Non-linear oscillations with multiple forcing terms

The problem of determining the transient response of a non-linear oscillator of the form ü + u = εƒ(u,u) + E(t) is studied by the method of multiple time scales, using the symbolic computation system MACSYMA. when the excitation E(t) consists of a finite number of harmonic forcing terms. Here ε is a small parameter and ƒ(u,u) is a non-linear function of its arguments. In particular, the Van der Pol and Duffing oscillators are studied in detail. It is found that when the forcing frequencies are not close to each other or close to the primary resonance of the system, then the response of the system is analogous to the behavior when only one forcing term is present. However, when the forcing frequencies are close to each other or close to the primary resonance, then the behavior is quite different, exhibiting certain oscillations not observed in the case of one forcing term.     

Some features of a turbulent wing–body junction vortical flow

Laser-Doppler velocimeter measurements of a wing/body junction flow field made within a plane to the side of the wing/wall junction and perpendicular both to a 3:2 elliptical nose—NACA 0020 tail wing, and a flat wall are presented. Reynolds number of the approach boundary layer was, Re_θ = 5940, and free-stream air velocity was, U_ref = 27.5 m/s. A large vortical structure residing in the outer region redirects the low-turbulence free-stream flow to the vicinity of the wing/wall junction, resulting in thin boundary layers with velocity magnitudes higher than free-stream flow. Lateral pressure gradients result in a three-dimensional separation on the uplifting side of the vortex. Additionally, a high vorticity vortical structure with opposite sense to the outer-layer vortex forms beneath the outer-layer vortex. Normal and shear stresses increase to attain values an order of magnitude larger compared to values measured in a three-dimensional boundary layer just outside the junction vortex. Bimodal histograms of the w fluctuating velocity occur under the outer-layer vortex near the wall due to the time-dependent nature of the horseshoe vortex. In such a flow the shear-stress angle (SSA) highly lags the flow-gradient angle (FGA), and the turbulence diffusion is highly altered due to presence of vortical structures.     

Reduced order nonlinear aeroelasticity of swept composite wings using compressible indicial unsteady aerodynamics

Nonlinear dynamic aeroelasticity of composite wings in compressible flows is investigated. To provide a reasonable model for the problem, the composite wing is modeled as a thin walled beam (TWB) with circumferentially asymmetric stiffness layup configuration. The structural model considers nonlinear strain displacement relations and a number of non-classical effects, such as transverse shear and warping inhibition. Geometrically nonlinear terms of up to third order are retained in the formulation. Unsteady aerodynamic loads are calculated according to a compressible model, described by indicial function approximations in the time domain. The aeroelastic system of equations is augmented by the differential equations governing the aerodynamics lag states to derive the final explicit form of the coupled fluid-structure equations of motion. The final nonlinear governing aeroelastic system of equations is solved using the eigenvectors of the linear structural equations of motion to approximate the spatial variation of the corresponding degrees of freedom in the Ritz solution method. Direct time integrations of the nonlinear equations of motion representing the full aeroelastic system are conducted using the well-known Runge–Kutta method. A comprehensive insight is provided over the effect of parameters such as the lamination fiber angle and the sweep angle on the stability margins and the limit cycle oscillation behavior of the system. Integration of the interpolation method employed for the evaluation of compressible indicial functions at any Mach number in the subsonic compressible range to the derivation process of the third order nonlinear aeroelastic system of equations based on TWB theory is done for the first time. Results show that flutter speeds obtained by the incompressible unsteady aerodynamics are not conservative and as the backward sweep angle of the wing is increased, post-flutter aeroelastic response of the wing becomes more well-behaved.     

