Corona-induced electrohydrodynamic instabilities in low conducting liquids

The rose-window electrohydrodynamic (EHD) instability has been observed when a perpendicular field with an additional unipolar ion injection is applied onto a low conducting liquid surface. This instability has a characteristic pattern with cells five to 10 times greater than those observed in volume instabilities caused by unipolar injection. We have used corona discharge from a metallic point to perform some measurements of the rose-window instability in low conducting liquids. The results are compared to the linear theoretical criterion for an ohmic liquid. They confirmed that the minimum voltage for this instability is much lower than that for the interfacial instability in high conducting liquids. This was predicted theoretically in the dependence of the critical voltage as a function of the non-dimensional conductivity. It is shown that in a non-ohmic liquid the rose window appears as a secondary instability after the volume instability.     

Evaluation of Euler fluxes by a high-order CFD scheme: shock instability

The construction of Euler fluxes is an important step in shock-capturing/upwind schemes. It is well known that unsuitable fluxes are responsible for many shock anomalies, such as the carbuncle phenomenon. Three kinds of flux vector splittings (FVSs) as well as three kinds of flux difference splittings (FDSs) are evaluated for the shock instability by a fifth-order weighted compact nonlinear scheme. The three FVSs are Steger–Warming splitting, van Leer splitting and kinetic flux vector splitting (KFVS). The three FDSs are Roe's splitting, advection upstream splitting method (AUSM) type splitting and Harten–Lax–van Leer (HLL) type splitting. Numerical results indicate that FVSs and high dissipative FDSs undergo a relative lower risk on the shock instability than that of low dissipative FDSs. However, none of the fluxes evaluated in the present study can entirely avoid the shock instability. Generally, the shock instability may be caused by any of the following factors: low dissipation, high Mach number, unsuitable grid distribution, large grid aspect ratio, and the relative shock-internal flow state (or position) between upstream and downstream shock waves. It comes out that the most important factor is the relative shock-internal state. If the shock-internal state is closer to the downstream state, the computation is at higher susceptibility to the shock instability. Wall-normal grid distribution has a greater influence on the shock instability than wall-azimuthal grid distribution because wall-normal grids directly impact on the shock-internal position. High shock intensity poses a high risk on the shock instability, but its influence is not as much as the shock-internal state. Large grid aspect ratio is also a source of the shock instability. Some results of a second-order scheme and a first-order scheme are also given. The comparison between the high-order scheme and the two low-order schemes indicates that high-order schemes are at a higher risk of the shock instability. Adding an entropy fix is very helpful in suppressing the shock instability for the two low-order schemes. When the high-order scheme is used, the entropy fix still works well for Roe's flux, but its effect on the Steger–Warming flux is trivial and not much clear.     

Dynamic instability of truncated conical shells under periodic axial load

Based on the Dynamic version of Donnell type basic equations neglecting bending deformations before instability, the parametric instability of truncated conical shells subjected to periodic axial load is studied under four different boundary conditions. Applying Galerkin's method, the basic equations are reduced to a system of coupled Mathieu equations, from which the instability regions are determined by using Hsu's results. As a numerical example, instability regions for a completely clamped shell are determined for relatively wide range of frequencies. The effects of static axial load as well as damping force on the instability regions are also examined.     

Estimating the Hydraulic Conductivity of Two-Dimensional Fracture Networks Using Network Geometric Properties

Based on a modified Darcy–Brinkman–Maxwell model, a linear stability analysis of a Maxwell fluid in a horizontal porous layer heated from below by a constant flux is carried out. The non-oscillatory instability and oscillatory instability with different hydrodynamic boundaries such as rigid and free surfaces at the bottom are studied. Compared with the rigid surface cases, onset of fluid motion due to non-oscillatory instability and oscillatory instability is found to occur both more easily for the system with a free bottom surface. The critical Rayleigh number for onset of fluid motion due to non-oscillatory instability is lower with a constant flux heating bottom than with an isothermal heating bottom, but the result due to oscillatory instability is in contrast. The effects of the Darcy number, the relaxation time, and the Prandtl number on the critical Rayleigh number are also discussed.     

