-up electromechanical model flapping wing to measure the aerodynamic forces and the three-dimensional flow structures on the flapping wing. The ground effect on the unsteady forces and the flow structures was also characterized. The present dynamically-scaled wing model could replicate the general stroke pattern of the beetle's hind wing kinematics during take-off flight. The instantaneous aerodynamic forces for four strokes during beetle's take-off were measured by the force sensor attached at the wing base. Flow visualization provided the general picture of the evolution of the three-dimensional leading edge vortex (LEV) on the beetle hind wing model. The LEV is stable during each stroke and increases radically with the distance from the root to the tip, forming a leading-edge spiral vortex. The force measurement results show that the vertical force generated by hind wing is large enough to lift the beetle up. For the beetle hind wing kinematics, the total vertical force production increases 18.4% and 8.6 % for the first and the second stroke, respectively, due to the ground effect.

In this paper, detailed development of a nonlinear aeroelastic coupled trim model of a twin-cyclocopter in forward flight is presented. Twin-cyclocopter consists of two cycloidal rotors as main thrusters and a conventional nose rotor for pitch-torque balance. It is shown that five control inputs (mean and differential rpm, mean and differential phase offset of cyclorotors, rpm of nose rotor) are needed to balance three moments and two forces on cyclocopter in forward flight while forces along lateral direction remain balanced at all stages. In this coupled trim procedure, blade aeroelastic response equations and vehicle trim equations are solved together by simultaneously updating control inputs and blade response. To obtain the blade response and forces for a given set of control inputs, an aeroelastic model of cyclorotor and an aerodynamic model of the conventional nose rotor in forward flight is developed. The nonlinear aeroelastic model of the cyclorotor is developed by coupling unsteady aerodynamic model of cyclorotor in forward flight with a geometrically exact beam based structural framework capable of predicting large bending and torsional deflections of rotor blade. Towards this, complex aerodynamics of the cyclorotor is thoroughly investigated and various underlying phenomena, such as dynamic virtual camber, effects of near and shed wake and leading-edge vortices are rigorously modeled. A modified Double Multiple Streamtube (D-MS) model is implemented to capture the complex dynamic inflow characteristics of cyclorotor in forward flight. The present model is validated with previously published in-house experimental data on the performance of a trimmed cyclorotor at different forward speeds.

We investigate experimentally the effect of aspect ratio ( Open image in new window ) on the time-varying, three-dimensional flow structure of flat-plate wings rotating from rest at 45° angle of attack. Plates of Open image in new window = 2 and 4 are tested in a 50 % by mass glycerin–water mixture, with a total rotation of ϕ = 120° and a matched tip Reynolds number of 5,000. The time-varying, three-component volumetric velocity field is reconstructed using phase-locked, phase-averaged stereoscopic digital particle image velocimetry in multiple, closely-spaced chordwise planes. The vortex structure is analyzed using the \(\mathcal{Q}\)-criterion, helicity density, and spanwise quantities. For both Open image in new window s, the flow initially consists of a connected and coherent leading-edge vortex (LEV), tip vortex (TV), and trailing-edge vortex (TEV) loop; the LEV increases in size with span and tilts aft. Smaller, discrete vortices are present in the separated shear layers at the trailing and tip edges, which wrap around the primary TEV and TV. After about ϕ = 20°, the outboard-span LEV lifts off the plate and becomes arch-like. A second, smaller LEV and the formation of corner vortex structures follow. For Open image in new window = 4, the outboard LEV moves farther aft, multiple LEVs form ahead of it, and after about ϕ = 50° a breakdown of the lifted-off LEV and the TV occurs. However, for Open image in new window = 2, the outboard LEV lift-off is not progressive, and the overall LEV-TV flow remains more coherent and closer to the plate, with evidence of breakdown late in the motion. Inboard of about 50 % span, the Open image in new window = 4 LEV is stable for the motion duration. Up to approximately 60 % span, the Open image in new window = 2 LEV is distinct from the TV and is similarly stable. The Open image in new window = 2 LEV exhibits substantially higher spanwise vorticity and velocity. The latter possesses a “four-lobed” distribution at the periphery of the LEV core having adjacent positive (outboard) and negative (inboard) components, corresponding to a helical streamline structure. Both Open image in new window s show substantial root-to-tip velocity aft of the stable LEV, which drives outboard spanwise vorticity flux; flux toward the root is also present in the front portion of the LEV. For Open image in new window = 2, there is a strong flux of spanwise vorticity from the outboard LEV to the tip, which may mitigate LEV lift-off and is not found for Open image in new window = 4. The TV circulation for each Open image in new window is similar in magnitude and growth when plotted versus the chord lengths travelled by the tip, prior to breakdown. Streamwise vorticity due to the TV induces high spanwise velocity, and for Open image in new window = 2, the tilted LEV creates further streamwise vorticity which corresponds well to spanwise-elongated regions of spanwise velocity. For Open image in new window = 2, the TV influences a relatively greater portion of the span and is more coherent at later times, which coupled with the tilted LEV strongly contributes to the higher overall spanwise velocity and vorticity flux.

