CONVECTIVE INSTABILITY OF A TWO-COMPONENT FLUID-FLUID SYSTEM

The stability of a plane interface of two immiscible liquids(both are finite thickness)with a perpendicular mass transfer is investigated by means of linear stability and energy methods.An analytical formula is derived for the linear stability boundary,whereas the numerical solutions are obtained for boundaries following from both linear and energy analyses. It is concluded that the difference in the chemical potential of.these two phases drives the convective flow and that a threshold Marangoni number existg for the instability to occur. It is also shown that the energy stability boundary does not coincide with that following from the linear analysis,so the subcritical instability is allowed in the region in between.     

Unstable Surface Waves in Running Water

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the rigid-wall setting testifies that the free surface has a destabilizing effect. For a class of unstable shear flows, the bifurcation of nontrivial periodic traveling waves is demonstrated at all wave numbers. We show the linear instability of small nontrivial waves that appear after bifurcation at an unstable wave number of the background shear flow. The proof uses a new formulation of the linearized water-wave problem and a perturbation argument. An example of the background shear flow of unstable small-amplitude periodic traveling waves is constructed for an arbitrary vorticity strength and for an arbitrary depth, illustrating that vorticity has a subtle influence on the stability of free-surface water waves.     

Effect of tilted electrostatic field on the Kelvin–Helmholtz instability in a liquid dielectric and gas flow

The effect of surface ponderomotive forces on the Kelvin–Helmholtz instability is studied in the linear formulation based on the equations and boundary conditions of the electrostatics and fluid dynamics of an ideal incompressible fluid. Conditions to be satisfied by the values of determining parameters of the problem for the transition of an unstable flow in zero electric field into a stable regime after the application of a horizontal electric field have been written in the form of inequalities. It has been shown that, at the stability bound, the wavelength of the most instable mode is independent of the ponderomotive forces. In case of a liquid with large permittivity a stable flow regime exists for which the stability condition only differs in small dimensionless values from the stability condition for the charged surface of a quiescent liquid conductor in contact with a gas at rest.     

高超声速椭圆锥边界层横流转捩特性大涡模拟

横流效应显著影响高超声速飞行器的三维边界层转捩过程, 深化对该流动机制的认识有助于提升和改善飞行器气动性能及热力学环境. 针对HIFiRE5椭圆锥绕流问题, 采用大涡模拟方法计算分析了超声速边界层横流转捩特性, 并揭示其中的流动机理. 参考HIFiRE5风洞模型试验条件, 数值模拟中椭圆锥来流入口处施加人工速度扰动以激发边界层内不稳定扰动波, 进而预测了高超声速边界层流动横流失稳、转捩过程等基本流动特征, 并基于转捩热流分布形态对比, 获得了与试验数据基本吻合的计算结果. 研究发现, 椭圆锥中心线流动汇聚形成的流向涡结构非常容易失稳, 另外在中心线及侧缘之间的中部区域存在较强的横流不稳定性, 两种机制共同作用影响边界层转捩过程. 此外, 分析了来流扰动幅值对边界层横流失稳转捩的影响, 并发现静来流条件下, 横流区域出现两组独立的定常横流涡结构, 而强噪声来流条件下, 中心线主涡和中部横流涡均发生失稳转捩, 且在椭圆锥表面形成多峰状的转捩阵面. 最后, 深入分析流场的压力脉动动力学特性, 揭示了三维边界层发生失稳转捩的非线性演化机制.      

ABSOLUTELY UNSTABLE WAVES IN INVISCID HYDROELASTIC SYSTEMS

The effect of inviscid plug flow on the stability of several hydroelastic systems is investigated by determining the absolute or convective nature of the instability from the linear dispersion relation. The fluid-structure systems consist of plates and membranes with bounded and unbounded flow. A method is proposed to derive systematically in parameter space the boundary between convective and absolute instability, based on the particular symmetries of the dispersion relation as originally noted by Crighton and Oswell. This method is then applied to the case of plates with superimposed tension, thick plates with rotary inertia and walls made of plates or membranes bounding channel flow, oscillating in a sinuous or varicose mode of deformation. A relation is drawn with solutions by previous authors for plates, for pipes and for the Kelvin-Helmholtz instability with surface tension. To illustrate these results some temporal evolutions are calculated by using an integration in the wavenumber space. Based on the large set of new cases solved in the paper some general trends are discussed as to the influence of flow velocity, confinement and structural stiffness on the existence of absolutely unstable waves in inviscid hydroelastic systems.     

