Conditions of aerodynamic instability of airfoil equilibrium positions

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 37, No. 5, pp. 29–34, September–October, 1996.     

Global aerodynamic instability of twin cylinders in cross flow

This paper comprises an in-depth physical discussion of the flow-induced vibration of two circular cylinders in view of the time-mean lift force on stationary cylinders and interaction mechanisms. The gap-spacing ratio T/D is varied from 0.1 to 5 and the attack angle α from 0° to 180° where T is the gap width between the cylinders and D is the diameter of a cylinder. Mechanisms of interaction between two cylinders are discussed based on time-mean lift, fluctuating lift, flow structures and flow-induced responses. The whole regime is classified into seven interaction regimes, i.e., no interaction regime; boundary layer and cylinder interaction regime; shear-layer/wake and cylinder interaction regime; shear-layer and shear-layer interaction regime; vortex and cylinder interaction regime; vortex and shear-layer interaction regime; and vortex and vortex interaction regime. Though a single non-interfering circular cylinder does not correspond to a galloping following quasi-steady galloping theory, two circular cylinders experience violent galloping vibration due to shear-layer/wake and cylinder interaction as well as boundary layer and cylinder interaction. A larger magnitude of fluctuating lift communicates to a larger amplitude vortex excitation.     

Implications of cubic physical/aerodynamic non-linearities on the character of the flutter instability boundary

The present paper deals with a study of the benign and catastrophic characters of the flutter instability boundary of 2-D lifting surfaces in a supersonic flow field. The objectives of this work are: (i) to contribute to a better understanding of the implications of aerodynamic and physical non-linearities on the character of the flutter boundary and (ii), to outline the effects exerted in the same respect by some important parameters of the aeroelastic system. With the aim of addressing this problem, the method based on the First Liapunov Quantity is used to study the bifurcational behavior of the aeroelastic system in the vicinity of the flutter boundary. The expected outcomes of this study are: (a) to greatly enhance the scope and reliability of the aeroelastic analysis and design criteria of advanced aircraft and, (b) to provide a theoretical basis for the analysis of more complex non-linear aeroelastic systems.     

Modulation instability of electrohydrodynamic waves on liquid jet

An analytical study of slow modulation has been made of cylindrical interface between two inviscid streaming fluids, in the presence of a relaxation of electrical charges at the interface, and stressed by an axial electric field. A new technique based on the perturbation theory, to derive the non-linear evolution equations has been introduced. These equations are combined to yield a non-linear Ginzburg–Landau equation and a non-linear modified Schrödinger equation describing the evolution of wave packets. The linear analysis showed that the streaming has a destabilizing effect and the electric field has stabilizing influence associated with parameters condition involving the electric conductivity and permittivity of the fluids. While the non-linear approach indicated that the streaming may become unstable for sufficiently high velocities, with a new condition on the material properties, involving weak electric relaxation times in both fluids.     

Experimental study on aerodynamic coefficients of yawed cylinders

This paper presents wind tunnel tests on a stationary cylinder inclined with the flow. The cylinder was positioned at different sets of yaw and vertical angles. The flow regime of the tests remained in the subcritical state. Two load cells were designed and installed to measure the aerodynamic forces, with enough sensitivity to measure vortex shedding frequencies. In this paper, the three aerodynamic force coefficients are normalized using the free stream velocity instead of its normal component. The results show that the drag coefficient and the resultant of the lift and side forces coefficients can be described by an empirical function of the incidence angle. The lift and side force coefficients remain however functions of both the horizontal yaw and vertical angles and cannot be expressed as functions of the incidence angle only. The Independence Principle was observed to become inaccurate for yaw angles larger than 40°. However, the measured Strouhal numbers indicate that the vortex shedding frequencies of a yawed cylinder can be predicted using the Independence Principle.     

Theoretical and experimental studies on the aerodynamic instability of a two-dimensional circular cylinder with a moving attachment

Rain–wind induced vibration of cables in cable-stayed bridges is a worldwide problem of great concern. The effect of the motion of water rivulets on the instability of stay cables has been recognized as one of the mechanisms of this complex phenomenon. In order to investigate how the motion of rivulets affects the unstable vibration of cables without considering the effects of axial flow and axial vortex, a real three-dimensional cable was modeled as a two-dimensional circular cylinder, around which an attachment representing the rivulet can move. This could also be regarded as a new kind of two-dimensional 2-dof dynamic system. This paper studies the aerodynamic instability of the system theoretically and experimentally. Equations governing the motions of the cylinder and the attachment are first established. The Lyapunov stability criterion is applied to the equations of motion to derive the criterion for the unstable balance angle of the attachment. Moreover, a new two-dimensional 2-dof cable model system with a movable attachment is designed and tested in a wind tunnel. Parametric studies are carried out to investigate the effects of major factors such as wind speed, frequency and damping of the dynamic system on the unstable balance angle of the rivulet attachment. Theoretical and experimental results match well. These results may be valuable in elucidating the mechanism of rain–wind induced vibration of stay cables.     