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 dragonfly (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 r 2 (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: when AR 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.

Unsteady aerodynamics of a rigid flapping wing at a Reynolds number of 10,000 for forward flight with an advance ratio of 0.5 is analyzed. A spiral leading-edge vortex with a strong spanwise flow along its core is formed during the downstroke, resulting in a peak lift and thrust. A negative spanwise flow formed due to the tip vortex prevents the removal of vorticity from the leading-edge vortex, leading to instability and separation of the leading-edge vortex. Analysis of different rotation timings shows that supination results in the leading-edge vortex formation near the base and its strength depends on the flapping velocity. A stronger vortex is formed for advanced rotation and it generates high lift. Delayed rotation affects thrust production during translation and results in low propulsive efficiency. Analysis of rotation duration shows that shorter rotation results in high instantaneous lift values, whereas continuous long-duration rotation results in high thrust and propulsive efficiency. Analysis of different angles of attack show that a moderate angle of attack, which results in a high thrust-to-lift ratio and complete shedding of the leading-edge vortex at the end of translation, is required for high propulsive efficiency.

The vortex dynamics during the initial rotation of a rotating blade were investigated using two-component and stereo digital particle image velocimetry. The structure and dynamics of spanwise vorticity in the leading-edge vortex (LEV) was investigated on two rotating at plates of aspect ratios (AR), 2 and 4. Reynolds numbers of 4,000, 8,000, and 16,000, based on tip velocity, and angles of attack of 25 , 35 , and 45 were investigated at ve azimuthal locations ( = 90 , 180 , 235 , 270 , and 320 ), and two span locations (25% and 50%). Circulation measurements of the leading-edge vortex structure exhibit trends of increasing circulation with increasing Reynolds number and angle of attack, independently, for both aspect ratios. In the particular case of the aspect ratio 4 plate at the 25% spanwise position and the aspect ratio 2 plate at the 50% spanwise position, measurements demonstrate that the LEV of the smaller aspect ratio plate has lower circulation for a given angle of attack and Reynolds number (based on the local velocity). A strong region of counter-rotating vorticity was observed on the surface of the plate due to the interactions of the LEV and the body. It is proposed that the interactions between the LEV and counterrotating surface vorticity play an important role in governing the dynamics and strength of the LEV which may ultimately determine whether the LEV remains attached. An analysis of vorticity transport in the LEV was conducted to estimate the relative contributions of spanwise ux, tilting, the shear layer, and annihilation to the rate of change of circulation of the LEV. Stereoscopic particle image velocimetry (SPIV) was implemented at three parallel chordwise planes to obtain the three components of velocity and vorticity vectors needed for the analysis. Results of the vorticity transport equation indicate that annihilation of the LEV due to entrainment of the surface vorticity is an important factor governing the dynamics of the LEV.

