应用变分法计算三角形截面毛管中的流动

以三角形截面管道中的流动为研究对象,在前人研究的基础上,进一步研究了牛顿流体和幂律流体在截面为三角形毛管中的流动,应用变分方法求出了毛管内速度分布的近似解,并通过对整个毛管进行积分,求出了类似泊肃叶定律的不同毛管内的流量与压差的定量关系.同时,又应用Matlab中的Pdetool工具对不同截面毛管中的层流流动进行了数值求解.变分结果、数值结果与有关文献解析解、数值解进行了对比,又进一步分析了幂律指数和截面形状对综合阻力系数、等效渗透率及流量-压差关系的影响.     

Existence of a Nonstationary Poiseuille Solution

The nonstationary Poiseuille solution describing the flow of a viscous incompressible fluid in an infinite cylinder is defined as a solution of the inverse problem for the heat equation. The existence and uniqueness of such nonstationary Poiseuille solution with the prescribed flux F(t) of the velocity field is studied. It is proved that under some compatibility conditions on the initial data and flux F(t) the corresponding inverse problem has a unique solution in Holder spaces.Original Russian Text Copyright © 2005 Pileckas K. and Keblikas V.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 649–662, May–June, 2005.     

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.     

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．     

一类具有偏差变元的高阶中立型Rayleigh方程周期解的存在性

利用重合度理论和不等式分析技巧,获得了一类具有偏差变元的高阶中立型Rayleigh方程(x(t)-cx(t-σ))~((m))+f(x'(t))+β(t)g(x(t-τ(t)))=p(t)周期解存在性的新的充分条件,有意义的是函数f(x)和非线性项前的系数β(t)可以变号.     

Asymptotic Behavior of Micropolar Fluid Flow Through a Curved Pipe

We study the stationary motion of a micropolar fluid in a thin (or long) curved pipe via rigorous asymptotic analysis. An asymptotic solution is found, showing explicitly the effects of pipe’s distortion and microstructure on the effective behavior of the flow. We justify the obtained model by proving the corresponding error estimate.     

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.     

Stability of the Poiseuille Flow in a Channel with Comb Grooves

The stability of the Poiseuille flow in a channel with longitudinal comb grooves on the lower wall is studied numerically. Dependences of the linear and energy critical Reynolds numbers on the groove spacing and height are obtained and analyzed. The results are compared with data available for wavy grooves, which tend to comb grooves as one of the groove parameters approaches infinity.     

多偏差变元中立型Rayleigh方程周期解问题

作者研究了一类多偏差变元中立型Rayleigh方程周期解问题,利用Mawhin重合度拓展定理得到了周期解存在性的新结果.     

On Stratified Shear Flow in Sea Straits of Arbitrary Cross Section

Equations and theorems governing the flow of an inviscid, incompressible, continuously-stratified fluid in a gradually varying channel with an arbitrary cross section are developed. The stratification and longitudinal velocity are assumed to be uniform in the transverse direction, an assumption that is supported under the assumption of gradual topographic variations. Extended forms of Long's model and the Taylor–Goldstein equation are developed. Interestingly, the presence of topographic variation does not alter the necessary condition for instability (Richardson number     ) nor the bounds on unstable eigenvalues (the semi-circle theorem). The former can be proved using a new technique introduced herein. For the special case of homogeneous shear flow, generalized versions of the theorems of Rayleigh and Fjørtoft do depend on the form of the topography, though no general tendency toward stabilization or destabilization is apparent. Previous results on the bounds and enumeration of neutral modes are also extended. The results should be of use in the hydraulic interpretation of exchange flow in sea straits.     

The Effect of the Backward-Facing Step Height on Flow in a Channel with Rectangular Cross Section

The investigation of a channel flow with a backward-facing step on one wall is described. The height of the incoming channel H is adjustable as to allow alter the ratio of step height h over H; h/H = 1 : 10, 1 : 4, 1.02 : 1(h + H = 0.275m). Mutual correlations between the extremes of static pressure distributions, limits of the separation zone and of the corner vortex structures and Reynolds number are discussed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effects of Flexion and Torsion on a Fluid Flow Through a Curved Pipe

We consider an injection of incompressible viscous fluid in a curved pipe with a smooth central curve γ . The one-dimensional model is obtained via singular perturbation of the Navier—Stokes system as ɛ , the ratio between the cross-section area and the length of the pipe, tends to zero. An asymptotic expansion of the flow in powers of ɛ is computed. The first term in the expansion depends only on the tangential injection along the central curve γ of the pipe and the velocity as well as the pressure drop are in the tangential direction. The second term contains the effects of the curvature (flexion) of γ in the direction of the tangent while the effects of torsion appear in the direction of the normal and the binormal to γ . The boundary layers at the ends of the pipe are studied. The error estimate is proved. Accepted 21 March 2001. Online publication 9 August 2001.     

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.     

微极各向同性弹性板中的Rayleigh-Lamb波

研究了无应力作用条件下，均匀、各向同性、圆柱形微极结构弹性板中波的传播．导出了对称和斜对称模式下波传播的特征方程．对短波这一极端情况，无应力圆板中对称和斜对称模态波的特征方程退化为Pmyle曲表面波频率方程．并得到薄板的计算结果．给出了位移和微转动分量，并绘制了相应图形．给出了若干特殊情况的研究结果及对称和斜对称模态特征方程的图示．     

一类反应扩散方程波前解的存在性

本文讨论一类反应扩散方程满足各种条件的单调波前解及振荡波前解的存在性；得到了一系列保证波前解存在的充分条件。     

Investigation of the Spectrum of the Problem of Normal Waves in a Closed Regular Inhomogeneous Dielectric Waveguide of Arbitrary Cross Section

Doklady Mathematics - The problem of normal waves in a closed (screened) regular waveguide of arbitrary cross section is considered. It is reduced to a boundary value problem for the longitudinal...     

直圆管突扩通道内宾汉流体湍流流场的数值研究

本文依据牛顿流体中建立的标准ｋ＿ε湍流模型这一基本思想，考虑宾汉流体的本构方程，建立了适用于求解宾汉流体湍流流动的控制方程·采用压力修正算法，实现了宾汉流体速度场与压力场的关联·在理论研究基础上，对直圆管突扩通道内宾汉流体湍流流动进行了数值研究，并探讨了直圆管突扩通道内宾汉流体湍流流动机理·     

Stability of Surface Rayleigh Waves in an Elastic Half‐Space

This paper is concerned with nonlinear analysis for the propagation of Rayleigh surface waves on a homogeneous, elastic half‐space of general anisotropy. We show how to derive an asymptotic equation for the displacement by applying the second‐order elasticity theory. The evolution equation obtained is a nonlocal generalization of Burgers' equation, for which an explicit stability condition is exhibited. Finally, we investigate examples of interest, namely, isotropic materials, Ogden's materials, compressible Mooney–Rivlin materials, compressible neo‐Hookean materials, Simpson–Spector materials, St Venant–Kirchhoff materials, and Hadamard–Green materials.