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.     

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.     

Calculation of nonlinear aerodynamic characteristics of a wing using a 3‐D panel method

The nonlinear aerodynamic characteristic of a wing is investigated using the frequency‐domain panel method. To calculate the nonlinear aerodynamic characteristics of a three‐dimensional wing, the iterative decambering approach is introduced into the frequency‐domain panel method. The decambering approach uses the known nonlinear aerodynamic characteristic of airfoil and calculates two‐variable decambering function to take into consideration the boundary‐layer separation effects for the each section of the wing. The multidimensional Newton iteration is used to account for the coupling between the different sections of wing. The nonlinear aerodynamic analyses for a rectangular wing, a tapered wing, and a wing with the control surface are performed. Present results are given with experiments and other numerical results. Computed results are in good agreement with other data. This method can be used for any wing having different nonlinear aerodynamic characteristics of airfoil. The present method will contribute to the analysis of aircraft in the conceptual design because the present method can predict the nonlinear aerodynamic characteristics of a wing with a few computing resources and significant time. Copyright © 2007 John Wiley & Sons, Ltd.     

排翼布局飞行器气动性能的实验研究

通过低速低湍流度风洞实验,研究了利用排翼布局改善充气飞机采用大厚度翼型机翼带来的气动效率偏低问题。首先比较了采用不同厚度翼型的单翼与排式双翼布局的气动特性。在此基础上,为了优化排翼布局的气动特性,研究了给后翼安装偏转角对排翼布局气动特性的影响。同时,基于NACA0030翼型,设计了波纹型外形的充气机翼,比较了此外形下单翼和排翼布局气动性能的差异。实验结果表明,采用排翼布局能够改善采用厚翼型单翼布局的气动性能,而给后翼安装一定偏转角可以进一步提高排翼布局的升力和升阻比。采用波纹外形和光滑外形机翼模型的对比结果表明,波纹外形能够在大迎角时改善充气机翼的失速性能。分析认为,造成这一现象的流动机理是由于波纹型机翼在实验条件下提前由层流转捩为湍流,使失速推迟,流动分离现象有所减弱。     

Mathematical simulation of unsteady flow past a wing with jets

The various approximate approaches to the investigation of the unsteady aerodynamic characteristics of an airfoil with jet flap [1–3] are applicable only for an airfoil, low jet intensity, and low oscillation frequencies. In the present paper, the method of discrete vortices [4] is generalized to the case of unsteady flow past a wing with jets and arbitrary shape in plan. The problem is solved in the linear formulation; the conditions used are standard: no flow through the wing and jet, finite velocities at the trailing edges where there is no jet, and also a dynamical condition on the jet. The wing and jet are assumed to be thin and the medium inviscid and incompressible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 139–144, May–June, 1982.     

Aerodynamic improvement of a delta wing in combination with leading edge flaps

Recently, various studies of micro air vehicle(MAV) and unmanned air vehicle(UAV) have been reported from wide range points of view. The aim of this study is to research the aerodynamic improvement of delta wing in low Reynold's number region to develop an applicative these air vehicle. As an attractive tool in delta wing, leading edge flap(LEF) is employed to directly modify the strength and structure of vortices originating from the separation point along the leading edge. Various configurations of LEF such as drooping apex flap and upward deflected flap are used in combination to enhance the aerodynamic characteristics in the delta wing. The fluid force measurement by six component load cell and particle image velocimetry(PIV) analysis are performed as the experimental method. The relations between the aerodynamic superiority and the vortex behavior around the models are demonstrated.     

Method of calculating subsonic gas flow with separation past wings

The steady nonlinear problem of subsonic compressible gas flow past a wing of arbitrary shape in plan is considered. A numerical method was devized for solving the problem; this is a further development of the method of discrete vortices. The surface of the body and the vortex wake behind it are simulated by systems of discrete vortex sections, but, in contrast to the case of an incompressible medium, it is necessary in this case for the sources to be distributed outside the wing. The circulations of the attached vortices, the strengths of the sources, and the shape of the wake are determined by iterations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 140–147, July–August, 1984.     

Aerodynamic characteristics of a deltawing in the case of harmonic oscillations with respect to the roll and yaw angles at high angles of attack

The aerodynamic characteristics of a delta wing in the case of harmonic oscillations with respect to the roll and yaw angles are obtained in a subsonic low-speed wind tunnel and analyzed. It is shown that at near-critical angles of attack the aerodynamic derivatives of the roll moment considerably depend on the reduced oscillation frequency. It is established that this dependence is due to a variation in the slip angle. A mathematical model that involves an ordinary linear differential first-order equation is used to describe the aerodynamic characteristics of the wing for the problems of aircraft flight dynamics at high angles of attack.     

Temperature factor effect on the structure of the separated flow within a supersonic gas stream

The effect of the temperature factor, that is, the ratio of the body temperature to the freestream stagnation temperature, on the structure of the separated flow formed in the presence of a concave corner in a supersonic stream is studied. The strong influence of the temperature factor on the separation zone length and the flow-generated aerodynamic characteristics is established. It is shown that for fairly large deflection angles this flow cannot be described by free interaction, or triple deck, theory.     