Stability,instability and interaction of solitary pulses in a composite medium

The questions of a dynamical stability and instability of soliton-like solutions (solitary pulses) of the Hamiltonian equations, describing planar waves in nonlinear elastic composites are considered, both in the presence as well as in the absence of the anisotropy. In the anisotropic case one has the slow and the fast two-parametric soliton families on the background of the quiescent state. In the absence of the anisotropy these two families coalesce into the unique three parametric family. It was shown recently that solitary pulses of the slow family in the anisotropic composite and pulses in the isotropic composite are stable when their speeds lie inside a certain range, the so-called range of stability. In the present paper, on the basis of numerical solving of the Cauchy problem for the basic governing equations, the classification is given of the types of instability of solitary pulses from the fast family for all range of speeds as well as in the case of the slow family and in the isotropic case, when the speeds of the pulses lie without the range of stability. The first type of instability is the blow-up instability for the slow anisotropic and isotropic pulses, living without the range of stability and also for high amplitude fast anisotropic pulses. The second type of instability is the instability resulting in energy exchange between the components of strain tensor for low amplitude fast anisotropic solitary pulses. The reasons of the both types of instability are discussed in detail.The interaction between the pairs of solitary pulses of different nature is investigated both analytically as well as numerically. It is found out that solitary pulses having the different polarization, i.e. different sign of amplitudes, can form bound states, oscillating about the common center, subjected to a motion with a constant speed, approximately equal to the average of speeds of two pulses when they are far apart.     

The instability mechanism of single and multilayer Newtonian and viscoelastic flows down an inclined plane

The instability mechanism of single and multilayer flow of Newtonian and viscoelastic fluids down an inclined plane has been examined based on a rigorous energy analysis as well as careful examination of the eigenfunctions. These analyses demonstrate that the free surface instability in single and multilayer flows in the limit of longwave disturbances (i.e., the most dangerous disturbances) arise due to the perturbation shear stresses at the free surface. Specifically, for viscoelastic flows, the elastic forces are destabilizing and the main driving force for the instability is the coupling between the base flow and the perturbation velocity and stresses and their gradient at the free surface. For Newtonian flows at finite Re, the driving force for the interfacial instability in the limit of longwaves depends on the placement of the less viscous fluid. If the less viscous fluid is adjacent to the solid surface then the main driving force for the instability is interfacial friction, otherwise the bulk contribution of Reynolds stresses drives the instability. For viscoelastic fluids in the limit of vanishingly small Re, the driving force for the instability is the coupling of the base flow and perturbation velocity and stresses and their gradients across the interface. In the limit of shortwaves the interfacial stability mechanism of flow down inclined plane is the same as plane Poiseuille flows (Ganpule and Khomami 1998, 1999a, b). Received: 20 October 2000/Accepted: 11 January 2001     

超重力作用下软材料薄膜失稳的有限元分析

软材料在自然界和工业应用中无处不在,其显著特点是对外界刺激极其敏感,相对于传统材料其弹性模量更小,容易发生表面形态的失稳现象．现有研究主要把光、声、电等作为诱导材料失稳的因素进行研究,而重力往往作为常量考虑．本文通过有限元模拟,建立超重力作用下环向受限的圆柱状软材料薄膜失稳模型,探究了薄膜材料的密度、厚度、半径、剪切模量等材料和几何参数对失稳临界超重力和临界失稳模态的影响．结果表明,触发薄膜失稳的超重力随薄膜厚度和密度增大而减小,随剪切模量增大而增大,随着薄膜半径增大快速减小并迅速趋于常数．另外,当径厚比R/H较小时,无量纲临界超重力随着径厚比增大而单调减小,但当径厚比R/H大于3 时,此量为一个常数．超重力作用下软材料的临界失稳模态与密度、剪切模量等参数无关,随径厚比R/H增大,临界失稳模态波数增大、波长减小．     

Instabilities in self-fluidized beds—II experiments

Experimental studies of the behavior of self-fluidized beds in both 2-D and 3-D are reported. The experimental system used was the drying of silica gel under vacuum, and wide ranges of particle sizes and drying rates were covered. Both flow visualization and dynamical measurements of flow rates were utilized in the study. The observations indicate that self-fluidization is always unstable above the source strength required for minimum fluidization. The instability takes one of two forms, depending upon the degree of supercriticality. The primary instability consists of a quasi-steady array of spatially periodic spouts. A secondary instability leads to the emergence and dominance of larger spouts, which are observed to appear and disappear in a cyclic fashion. Measurements are made of wavelengths of the primary instability and the frequency of the secondary instability as functions of the operating variables, and the secondary instability is seen to occur at the same normalized flow rate for all the particles studied. Plausible mechanisms for these instabilities are proposed and discussed.     