Flight dynamics modeling and analysis for a Mars helicopter

Analytical prediction of trajectories of ice pieces after release in an airstream

To investigate the aerodynamic performance of a flexible flapping wing aircraft, a flapping-wing system were design and an experiment were set up to measure the unsteady aerodynamic forces of the flapping motion. The thrust formula and resistance formula described aerodynamic forces. The lift and thrust of this mechanism were measured for different angles of attack and wind velocities. Results indicate that the thrust increases with the flapping frequency and the lift increase with the wind velocity, while the lift coefficient decreases while the velocity increases. It is realized that the wing’s transformation which imitated birds leads less resistance when flapping upward which impacts the aerodynamic lift generation and the bionic winglet leads to a change in the leading edge vortex and span-wise flow structures, which decrease the airflow’s backward pull. Models were introduced which were used in the design process and show its aerodynamic performance. The flexible flapping wing vehicle is still an open research area.

The synthesis of a comprehensive theory of force production in insect flight is hindered in part by the lack of precise knowledge of unsteady forces produced by wings. Data are especially sparse in the intermediate Reynolds number regime (10<Re<1000) appropriate for the flight of small insects. This paper attempts to fill this deficit by quantifying the time-dependence of aerodynamic forces for a simple yet important motion, rapid acceleration from rest to a constant velocity at a fixed angle of attack. The study couples the measurement of lift and drag on a two-dimensional model with simultaneous flow visualization. The results of these experiments are summarized below. At angles of attack below 13.5°, there was virtually no evidence of a delay in the generation of lift, in contrast to similar studies made at higher Reynolds numbers.At angles of attack above 13.5°, impulsive movement resulted in the production of a leading edge vortex that stayed attached to the wing for the first 2 chord lengths of travel, resulting in an 80% increase in lift compared to the performance measured 5 chord lengths later. It is argued that this increase is due to the process of detached vortex lift, analogous to the method of force production in delta-wing aircraft.As the initial leading edge vortex is shed from the wing, a second vortex of opposite vorticity develops from the trailing edge of the wing, correlating with a decrease in lift production. This pattern of alternating leading and trailing edge vortices generates a von Karman street, which is stable for at least 7.5 chord lengths of travel.Throughout the first 7.5 chords of travel the model wing exhibits a broad lift plateau at angles of attack up to 54°, which is not significantly altered by the addition of wing camber or surface projections.Taken together, these results indicate how the unsteady process of vortex generation at large angles of attack might contribute to the production of aerodynamic forces in insect flight. Because the fly wing typically moves only 2–4 chord lengths each half-stroke, the complex dynamic behavior of impulsively started wing profiles is more appropriate for models of insect flight than are steady-state approximations.

When a compound high-speed helicopter is in forward flight, there are serious aerodynamic disturbances among the fuselage components, among which the tail configuration has a greater influence on its aerodynamic performance. To study the influence of different tail configurations on aerodynamic performance, the flow field of a compound high-speed helicopter in forward flight was numerically simulated based on the commercial software XFlow. Firstly, the ROBIN standard helicopter fuselage model was calculated to verify the scientific validity of the method. Then, the aerodynamic data of a high-speed helicopter was analyzed for different tail configurations in forward flight with different angles of attack and yaw. The results show that the V-tail configuration has the lowest lift and resistance coefficients and the best longitudinal manoeuvrability and stall characteristics; the conventional tail configuration has the highest lift-to-resistance ratio and the fastest wake decay; the lateral stability of the V-tail and conventional tail configurations is weaker than that of the H-tail and fixed tail configurations; and the presence of the vertical tail in the tail increases the pressure value around the wing surface.

Free forward flight of cicadas is investigated through high-speed photogrammetry, three-dimensional surface reconstruction and computational fluid dynamics simulations. We report two new vortices generated by the cicada's wide body. One is the thorax-generated vortex, which helps the downwash flow, indicating a new phenomenon of lift enhancement. Another is the cicada posterior body vortex, which entangles with the vortex ring composed of wing tip, trailing edge and wing root vortices. Some other vortex features include: independently developed left- and right-hand side leading edge vortex (LEV), dual-core LEV structure at the mid-wing region and near-wake two-vortex-ring structure. In the cicada forward flight, approximately 79% of the total lift is generated during the downstroke. Cicada wings experience drag in the downstroke, and generate thrust during the upstroke. Energetics study shows that the cicada in free forward flight consumes much more power in the downstroke than in the upstroke, to provide enough lift to support the weight and to overcome drag to move forward.