Numerical Investigation of Unipolar Injection in the Presence of Electroconvective Motion in a Plane Layer of Transformer Oil

The effect of unipolar injection of charges on the electroconvective motion of a weakly conducting liquid in a plane-parallel electrode system is investigated. By means of a numerical experiment it is confirmed that the crisis in the stability of a plane layer of weakly conducting liquid with unipolar injection conductivity depends significantly on the electrochemical processes in the electrode layer. A~dependence of the unipolar charge injection on the initial conductivity for a solution of molecular iodine in transformer oil is obtained.     

The three-dimensional stationary instability in dynamic thermocapillary shallow cavities

In various configurations with thermal convection, three-dimensional stationary patterns occur that consist of pairs of counter-rotating longitudinal rolls. These rolls are investigated in this paper under a variety of experimental conditions. The liquids used are ethanol and the silicone oil hexamethyldisiloxane. The upper surface of the liquid volume is free and very flat because measures against menisci at the side and end walls have been taken. The temperature gradient is applied horizontally via thermally conducting but transparent sapphire end walls, leading to thermocapillary forces at the free surface in addition to the buoyant forces at normal earth's gravity. The geometry of the liquid volume is either rectangular or axisymmetrical (annular). The rectangular set-up is transparent and especially suited for optical observations of tracers in the bulk of the liquid. The annular set-up has the advantages of a large azimuthal (transversal) extent and the absence of side walls. In it a wavelength of λ≈1.3d was observed (where d is the depth of the liquid volume). Temperatures and velocities are measured and used to characterize the instability. Also the region of existence of the instability is studied in layers shallower than in earlier experiments in order to give a larger ratio between thermocapillary and buoyant forces. To find the onset of the instability when increasing the temperature gradient, the amplitude of the instability was derived from measurements and extrapolated. This yields a significantly lower threshold (Ma^c=2300 ± 1000 for d=5 mm) than previous experimental studies. One implementation of the annular gap experiment was performed under microgravity (experiment MAGIA), the other experiments under normal gravity. The results of the experiment under microgravity indicate the absence of the three-dimensional stationary pattern under the absence of gravity. Received: 14 August 2000/Accepted: 17 April 2001     

Electrohydromagnetic instability of superposed fluids

The problem of stability of superposed viscous liquids subject simultaneously to electric and magnetic fields is investigated using the normal mode analysis. A configuration of an electrically conducting liquid topped by a dielectric liquid is envisaged in a downward gravity field. The electric field is assumed along the gravity field, while the magnetic field is taken to be either along or normal to the electric field. Criteria of instability are derived in both cases. It is found that a vertical electric field has a destabilizing influence and renders an otherwise stable configuration (bottom heavy arrangement) unstable for small wavelengths, while the effect of the magnetic field is stabilizing.     

Parametric convection of a low-conducting liquid in an alternating electric field

The development of parametric electroconvective instability of a low-conducting liquid in a horizontal capacitor under the action of an alternating electric field is studied. The conditions on which the free charge is generated due to autonomous unipolar injection are considered. The charge distributions over the liquid at rest are determined analytically and numerically, respectively, for low and arbitrary amplitudes of the external field. The limits of parametric electroconvective instability are found within the framework of the linear theory. It is shown that the perturbations can manifest themselves in different ways depending on the modulation amplitude and frequency of the electric field and be of the subharmonic, synchronous, or quasiperiodic type of the response. The characteristics of the resonance action, namely, the amplitudes and the frequencies necessary for the efficient generation of electroconvection, are determined.     

电场作用下导电射流稳定性的理论与实验研究

建立导电射流在径向电场作用下的线性稳定性粘性模型,通过正则模方法,推导了轴对称和非轴对称模态下的色散关系,通过计算求得增长率随波数及电欧拉数的变化,并在理论上预测了最有可能波长.选用酒精和酒精甘油混合物作实验液体,观察了径向电场对射流不稳定性行为的影响规律,并测量射流表面波的波长.实验结果和理论结果在定性方面取得了较好的一致.但通过与实验比较,理论预测的最有可能波长在非轴对称模态出现较大偏差,普遍比实验结果小.而且,实验表明,最大增长率并不是判断主导模态的好标准,因为在非轴对称的最大增长率小于轴对称的最大增长率情况下,实验显示非轴对称模态要比轴对称模态明显了.因此,对于非轴对称的不稳定机理,需要进一步研究.对轴对称模态,理论给出了较好的预测.     

