Hydroelastic instability of orthotropic panels with infinite width under shearing load

An analysis is presented of the hydroelastic instability of an orthotropic plate with finite length and infinite width exposed to an incompressible inviscid flow over its upper surface and subjected to shearing loads along both its edges. On the basis of the small deflection plate theory and the classical linearized potential flow theory, the problem is solved for two different boundary conditions by means of the Galerkin method and Fourier transforms. It is found that an increase of the shearing load larger than about one half of the buckling load reduces rapidly the divergence velocity and increases discontinuously the divergence wavelength.     

A piecewise linear mean flow model for studying stability in a lined channel

Acoustic liners are used to reduce sound emission by turbofan engines. Under grazing flow they may sustain hydrodynamic instabilities and these are studied using a stability analysis, based on a simplified model: the liner is a mass–spring–damper system, the base channel flow is piecewise linear, and the inviscid, incompressible Rayleigh equation is used. The model is an extension to the channel case of a boundary layer model by Rienstra and Darau. The piecewise linear profile introduces a finite boundary layer thickness which ensures well-posedness, allowing an initial value problem to be conducted to investigate absolute stability. For typical values in aeronautics the flow above the liner is unstable. Absolute instability is obtained for somewhat extreme values of the mean flow (tiny boundary layer thickness), and under realistic conditions the flow is convectively unstable. The effect of finite channel height is investigated in both cases. In particular, for large boundary layer thicknesses associated with convective instability the channel height has little effect on the unstable mode. Favorable outcomes and failures of the model are shown by comparison to a published experimental work.     

Solid-state traveling-wave amplifiers and oscillators in the THz range: effect of electron collisions

Due to their high plasma frequencies, drifting semiconductor plasmas interacting with slow electromagnetic waves hold promise for terahertz amplifiers and oscillators. In these devices, the gain and the type of instabilities are influenced by electron collisions. To study the effect of collisions, we developed a two-wave model describing the interaction between drifting solid-state plasmas and electromagnetic waves. This paper analyzes the two-wave dispersion relation for representative examples. As the examples show, convective and absolute instabilities can occur at high and low collision frequencies depending on the relationship between the collision frequency and the coupling coefficient. Surprisingly, an absolute instability occurs when collision-dominated plasmas interact with backward waves. The model can be used to determine the potential of a particular configuration in a solid-state amplifier or oscillator.     

高超声速边界层中由粗糙元引起强制转捩的机理

由大粗糙元引起的高超声速边界层强制转捩在航天技术中有实际应用, 因而近年来受到人们的广泛关注.虽然目前导致该转捩过程的内在机理尚不完全清楚, 但有一点是明确的, 即粗糙元的尾迹流场中存在强对流不稳定性.文章的出发点是研究这种对流不稳定模态是如何触发转捩的.首先通过CFD方法, 计算出高超声速边界层中粗糙元的尾迹流场, 并对其进行二维稳定性分析.结果发现, 在传统不稳定Tollmien-Schlichting(T-S)模态出现的临界Reynolds数之前, 存在高增长率的无黏不稳定模态, 表现为对称的余弦模态和反对称的正弦模态.然后对该不稳定模态在粗糙元尾迹流中的演化进行了模拟, 验证了二维稳定性分析的结果, 并考察了非平行性效应的影响.最后通过直接数值模拟, 研究由这些不稳定模态触发转捩的全过程.结果表明, 对流不稳定模态确实是导致边界层转捩的关键机制.该转捩过程的特点是, 局部湍斑首先在不稳定模态特征函数的峰值附近出现, 然后向全流场扩散.就文章研究的工况而言, 余弦和正弦模态的相互作用对转捩的影响并不明显, 且后者在转捩过程中起主导作用.      

Hydroelastic oscillations of a viscous infinitely long liquid column

The coupled frequencies of hydroelastic systems in zero gravity consisting of an elastic shell and a viscous liquid layer with a free surface have been treated. The system exhibits either an annular liquid layer around an elastic cylindrical center shell or a liquid layer inside an elastic infinitely long container. The first case has been evaluated numerically, where the influence of the liquid surface tension parameter, the elasticity parameter of the shell, its axial deflection wave length l and the thickness of the layer have been determined. In contrast to the hydroelastic system with an ideal liquid, the system with viscous liquid exhibits instability of the liquid surface as well as the shell.     