Aspect ratio effect on natural convection in water near its density maximum temperature

The effect of the aspect ratio on natural convection in water subjected to density inversion has been investigated in this study. Numerical simulations of the two-dimensional, steady state, incompressible flow in a rectangular enclosure with a variety of aspect ratios, ranging from 0.125 to 100, have been accomplished using a finite element model. Computations cover Rayleigh numbers from 10³ to 10⁶. Results reveal that the aspect ratio, A, the Rayleigh number, Ra, and the density distribution parameter, R, are the key parameters to determine the heat transfer and fluid flow characteristics for density inversion fluids in an enclosure. A new correlation for predicting the maximum mean Nusselt number is proposed in the form of , with the constants a and b depending on density distribution number R. It is demonstrated that the aspect ratio has a strong impact on flow patterns and temperature distributions in rectangular enclosures. The stream function ratio Ψ_inv/|Ψ_reg| is introduced to describe quantitatively the interaction between inversional and regular convection. For R=0.33, the density inversion enhancement is observed in the regime near A=3.     

模型昆虫翼作非定常i运动时的气动力特性

基于Navier-Stokes方程的数值解,研究了一模型昆虫翼在小雷诺数(Re=100)下作非定常运动时的气动力特性.这些运动包括翼启动后的常速转动,快速加、减速转动,常速转动中快速上仰(模拟昆虫翼的上挥或下拍、翻转等运动).有如下结果在小雷诺数下,模型昆虫翼以大攻角(α=35°)作常速转动运动时,由于失速涡不脱落,可产生较大的升力系数.其机理是翼转动时,翼尖附近(该处线速度大)上翼面压强比翼根附近(该处线速度小)的小得多,因而存在展向压强梯度,同时存在着沿展向的离心力,此展向压强梯度和离心力导致的展向流动在失速涡的轴向方向,其可避免失速涡脱落.模型昆虫翼在快速加、减速转动和快速上仰运动中,虽然雷诺数小,但由于在短时间内产生了大涡量,也可产生十分大的气动力,例如在快速上仰运动中,升力系数可大于10.     

80°/65°双三角翼摇滚特性风洞实验研究

介绍了在FL-23高速风洞中研究自由摇滚的装置、试验方法、数据采集等试验技术.在马赫数从0.3到0.6范围内,对应的雷诺数从0.56×107/m至1.126×107/m范围内,开展了双三角翼大迎角下的摇滚特性的研究,包括迎角、马赫数、初始释放等参数的影响,给出了典型的结果.结果表明,随着模型迎角的增加,双三角翼呈现不同的滚转运动形态,包括静态稳定、准极限环摇滚、双周期震荡等;试验中马赫数提高对翼摇滚起抑制作用;摇滚运动的最终平衡状态和摇滚幅值与初始状态无关.     

The effect of the Reynolds number on the Reynolds stresses and vorticity in a turbulent far-wake

Using two orthogonal arrays of 16 X-wires, eight in the (x,y)-plane and eight in the (x,z)-plane, the effect of the Reynolds number in a turbulent plane far-wake has been investigated for two values of Re_θ (based on the free stream velocity and the momentum thickness), i.e. 1350 and 4600. It is observed that as the Reynolds number increases the magnitudes of the measured Reynolds stresses increase, as does the size of two-point vorticity correlation iso-contours. Discernible differences are also observed in probability density function, spectra and three-dimensional topologies. The Reynolds number dependence seems to vanish when Re_θ5000.     

Flow past a delta wing with a sinusoidal leading edge: near-surface topology and flow structure

The near-surface flow structure and topology on a delta wing of low sweep angle, having sinusoidal leading edges of varying amplitude and wavelength, are investigated using a stereoscopic technique of high-image-density particle image velocimetry at a Reynolds number of 15,000. Identification of critical points, in conjunction with surface-normal vorticity and velocity, provides a basis for determining the effectiveness of a given leading edge. At high angle of attack, where large-scale three-dimensional separation occurs from the wing with a straight leading edge, an amplitude of the leading-edge protuberance as small as one-half of one percent of the chord of the wing can substantially alter the near-surface topology. When the amplitude reaches a value of four percent of the chord, it is possible to completely eradicate the negative focus of large-scale, three-dimensional separation, in favor of a positive focus of attachment. Moreover, alteration of the near-surface topology is most effective when the ratio of the wavelength to amplitude of the sinusoidal leading edge is maintained at a small value.     