Injection and coalescence of bubbles in a quiescent inviscid liquid

Time periodic generation and coalescence of bubbles by injection of a gas at a constant flow rate through an orifice at the bottom of a quiescent inviscid liquid is investigated numerically using a potential flow formulation. The volume of the bubbles is determined for different values of a Weber number and a Bond number. Single bubbling and different regimes of coalescence are described by these computations. The numerical results show qualitative agreement with well-known experimental results for liquids of low viscosity, suggesting that bubble interaction and coalescence following gas injection is to a large extent an inviscid phenomenon for these liquids, many aspects of which can be accounted for without recourse to wake effects or other viscosity-dependent ingredients of some current models.     

Charging of disperse particles in two-phase media with unipolar charge

Charging of disperse particles with good conduction in two-phase media with unipolar charge is considered in the case when the volume concentration of the particles is low. For this, in the framework of electrohydro-dynamics [1, 2], a study is made of the charge of one perfectly conducting liquid particle in a gas (or liquid) with unipolar charge in a fairly strong electric field. The influence of the inertial and electric forces on the motion of the gas is ignored, and the velocities are found by solving the Hadamard—Rybczynski problem. We consider the axisymmetric case when the gas velocity and electric field intensity far from the particle are parallel to a straight line. The analogous problem for a solid spherical particle was solved in [3–6] (in [3], the relative motion of the gas was ignored, while in [4–6] Stokes flow around the particle was considered). The two-dimensional problem of the charge of a solid circular, perfectly conducting cylinder in an irrotational flow of gas with unipolar charge was studied in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 108–115, November–December, 1980.We thank L. I. Sedov and V. V. Gogosov for a helpful discussion of the present work.     

Analyse par simulation numérique du développement de l'instabilité électro-convective d'une couche de liquide diélectrique infinie soumise à une injection unipolaire

In this article electroconvective phenomenon, which take place in a dielectric liquid layer submitted to an unipolar injection, are studied by numerical simulations means. For the first time the full and coupled resolution of the Electro-Hydro-Dynamic equations are achieved. The results are compared with those coming from stability analysis especially for the linear and non-linear criteria in strong and weak injection cases. The hysterical behavior of the development of this instability is accurately reproduced. To cite this article: P. Traoré et al., C. R. Mecanique 337 (2009).     

Surface instability and primary atomization characteristics of straight liquid jet sprays

Using the detailed numerical simulation data of primary atomization, the liquid surface instability development that leads to atomization is characterized. The numerical results are compared with a theoretical analysis of liquid–gas layer for a parameter range close to high-speed Diesel jet fuel injection. For intermittent and short-duration Diesel injection, the aerodynamic surface interaction and transient head formation play an important role. The present numerical setting excludes nozzle disturbances to primarily investigate this interfacial instability mechanism and the role of jet head. The first disturbed area is the jet head region, and the generated disturbances are fed into the upstream region through the gas phase. This leads to the viscous boundary layer instability development on the liquid jet core. By temporal tracking of surface pattern development including the phase velocity and stability regime and by the visualization of vortex structures near the boundary layer region, it is suggested that the instability mode is the Tollmien–Schlichting (TS) mode similar to the turbulent transition of solid-wall boundary layer. It is also demonstrated that the jet head and the liquid core play an interacting role, thus the jet head cannot be neglected in Diesel injection. In this study, this type of boundary layer instability has been demonstrated as a possible mechanism of primary atomization, especially for high-speed straight liquid jets. The effect of nozzle turbulence is a challenging but important issue, and it should be examined in the future.     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

Numerical investigation of injection-induced electro-convection in a dielectric liquid between two eccentric cylinders

