Some Aspects of the Lift Force on a Spherical Bubble

Several situations in which a spherical bubble experiences a lift force are examined, especially through the use of computational results obtained by solving the full Navier–Stokes equations. The lift force is computed over a wide range of Reynolds number for the case of pure shear flow, pure strain and solid body rotation. Using these results, the validity of asymptotic solutions derived in the limit of low Reynolds number or inviscid flow is discussed. A general expression of the lift force valid for low to moderate shears is proposed. It is shown that for such shears, the lift force in a complex flow can be predicted by superposing the results obtained in pure strain flow and solid body rotation flow. Finally, the interaction force experienced by two bubbles rising side-by-side is studied. The computational results reveal that, at variance with the predictions of potential theory, the sign of this force changes when the Reynolds number or the separation distance between the bubbles decreases below a critical value. All these results are discussed in terms of vorticity. The respective role played by the vorticity generated at the bubble surface and by the one that is eventually present in the unperturbed flow is emphasized.     

Lift Force Acting on a Heavy Solid in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

The dynamics of a heavy cylindrical body in a liquid-filled horizontal cylindrical cavity with a time-varying rotation rate is experimentally investigated. The body is near the cavity boundary under a centrifugal force and undergoes solid-body rotation together with the liquid and the cavity at a fixed rotation rate. The dependence of the body dynamics on the amplitude and frequency of modulation of the rotation rate is investigated. It is found that at a critical amplitude of modulation (at definite frequency), the heavy body repulses from the cavity boundary and comes into a steady state at some distance from the wall. It is found that the average lift force (repulsive one) is generated by the azimuthal oscillation of the body in the rotating frame of reference and manifests itself at a distance comparable to the thickness of the viscous boundary layer. In the experiments, we observed azimuthal drift of the body due to asymmetric azimuthal oscillations of the body. In the limit of high frequency of the rotation rate modulation, the dependence of the lift force coefficient on the gap between the body and the wall is determined.     

Optimal Control of a Vortex Trapped by an Airfoil with a Cavity

An airfoil with a cavity traps a vortex; the lift increases but the vortex shows great receptivity to upstream disturbances. A simple potential flow model confirms that the vortex stability basin is of a reduced extent. In this paper we present a control technique stabilizing the vortex position based on a potential flow model. The actuators are sources/sinks at the wall and the suction/blowing law is obtained by the adjoint optimization method. This revised version was published online in July 2006 with corrections to the Cover Date.     

可变形儒可夫斯基翼型非定常气动力的研究

对于翼面变形法向运动速度远小于来流速度的儒可夫斯基机翼,将解析解和离散涡方法相结合计算变形机翼的流场及非定常气动力,较详细地分析了变形机翼升力系数的准定常计算方法的误差来源,并给出修正方法.计算结果显示脱落涡尾迹对升力系数和机翼绕流环量的影响很小,变形机翼升力系数准定常计算方法的误差丰要来源于流体非定常运动引起的虚拟质量力,该非定常附加升力仅与当前时刻飞行姿态及翼犁形状和变形速率有关,与具体的变形历史过程无关,变形机翼的升力近似等于准定常计算结果叠加上相应的虚拟质量力.     

可变形儒可夫斯基翼型亚音速非定常气动力的研究

对于翼面变形速度远小于来流速度情况下的儒可夫斯翼型亚音速绕流问题,通过仿射变换将可压缩流动转换成不可压缩流动,将解析解和离散涡方法相结合计算变形机翼的不可压缩流动速度场,再利用逆变换得到变形机翼的亚音速流动速度场,进而分析非定常气动力特性,建立变形机翼的准定常升力系数和非定常附加升力系数在可压缩和不可压缩两种状态下的简单近似对应关系。计算结果显示变形机翼的非定常气动升力近似等于准定常计算结果叠加上虚拟质量力导致的非定常附加升力,该非定常附加升力随翼型变形速率呈线性关系,由机翼当前时刻飞行姿态、翼型及其变形速率确定,与具体变形历史过程无关。低来流马赫数时虚拟质量力导致的非定常效应显著,高亚音速流动时准定常升力起主导作用。同时还分析了不同马赫数下机翼往复变形过程中升力的变化特性,指出尽管高亚音速变形机翼的气动升力近似等于准定常气动升力,但不能忽视非定常附加升力的影响,非定常附加升力将导致完成往复变形需要外界输入正比于Ma∞/[(1-Ma2∞)]的功。     

Hydrodynamic Mechanisms of the Influence of an Elastic Constraint on the Propulsive Force of Airfoil under Semideterministic Oscillations in Viscous Fluid Flow

Fluid Dynamics - The results of investigation of oscillations of an airfoil on an elastic hinge that performs transverse sinusoidal oscillations in the free stream of a viscous incompressible fluid...     