Calculation of aerodynamic characteristics of a wing profile with discharge of a controllable jet into the external flow

A wing profile of infinite span, whose lower surface is replaced by a system of guide vanes, is placed in a flow of an ideal incompressible fluid. Fluid flows out through the system of guide vanes from the internal cavity of the wing into the external stream, forming a jet in the wake (Fig. 1). The total pressure in the wing cavity and in the jet differs from the total pressure in the outer free stream. The jet boundaries are streamlines extending to infinity, along which there is a discontinuity of the velocity value. The flow of fluid in the internal wing cavity is simulated by a flow caused by a system of suitably located sources, and the system of guide vanes is replaced by discrete vortices.The form of the profile arc is selected so that the fluid flow from the sources in the direction which is nearly opposite the direction of the freestream velocity is restrained by the segment of the contour with high curvature in the vicinity of the leading edge. We consider the flow regime about the profile with an exhausting jet for which the two ends of the arc the points of detachment of the stream and the velocity discontinuity line (profile arc, jet boundary) is a smooth curve, which imposes an additional condition on the magnitude of the circulation. As the model for the study of the flow about a profile with jet blowing we take the arc of a logarithmic spiral.Formulas are obtained for determining the over-all characteristics of the stream forces acting on the profile in the presence of the jet and the total pressure discontinuity. On the basis of the calculations made for a thin wing a qualitative analysis is made for the stream force acting on the profile.The authors wish to thank S. A. Khristianovich for formulating the problem and for his advice.     

Aerodynamic Performance of a Gliding Swallowtail Butterfly Wing Model

In the present study, we perform a wind-tunnel experiment to investigate the aerodynamic performance of a gliding swallowtail-butterfly wing model having a low aspect ratio. The drag, lift and pitching moment are directly measured using a 6-axis force/torque sensor. The lift coefficient increases rapidly at attack angles less than 10° and then slowly at larger attack angles. The lift coefficient does not fall off rapidly even at quite high angles of attack, showing the characteristics of low-aspect-ratio wings. On the other hand, the drag coefficient increases more rapidly at higher angles of attack due to the increase in the effective area responsible for the drag. The maximum lift-to-drag ratio of the present modeled swallowtail butterfly wing is larger than those of wings of fruitfly and bumblebee, and even comparable to those of wings of birds such as the petrel and starling. From the measurement of pitching moment, we show that the modeled swallowtail butterfly wing has a longitudinal static stability. Flow visualization shows that the flow separated from the leading edge reattaches on the wing surface at α < 15°, forming a small separation bubble, and full separation occurs at α ≥ 15°. On the other hand, strong wing-tip vortices are observed in the wake at α ≥ 5° and they are an important source of the lift as well as the main reason for broad stall. Finally, in the absence of long hind-wing tails, the lift and longitudinal static stability are reduced, indicating that the hind-wing tails play an important role in enhancing the aerodynamic performance.     

Supersonic Flow Past a Bent Delta Wing and Its Aerodynamic Characteristics

The supersonic flow past a bent delta wing and its aerodynamic characteristics, both local and integral, are studied using approximate analytic estimates and numerical calculations. The flow regimes with the shock attached to the leading edges are considered. It is established that at M = 4–6 and angles of attack as high as 6° the lift-drag ratio of the wing can be increased by 10% by deflecting the wing nose downwards. This is confirmed by the results obtained earlier in the hypersonic thin-shock-layer approximation. The effect is also obtained in calculations made within the framework of the Navier-Stokes equations.     

三角翼大迎角流场结构和气动力特性的数值分析研究

采用数值计算方法对亚音速三角翼纵向及带有小侧滑情况下的流场结构和气动力特性进行了计算。文中给出了三角翼大迎角纵向情况下气动力、机翼前缘分离涡轴线位置和旋涡破裂位置随迎角的变化规律，以及带有横侧小扰动和小侧滑情况下流场结构的非对称性对气动力的影响。计算结果表明与实验结果符合较好。     

Oscillations of a plate cascade in a transonic gas flow

The transonic unsteady flow of a gas through a cascade of thin, slightly curved plates is quite complex and has received little study. The main difficulties are associated with the nonlinear dependence of the aerodynamic characteristics on the plate thickness. In [1] it is shown that, for a single thin plate performing high-frequency oscillations in a transonic gas stream, the variation of the unsteady aerodynamic characteristics with plate thickness may be neglected. For a plate cascade, the flow pattern is complicated by the aerodynamic interference between the plates, which may depend significantly on their shape. A solution of the problem of transonic flow past a cascade without account for the plate thickness has been obtained by Hamamoto [2].The objective of the present study is the clarification of the dependence of the aerodynamic characteristics of a plate cascade on plate thickness in transonic unsteady flow regimes. The nonlinear equation for the velocity potential is linearized under the assumption that the motionless plate causes significantly greater disturbances in the stream than those due to the oscillations. A similar linearization was carried out for a single plate in [3]. The aerodynamic interference between the plates is determined by the method presented in [4]. As an example, the aerodynamic forces acting on a plate oscillating in a duct and in a free jet are calculated.     