Numerical analysis of the 2D radial and azimuth electro-convection (EC) flow of dielectric liquid between two eccentric cylindrical electrodes driven by unipolar injection of ions is presented. The finite volume method is used to resolve the spatiotemporal distributions of the flow field, electric field, and charge density. The flow instability is studied in various scenarios where the radius ratio Γ = R_i/R_o ranges between 0.1 and 0.7 and the eccentricity η between 0.1 and 0.5. The bifurcation of the flow patterns depends on the electric Rayleigh number T, a ratio of the electric force to viscous force, and the two geometric parameters Γ and η. For an increasing T, the EC system develops from a weak steady convective state to chaos via different intermediate states experiencing pitchfork and Hopf bifurcations. The influence of Γ and η on the bifurcation behavior is also investigated. When Γ lies between 0.1 and 0.3, a novel periodic oscillation of the flow patterns has been observed.     

三维方腔介电液体电对流的数值模拟研究

本文对封闭方腔内介电液体电对流进行了三维数值模拟研究.方腔的6个边界为固壁;4个侧边界为电绝缘边界;上下界面为两个电极.直流电场作用在从底部电极注入的自由电荷上,从而对液体施加库伦体积力并驱动流体流动形成电对流.为了求解这一物理问题,发展了一种二阶精度的有限体积法来求解完整的控制方程,包括Navier-Stokes方程和一组简化的Maxwell方程.考虑到电荷密度方程的强对流占优特性,采用了全逆差递减格式来求解该方程,获得了准确有界的解.通过研究发现,该流动在有限振幅区内的分叉类型为亚临界,即系统存在一个线性和非线性临界值,分别对应流动的开始和终止.由于非线性临界值比线性值小,因此两个临界值之间有一个迟滞回线.与无限大域中的自由对流相比,侧壁施加的额外约束改变了流场结构,使这两个临界值均有所增大.此外,还讨论了电荷密度和速度场的空间分布特征,发现电荷密度分布中存在电荷空白区.最后对更小空间尺寸情况计算结果表明,流动的线性分叉类型为超临界.本文的结果拓展了已有的二维有限空间内电对流的研究,并为三维电对流的线性和弱非线性理论分析提供参考.      

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.     

一类轴对称充液陀螺系统自旋运动稳定性研究

研究了一类复杂充液旋转对称陀螺（其圆柱形容腔充有互不相溶的双元液体，且带充液圆柱中心杆）的章动振荡与其所充双元液体自由振荡之耦合问题．利用留数方法研究了系统的自旋稳态运动的稳定性条件     

Thermocapillary instability of the interface between two immiscible liquids in the presence of volume heat sources

The problem of the stability of the interface between two infinite layers of different immiscible liquids is considered. It is assumed that within the liquid a distributed volume heat source, simulating Joule heating, is given. The stability of the rest state with respect to small unsteady disturbances is investigated. The investigation is carried out using the real boundary conditions at the interface between the two liquids rather than the model boundary conditions usually employed in such problems [5]. The problem considered is related to the practical question of the stability of electrolyzer processes. In the present case a possible threshold mechanism of development of oscillations of the electrolyte-aluminum interface is examined. A numerical example with liquid parameters that coincide with those of the electrolyte and aluminum shows that the thermocapillary instability mechanism can, in fact, be the source of surface waves at the electrolyte-aluminum interface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 156–160, September–October, 1990.     

Formation of shock waves in gas-liquid foams

The purpose of the present investigation is to analyze the phenomenon of shock wave formation in gas-liquid foams and to explain the qualitative differences which are found when comparing results from shock tube experiments performed with foams and bubbly liquids. It is well known that oscillatory pressure waves in bubbly liquids may reach an amplitude twice as large as that of the original pressure impulse. However, experiments showed that pressure disturbances in foams always attenuate without significant change in the wave pressure profile. In the present study this behavior is explained by analyzing shock wave formation using the Burgers equation which is derived from the conservation laws for a bubbly liquid. It is shown that the parameter of non linearity in the Burgers equation describing wave propagation in bubbly liquids is about 40 times higher than in foams. At the same time coefficient of bulk viscosity of a foam is about 10³ times greater than that of a bubbly liquid. This explains why in shock tube experiments with foams shock waves are not detected while they are easily observed when bubbly liquids are used under similar conditions.     