Analytic Solution in the Problem of Constructing an Airfoil with Minimum Wave Drag

A solution of the problem of optimization of an airfoil in a supersonic flow is proposed. A symmetric airfoil with minimum wave drag for a given longitudinal cross-sectional area is constructed within the framework of a local analysis of variations of the shape with respect to the exact solution for a wedge and a rhombus. Analytic dependences representing the shape of the airfoil and its drag are found. The solution obtained is tested numerically within the framework of the Euler model.     

Nonuniqueness of the Transonic Flow past an Airfoil

The inviscid transonic flow past a symmetric airfoil having a curvature minimum in the middle is numerically investigated. It is shown that at zero angle of attack both symmetric and asymmetric steady-state flow patterns can exist on a certain freestream Mach number range M_min < M_max. On this range, the asymmetric flows are stable against small perturbations, whereas the symmetric flows are stable only if M does not coincide with a singular Mach number at which small variations in M or can result in flow restructuring.     

圆形坚冰影响翼型气动性能的数值分析

本文用FLUENT软件模拟了结冰后NACA 0012翼型周围流场的变化,并与结冰前NACA 0012翼型的气动性能进行了对比.工作中首先以未结冰的NACA 0012翼型(干净翼型)为标准模型进行了数值验证计算,再以经过检验的方法计算结冰模型,并与结冰风洞试验数据进行了对比.本文计算攻角为0°～20°,温度为250.37K,雷诺数为2,400,000,冰型为圆形坚冰.通过对比升力阻力性能,发现与干净翼型相比,结冰翼型的最大升力系数大约减少了50%,阻力系数增加了约65%,失速攻角降低了4°.结冰后翼型提前失速是造成气动性能恶化的主要原因.     

水平油气输送管线中液滴升力的理论预测

通过对油气输送条件下液滴运动状态的分析，提出了考虑相间局部滑移和局部剪切速率分布的水平布置管线中液滴局部升力的计算方法。研究表明液滴升力值在靠近液膜表面位置存在一最大值，可达液滴重力的33％，这时液滴将在剪切气流的作用下被强有力地抬升到气核中去，而气核中液滴的平均升力约为液滴重力的10％。因此，在研究油气输送条件下液滴扩散和空间分布规律时应当合理计及液滴升力的作用。     

Mathematical Modeling of Time-Dependent Aerodynamic Loads on an Airfoil with Dynamic Deflection of a Control on the Trailing Edge

The linear problem of the time-dependent inviscid flow past a thin symmetric airfoil with a control on its trailing edge deflected in accordance with an arbitrary law is considered. The aerodynamic loads on the airfoil are calculated. The intensity of the vortex wake shed from the airfoil is determined by numerically solving a Volterra integral equation of the first kind. Questions of the mathematical modeling of the time-dependent aerodynamic loads in a form convenient for the joint solution of the problems of aerodynamics and flight dynamics are also considered. The results of the modeling are compared with the numerical solutions obtained.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 157–169.Original Russian Text Copyright © 2005 by Khrabrov.     

Deformable-Drop Dynamics near an Airfoil Surface in Viscous Air

A locally monodisperse air-supercooled water drop flow past an airfoil is studied. The influence of the viscous boundary layer on the force exerted on the drops by the carrier gas and the effect of deformation of the drops on (i) their trajectories, (ii) the water mass flux density over the airfoil surface, and (iii) the wetted-surface length are considered. The effect of an airfoil electrostatic field on the dynamics of charged atmospheric drops is estimated. The role of the governing parameters, i.e. the airfoil angle of attack, the radius of the undisturbed spherical drop, and the drop charge is investigated.The possible origins of the discrepancy between the numerical and experimental results of foreign researchers are indicated.     

Vortex Cell with a Cylinder Rotating inside it on the Surface of an Airfoil Section at High Reynolds Numbers

An algorithm for eliminating flow separation in the nose region of a symmetric airfoil section at nonzero angle of incidence is proposed. Below the separation-prone region of the section, to increase the critical angle of incidence, a vortex cell with a cylinder rotating inside is located. The shape of the vortex cell and the precise location of the cylinder are so chosen as to create the same pressure gradient in the mixing layer as in the external flow.     

Equilibrium of an Inverted Mathematical Double-Link Pendulum with a Follower Force

A discrete model of an elastic pendulum with a follower force is studied. This model is an inverted mathematical two-link pendulum with viscoelastic hinges. It is shown that divergent bifurcations are possible for some absolute values of the follower force and the stiffness of the restraint of the pendulum's upper end. As a result, the vertical position of the equilibrium becomes unstable and two new nonvertical stable equilibrium states (fork bifurcation) occur.     