高径比对GaAs熔体液桥热毛细对流失稳的影响

采用基于谱元法线性稳定性分析方法,研究了高径比对GaAs熔体(Pr=0.068)液桥热毛细对流失稳的影响,同时结合能量分析揭示了热毛细对流的失稳机制.研究结果表明:与典型低普朗特数(例如Pr=0.011)熔体静态失稳模式和典型高普朗特数(例如Pr>1)熔体振荡失稳模式不同,GaAs熔体热毛细对流失稳模式依赖于液桥高径比...     

Nonlocal instability analysis of FCC bulk and (1 0 0) surfaces under uniaxial stretching

The objective of this paper is to examine the instability characteristics of both a bulk FCC crystal and a (1 0 0) surface of an FCC crystal under uniaxial stretching along a 〈1 0 0〉 direction using an atomistic-based nonlocal instability criterion. By comparison to benchmark atomistic simulations, we demonstrate that for both the FCC bulk and (1 0 0) surface, about 5000–10,000 atoms are required in order to obtain an accurate converged value for the instability strain and a converged instability mode. The instability modes are fundamentally different at the surface as compared to the bulk, but in both cases a strong dependence of the instability mode on the number of atoms that are allowed to participate in the instability process is observed. In addition, the nonlocal instability criterion enables us to determine the total number of atoms, and thus the total volume occupied by these atoms, that participate in the defect nucleation process for both cases. We find that this defect participation volume converges as the number of atoms increases for both the bulk and surface, and that the defect participation volume of the surface is smaller than that of the bulk. Overall, the present results demonstrate both the necessity and utility of nonlocal instability criteria in predicting instability and subsequent failure of both bulk and surface-dominated nanomaterials.     

邻近爆破对矩形岩柱稳定性影响的突变理论分析

运用突变理论,建立了邻近爆破扰动诱发矩形岩柱失稳的非线性动力学模型,导出了岩柱发生动 力失稳的充分必要条件。根据建立的尖点突变模型,分析了竖向压力、爆破扰动强度及频率对矩形岩柱失稳 机理的影响。结果表明:(1)借助突变理论分析邻近爆破扰动诱发岩柱失稳机理是可行的;(2)邻近爆破扰动 强度越大,岩柱越容易发生失稳破坏;(3)竖向荷载越大,满足岩柱失稳条件所对应的爆破扰动强度越小,岩柱 发生失稳的可能性越大;(4)岩柱发生动力失稳破坏,爆破扰动频率必须满足一定条件。     

A strain localization analysis using a viscoplastic softening model for clay

Strain localization has become an attractive subject in geomechanics during the past decade. Shear bands are well known to develop in clay specimens during the straining process. Strain localization is closely related to plastic instability. In the present paper, a non-linear instability condition for the viscoplastic strain softening model during the creep process is firstly obtained. It is found that the proposed viscoplastic model is capable of describing plastic instability. Secondly, a two-dimensional linear instability analysis is performed and the preferred orientation for the growth of fluctuation and the instability condition are derived. It is worth noting that the two instability conditions are equivalent. Finally, the behavior of the clay is numerically analyzed in undrained plane-strain compression tests by the finite element method, considering a transport of pore water in the material at a quasi-static strain rate. The numerical results show that the model can predict strain localization phenomena, such as shear banding. From the numerical calculations, the effects of strain rate and permeability are discussed.     

Instability conditions for a class of switched linear systems with switching delays based on sampled-data analysis: applications to DC–DC converters

General instability (critical) conditions for a class of switched linear systems (such as DC–DC converters) with switching delays are derived. Many instability conditions for the systems with fixed/variable-switching frequency under various control schemes are also derived. The conditions also show the required ramp slopes to stabilize the converters. Some previously known instability conditions become special cases in this generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the instability condition for that control scheme. Different control schemes (such as \(V^{2}\) control and voltage/current mode control, for example) are shown to have similar forms of instability conditions.     

