Some aspects of calculating subsonic flow over wings of complex planform

The use of wings of complex planform is characteristic of the present stage of development of aviation; with discontinuities along the leading and trailing edges; with curved edges; with variable geometry (by pivoting the wing panels). This article considers some aspects of the calculation of the over-all and distributed aerodynamic characteristics of such wings for low and high subsonic velocities. The methods, based on the lifting surface scheme and the use of discrete vortical singularities, enable quite efficient and reliable digital computation of the flow about these wings at moderate angles of attack. For steady motion of the wing a further development of the method of [1] is obtained, for harmonic oscillations an extension of [2] is obtained, and for aperiodic motions of the wing and gust inputs a modification of the method of [3] is found.The author wishes to thank T. M. Muzychenko and N. G. Lavrenko for carrying out the calculations of the examples.     

Wing of simple planform in a sharp-edged gust

The entry of a wing into the zone of a sharp-edged gust is considered in the linear formulation. The case is studied when the wing velocity is supersonic and its edges satisfy the supersonic flow condition. The gust intensity is considered to be variable, and its edge may move into the undisturbed medium. Equations in finite form are obtained for the forces and moments for a rectangular wing of infinite span, and also for triangular wings with positive and negative sweep, for the case when the gust intensity varies linearly. Sudden envelopment of the wing and penetration of the wing into a gust whose edge is fixed relative to the undisturbed medium are considered.     

A simulation-based study on longitudinal gust response of flexible flapping wings

Winged animals such as insects are capable of flying and surviving in an unsteady and unpredictable aerial environment. They generate and control aerodynamic forces by flapping their flexible wings. While the dynamic shape changes of their flapping wings are known to enhance the efficiency of their flight, they can also affect the stability of a flapping wing flyer under unpredictable disturbances by responding to the sudden changes of aerodynamic forces on the wing. In order to test the hypothesis, the gust response of flexible flapping wings is investigated numerically with a specific focus on the passive maintenance of aerodynamic forces by the wing flexibility. The computational model is based on a dynamic flight simulator that can incorporate the realistic morphology, the kinematics, the structural dynamics, the aerodynamics and the fluid–structure interactions of a hovering hawkmoth. The longitudinal gusts are imposed against the tethered model of a hovering hawkmoth with flexible flapping wings. It is found that the aerodynamic forces on the flapping wings are affected by the gust, because of the increase or decrease in relative wingtip velocity or kinematic angle of attack. The passive shape change of flexible wings can, however, reduce the changes in the magnitude and direction of aerodynamic forces by the gusts from various directions, except for the downward gust. Such adaptive response of the flexible structure to stabilise the attitude can be classified into the mechanical feedback, which works passively with minimal delay, and is of great importance to the design of bio-inspired flapping wings for micro-air vehicles.     

Influence of wing flexibility on the aerodynamic performance of a tethered flapping bumblebee

The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight. In this study, a mass-spring system is used to model wing structural dynamics as a thin, flexible membrane supported by a network of veins. The vein mechanical properties can be estimated based on their diameters and the Young's modulus of cuticle. In order to analyze the effect of wing flexibility, the Young's modulus is varied to make a comparison between two different wing models that we refer to as flexible and highly flexible. The wing models are coupled with a pseudo-spectral code solving the incompressible Navier–Stokes equations, allowing us to investigate the influence of wing deformation on the aerodynamic efficiency of a tethered flapping bumblebee. Compared to the bumblebee model with rigid wings, the one with flexible wings flies more efficiently, characterized by a larger lift-to-power ratio.     