Effect of Localization of Pulsed Energy Addition on the Wave Drag of an Airfoil in a Transonic Flow

The possibility of controlling the aerodynamic characteristics of airfoils with the help of local pulsed-periodic energy addition into the flow near the airfoil contour at transonic flight regimes is considered. By means of the numerical solution of two-dimensional unsteady equations of gas dynamics, changes in the flow structure and wave drag of a symmetric airfoil due to changes in localization and shape of energy-addition zones are examined. It is shown that the considered method of controlling airfoil characteristics in transonic flow regimes is rather promising. For a zero angle of attack, the greatest decrease in wave drag is obtained with energy addition at the trailing edge of the airfoil.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 60–67, September–October, 2005.     

Airfoil boundary layer measurements at low Re in an accelerating flow from a nonzero velocity

The effects of an accelerating freestream from a nonzero velocity on the transitional separation bubble characteristics were investigated quantitatively. Hot wire anemometry was used to determine the boundary layer velocity profile repsonse to the acceleration at selected chordwise locations on a Wortmann FX 63-137 airfoil at 7 ° angle of attack. Both positive and negative accelerations were studied from base chord Reynolds number of 100,000 and 150,000, respectively. The purpose of this experiment was to verify the trends witnessed in previous research concerning a sinusoidally oscillating freestream velocity by uncoupling the accelerating and decelerating boundary layer effects. The experimental results indicate that as a result of a freestream acceleration, the separation bubble position shifts in the direction opposite to the chordwise direction it would move for a quasi-steady velocity change. The transition location was more responsive to the acceleration than was the separation position. This supports the oscillating freestream experiment conclusions.This research was supported by the U.S. Navy Office of Naval Research under contract N00014-83-K-0239     

Experimental Investigation of the Interaction between an Electric Arc and a Gas Flow

The results of investigating the shape of an electric arc carrying an electric current of less than 100 A and exposed to an air, nitrogen, or argon stream at a stream velocity of from zero to 20 m/s, when the interelectrode gap is less than 20 mm, are reported. The shape of the arc is qualitatively investigated as a function of the gas type, blowing velocity, and interelectrode gap. It is shown that an arc burning in a channel with insulated walls is much more stable under these conditions than an arc with the same parameters burning in free space.     

Modeling of Ice Accretion on the Airfoil Surface in an Air Flow Containing Ice Particles

The process of airfoil icing caused by incidence of ice crystals is considered. A physicomathematical model of motion of spheroidal crystals in the gas flow and their interaction with the body is formulated. The model takes into account the non-spherical particle orientation with respect to the velocity vector of the gas flow. It is assumed that the particle impact onto the body surface leads to partial destruction of the particle under the action of normal and tangential stresses, and some part of the particle mass remains in the vicinity of the impact point. An inviscid flow around the airfoil with a time-dependent shape is calculated by the method of approximate conformal mapping.     

开关柜内部电弧故障产生力和热的计算模型

开关柜内部电弧故障会引起许多效应。在电弧周围引起压力升高 ,并在柜体内和空气中引起温度升高。建立的模型对内部电弧故障引起的力和热的效应规律进行研究 ,并对这两种效应进行了数值求解。结果表明 ,对于持续时间为 1s的电弧故障 ,柜体内部压力在最初阶段上升很快 ,在达到一个峰值后下降直至消失 ,但热效应持续时间较长。     

Effect of Inflow Turbulence on an Airfoil Flow with Laminar Separation Bubble: An LES Study

The present paper is concerned with numerical investigations on the effect of inflow turbulence on the flow around a SD7003 airfoil. At a Reynolds number Re_c =?60,000, an angle of attack α =?4^° and a low or zero turbulence intensity of the oncoming flow, the flow past the airfoil is known to be dominated by early separation, subsequent transition and reattachment leading to a laminar separation bubble with a distinctive pressure plateau. The objective of the study is to investigate the effect of inflow turbulence on the flow behavior. For this purpose, a numerical methodology relying on a wall-resolved large-eddy simulation, a synthetic turbulence inflow generator and a specific source term concept for introducing the turbulence fluctuations within the computational domain is used. The numerical technique applied allows the variation of the free-stream turbulence intensity (TI) in a wide range. In order to analyze the influence of TI on the arising instantaneous and time-averaged flow field past the airfoil, the present study evaluates the range 0% ≤ TI ≤?11.2%, which covers typical values found in atmospheric boundary layers. In accordance with experimental studies it is shown that the laminar separation bubble first shrinks and finally completely vanishes for increasing inflow turbulence. Consequently, the aerodynamic performance in terms of the lift-to-drag ratio increases. Furthermore, the effect of the time and length scales of the isotropic inflow turbulence on the development of the flow field around the airfoil is analyzed and a perceptible influence is found. Within the range of inflow scales studied decreasing scales augment the receptivity of the boundary layer promoting an earlier transition.