Instability of Streaming Viscoelastic Fluids in the Presence of ��Effective Interfacial Tension�� Through Porous Medium

The ??effective interfacial tension?? effect on the instability of the plane interface between two uniform, superposed, and streaming Rivlin?CEricksen viscoelastic fluids through a porous medium is considered. The case of two uniform streaming Rivlin?CEricksen viscoelastic fluids separated by a horizontal boundary is studied. In the absence of ??effective interfacial tension??, stability/instability of the system as well as perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if the perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions, there exists instability for a certain wave number range. ??Effective interfacial tension?? is able to suppress this Kelvin?CHelmholtz instability for small wavelength perturbations, the medium porosity reduces the stability range given in terms of a difference in streaming velocities.     

A numerical study on nonlinear dynamics of three-dimensional time-depended viscoelastic Taylor-Couette flow

In this paper, three-dimensional viscoelastic Taylor-Couette instability between concentric rotating cylinders is studied numerically. The aim is to investigate and provide additional insight about the formation of time-dependent secondary flows in viscoelastic fluids between rotating cylinders. Here, the Giesekus model is used as the constitutive equation. The governing equations are solved using the finite volume method (FVM) and the PISO algorithm is employed for pressure correction. The effects of elasticity number, viscosity ratio, and mobility factor on various instability modes (especially high order ones) are investigated numerically and the origin of Taylor-Couette instability in Giesekus fluids is studied using the order of magnitude technique. The created instability is simulated for large values of fluid elasticity and high orders of nonlinearity. Also, the effect of elastic properties of fluid on the time-dependent secondary flows such as wave family and traveling wave and also on the critical conditions are studied in detail.     

The effect of the production and loss reactions on the parametric instability

In this paper, the effect of the loss and production reactions on the parametric instability in plasma is investigated. Based on the hydrodynamic equations, we derive the wave equations for the electron plasma oscillation and ion-acoustic oscillation and obtain the threshold and the growth rate for the parametric instability. It is shown that (1) there is no effect of production reaction on the parametric instability; (2) the effect of loss reaction on the parametric instability is a slight damping; (3) the higher threshold is needed to excite the parametric instability in plasma with the loss reaction; (4) if taking the loss reaction into account, the growth rate for parametric instability will decrease by one half of the loss rate; and (5) the growth rate increases as the external field increases.     

井壁失稳区域确定方法及影响因素分析简

井壁失稳区域及其面积能够反映井壁失稳破坏特性及其严重程度,以井壁安全系数作为识别准则,建立了井壁失稳区域识别方法,并基于Monte-Carlo 方法,给出了井壁失稳面积的计算方法. 以井壁坍塌为例,分析了钻井液密度、井斜角及方位角对井壁失稳区域特性的影响,以本文建立的失稳区面积计算方法,分析了不同地应力场中井眼轨迹对井壁失稳区大小的影响,评价结果符合工程实际,表明能够利用本文方法评价井壁失稳特性及其严重程度.     

Non-conservative stability of intermediate spring supported columns with an elastically restrained end support

The non-conservative stability of an intermediate spring supported uniform column clastically restrained at one end and subjected to a follower force at the other unsupported end is studied. It is found that when the intermediate spring support is far from the unsupported end, the instability mechanism is flutter. As the intermediate spring support approaches the unsupported end, the instability mechanism is changed from flutter to divergence with the increase of intermediate spring stiffness. For the hinged-intermediate and guided-intermediatc spring supported columns, the critical buckling load of flutter instability will first decrease, then increase as the intermediate spring stiffness is increased. Nevertheless, when the instability mechanism is divergence, the critical buckling load depends on the location of the intermediate spring support only, whereas for the clamped-intermediate spring supported column the critical buckling load of divergence instability decreases monotonically to a fixed value as the intermediate spring stiffness is increased. Finally, the influence of elastic end restraints on the stability of the column is also investigated.     

The influence of prestressing on the twisting phenomenon of beams

The prestressing technique is often employed in engineering practice to increase the bearing capacity of concrete beams in bending. Nevertheless, prestressing has been also applied successfully in numerous cases of steel members, bars or trusses. Whilst in members with concrete sections buckling instability is unlikely to occur, the phenomenon of twisting instability may appear in prestressed steel beams under bending as a special case of the lateral-torsional instability. In the present work, the influence of prestressing on the stability (twisting instability) of a simply supported beam induced by a rectilinear tendon is thoroughly studied. Useful results are gathered and presented in the form of interaction axial force—moment diagrams that can be used for a preliminary design of beams against twisting instability.