Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments.

A novel method of calculating static derivatives and acceleration derivatives using Computational Fluid Dynamics is presented. This method uses field velocity approach to simulate the unsteady forced-plunging flow field over the aircraft without updating the field grids during each time step. This provides an improvement in computational efficiency over similar precision without loss of generality. Finally, to verify the present method, the Basic Finner missile as the benchmark example was taken to calculate its acceleration derivatives at various Mach number. Results are in fairly good agreement with traditionally method and the tunnel experimental results. Comparisons with the results of time-dependent simulations are also included.

The unsteady aerodynamic forces of a model fruit fly wing in flapping motion were investigated by numerically solving the Navier-Stokes equations. The flapping motion consisted of translation and rotation [the translation velocity (u(t)) varied according to the simple harmonic function (SHF), and the rotation was confined to a short period around stroke reversal]. First, it was shown that for a wing of given geometry with u(t) varying as the SHF, the aerodynamic force coefficients depended only on five non-dimensional parameters, i.e. Reynolds number (Re), stroke amplitude (Phi), mid-stroke angle of attack (alpha(m)), non-dimensional duration of wing rotation (Delta tau(r)) and rotation timing [the mean translation velocity at radius of the second moment of wing area (U), the mean chord length (c) and c/U were used as reference velocity, length and time, respectively]. Next, the force coefficients were investigated for a case in which typical values of these parameters were used (Re=200; Phi=150 degrees; alpha(m)=40 degrees; Delta tau(r) was 20% of wingbeat period; rotation was symmetrical). Finally, the effects of varying these parameters on the force coefficients were investigated. In the Re range considered (20-1800), when Re was above approximately 100, the lift ((L)) and drag ((D)) coefficients were large and varied only slightly with Re (in agreement with results previously published for revolving wings); the large force coefficients were mainly due to the delayed stall mechanism. However, when Re was below approximately 100, (L) decreased and (D) increased greatly. At such low Re, similar to the case of higher Re, the leading edge vortex existed and attached to the wing in the translatory phase of a half-stroke; but it was very weak and its vorticity rather diffused, resulting in the small (L) and large (D). Comparison of the calculated results with available hovering flight data in eight species (Re ranging from 13 to 1500) showed that when Re was above approximately 100, lift equal to insect weight could be produced but when Re was lower than approximately 100, additional high-lift mechanisms were needed. In the range of Re above approximately 100, Phi from 90 degrees to 180 degrees and Delta tau(r) from 17% to 32% of the stroke period (symmetrical rotation), the force coefficients varied only slightly with Re, Phi and Delta tau(r). This meant that the forces were approximately proportional to the square of Phi n (n is the wingbeat frequency); thus, changing Phi and/or n could effectively control the magnitude of the total aerodynamic force. The time course of (L) (or (D)) in a half-stroke for u(t) varying according to the SHF resembled a half sine-wave. It was considerably different from that published previously for u(t), varying according to a trapezoidal function (TF) with large accelerations at stroke reversal, which was characterized by large peaks at the beginning and near the end of the half-stroke. However, the mean force coefficients and the mechanical power were not so different between these two cases (e.g. the mean force coefficients for u(t) varying as the TF were approximately 10% smaller than those for u(t) varying as the SHF except when wing rotation is delayed).

A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack. >

Fluidelastic instability (FEI) remains the most important mechanism of flow-induced vibrations that can potentially cause large amplitude vibrations and early failure of nuclear steam generator tubes. In the present work, experimental tests are conducted to measure the unsteady and quasi-steady fluid forces acting on a normal triangular tube array of P/D=1.5 subjected to single-phase (water) cross-flow. The quasi-steady forces together with unsteady fluid forces are then used to estimate the time delay between the central tube motion and fluid forces on the tube itself. The time delay effect for the quasi-steady fluidelastic instability model is derived in the frequency domain in the form of an Equivalent Theodorsen Function. The results are compared to the first Equivalent Theodorsen function developed for rotated triangular array by Li and Mureithi [1]. Using the Equivalent Theodorsen Function, a stability analysis is carried out to predict the critical velocity for fluidelastic instability in a normal triangular array subjected to single-phase flow. The predicted stability threshold is consistent with previous published experimental data. The results show that the normal triangular array is more stable than the rotated triangular array.

