非定常修正下平面Poiseuille流动的线性稳定性性质

本文在文[1]的基础上,用多重尺度法进一步研究了在非定常修正剖面作用下平面Poiseuille流动的线性稳定性性质,发现文[1]所给出的修正剖面在扰动发展的初期,在一定条件下会促进扰动的发展,从而增大流动失稳的可能性.     

Linear Stability of Pipe Poiseuille Flow at High Reynolds Number Regime

In this paper, we prove the linear stability of the pipe Poiseuille flow for general perturbations at high Reynolds number regime. This has been a long-standing problem since the experiments of Reynolds in 1883. Our work lays a foundation for the theoretical analysis of hydrodynamic stability of pipe flow, which is one of the oldest yet unsolved problems in fundamental fluid dynamics. © 2022 Wiley Periodicals LLC.     

非牛顿幂级数流体平面泊肃叶流的非线性稳定性*

非牛顿流体在现代工业生产中,广泛地作为加工的对象,因此非牛顿流体的流动稳定性问题有着重要的生产实际背景。本文选择在聚合物加工时将熔体压入成板口模时形成平面泊肃叶流这一生产背景,研究其非线性稳定性问题,计算其亚临界阈值。     

Wave-Mean Flow Interactions in Thermally Stratified Poiseuille Flow

We consider nonlinear wave motions in thermally stratified Poiseuille flow. Attention is focused on short wavelength wave modes for which the neutral Reynolds number scales as the square of the wave number. The nonlinear evolution of a single monochromatic wave is governed by a first harmonic/mean-flow interaction theory in which the wave-induced mean flow is comparable in size to the wave component of the flow. An integrodifferential equation is derived which governs the normal variation of the wave amplitude. This equation admits finite-amplitude solutions which bifurcate supercritically from the linear neutral point(s).     

高雷诺数下平面Poiseuille流稳定性渐近分析

本文主要讨论高雷诺数下平面Poiseuille流稳定性问题.应用多层结构分析理论,求出了描述该流体稳定性的Orr-Sommerfeld方程特征值的较为合理的逼近式及相应的特征函数的渐近解析解.     

Weakly Nonlinear Analysis of a Localized Disturbance in Poiseuille Flow

In this article, we investigate, via a perturbation analysis, some important nonlinear features related to the process of transition to turbulence in a wall-bounded flow subject to a spatially localized disturbance that is harmonic in time. We show that the perturbation expansion, truncated at second order, is able to capture the generation of streamwise vorticity as a weakly nonlinear effect. The results of the perturbation approach are discussed in comparison with direct numerical simulation data for a sample case by extracting the contribution of the different orders. The main aim is to provide a tool to select the most effective nonlinear interactions to enlighten the essential features of the transitional process.     

Initial Development of Diffusion in Poiseuille Flow

The combined effect of diffusion, and of convection by Poiseuilleflow, on the distribution of a small quantity of miscible additiveinjected into a tube of radius a, is to spread it longitudinallywith a Taylor "effective diffusion coefficient", to an approximationthat is good at times greater than about 0.5a²/D (Bailey &Gogarty, 1962), where D is the molecular diffusion coefficient.The present theory, complementary to the Taylor theory, determinesthe initial action of diffusion on the front of the concentrationdistribution, to an approximation that is good at times t lessthan about 0.1a²/D. The theory is exact wherever the added substancedoes not yet interact with the tube wall, and predicts thatthe spread in the front due to diffusion extends (Fig. 2) overa distance of order DUt²/a², where U is the velocity on theaxis of the tube. The transition between distributions characteristicof the two theories is illustrated (Fig. 4); and the introductionindicates the relevance of the new theory to work (Caro, 1966)on tracers used in study of the blood circulation.     

Poiseuille流的谱问题

对Poiseuille流问题的Orr-Sommerfeld方程严格求解.得到的正规解不含外来奇点.从而谱方程可作解析的显式分析.本文结果可以进一步讨论分岔解.     