EFFECTS OF STEADY ANGLE OF ATTACK ON NONLINEAR GUST RESPONSE OF A DELTA WING MODEL

The effects of a steady angle of attack on the nonlinear aeroelastic response of a delta wing model to a periodic gust have been studied. For the theoretical analysis, a three-dimensional time-domain vortex lattice aerodynamic model and a reduced order aerodynamic technique were used and the structure was modelled using von Karman plate theory that allows for geometric strain–displacement nonlinearities in the delta wing structure. Also, an experimental investigation has been carried out in the Duke wind tunnel using a rotating slotted cylinder gust generator and an Ometron VPI 4000 Scanning Laser Vibrometer measurement system to measure deflections (velocities) of a delta wing test model. The fair to good quantitative agreement between theory and experiment verifies that the present analytical approach has reasonable accuracy and good computational efficiency for nonlinear gust response analysis in the time-domain. The results also contribute to a better physical understanding of the nonlinear aeroelastic response of a delta wing model to gust loads when the steady angle of attack is varied.     

Hypersonic flow past conical V-shaped wings

Hypersonic flow past delta wings with a V-shaped cross-section has been investigated both theoretically and experimentally. Much attention is given to the examination and classification of possible conical flow patterns in the vicinity of the windward surface using the thin shock layer method. Solutions for shocks both attached to and detached from the leading edges them are obtained. It is shown that qualitatively new flow patterns can appear in the flow past V-shaped wings as compared with the case of a planar wing.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 170–178, September–October, 1996.     

Investigation on the planform and kinematic optimization of bio-inspired nano air vehicles for hovering applications

Wing shape and kinematics of flapping wing nano air vehicles are two important factors in their design process. These factors require an optimal design in terms of decreasing the needed aerodynamic power. Since, insects are regarded as the best natural flier in hovering flight, seven of their wings are considered in order to determine the best wing shape for hovering applications. Because of the difference in the original bio-inspired shape of these wings, two scenarios are studied, namely, considering the same wingspan and same wing surface. Using the quasi-steady approximation to model the aerodynamic loads and a basic gradient approach to optimize the kinematics of the wing, the optimum Euler angles, required aerodynamic power, and hence the best wing shape for each scenario are analytically determined. The results show that the wing shape and surface strongly impact the aerodynamic characteristics and performances of the chosen wing shapes. It is demonstrated that the twisted parasite wing shape is a good candidate to minimize the required aerodynamic power during hovering. The strategy used in this analysis can be used to evaluate the performance of any realistic wing shape design and could provide a guideline for selecting the best wing shape and kinematics for flapping wing nano air vehicles with hovering capabilities.     

Method of calculating unsteady aerodynamic characteristics of a lifting surface at high subsonic speed

A method is presented for calculating the unsteady aerodynamic characteristics of harmonically oscillating thin wings traveling at high subsonic speed. The medium is assumed ideal. The aerodynamic coefficients are expressed in terms of the rotational derivatives, which are determined for a Strouhal number of zero. The calculation of the rotational derivatives of the aerodynamic coefficients in a compressible medium reduces to the conversion of the corresponding characteristics of a transformed wing, determined in an incompressible medium for altered boundary conditions. To calculate the aerodynamic characteristics of the transformed wing in the incompressible medium we use a technique based on replacement of the lifting surface by a system of discrete unsteady vortices. The problem is solved in general form, and together with the new relations for the rotational derivatives with dots we derive the known formulas for the rotational derivatives without dots.     

Experimental analysis of the flow field over a novel owl based airfoil

The aerodynamics of a newly constructed wing model the geometry of which is related to the wing of a barn owl is experimentally investigated. Several barn owl wings are scanned to obtain three-dimensional surface models of natural wings. A rectangular wing model with the general geometry of the barn owl but without any owl-specific structure being the reference case for all subsequent measurements is investigated using pressure tabs, oil flow pattern technique, and particle-image velocimetry. The main flow feature of the clean wing is a transitional separation bubble on the suction side. The size of the bubble depends on the Reynolds number and the angle of attack, whereas the location is mainly influenced by the angle of attack. Next, a second model with a modified surface is considered and its influence on the flow field is analyzed. Applying a velvet onto the suction side drastically reduces the size of this separation at moderate angles of attack and higher Reynolds numbers.     