65°三角翼亚音速复杂流场计算和数据可视化

提出一种基于非结构混合网格和有限体积法的有效计算策略,对第二期国际涡流试验项目(second international vortex flow experiment,VFE-2)的尖前缘65°三角翼在马赫数0.4,迎角20.3°,雷诺数2×10~6条件下的亚音速复杂流场结构进行数值模拟,重点探讨了基于计算数据进行该类型复杂涡系干扰表面和空间流场关键特征提取和数据可视化问题.通过与相关试验类比,建立了与先进试验流动显示技术相比拟的定性和定量分析方法,为三角翼这类复杂流场结构的精细分析奠定了技术基础.采用上述方法,细致分析了亚音速三角翼的大迎角复杂旋涡流场结构,得到了与试验一致的结论.研究证实:在大迎角条件下,三角翼流动物理复杂,黏性效应耦合严重,只有通过N-S方程计算才能准确地捕捉主涡和二次涡的发展.     

Simulation of leading-edge vortex flows

An implicit upwind-relaxation finite-difference algorithm solving the incompressible Navier-Stokes equations is employed to simulate low-speed, three-dimensional, laminar, leadingedge vortex flows over three round-edged low-aspect-ratio wings. The effects of grid density, angle of attack, Reynolds number, and wing planform on the flowfield structures and integral values are studied. Computed results are presented and compared with experimental data.The work of the first author was supported by the NASA Langley Research Center under Contract NAS1-18585.     

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.      

微型飞行器低雷诺数空气动力学

微型飞行器(MAVs)设计绝不是常规飞行器在尺度上的简单缩小,面临许多技术难题.其中微型飞行器低雷诺数空气动力学是其最为根本的技术瓶颈之一,也是当前受到广泛关注的热点之一.本文紧密结合微型飞行器技术,对这一领域中所面临的低雷诺数空气动力学问题和近两年来该方向国内一些新的进展进行了较为详细的介绍.按照MAVs飞行方式和结构特性进行分类,简单介绍微型飞行器研究中的低$Re$数空气动力学问题.首先介绍了二维和三维固定翼低雷诺数空气动力学问题:包括层流分离泡,翼型升力系数小攻角非线性效应,静态迟滞效应,以及低$Re$数小展弦比机翼气动特性.第2,介绍了拍动翼低雷诺数空气动力学方面的研究工作.包括前人提出的昆虫低$Re$数下获得高升力的多种非定常拍动翼飞行机制:Wagner效应、Weis-Fogh效应(clap-and-fling)、延迟失速效应(delayedstall)、Kramer效应(rotational forces)、尾迹捕获效应(wakecapture)、附加质量效应(addedmass)等.以及国内学者近几年在拍动翼方面取得的一些研究成果.第3,介绍了柔性翼低雷诺数气动问题.研究表明柔性翼对于固定翼微型飞行器提高抗阵风能力,拍动翼微型飞行器产生足够的升力和推力.最后简单介绍了可变形翼(morphingwing)微型飞行器方面的一些研究工作,指出微型飞行器技术可以通过采用可变形翼设计,突破众多的技术瓶颈.另一方面,可变形翼概念可以通过在低成本,低速的MAVs上进行飞行试验,获得非常好的验证平台.      