圆管Poiseuille流动中平均速度的一种修正剖面及其稳定性研究

本文给出了圆管Poiseuille流动中Hagen-Poiseuille速度剖面的一种修正剖面.这种剖面可看作是轴对称扰动各谐波分量非线性相互作用对平均流影响的一般体现.通过对这种速度剖面的稳定性研究,本文首次得到轴对称扰动造成失稳的结果,提出了Hagen-Poiseuille流动一种新的产生失稳的可能途径.     

纤维悬浮槽流空间模式稳定性分析

采用扰动的空间发展模式而非通常的时间发展模式,对含有悬浮纤维的槽流进行了线性稳定性分析。建立了适用于纤维悬浮流的稳定性方程并针对较大范围的流动Re数及扰动波角频率进行了数值求解。计算结果表明,纤维轴向抗拉伸力与流体惯性力之比H可以反映纤维对流动稳定性的影响。H增大使临界Re数升高,对应的扰动波数减小,扰动空间衰减率增加,扰动速度幅值的峰值降低,不稳定扰动区域缩小,长波扰动所受影响相对较大。纤维的存在抑制了流场的失稳。     

Nonlinear Stability of Baroclinic Fronts in a Channel with Variable Topography

The governing equations describing baroclinic bottom-trapped fronts in a channel with variable bottom topography are shown to be a noncanonical Hamiltonian system. The Hamiltonian formalism is exploited to derive a variational principle for arbitrary steady solutions based on an appropriately constrained energy functional. The variational principle is exploited to obtain formal and nonlinear stability conditions. In the infinitesimal amplitude limit, these stability conditions reduce to previously obtained normal mode results for the transverse gradient of the mean frontal potential vorticity.     

张量封闭模型与三维取向分布对纤维悬浮槽流稳定性的影响

应用3种不同的纤维方向张量封闭模型,数值模拟了纤维悬浮槽流的流动稳定性问题,从而研究封闭模型和纤维的三维取向分布对稳定性分析的影响．结果发现,采用3种不同封闭模型所得到的流动稳定特性与纤维参数之间的关系是相同的,但采用三维混合封闭模型时,由于纤维的取向与流向的偏差程度较大,所以纤维对流动的不稳定性具有最强的抑制作用．而采用二维混合封闭模型时,由于纤维在平面取向条件下,其轴线整体上趋于呈流向排列,使得对流体的作用削弱,导致纤维对流动不稳定性抑制的作用最弱．     

周期压力驱动下管壁局部不规则的圆管Poiseuille流感受性问题

采用渐近分析方法,建立了在周期压力驱动下,完全发展的圆管Poiseuille流当管壁存在局部不规则几何形状时的感受性问题模型．通过特征函数的双正交系统,应用Chebyshev配点法进行数值求解．通过算例计算,获得周期压力和矩形突起激发起的流体系统中的各种空间发展模态以及相应的感受性系数．从计算和分析可以知道,在流场的不同发展阶段不同的模态起着主导作用,这与在试验中观察到的扰动流场在不同位置的特性是一致的．     

DNS and Experiment of a Turbulent Channel Flow with StreamwiseRotation - Study of the Cross Flow Phenomena

Modelling of rotating turbulent flows is a major issue in engineering applications. Intensive research has been dedicated to rotating channel flows in spanwise direction such as by [1], [2] to name only two. In this work a turbulent channel flow rotating about the streamwise direction is presented. The theory is based on the investigations of [4] employing the symmetry theory. It was found that a cross flow in the spanwise direction is induced. A series of direct numerical simulations (DNS) at different rotation numbers is carried out to examine these effects. Further, the results of the DNS are compared to the measuremets of a corresponding experiment. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow Structure behind a Shock Wave in a Channel with Periodically Arranged Obstacles

We study the propagation of a pressure wave in a rectangular channel with periodically arranged obstacles and show that a flow corresponding to a discontinuity structure may exist in such a channel. The discontinuity structure is a complex consisting of a leading shock wave and a zone in which pressure relaxation occurs. The pressure at the end of the relaxation zone can be much higher than the pressure immediately behind the gas-dynamic shock. We derive an approximate formula that relates the gas parameters behind the discontinuity structure to the average velocity of the structure. The calculations of the pressure, velocity, and density of the gas behind the structure that are based on the average velocity of the structure agree well with the results of gas-dynamic calculations. The approximate dependences obtained allow us to estimate the minimum pressure at which there exists a flow with a discontinuity structure. This estimate is confirmed by gas-dynamic calculations.     