Combined aerodynamic and electrostatic atomization of dielectric liquid jets

The electrical and atomization performance of a plane?Cplane charge injection atomizer using a dielectric liquid, and operating at pump pressures ranging from 15 to 35?bar corresponding to injection velocities of up to 50?m/s, is explored via low current electrical measurements, spray imaging and phase Doppler anemometry. The work is aimed at understanding the contribution of electrostatic charging relevant to typical higher pressure fuel injection systems such as those employed in the aeronautical, automotive and marine sectors. Results show that mean-specific charge increases with injection velocity significantly. The effect of electrostatic charge is advantageous at the 15?C35?bar range, and an arithmetic mean diameter D ₁₀ as low as 0.2d is achievable in the spray core and lower still in the periphery where d is the orifice diameter. Using the data available from this higher pressure system and from previous high Reynolds number systems (Shrimpton and Yule Exp Fluids 26:460?C469, 1999), the promotion of primary atomization has been analysed by examining the effect that charge has on liquid jet surface and liquid jet bulk instability. The results suggest that for the low charge density Q _v?~?2?C/m³ cases under consideration here, a significant increase in primary atomization is observed due to a combination of electrical and aerodynamic forces acting on the jet surface, attributed to the significantly higher jet Weber number (We _j) when compared to low injection pressure cases. Analysis of Sauter mean diameter results shows that for jets with elevated specific charge density of the order Q _v?~?6?C/m³, the jet creates droplets that a conventional turbulent jet would, but with a significantly lower power requirement. This suggests that ??turbulent?? primary atomization, the turbulence being induced by electrical forces, may be achieved under injection pressures that would produce laminar jets.     

The effect of surfactants on the instability of a rotating liquid jet

It has long been known that the presence of surfactants on the free surface of a liquid jet can create surface tension gradients along the interface. The resulting formation of tangential stresses along the surface lead to Marangoni type flows and greatly affect the resulting dynamics of rupture. In this way surfactants can be used to manipulate the breakup of a liquid jet and control the size of droplets produced. In this paper we investigate the effects of insoluble surfactants on the breakup of rotating liquid jets with applications to industrial prilling. Using a long wavelength approximation we reduce the governing equations into a set of one-dimensional equations. We use an asymptotic theory to find steady solutions and then carry out a linear instability analysis on these solutions. We show that steady state centreline solutions are independent of viscosity to leading order and that the most unstable wavenumber and growth rate of disturbances decrease as the effectiveness of surfactants is increased. We also numerically solve these equations using a finite difference scheme to investigate the effects of changing the initial surfactant concentration and other fluid parameters. Our results show that differences in breakup lengths between rotating surfactant-laden jets and surfactant-free jets increase with the rate of rotation. Moreover, we find that satellite droplet sizes decrease as the rate of rotation is decreased with the effect of surfactants amplifying the reduction in sizes. Furthermore, the presence of surfactants at fixed rotation rates is shown to produce larger main droplets at low disturbance wavenumbers whilst satellite droplets are smaller for moderate disturbance wavenumbers κ≈0.7.     

Influence of a sureactant on the instability of a falling liquid film

The hydrodynamic instability of a film flow of a weak solution containing a soluble volatile surfactant is investigated. Diffusion of the surfactant in the liquid, its evaporation into the boundary gas medium, and the adsorption and desorption processes in the near-surface layer are taken into account. A system of evolutionary equations is derived and a steady-state solution film flow along a vertical surface and the stability of this flow are investigated for the simultaneous action of body and capillary forces and the Marangoni effect. Hydrodynamic and diffusion instability modes are detected and their properties are investigated for constant and variable surfactant concentration in the adsorbed sublayer. Moscow, Madrid. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 56–67, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (project No. 97-01-00153) and the Spanish Ministry of Higher Education (program DGICYT (Spain), project No. PB 96-599).     

Characteristics of liquid sheets formed by splash plate nozzles

An experimental study was conducted to identify the effect of viscosity on the characteristics of liquid sheets formed by a splash plate nozzle. Various mixtures of corn syrup and water are used to obtain viscosities in the range 1–170 mPa.s. Four different splash plates with nozzle diameters of 0.5, 0.75, 1, and 2 mm, with a constant plate angle of 55° were tested. Liquid sheets formed under various operating conditions were directly visualized. The sheet atomization process for the range of parameters studied here is governed by two different mechanisms: Rayleigh–Plateau (R–P) and Rayleigh–Taylor (R–T) instabilities. R–P occurs at the rim and R–T occurs on the thin sheet. The rim instability can be laminar or turbulent, depending on the jet Reynolds number. The R–T instability of the sheet is observed at the outer edges of the radially spreading sheet, where the sheet is the thinnest. It can also occur inside the sheet, due to formation of holes and ruptures.     