The downstroke-to-upstroke transition of many insects is characterized by rapid wing rotation. The aerodynamic consequences of these rapid changes in angle of attack have been investigated using a mechanical model dynamically scaled to the Reynolds number appropriate for the flight of small insects such as Drosophila. Several kinematic parameters of the wing flip were examined, including the speed and axis of rotation, as well as the duration and angle of attack during the wing stroke preceding rotation. Alteration of these kinematic parameters altered force generation during the subsequent stroke in a variety of ways. 1. When the rotational axis was close to the trailing edge, the model wing could capture vorticity generated during rotation and greatly increase aerodynamic performance. This vortex capture was most clearly manifested by the generation of lift at an angle of attack of 0°. Lift at a 0° angle of attack was also generated following rotation about the leading edge, but only if the downstroke angle was large enough to generate a von Karman street. The lift may be due to an alteration in the effective angle of attack caused by the inter-vortex stream in the downstroke wake. 2. The maximum lift attained (over all angles of attack) was substantially elevated if the wing translated backwards through a wake generated by the previous stroke. Transient lift coefficient values of nearly 4 were obtained when the wing translated back through a von Karman street generated at a 76.5° angle of attack. This effect might also be explained by the influence of the inter-vortex stream, which contributes a small component to fluid velocity in the direction of translation. 3. The growth of lift with angle of attack was significantly elevated following a 7.5 chord stroke with a 76.5° angle of attack, although it was relatively constant under all other kinematic conditions. 4. The results also indicate the discrepancies between transient and time-averaged measures of performance that arise when unsteady mechanisms are responsible for force generation. Although the influence of wing rotation was strong during the first few chords of translation, averaging the performance over as little as 6.5 chords of motion greatly attenuated the effects of rotation. 5. Together, these modeling results suggest that the unsteady mechanisms generated by simple wing flips could provide an important source for the production of aerodynamic forces in insect flight. Furthermore, the extreme sensitivity to small variations in almost all kinematic parameters could provide a foundation for understanding the aerodynamic mechanisms underlying active flight control.

The desire to match the bow shock of a hypersonic vehicle to the lip of the engine cowl provides for a design constraint on the hypersonic forebody. For in viscid flow, it is shown that there is one particular wedge angle which provides for shock matching which is insensitive to steady-state changes in vehicle angle of attack, though it is not possible to match against changes in flight Mach number. The angle-of-attack sensitivity of a hypersonic boundary layer makes this matching process more difficult. Design rules for cowl matching with secondary shocks are presented, though it is shown that it is never possible to fix them against changes in angle of attack.

Hovering flight is one of the most energetically demanding forms of animal locomotion. Despite the cost, hummingbirds regularly hover at high elevations, where flight is doubly challenging because of reduced air density and oxygen availability. We performed three laboratory experiments to examine how air density and oxygen partial pressure influence wingbeat kinematics. In the first study, we experimentally lowered air density but maintained constant oxygen partial pressure. Under these hypodense but normoxic conditions, hummingbirds increased stroke amplitude substantially and increased wingbeat frequency slightly. In the second experiment, we maintained constant air density but decreased oxygen partial pressure. Under these normodense but hypoxic conditions, hummingbirds did not alter stroke amplitude but instead reduced wingbeat frequency until they could no longer generate enough vertical force to offset body weight. In a final combined experiment, we decreased air density but increased oxygen availability, and found that the wingbeat kinematics were unaffected by supplemental oxygen. We also studied hovering and maximally loaded flight performance for 43 hummingbird species distributed along a natural elevational gradient in Peru. During free hovering flight, hummingbirds showed increased stroke amplitude interspecifically at higher elevations, mirroring the intra-individual responses in our first laboratory experiment. During loaded flight, hummingbirds increased both wingbeat frequency and wing stroke amplitude by 19% relative to free-flight values at any given elevation. We conclude that modulation of wing stroke amplitude is a major compensatory mechanism for flight in hypodense or hypobaric environments. By contrast, increases in wingbeat frequency impose substantial metabolic demands, are only elicited transiently and anaerobically, and cannot be used to generate additional sustained lift at high elevations.