Absolute instability of a liquid jet in a coflowing stream

Cylindrical liquid jets are inherently unstable and eventually break into drops due to the Rayleigh-Plateau instability, characterized by the growth of disturbances that are either convective or absolute in nature. Convective instabilities grow in amplitude as they are swept along by the flow, while absolute instabilities are disturbances that grow at a fixed spatial location. Liquid jets are nearly always convectively unstable. Here we show that two-phase jets can breakup due to an absolute instability that depends on the capillary number of the outer liquid, provided the Weber number of the inner liquid is >O(1). We verify our experimental observations with a linear stability analysis.     

Stabilization of solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle

The stability of dark solitons generated by supersonic flow of a Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to the decay of disturbances of solitons at a fixed distance from the obstacle and the formation of effectively stable dark solitons. This phenomenon explains the surprising stability of the flow picture that has been observed in numerical simulations.     

Porous structure of membranes of an acrylonitrile copolymer. Porosity, 1H-NMR permeability

Nanoporous polymer membranes (porosity ) used for dialysis are studied from NMR relaxation times of water confined in the pore space. Fast interpore water diffusion is observed. Two structural parameters are evidenced: i) a reduced NMR relaxation time, , which reflects the width of the pore-size distribution; ii) the average polymer-grain size of the solid matrix deduced from NMR experiments performed on membranes partially filled by water. A relation is found between the ratio , where k is the permeability to water and the porosity. This relation is in qualitative agreement with numerical simulations reported in the literature on low-porosity systems and with experimental results obtained for sedimentary rocks and for fused glass model systems. It supports the idea that is the relevant structural parameter to describe convective transport in a wide class of porous systems. Received 8 July 1999     

A theoretical investigation of flow-induced instabilities in compliant coatings

The flow-induced instabilities of a fairly general class of compliant coatings are investigated theoretically. The coatings are of finite length and consist of elastic plates or membranes stretched over a fluid substrate having a density which may be different from the main flow. Provision is also made for the plate to be backed by an elastic foundation of arbitrary spring stiffness. Fairly standard aeroelastic methods are followed. The aerodynamic forces generated by the main flow are calculated by using thin aerofoil theory with a correction factor to allow for the presence of a boundary layer. The pressure induced in the substrate fluid is calculated by assuming potential flow and applying the method of images. A single-mode analysis shows that coatings with laminar boundary layers suffer a divergence-type instability in contrast to turbulent boundary layers which always give rise to a flutter-type instability with a higher critical velocity. The order of the most dangerous mode is calculated and found to rise with an increase in equivalent spring stiffness for fixed tension or flexural rigidity. Results are presented for plates and membrane coatings with an air stream over air and water substrates. Taking account of the substrate fluid dynamics reduces the growth rate of the instability by an order of magnitude and completely suppresses flutter with water substrates. Single-, double- and triple-mode analyses are carried out and the results compared. The critical velocity is adequately predicted by single-mode analysis but a coupling of odd and even modes can lead to flutter even with a laminar boundary layer.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Optical fiber systems are convectively unstable

We theoretically and experimentally evidence that fiber systems are convective systems since their nonlocal inherent properties, such as the dispersion and Raman effects, break the reflection symmetry. Theoretical analysis and numerical simulations carried out for a fiber ring cavity demonstrate that the third-order dispersion term leads to the appearance of convective and absolute instabilities. Their signature is an asymmetry in the output power spectrum. Using this criterion, experimental evidence of convective instabilities is given in a fiber cavity pumped by a pulsed laser.     

Faraday instability with a polymer solution

We present an experimental study of the Faraday instability in which we compare the behavior of a Newtonian fluid (water-glycerine mixture) with that of a semi-dilute non-Newtonian solution of high molecular weight polymer. We show that although the dispersion relation of surface waves, derived for a layer of inviscid fluid, remains valid in that particular non-Newtonian case, the behavior of the instability threshold with frequency strongly differs from the Newtonian case. We explain this effect as a result of a frequency-dependent viscosity. The linear stability analysis of the non-Newtonian case shows a perfect agreement with the experimental results both for the dispersion relation and for the reduction of the instability threshold. We discuss the use of the characteristics of the Faraday experiment as a measurement tool to determine frequency dependent properties of non-Newtonian fluids. Received 5 January 1999     

热电子等离子体的低频交换不稳定性

本文用磁流体理论,导出了包含导电端板“线结”效应的热电子等离子体低频交换模的色散关系,分析了热电子环的稳定作用,求出了稳定性判据。“线结”效应能大大降低交换模的增长率。取热电子密度为零,就得到简单流体等离子体的结果。     

Surface effect on the necking of hyperelastic materials

Necking is a widely observed instability phenomenon. Surface tension often plays a significant role in the deformation of soft materials, especially at the micro scale, but its influence on the necking behavior of soft structures remains unclear. In this paper, we use the energy method to explore surface effects on the necking of soft plates and cylindrical bars under uniaxial tension. Analytical solutions are derived for the critical conditions of necking instability in the two types of structural components with a power-law constitutive relation. It is found that surface energy shows different impacts on their necking behaviors – it tends to postpone the occurrence of necking in soft plates but promote that in soft cylinders. This work not only deepens our understanding of the instability of soft materials but also helps design soft devices and robots.     