相邻双侧边盖驱动方腔流动的三维线性整体稳定性

文章考察了相邻双侧边盖驱动方腔流动（即上壁面向右运动和左侧壁面向下运动）的三维线性整体稳定性.首先,采用Taylor-Hood有限元方法并经由Newton迭代过程计算得到双侧边盖驱动方腔流动的二维稳态基本流.其次,Taylor-Hood有限元在Chebyshev Gauss配置点上进行离散,同时Gauss配置点也可以用于线性稳定性方程的高阶有限差分格式离散.然后,离散得到的矩阵形式的广义特征值问题可以结合shift-and-invert算法采用隐式重启Arnoldi方法计算.最后,通过对线性稳定性方程特征值的计算,发现了一个最不稳定的驻定模态和两对对称行波模态.最不稳定的三维驻定模态的临界Reynolds数为Re_c=261.5,远远小于二维不稳定的临界Reynolds数Re_c2d=1 061.7.通过画出这3类三维不稳定模态的流向扰动速度和扰动涡量的空间等值面图像,可以发现不稳定扰动位于稳态基本流的两个主涡区域,因此可以认为主涡区域是三维扰动失稳的主要能量来源地.      

A simplified approximate analytical model for Rayleigh–Taylor instability in elastic–plastic solid and viscous fluid with thicknesses

A simplified theoretical model for the linear Rayleigh-Taylor instability of finite thickness elastic-plastic solid constantly accelerated by finite thickness viscous fluid is performed.With the irrotational assumption,it is possible to consider viscosity,surface tension,elasticity or plasticity effects simultaneously.The model considers thicknesses at rigid wall boundary conditions with the velocity potentials,and deals with solid elastic-plastic transition and fluid viscosity based on the velocity continuity and force equilibrium at contact interface.The complete analytical expressions of the amplitude motion equation,the growth rate,and the instability boundary are obtained for arbitrary Atwood number,viscosity,thicknesses of solid and fluid.The thicknesses effects of two materials on the growth rate and the instability boundary are discussed.     

合成冷/热射流控制超声速边界层流动稳定性

为了探究超声速边界层流动稳定性及其转捩控制机理,提出基于合成冷/热射流的边界层速度-温度耦合控制方法,并通过数值模拟研究了Ma=4.5超声速平板边界层不稳定波的传播,采用线性稳定性理论中的时间模式分析了壁面吹吸、射流温度、扰动频率、扰动振幅等对不稳定波控制效果的影响.结果表明:无射流控制时,边界层内同时存在不稳定的第一模态扰动波和第二模态扰动波,且二维波形式的第二模态占主导地位;壁面吹吸作用下,仅出现更加不稳定的第二模态,第一模态被抑制;速度-温度耦合控制下,射流温度对扰动模态的不稳定区域大小及扰动增长率影响显著,射流温度与来流温度不同时,温度的脉动使得流动转捩为湍流的速度加快,边界层速度型更加饱满,抗干扰能力增强,流动稳定性提高;高频的吹吸扰动对流场的控制效果优于低频扰动,扰动频率超过400 Hz时,第二模态扰动波时间增长率降低,扰动分量对边界层速度剖面和温度剖面的修正加快,第二模态更加稳定;扰动振幅减小为主流速度的1%时,仅出现时间增长率较小的第二模态,控制效果较好,进一步减小时,第一模态重新出现,并且波数范围与第二模态先重合后分离,对应的时间增长率先增加后减小.研究结果为边界层转捩控制技术提供了新的思路.     

泵驱动两相系统流动稳定性的时域理论研究

蒸汽发生器中可能出现的两相流不稳定现象会导致二回路流量、压力和温度的脉动,不仅干扰控制系统,还可能引起传热管热疲劳损坏.首先,采用集总参数法和小扰动线性化方法,建立了由泵驱动的两相系统的时域理论模型.然后对比分析了泵驱动边界条件和恒定压降边界条件,以及泵特性曲线的斜率对系统稳定性的影响.结果 表明,随着泵特性曲线斜率绝...     

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.     

Linear mechanism of surface gravity wave generation in horizontally sheared flow

An analysis is presented of a linear mechanism of surface gravity wave generation in a horizontally sheared flow in a fluid layer with free boundary. A free-surface flow of this type is found to be algebraically unstable. The development of instability leads to the formation of surface gravity waves whose amplitude grows with time according to a power law. Flow stability is analyzed by using a nonmodal approach in which the behavior of a spatial Fourier harmonic of a disturbance is considered in a semi-Lagrangian frame of reference moving with the flow. Shear-flow disturbances are divided into two classes (wave and vortex disturbances) depending on the value of potential vorticity. It is shown that vortex disturbances decay with time while the energy of wave disturbances increases indefinitely. Transformation of vortex disturbances into wave ones under strong shear is described.     

The electric double layer effect on the microchannel flow stability and heat transfer

The effect of the electric double layer (EDL) on the linear stability of Poiseuille planar channel flow is reported. It is shown that the EDL destabilises the linear modes, and that the critical Reynolds number decreases significantly when the thickness of the double layer becomes comparable with the height of the channel. First results coming from direct numerical simulations on the non-linear effects show also that the by-pass transition is much more rapid in the presence of EDL. There is an acceptable qualitative correspondence between the estimated transitional Reynolds numbers and some experiments, showing that early transition is plausible in microchannels under some conditions. Several questions remain however unanswered such as the surface conduction effect on EDL.     