When a flat plate falls freely in periodic oscillating motion regime, unsteady fluid forces create additional lift force contributions due to the rotational behaviour. Computational fluid dynamics is used to simulate the free fall behaviour of a flat plate with aspect ratio β = 20 falling in two-dimensional flow with Reynolds number Re ≈ 10,000 and non-dimensional moment of inertia I* = 0.115. To validate the free fall trajectory obtained by computational fluid dynamics, video recordings are used. Based on the validated free fall computational fluid dynamics simulation, the instantaneous fluid forces and torques on the plate are obtained. The validated simulations show significant deviations in per-pendicular and tangential force coefficients at the same angle of attack depending on the trajectory history of the plate. At low angles of attack below 5 deg, the tangential force differs significantly. Oppositely, the difference in the perpendicular force is most pronounced at high angles of attack. During a free fall, the angle of attack is below 5 deg in 70 % of the time. Furthermore, the angle of attack is only above 45 deg in less than 5 % of the time. Therefore, effort must be put into a more detailed description of the tangential force component, in order to improve the existing modelling framework for non-spherical particles.

The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (Levin & Johnson, Am. J. Phys., vol. 79, issue 8, 2011, pp. 843–849), a result that follows from an energy theorem in electrostatics. Based on the analogous minimum energy theorem of Kelvin (Camb. Dublin Math. J., vol. 4, 1849, pp. 107–112), valid in the theory of ideal fluids, we show corresponding effects on steady and unsteady fluid forces in the presence of boundaries. Two main results are presented regarding the unsteady force. First, the added mass is proven to always increase in the presence of boundaries. Second, in a model of a body approaching a boundary, where the unsteady force is typically repulsive (Lamb, Hydrodynamics, 1975, § 137, University Press), we present a geometry where the force can be attractive. As for the steady force, there is one main result: in a model of a Bernoulli suction gripper, for which the steady force is typically attractive, we show that the force becomes repulsive in some geometries. Both the unsteady and steady forces are shown to reverse sign when boundaries approximate flow streamlines, at energy minima predicted by Kelvin's theorem.

For the design and certification of wind turbines, it is essential to provide fast and accurate unsteady aerodynamic load prediction models for the whole operational range of angle of attack, up to 180° for vertical-axis and 90° for horizontal-axis wind turbines. This work describes a computationally efficient unsteady forces prediction model based on a deep learning approach, namely the bidirectional long short-term memory (BiLSTM) algorithm, for an airfoil pitched over the full operational range of angles of attack up to 180°. No model has been developed to capture the unsteady forces at high angles of attack. Novel features based on operating conditions and the steady polars of the airfoil are used as inputs for the BiLSTM model. Direct measurements of steady and unsteady forces on a NACA 0021 airfoil model were conducted at reduced frequencies up to 0.075 and a Reynolds number of 120 000 in an open-jet wind tunnel for model learning and testing. The unsteady forces vary significantly from the steady values at high pitching amplitudes and post-stall angles, which, if not accounted for when simulating wind turbine performance, would result in inaccurate predictions. Furthermore, measurements revealed the effect of unsteady vorticity development and shedding on aerodynamic forces under forward and reverse flow conditions. The BiLSTM model is capable of capturing the underlying physics of unsteady aerodynamic forces under extreme operating conditions.

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.

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.