雷诺数效应对翼型抖振特性的影响

飞行器抖振是一种非线性气动弹性问题,当飞行器进入抖振阶段时,将会对飞行器的性能产生严重影响。而在跨声速条件下,激波附面层相互作用会诱导机翼抖振。本文开展了跨声速条件下翼型抖振特性雷诺数效应的实验研究,揭示了翼型跨声速抖振起始迎角、激波运动前缘边界、频谱特性、抖振频率与雷诺数变化的基本规律。结论如下:雷诺数变化会导致抖振起始边界的改变,对抖振起始迎角下的功率谱密度峰值有明显影响;随着雷诺数的增大,激波运动的前缘后移。雷诺数变化对抖振频率有明显影响,随着马赫数增大,雷诺数效应增强。     

Entropy effects in hypersonic flow over blunt delta wings

The problem of hypersonic flow over blunt delta wings is considered. It is shown that in the case of large wing lengths x -100, where x is the longitudinal coordinate measured in blunt nose radii, extremal flow regimes characterized by an essentially nonuniform distribution of the gas dynamic parameters (density, entropy, Mach number) may be realized in the shock layer near the windward surface of the wing. The location of the zones of flow convergence or divergence on the surface of a delta wing with sweep angle x=75° is established. For the same wing the ranges of Mach numbers M and angles of attack leading to extremal flow regimes are indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 178–181, March–April, 1991.     

Numerical and experimental study of turbulent impinging twin-jet flow

The two dimensional impinging circular twin-jet flow with no-cross flow is studied numerically and experimentally. The theoretical predications are carried out through numerical procedure based on finite volume method to solve the governing mass, momentum, turbulent kinetic energy and turbulent kinetic energy dissipation rate. The parameters studied were jet Reynolds number (9.5 × 10⁴  Re  22.4 × 10⁴), nozzle to plate spacing (3  h/d  12), nozzle to nozzle centerline spacing (l/d = 3, 5 and 8) and jet angle (0°  θ  20°). It is concluded that the stagnation primary point moves away in the radial main flow direction by increasing the jet angle. This shift becomes stronger by increasing the nozzle to nozzle centerline spacing (l/d). A secondary stagnation point is set up between two jets. The value of pressure at this point decreases by decreasing Reynolds number and/or increasing the jet angle.

The sub atmospheric region occurs on the impingement plate. It increases strongly by increasing Reynolds number and decreases as the jet angle and/or a nozzle to plate spacing increases. The spreading of jet decreases by increasing nozzle to plate spacing. The intensity of re-circulation zone between two jets decreases by increasing of h/d and jet angle. The increase of turbulence kinetic energy occurs within high gradient velocity.     

Aeroelastic analysis of swept pre-twisted wings

In this paper, aeroelastic modeling of aircraft wings with variations in sweep angle, taper ratio, and variable pre-twist angle along the span is considered. The wing structure is modeled as a classical beam with torsion and bending flexibility. The governing equations are derived based on Hamilton’s principle. Moreover, Peters’ finite state aerodynamic model which is modified to take into account the effects of the wing finite-span, the wing sweep angle, and the wing pre-twist angle, is used to simulate the aerodynamic loads on the wing. The coupled partially differential equations are discretized to a set of ordinary differential equations using Galerkin’s approach. By solving these equations the aeroelastic instability conditions are derived. The results are compared with some experimental and analytical results of previous published papers and good agreement is attained. Effects of the wing sweep angle, taper ratio, bending to torsional rigidity, and pre-twist angle on the flutter boundary in several cases are studied. Results show that these geometrical and physical parameters have considerable effects on the wing flutter boundary.     

Multigrid convergence of inviscid fixed‐ and rotary‐wing flows

The affect of multigrid acceleration implemented within an upwind‐biased Euler method is presented, and applied to fixed‐wing and rotary‐wing flows. The convergence of fixed‐ and rotary‐wing computations is shown to be vastly different, and multigrid is shown to be less effective for rotary‐wing flows. The flow about a hovering rotor suffers from very slow convergence of the inner blade region, where the flow is effectively incompressible. Furthermore, the vortical wake must develop over several turns before convergence is achieved, whereas for fixed‐wing computations the far‐field grid and solution have little significance. Results are presented for single mesh and two, three, four, and five level multigrid, and using five levels a reduction in required CPU time of over 80 per cent is demonstrated for rotary‐wing computations, but 94 per cent for fixed‐wing computations. It is found that a simple V‐cycle is the most effective, smoothing in the decreasing mesh density direction only, with a relaxed trilinear prolongation operator. Copyright © 2002 John Wiley & Sons, Ltd.     