Nonlinear flutter of a two-dimension thin plate subjected to aerodynamic heating by differential quadrature method

The problem of nonlinear aerothermoelasticity of a two-dimension thin plate in supersonic airflow is examined. The strain-displacement relation of the von Karman＇s large deflection theory is employed to describe the geometric non-linearity and the aerodynamic piston theory is employed to account for the effects of the aerodynamic force. A new method, the differential quadrature method （DQM）, is used to obtain the discrete form of the motion equations. Then the Runge-Kutta numerical method is applied to solve the nonlinear equations and the nonlinear response of the plate is obtained numerically. The results indicate that due to the aerodynamic heating, the plate stability is degenerated, and in a specific region of system parameters the chaos motion occurs, and the route to chaos motion is via doubling-period bifurcations.     

基于雨燕翅膀的仿生三角翼气动特性计算研究

针对低雷诺数微型飞行器的气动布局,设计出类似雨燕翅膀的一组具有不同前缘钝度的中等后掠(Λ=50?)仿生三角翼.为了定量对比研究三角翼后缘收缩产生的气动效应,设计了一组具有同等后掠的普通三角翼.为了深入研究仿生三角翼布局的前缘涡演化特性以及总体气动特性,采用数值模拟方法详细地探索了低雷诺数(Re=1.58×104)流动条...     

Asymptotic theory of flow separation from wings of low aspect ratio

Numerous methods have been developed to calculate the aerodynamic characteristics of wings of low aspect ratio in the case when there is flow separation from the wing edges. Among the methods based on direct solution of the three-dimensional Euler equations there are the method of discrete vortices [1, 2] and the panel method [3]. In addition, numerical and asymptotic methods [4, 5] based on the theory of slender bodies [6] are used. One of the most important shortcomings of this theory is the dependence of the flow pattern at a given section of the wing on only the upstream flow. The obtained solutions therefore contain no information about the influence of the trailing edge of the wing, on which, as is well known, the Chaplygin-Zhukovskii condition is satisfied. The aim of the present paper is to construct an asymptotic theory of higher approximation and a corresponding numerical method for calculating flow separation from wings of low aspect ratio in which this shortcoming is absent.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 141–147, July–August, 1982.     

翼反角对高压捕获翼构型亚声速气动特性影响分析研究

高压捕获翼新型气动布局在高超声速设计状态下具有较好的气动性能, 新升力面的引入使其在亚声速条件下也具有较大的升力, 但在亚声速下的稳定特性还有待研究. 基于高压捕获翼气动布局基本原理, 在机身-三角翼组合体上添加单支撑和捕获翼, 设计了一种参数化高压捕获翼概念构型. 以捕获翼和机体三角翼上/下反角为设计变量, 采用均匀试验设计、计算流体力学数值计算方法及Kriging代理模型方法, 研究了0° ~ 10°攻角状态下不同翼反角对高压捕获翼构型亚声速气动特性的影响, 重点分析了升阻特性、纵向和横航向稳定性的变化规律以及流场涡结构等. 结果表明, 小攻角状态下翼反角对升阻比的影响比大攻角更加显著, 捕获翼上反时, 升阻比略微增大, 下反则升阻比减小; 三角翼上反时, 升阻比减小, 下反则升阻比先略微增大后缓慢减小; 翼反角对纵向稳定性的总体影响较小, 捕获翼上反会稍微提高纵向稳定性, 而三角翼上反则会降低纵向稳定性; 捕获翼或三角翼上反都会增强横向稳定性, 下反则减弱横向稳定性, 但大攻角状态时, 三角翼上反角过大对提升横向稳定性作用有限; 捕获翼上反航向稳定性增强, 下反航向稳定性则减弱, 而三角翼下反对提升航向稳定性的整体效果比上反更加显著.      

高速列车头型长细比对气动噪声的影响

高速列车的头尾车外形对气动噪声具有重要的影响.工程实践中随着车速的增加,车辆头部越来越细长,日本高速磁悬浮列车实践中甚至出现了具有极端长细比的头部形状.本文以讨论头型长细比对列车气动噪声的影响规律为出发点,应用非线性声学求解器(NLAS)和FW-H声学比拟法的混合算法,在3种运行速度下对基于CRH380A高速列车头型概化的4种不同头型长细比的模型车的气动噪声进行了数值模拟.给出了不同头型长细比列车的流场特征、气动阻力和气动噪声.结果表明,列车的气动总阻力随头型长细比的增大而减小,且头型长细比对列车总气动阻力的影响随运行速度的增加而增强.而头型长细比对气动噪声的影响呈现出较为复杂的影响,并不存在单调的影响关系;综合考虑气动阻力和气动噪声,长细比最大的头型综合性能较优,但差异并不显著,因此在不考虑微气压波等因素的条件下,简单增加车头长细比并不一定能带来明显的气动噪声性能提升.     

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.