The minimum drag of thin wings at supersonic speed according to Kogan's theory

In the theory of thin lifting surfaces the minimum drag consistent with a given total lift occurs when the downwash, averaged between forward and reversed motion of the wing, has the same value at all points of the wing planform. In Kogan's theory the conditions for minimum drag are determined on the forward sloping characteristic surface touching the trailing edge of the wing and it is shown that such a surface plays the role of the Trefftz plane familiar in subsonic wing theory. This paper shows how Kogan's theory may be applied to determine the drag of elliptic wings at supersonic speed. It appears that such wings have lower drag than the conventional delta wing.     

ANALYSIS OF THE HIGH-ASPECT-RATIO WING GUST RESPONSE BY TRANSFER FUNCTION METHOD1)

将传递函数法应用于大展弦比机翼的阵风响应分析。首先,基于二元机翼的运动方程和准定常片条理论建立机翼的阵风响应微分方程,对其进行Laplace变换,并转换为状态空间方程形式。然后,运用传递函数方法,获得机翼响应在频域的解析解,通过Laplace数值逆变换求得机翼在时域内的响应。通过与已有文献结果对比,验证了本文方法的正确性。最后,采用该方法求解了“1-cos”型阵风和连续大气湍流作用下的机翼响应,并对结果进行了分析讨论。     

Gust response: Simulation of an aeroelastic experiment by a fluid–structure interaction method

In this paper fluid–structure interaction simulations regarding a gust generator experiment are presented, which has been conducted in 2010 in the Transonic Wind Tunnel in Göttingen (DNW-TWG), Germany. The main objective of the experiment was the investigation of the dynamic response problem of an elastic wing model concerning an encountering generic gust induced by a gust generator. Fluid–structure simulations, using a finite element structural model and a computational fluid dynamics model based on time-accurate, Reynolds-averaged Navier–Stokes equations, are compared to the experiment to validate the numerical methodology. Comparisons include steady and unsteady deflections of the elastic wing and pressure distributions. Finally, the results of simulated transfer functions of the gust generator to the elastic wing are presented in comparison to the test data.     

Exploration of plasma-based control for low-Reynolds number airfoil/gust interaction

Large-eddy simulation (LES) is employed to investigate the use of plasma-based actuation for the control of a vortical gust interacting with a wing section at a low Reynolds number. Flow about the SD7003 airfoil section at 4° angle of attack and a chord-based Reynolds number of 60,000 is considered in the simulation, which typifies micro air vehicle (MAV) applications. Solutions are obtained to the Navier–Stokes equations that were augmented by source terms used to represent body forces imparted by the plasma actuator on the fluid. A simple phenomenological model provided these body forces resulting from the electric field generated by the plasma. The numerical method is based upon a high-fidelity time-implicit scheme and an implicit LES approach which are used to obtain solutions on a locally refined overset mesh system. A Taylor-like vortex model is employed to represent a gust impinging upon the wing surface, which causes a substantial disruption to the undisturbed flow. It is shown that the fundamental impact of the gust on unsteady aerodynamic forces is due to an inviscid process, corresponding to variation in the effective angle of attack, which is not easily overcome. Plasma control is utilised to mitigate adverse effects of the interaction and improve aerodynamic performance. Physical characteristics of the interaction are described, and several aspects of the control strategy are explored. Among these are uniform and non-uniform spanwise variations of the control configuration, co-flow and counter-flow orientations of the directed force, pulsed and continuous operations of the actuator and strength of the plasma field. Results of the control situations are compared with regard to their effect upon aerodynamic forces. It was found that disturbances to the moment coefficient produced by the gust can be greatly reduced, which may be significant for stability and handling of MAV operations.     

Iteration schemes for rapid post‐stall aerodynamic prediction of wings using a decambering approach