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

Tomographic particle image velocimetry was used to explore the evolution of three-dimensional flow structures of revolving low-aspect-ratio flat plates in combination with force measurements at a Reynolds number of 10,000. Two motion kinematics are compared that result in the same terminal condition (revolution with constant angular velocity and $$45^{\circ }$$ angle of attack) but differ in the motion during the buildup phase: pitching while revolving at a constant angular velocity; or surging with a constant acceleration at a fixed angle of attack. Comparison of force histories shows that the pitching wing generates considerably higher forces during the buildup phase which is also predicted by a quasi-steady model quite accurately. The difference in the buildup phases affects the force histories until six chords of travel after the end of buildup phase. In both cases, a vortex system that is comprised of a leading-edge vortex (LEV), a tip vortex and a trailing edge vortex is formed during the initial period of the motion. The LEV lifts off, forms an arch-shaped structure and bursts into substructures, which occur at slightly different phases of the motions, such that the revolving–surging wing flow evolution precedes that of the revolving–pitching wing. The delay is shown to be in accordance with the behavior of the spanwise flow which is affected by the interaction between the tip vortex and revolving dynamics. Further analysis shows that the enhanced force generation of the revolving–pitching wing during the pitch-up phase originates from: (1) increased magnitude and growth rate of the LEV circulation; (2) relatively favorable position and trajectory of the LEV and the starting vortex; and (3) generation of bound circulation during the pitching motion, whereas that of the revolving–surging wing is negligible in the acceleration phase.

Euler's equations, the shock wave relations, and the surface boundary condition are used to derive a hypersonic slender body theory applicable to angles of attack from zero to 90 degrees. The theory is not based on small disturbances, but it gives Van Dyke's theory for small angles of attack, Sychev's similarity for moderate angles of attack, and strip theory for large angles of attack. The new similarity parameters are Meo~, 0 cos a/~, and y (where ~=o cos a + sin a). They are shown to be a combination of Sychev's parameters and can be used to modify equations for pressure and force coefficients at small angles of attack for moderate and large angle of attack applications. B(X,y,Z) CA CA CD CD CN CN Cp Cp d D Db A n p,p S(x,y,Z) T Nomenclature scaled function for body geometry axial force coefficient, based on ref. area ::: 2Ld scaled axial force coefficient given by eq. (50) drag coefficient, based on ref. area ::: 2Ld scaled drag coefficient given by eq. (51) normal force coefficient based on ref. area ::: 2Ld scaled normal force coefficient given by eq. (19) pressure coefficient, eq. (47) ... scaled pressure coefficient given by eq. (47) base height of lower surface, see Fig. 1 parameter defined by eq. (2) parameter defmed by eq. (44) unit vectors in x, y, z directions, respectively similarity parameter, 0 cos a~ similarity parameter, Moo~ body length freestream Mach number unit vector normal (inner) to surface static pressure and scaled static pressure, eq. (25) scaled function for shock surface temperature * Professor of Mechanical and Aerospace Engineering, Associate Fellow AlAA. Copyright© 1992 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 542 u,v,w u,v,w ~ Veo,VOQ x,y,z x,y,z a ~ y o ~ Cartesian velocity components in x,y,z directions, respectively scaled (nondimensional) velocity components freestream velocity vector and magnitude Cartesian coordinates, see Fig. 1 x/L, y/d, z/d, respectively angle of attack shockwave angle ratio of specific heats, 1.4 for air lower surface thickness ratio, d/L, see Fig. 1 --'> lower surface thickness ratio relative to V 00' see Fig. 1 and eq. (15) p,p density and scaled density, eq. (22) circumferential angle, =0 in windward plane SUbscripts c Cone b body s shock wave 00 freestream value Introduction Analysis of inviscid, hypersonic flow past slender bodies has been developed by Van Dyke l for small angles of attack and by Sychev2 for large angles of attack. The small angle of attack analysis is based on small disturbance theory and the similarity parameters are Moo 0, a/o, and y. At large angles of attack the Sychev similarity parameters are Moo sin a, 0 cot a, and y. Hemsch3 showed that the large angle of attack similarity parameters can be combined to yield the small angle of attack parameters when a is small, i.e. (MOQ sin a) (0 cot a) --'> Moo 0 and 0 cot a --'> o/a. Cox and Crabtree4 and Hayes and Probstein5 discuss hypersonic small disturbance theory and Sychev similarity. BarnweU6 showed that Sychev's analysis is applicable to all slender-body flows with crossflow Mach numbers greater than sonic and hence is not restricted to hypersonic values of the cross flow Mach number. In addition, he showed that Sychev similarity applied to a number of slender-body flows with subsonic crossflow Mach numbers, including incompressible flow. Hemsch3 demonstrated empirically that Sychev similarity holds for any value of the cross-flow Mach number if the axial flow component is 4