Spatial instability of a viscous liquid sheet

In the present study, the spatial instability for a two‐dimensional viscous liquid sheet, which is thinning with time, has been analysed. The study includes the derivation of a spatial dispersion equation, numerical solutions for the growth rate of sinuous disturbances, and parameter sensitivity studies. For a given wave number, the growth rate of the disturbance is essentially a function of Weber number, Reynolds number, and gas/liquid density ratio. The analysis indicates that the cut‐off wave number of the disturbance becomes larger with an increase in Weber number or gas/liquid density ratio. Thus, the liquid sheet should produce finer drops. When the Reynolds number decreases, the higher viscosity has a greater damping effect on shorter waves than longer waves. This could explain that only large drops and ligaments were observed in past measurements for the disintegration of a very viscous sheet. The spatial instability results of the present study were also compared with the temporal theory. The importance of spatial analysis was found and demonstrated for the cases of low Weber numbers. The temporal theory underestimates growth rates when the Weber number is less than 100. The discrepancy between the two theories increases as the Weber number further decreases. Copyright © 2005 John Wiley & Sons, Ltd.     

Convective oscillatory instability of a compressible liquid

Oscillatory instability can arise in a compressible, viscous, and thermally conducting liquid only near the critical liquid-vapor point, where there are singularities in the thermodynamic derivatives that enter into the stability criteria. Expressions are derived for the oscillatory instability criterion and the frequency of the neutral oscillations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 185–190, May–June, 1971.I am indebted to M. Sh. Giterman for continuous interest in the work and for valuable comments.     

Thermocapillary instability of a deformable liquid film

The instability of a plane liquid film with a uniform transverse temperature gradient under conditions of weightlessness is considered. The surface tension is assumed to depend linearly on the temperature. On the basis of an exact solution of the neutral perturbation problem for a layer with deformable boundaries, the instability domains, the dispersion curves, and the shape of the perturbations are determined. It is shown that on the interval of low Prandtl numbers both thermocapillary waves with predominantly longitudinal flow and capillary waves, supported by the thermocapillary effect, with intense transverse liquid flow can develop on the film.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 30–36, September–October, 1996.     

Orientation instability of the layer of a nematic liquid crystal

The origin of periodic structures in a layer of a lyotropic nematic liquid crystal observed in the director (vector, describing the anisotropic properties of the medium) reorientation experiment is studied. Such perturbations with the wavevector perpendicular to the initial orientation can develop in a liquid crystal layer in the unstable equilibrium state when the director is parallel to the walls under the condition that its orthogonality to the boundary corresponds to the minimum anchoring energy. It is shown that the linear dependence of the domain period on the layer thickness observed experimentally can be theoretically described when the Frank orientation elasticity energy is considered in the most general form taking the divergence terms into account and the anchoring energy of orientation is small as compared with the bulk energy. A relation between the coefficient of the divergence terms (saddlesplay elastic constant) and two other coefficients in the Frank energy is obtained.     

Conjugate problem of aerodynamic extrusion of jets of heated viscous liquid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 148–153, November–December, 1988.     

A finite element study on the large amplitude flexural vibration characteristics of FGM plates under aerodynamic load

The large amplitude flexural vibration characteristics of functionally graded material (FGM) plates are investigated here using a shear flexible finite element approach. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of the constituents. The effective material properties are then evaluated based on the rule of mixture. The FGM plate is modeled using the first-order shear deformation theory based on exact neutral surface position and von Kármán’s assumptions for large displacement. The third-order piston theory is employed to evaluate the aerodynamic pressure. The governing equations of motion are solved by harmonic balance method to study the vibration amplitude of FGM plates under supersonic air flow. Thereafter, the non-linear equations of motion are solved using Newmark’s time integration technique to understand the flexural vibration behavior of FGM plates in time domain (simple harmonic or periodic or quasi-periodic). This work is new in the sense that it deals with the non-linear flutter characteristics of FGM plates under high supersonic airflow accounting for both the geometric and aerodynamic non-linearities. Some parametric study is conducted to understand the influence of these non-linearities on the flutter characteristics of FGM plates.     

内爆加载金属界面不稳定性的数值分析

采用自行研制的多介质弹塑性流体力学欧拉程序,对柱形内爆加载金属界面不稳定性进行了数值研究,数值模拟结果与文献实验数据吻合较好。数值结果表明:材料强度对界面不稳定性发展有不可忽略的抑制作用;材料屈服强度对较高模数不稳定性增长的抑制较强,而剪切模量对不稳定性发展的影响相似但敏感性相对较弱;金属界面不稳定性增长存在最不稳定模数,最不稳定模数随屈服强度增加而减小,并近似与屈服强度的对数呈线性关系;随着壳的厚度减小,扰动增长加快。     

Dynamic instability of vibrating carbon nanotubes near small layers of graphite sheets based on nonlocal continuum elasticity

This article presents a new asymptotic method to predict dynamic pull-in instability of nonlocal clamped–clamped carbon nanotubes (CNTs) near graphite sheets. Nonlinear governing equations of carbon nanotubes actuated by an electric field are derived. With due allowance for the van der Waals effects, the pull-in instability and the natural frequency–amplitude relationship are investigated by a powerful analytical method, namely, the parameter expansion method. It is demonstrated that retaining two terms in series expansions is sufficient to produce an acceptable solution. The obtained results from numerical methods verify the strength of the analytical procedure. The qualitative analysis of system dynamics shows that the equilibrium points of the autonomous system include center points and unstable saddle points. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.