Nonlinear aerodynamics of wings may be evaluated using an iterative decambering approach. In this approach, the effect of flow separation due to stall at any wing section is modeled as an effective reduction in section camber. The approach uses a wing analysis method for potential‐flow calculations and viscous airfoil lift curves for the sections as input. The calculation procedure is implemented using a Newton–Raphson iteration to simultaneously satisfy the boundary condition, which comes from potential‐flow wing theory, and drive the sectional operating points toward their respective viscous lift curves, as required for convergence. Of particular interest in this research is the calculation of the residuals during the Newton iteration. Unlike a typical implementation of the Newton iteration, the residual calculation is not performed via a straightforward function evaluation, but rather by estimating the target operating points on the input viscous lift curves. Estimation of these target operating points depends on the assumptions made in the cross‐coupling of the decambering at the different sections. This paper presents four residual calculation schemes for the decambering approach. The residual calculation schemes are compared against each other to assess computational speed and robustness. Decambering results are also compared with higher‐order computational fluid dynamics (CFD) solutions for rectangular and swept wings. Results from the best scheme compare well with the CFD solutions for the rectangular wing, motivating further development of the method. Poor predictions for the swept wings are traced to spanwise propagation of separated flow at stall, highlighting the limitations of the current approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of thrust on the aeroelastic instability of a composite swept wing with two engines in subsonic compressible flow

This paper aims to investigate aeroelastic stability boundary of subsonic wings under the effect of thrust of two engines. The wing structure is modeled as a tapered composite box-beam. Moreover, an indicial function based model is used to calculate the unsteady lift and moment distribution along the wing span in subsonic compressible flow. The two jet engines mounted on the wing are modeled as concentrated masses and the effect of thrust of each engine is applied as a follower force. Using Hamilton's principle along with Galerkin's method, the governing equations of motion are derived, then the obtained equations are solved in frequency domain using the K-method and the aeroelastic instability conditions are determined. The flutter analysis results of four example wings are compared with the experimental and analytical results in the literature and good agreements are achieved which validate the present model. Furthermore, based on several case studies on a reference wing, some attempts are performed to analyze the effect of thrust on the stability margin of the wing and some conclusions are outlined.     

An investigation on the lift force of a wing pitching in dynamic stall for a comfort control vessel

On the basis of a comfort control system for ocean vessels, the control forces and moments in the form of lift forces from active wings are of important interest. In an ocean vessel comfort control system, active wings or fins are commonly used and constantly adjust their angles of attack to produce optimal sea-keeping conditions. The unsteady nature of the flow field around a wing, and the behaviour of the generated lift force must be understood in order to optimize the comfort control system. This paper presents experimental data on the flow past a pitching wing, paying particular attention to the lagging effects between the fluid dynamic lift force and the motion of the wing at large angles of attack as a function of peak angle of attack and reduced frequency of oscillation. The range of motion investigated has been chosen according to the applicability of a comfort control wing surface. Numerical data is also included to aid explanation on some of the witnessed phenomena.     

Passage of a supersonic flow over intersecting surfaces

Using the linear formulation, the problem of passage of a supersonic flow over slightly curved intersecting surfaces whose tangent planes form small dihedral angles with the incident flow velocity at every point is considered. Conditions on the surfaces are referred to planes parallel to the incident flow forming angles 0≤γ≤2π at their intersection [1]. The problem reduces to finding the solution of the wave equation for the velocity potential with boundary conditions set on the surfaces flowed over and the leading characteristic surface. The Volterra method is used to find the solution [2]. This method has been applied to the problem of flow over a nonplanar wing [3] and flow around intersecting nonplanar wings forming an angle γ=π/n (n=1, 2, 3, ...) with consideration of the end effect on the wings forming the angle [4]. In [5] the end effect was considered for nonplanar wings with dihedral angle γ=m/nπ. In the general case of an arbitrary angle 0≤γ≤2π the problem of finding the velocity potential reduces to solution of Volterra type integrodifferential equations whose integrands contain singularities [1]. It was shown in [6] that the integrodifferential equations may be solved by the method of successive approximation, and approximate solutions were found differing slightly from the exact solution over the entire range of interaction with the surface and coinciding with the exact solution on the characteristic lines (the boundary of the interaction region, the edge of the dihedral angle). The solution of the problem of flow over intersecting plane wings (the conic case) for an arbitrary angle γ was obtained in terms of elementary functions in [7], which also considered the effect of boundary conditions set on a portion of the leading wave diffraction. In [8, 9] the nonstationary problem of wave diffraction at a plane angle π≤γ≤2π was considered. On the basis of the wave equation solution found in [8], this present study will derive a solution which permits solving the problem of supersonic flow over nonplanar wings forming an arbitrary angle π≤γ≤2π in quadratures. The solutions for flow over nonplanar intersecting surfaces for the cases 0≤γ≤π [6] and π≤γ≤2π, found in the present study, permit calculation of gasdynamic parameters near a wing with a prismatic appendage (fuselage or air intake). The study presents a method for construction of solutions in various zones of wing-air intake interaction.     