明渠层流失稳与沙纹成因机理研究

动床水流中,泥沙起动之后,往往要出现沙纹,沙纹成因各家的解释不一。白玉川,罗纪生的观点是:沙纹的尺度较小,主要是由于明渠层流不稳定性波或床面近壁流层中小尺度拟序结构发展演化所致。当床面边界附近扰动波或拟序结构以及水流自身所产生的床面底部切应力大于Shields切应力后,床面即产生响应,形成沙纹;如果扰动所产生的扰动切应力频率接近床面泥沙固有频率,则产生与泥沙颗粒的共振,这种现象也称之为“泥沙的检波性质”,此时床面发生最大响应,沙纹发展速度也最快。     

Existence of Neutral Rayleigh Waves in the Hagen–Poiseuille Flow Through a Pipe of Circular Cross Section

The inviscid neutral stability of Hagen–Poiseuille flow through a circular pipe is studied using both analytical and numerical techniques. A zero phase shift is applied across the critical surface to represent the effects of strong nonlinearity. Using a form of Sturm's comparison theorem it is possible to prove that no neutral solutions exist if a combination of the axial and azimuthal wave numbers of the perturbation exceeds a critical value. As a consequence, the physical problem admits only neutral solutions for an azimuthal wave number of unity.     

Initial Algebraic Growth of Small Angular Dependent Disturbances in Pipe Poiseuille Flow

The evolution of small, angular dependent velocity disturbances in laminar pipe flow is studied. In particular, streamwise independent perturbations are considered. To fully describe the flow field, two equations are required, one for the radial and the other for the streamwise velocity perturbation. Whereas the former is homogeneous, the latter has the radial velocity component as a forcing term. First, the normal modes of the system are determined and analytical solutions for eigenfunctions, damping rates, and phase velocities are calculated. As the azimuthal wave number (n) increases, the damping rate increases and the phase velocities decrease. Particularly interesting are results showing that the phase velocities associated with the streamwise eigenfunctions are independent of the radial mode index when n = 1, and when n = 5 the same is obtained for phase velocities associated with the eigenfunctions of the radial component. Then, the initial value problem is treated and the time development of the disturbances is determined. The radial and the azimuthal velocity components always decay but, owing to the forcing, the streamwise component shows an initial algebraic growth, followed by a decay. The kinetic energy density is used to characterize the induced streamwise disturbance. Its dependence on the Reynolds number, the radial mode, and the azimuthal wave number is investigated. With a normalized initial disturbance, n = 1 gives the largest amplification, followed by n = 2 etc. However, for small times, higher values of n are associated with the largest energy density. As n increases, the distribution of the streamwise velocity perturbation becomes more concentrated to the region near the pipe wall.     

Forms of Unsteady Flow in a 2-D Channel

The paper describes results of a numerical simulations of air flow in a turned off, 2D channel with the plain nozzle. Simulations are based on an earlier experiment, carried out by Dyban, Mazur and Epik (1971). In the featured channel it has been observed several bifurcation forms, depending on the flow velocity and geometry relations. Basing on the numerical simulations results, the integral characteristics of the flow areas has also been presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DNS of a Turbulent Channel Flow with Streamwise Rotation - Study of the Reverse Effect of the Cross Flow

Modeling of rotating turbulent flows is a major issue in engineering applications. In this work a turbulent channel flow rotating about the streamwise direction is presented. The theory is based on the investigations of [3] employing Lie group analysis. It was found that a cross flow in spanwise direction is induced. A series of direct numerical simulations (DNS) has been conducted for both different rotation rates and different Reynolds numbers to validate the cross flow. In addition some new interesting effects were observed. The averaged profile ū₃ of the cross flow is formed like a ‘S’ that means it exhibits a triple zero-crossing which denotes regions of reverse flow. Alaso a reverse effect is seen which means that for small rotation rates up to Ro=10 the spanwise mean velocity profiles increase and at rotation number Ro=14 this effect appears to reverse. Both effects were observed at two different Reynolds numbers Re = 180 and Re = 270. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)