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.     

Suppression of Helmholtz resonance using inside acoustic liner

When a Helmholtz resonator is exposed to grazing flow, an unstable shear layer at the opening can cause the occurrence of acoustic resonance under appropriate conditions. In this paper, in order to suppress the flow-induced resonance, the effects of inside acoustic liners placed on the side wall or the bottom of a Helmholtz resonator are investigated. Based on the one-dimensional sound propagation theory, the time domain impedance model of a Helmholtz resonator with inside acoustic liner is derived, and then combined with a discrete vortex model the resonant behavior of the resonator under grazing flow is simulated. Besides, an experiment is conducted to validate the present model, showing significant reduction of the peak sound pressure level achieved by the use of the side-wall liners. And the simulation results match reasonably well with the experimental data. The present results reveal that the inside acoustic liner can not only absorb the resonant sound pressure, but also suppress the fluctuation motion of the shear layer over the opening of the resonator. In all, the impact of the acoustic liners is to dampen the instability of the flow-acoustic coupled system. This demonstrates that it is a convenient and effective method for suppressing Helmholtz resonance by using inside acoustic liner.     

Linear instability of planar shear banded flow

We study the linear stability of planar shear banded flow with respect to perturbations with wave vector in the plane of the banding interface, within the nonlocal Johnson-Segalman model. We find that perturbations grow in time, over a range of wave vectors, rendering the interface linearly unstable. Results for the unstable eigenfunction are used to discuss the nature of the instability. We also comment on the stability of phase separated domains to shear flow in model H.     

Surface instability of the liquid turbulent flows in the open inclined channels

The flow of a viscous liquid layer in an open inclined channel under the turbulent mode is considered in this paper. To describe turbulent viscosity, the Van Driest model is used. The spectrum of characteristic values of the problem on linear stability of a plane-parallel flow is studied numerically. Parameters of the maximal growth waves are found out, the surface tension effect is studied, and theoretical results are compared with experimental data. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 05-08-33585a).     

多孔表面推迟高超声速边界层转捩的机理

利用线性稳定性理论分析（LST）结合直接数值模拟（DNS）研究高超声速多孔表面边界层流动的失稳特征,分析多孔表面推迟高超声速边界层转捩的机理.在Ma=6,Re=2.0×10⁴（参考长度为入口处边界层位移厚度）条件下获得平板边界层及不同孔隙排列情形下平板边界层的典型流动特征,并采用LST方法分析光滑平板及多孔平板扰动的增长率及累计放大率.研究表明三维顺排及错排多孔表面都可以抑制第二模扰动的发展,推迟高超声速边界层转捩,但顺排多孔表面推迟高超声速边界层转捩能力更强.     

Effects of dimples on laminar boundary layers

A series of direct numerical simulations of the flow past a flat plate with two and eight rows of dimples in a staggered arrangement is carried out. The Reynolds number based on the boundary layer thickness and freestream velocity near the inflow plane is 1000 and the dimples are spherical with a depth to diameter ratio of 0.1. The incoming flow is laminar and the boundary layer thickness before the dimples is half the dimple depth. At this low Reynolds number the flow is expected to remain laminar over a smooth flat plate. The presence of the dimples triggers instabilities that cause significant momentum transport. It is shown that the shear layer that forms as the flow separates over the first two rows of dimple becomes unstable and sheds coherent vortex sheets. The vortex sheets become unstable and are transformed into packets of horseshoe vortices. When these vortices evolve over a flat plate or over a series of dimples the flow dynamics are very different with important changes in momentum transport across the boundary layer.     

A note on the interaction of unsteady flow with an acoustic liner

The effects of a mean grazing flow on the energy exchanges involved in the interaction of a bias-flow acoustic liner with, respectively, incident sound and boundary layer turbulence are contrasted. The analysis of model problems which make use of a line vortex to simulate large scale, unsteady boundary layer structures indicates that, whereas acoustic waves may be effectively attenuated, dissipation caused by “jetting” in the apertures of the liner can result in a net transfer of energy from the mean flow to the turbulence in the boundary layer.     

Stability of the heated liquid film in the presence of the thermocapillary effect

Stability of the flow of the heated liquid film is studied in the presence of the thermocapillary effect. To describe the waves in the film, the integral model is used. According to results of linear analysis of stability, the thermocapillary effect expands the area of instability only at low values of Peclet number Pe, and at high values of Pe, the instability area narrows. Wave evolution in the film on a substrate with the fixed temperature was simulated numerically. Results of numerical simulations agree with the linear theory of stability.