Experimental study of the instability of a film flowing down a vertical fiber

The wavy dynamics of a viscous film flowing axisymmetrically on a vertical fiber is characterized experimentally. The study of the initial response of the flow to natural noise shows a well-defined transition between a convective and an absolute instability [1]. In the convective case, disturbances of controlled frequencies have been applied at inlet. The flow responds to inlet excitation at frequencies lower than a well-defined cut-off frequency. A good agreement has been found with the linear stability analysis and with the solution to a two-equation model [2] in the nonlinear regime.     

Hydroelastic interaction between water waves and a thin elastic plate of arbitrary geometry

An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow.Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system.According to the surface boundary conditions,the fluid domain is divided into two regions,namely,an open water region and a plate-covered reg...     

Behavior of viscous solutions in Lagrangian formulation

In this paper, the behavior of shock-capturing methods in Lagrangian coordinate is investigated. The relation between viscous shock and inviscid one is analyzed quantitatively, and the procedure of a viscous shock formation and propagation with a jump type initial data is described. In general, a viscous shock profile and a discontinuous one include different energy and momentum, and these discrepancies result in the generation of waves in all families when a single wave Riemann problem (shock or rarefaction) is solved. Employing this method, some anomalous behavior, such as, viscous shock interaction, shock passing through ununiform grids, postshock oscillations and lower density phenomenon is explained well. Using some classical schemes to solve the inviscid flow in Lagrangian coordinate may be not adequate enough to correctly describe flow motion in the discretized space. Partial discrepancies between von Neumann artificial viscosity method and Godunov method are exhibited. Some reviews are given to those methods which can ameliorate even eliminate entropy errors. A hybrid scheme based on the understanding to the behavior of viscous solution is proposed to suppress the overheating error.     

Waves in an active medium guided by a reactive surface with reactance of gain modulation

The characteristics of surface waves (i) in a passive medium supported by a passive surface with reactance modulation and an active surface with the modulation of either the reactance or the negative resistance, and (ii) in an active medium supported by a passive surface with a reactance modulation are investigated with emphasis on the band regions. The periodic variation is sinusoidal and is in the propagation direction. For a passive medium terminated by a passive surface with a reactance modulation, there are stop bands in frequency for the surface waves and the structure of the first two stop bands is analyzed. For a passive medium terminated by an active surface and for an active medium terminated by a reactance-modulated passive surface, the characteristics of the absolute instabilities occurring in the first-order band are examined. The nature of the convective instability taking place in the second-order band for an active medium terminated by a reactance-modulated surface is discussed. Analytical expressions for the frequency shift of the second-order band are deduced. The Floquet theory is used to obtain the exact dispersion relation in the form of a continued fraction which is analyzed by singular expansions.     

Condition for convective instability of dark solitons

Simple derivation of the condition for the transition point from absolute instability of plane dark solitons to their convective instability is suggested. It is shown that unstable wave packet expands with velocity equal to the minimal group velocity of the disturbance waves propagating along a dark soliton. The growth rate of the length of dark solitons generated by the flow of Bose-Einstein condensate past an obstacle is estimated. Analytical theory is confirmed by the results of numerical simulations.     

Further improvement and analysis of CCD scheme: Dissipation discretization and de-aliasing properties

In this paper, we further analyze a combined compact difference (CCD) scheme proposed recently [T.K. Sengupta, V. Lakshmanan, V.V.S.N. Vijay, A new combined stable and dispersion relation preserving compact scheme for non-periodic problems, J. Comput. Phys. 228 (8) (2009) 3048–3071] for its dissipation discretization properties to show that its superiority also helps in controlling aliasing error for a benchmark internal flow. However, application of the same CCD method to study the receptivity of a boundary layer experiencing adverse pressure gradient is not successful. This is traced to the nature of the equilibrium flow where the better dissipation property is not helpful in the inviscid part of the flow, where the aliasing problems continue to persist. A further modification is proposed to the CCD method here to solve complex physical problems requiring information on higher order disturbance quantities – as in problems of flow receptivity and instability.