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.     

Temporal evolution and instability in a viscoelastic dielectric elastomer

Dielectric elastomer transducers are being developed for applications in stretchable electronics, tunable optics, biomedical devices, and soft machines. These transducers exhibit highly nonlinear electromechanical behavior: a dielectric membrane under voltage can form wrinkles, undergo snap-through instability, and suffer electrical breakdown. We investigate temporal evolution and instability by conducting a large set of experiments under various prestretches and loading rates, and by developing a model that allows viscoelastic instability. We use the model to classify types of instability, and map the experimental observations according to prestretches and loading rates. The model describes the entire set of experimental observations. A new type of instability is discovered, which we call wrinkle-to-wrinkle transition. A flat membrane at a critical voltage forms wrinkles and then, at a second critical voltage, snaps into another state of winkles of a shorter wavelength. This study demonstrates that viscoelasticity is essential to the understanding of temporal evolution and instability of dielectric elastomers.     

Wall slip phenomena in concentrated ionic liquid-based magnetorheological fluids

Ionic liquids (ILs) have been recently proposed as carrier for magnetorheological (MR) fluids. Their special properties, such as very low vapor pressure and high thermal stability, make ILs highly suitable dispersion media to increase the broad range of technological applications that magnetorheological fluids already have. It has been just reported that using ILs as carriers in MR fluids an improvement in the colloidal stability and suspension redispersibility is obtained. In this work, the magnetorheological behavior of highly concentrated suspensions in ILs is studied. Two kinds of suspensions were analyzed: using an ionic liquid of low conductivity and a mineral oil as carriers. In both cases, silica-coated iron microparticles were used as solid phase, being the solid volume concentration of 50% vol. A complete magnetorheological analysis focused on the wall slip phenomenon was performed. Steady-state and oscillatory experiments were carried out. In order to study wall slip effects, all experiments were performed with a plate–plate system, using both smooth and rough measuring surfaces. A significant effect of wall slip was observed when the experiments were performed using smooth surfaces. The novelty of this paper is mainly based on (1) the use of an ionic liquid as carrier to prepare magnetic suspensions, and?(2) the analysis of wall slip phenomena in MR fluids with a particle content close to the maximum packing fraction.     

Stability of a liquid jet into incompressible gases and liquids: Part 2. Effects of the irrotational viscous pressure

In this paper we investigate the effects of an irrotational, viscous pressure on the stability of a liquid jet into gases and liquids. The analysis extends our earlier work (part 1) in which the stability of the viscous jet was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. The liquid jet is always unstable; at high Weber numbers the instability is dominated by capillary instability; at low W the instability is dominated by Kelvin–Helmholtz (KH) waves generated by pressures driven by the discontinuous velocity. In the irrotational analysis the viscosity is important but the effects of shear are neglected. In fact a discontinuous velocity is not compatible with the continuity of the tangential components of velocity and shear stress so that KH instability is not properly posed for exact study using the no-slip condition but some of the effects of viscosity can be ascertained using viscous potential flow. The theory is called viscous potential flow (VPF). Here we develop another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by selecting viscous contributions to the irrotational pressure. These pressures generate a hierarchy of potential flows in powers of the viscosity, but only the first one, linear in viscosity, in the irrotational viscous stress, is thought to have physical significance. The tangential velocity and shear stress in an irrotational study cannot be made continuous, but the effects of the discontinuous velocity and stress in the mechanical energy balance can be removed “in the mean.” This theory with the additional viscous pressure is called VCVPF, viscous correction of VPF. VCVPF is VPF with the additional pressures. The theory here cannot be compared with an exact solution, which would not allow the discontinuous velocity and stress. In other problems, like capillary instability, in which VCVPF can be compared with an exact solution, the agreements are uniformly excellent in the wave number when one of the fluids is gas and in good but not uniform, agreement when both fluids are liquids.