Calculation of the flow around wings of arbitrary planform over a wide range of angles of attack

A numerical method is described for the calculation of the distributed and total aerodynamic characteristics of a thin wing of any planform. We use only the generally accepted hypotheses-smoothness of flow around the wing and the Chaplygin-Zhukovskii condition of finite velocity at the trailing edges. The medium is considered ideal and incompressible.The development of a nonlinear theory for the wing of small aspect ratio in a compressible medium is one of the most important and difficult problems of wing theory. It has long attracted the attention of the aerodynamiscists. Chaplygin touched on this question in his 1913 report On the vortex theory of the finite span wing, presented to the Moscow Mathematical Society. Several interesting ideas and schemes were proposed by Golubev (see, for example, [2]). The first adequately correct and effective attempt to determine theoretically the nonlinear variation of wing normal force with angle of attack was that of Bollay [3]. In this work he studied rectangular wings of very small aspect ratio. The circulation variation law along the span was taken to be constant, and along the chord it was taken the same as for a flat plate of infinite span. It was also assumed that the centerlines of the free vortices trailing from the wing tips are straight lines and form the same angle with the plane of the wing. The magnitude of this angle was calculated from the average value of the relative velocity. The boundary condition at the wing was satisfied at a single point.In several later studies [4–8] attempts have been made to extend this approach somewhat. In [7] the circulation variation law along the wing chord is calculated, and the boundary conditions are satisfied more exactly. However, attempts to convert to the study of wings of more complex planform, when the circulation can no longer be considered constant along the span, are hydrodynamically incorrect [5, 6, 8]. In these studies schemes are used in which with smooth flow around the wing the free vortices stand off from the wing surface. The angles which the vortex centerlines form with the wing surface are assumed or are calculated on the basis of very arbitrary hypotheses.In the present paper the vortex layer which simulates the wing surface, just as in the linear theory [9, 10], is replaced by a system of discrete vortices. The free vortices away from the wing then are discrete curvilinear vortex filaments. Each of them is replaced by a series of rectilinear vortex segments. The number of bound and free discrete vortices may be increased without limit. The position of the free vortex segments is determined in the computation process, which is carried out sequentially for a series of angles of attack , beginning with 0 when the linear theory scheme holds. We note that the question of accounting for the effect of the leading-edge free vortex sheet is not considered here, although the method described may also be used to obtain results for this problem.The proposed method turned out to be very general, flexible and convenient for the digital computer. It permits studying the practical convergence of the solution, and also permits obtaining not only the total and distributed characteristics of the wing of arbitrary planform, but also studying such delicate questions as the rollup of the vortex sheet behind the wing.The author wishes to thank O. N. Sokolov and T. M. Muzychenko for the example calculations.     

Aerodynamic Coefficients and Deformation Measurements on Flexible Micro Air Vehicle Wings

This paper documents the elastic deformations and corresponding aerodynamic coefficients of flexible wings used for micro air vehicles (MAVs). These low-aspect ratio wings, developed and fabricated at the University of Florida, incorporate an elastic latex membrane skin covering a thin carbon fiber skeleton. The wings were tested in a unique low-speed wind tunnel facility integrating a visual image correlation (VIC) system with a six-component strain gauge sting balance. Model characteristics are presented, along with the appropriate specimen preparation techniques and wind tunnel instrumentation. The static response characteristics, including full-field displacements and plane strain measurements, for three distinct MAV wing designs are presented. The full-field deformation results show how passive wing flexibility preferably affects aerodynamic performance when compared to a rigid model of similar geometry.