Stationary flow past the lower surface of a piecewise planar delta wing with supersonic leading edges

The considered wing has any finite number of inflections in its plane with lines of inflection intersecting at the point of inflection of the leading edge. In the present paper, this generalizes the author's earlier work [1] on flow past the undersurface of a flat wing at unite angle of attack with finite angle of slip and supersonic leading edges. In [1], calculations were not given. The special case of flow without slip in the same situation was considered later in [2], However, this paper contains errors, indicated at the end of the present paper. The calculations given in [2] are not correct. In the quoted papers, the gas flow is assumed to be a perturbation of a homogeneous flow behind a plane oblique shock wave. Such flows are treated systematically in [3]. Here and in [1], we use and generalize the representation of the linearized conservation laws across the shock front as the conditions of a boundary-value problem for an analytic function of a complex variable as obtained in [4, 5]. Calculations are given of the pressure distribution over the span for a number of different flow regimes and the pressure coefficients in the middle of the wing are compared with a numerical solution presented partly in [6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 80–90, September–October, 1979.I am very grateful to V. I. Lapygin for making available a large number of variants of his numerical solution, and to L. E. Pekurovskii for assistance in the calculations.     

机翼尺度效应对等离子体分离流动控制特性的影响

等离子体流动控制技术是一种以等离子体气动激励为控制手段的主动流动控制技术. 为了进一步提高等离子体激励器可控机翼尺度, 以超临界机翼SC(2)-0714大迎角分离流为研究对象, 以对称布局介质阻挡放电等离子体为控制方式, 以测力、粒子图像测速仪为研究手段, 从等离子体激励器特性研究出发, 深入开展了机翼尺度效应对等离子体控制的影响研究, 提出了适用于分离流控制的能效比系数, 探索了分离流等离子体控制机理, 掌握了机翼尺度对分离流控制的影响规律. 结果表明: (1)随着机翼尺度的增大, 布置到机翼上的激励器电极长度会相应增加; 在本文的参数研究范围内, 激励器的平均消耗功率不会随电极长度的增加而线性增大; 当电极长度达到一定阈值时, 激励器的平均消耗功率趋于定值; (2)在固定雷诺数的情况下, 随着机翼尺度的增大, 等离子体的控制效果并未降低, 激励器能效比系数提高; (3)等离子体在主流区诱导的大尺度展向涡与在壁面附近产生的一系列拟序结构成为分离流控制的关键. 研究结果为实现真实飞机的等离子体分离流控制, 推动等离子体流动控制技术工程化应用提供了技术支撑.      

On the departure behaviors of bubble at nucleate pool boiling

Dimensionless scales of radius and time, proposed by the authors in a previous study, were used to quantitatively analyze the bubble departure radius and time during nucleate pool boiling. The results obtained from dimensional analysis were compared with experimental data reported in many studies. These experimental data are including partial nucleate pool boiling data with constant heat flux and temperature conditions acquired over the past 40 years at atmospheric and sub-atmospheric pressures, as well as data obtained at subcooled, saturated, and superheated pool temperature conditions.It was shown that the departure radius and time could be well correlated with respect to Jakob number as proposed by the previous studies. And the bubble departure behaviors well categorized between atmospheric and sub-atmospheric pressure, which is occurred from the different growth rate near the departure time partial nucleate pool boiling.For almost all obtained under atmospheric pressure, the dimensionless departure radius and time scales were about 25 and 60, respectively. For higher Jakob number, the square root of Bond number was proportional to the power of 0.7 of Jakob number, little different from the previous correlations. The dimensional departure radius and time estimated from the relationships proposed in this study were compared with measured departure scales and the results obtained with the previous correlations. And it was shown that the relationships could well predict and describe the departure behaviors of bubble during nucleate pool boiling.