半无穷长圆管内的低雷诺数入口流

1969年Lew及Fung[1]计算了圆管内的低雷诸数入口流.1982年Dagan等人[2]得到了有限长圆柱形孔道内蠕动流的级数解.[1]中所得的数值解实质上代表有限长圆管内的低雷诺数入口流,因为一般解中的富氏积分已用富氏级数代替.本文直接计算富氏积分,更精确地求出了真正的半无穷长圆管内Stokes入口流的速度分布,压力分布以及流函数,与此对应的入口段长度为圆管半径的1.2倍,接近于Lew及Fung得到的结果1.3倍.此外,本文还研究了配置法的收敛性,证明了此法在入口流问题中具有很好的收敛性,因此可以在其他类似的问题中采用.     

风沙两相流中的跃移运动

从单个跃移沙粒在气流中的运动方程出发 ,导出了风沙两相流中沙粒相速度分布函数的Boltzmann方程 ;并以此将单相颗粒流理论中的广义平衡方程推广到气固两相流的情形 .提出用Grad方法将粒子相速度分布函数展成无穷级数 ,并引入Gauss分布取代单相颗粒流理论中传统的Maxwell分布 .在保留到 3次项的情况下 ,建立了气体 颗粒两相湍流边界层三阶矩封闭理论的动力学方程组 .并在风洞频闪摄影实验的基础上 ,对理论进行简化 ,得到便于工程应用的简化方程     

解任意形状扁轴对称体Stokes流动的连续奇点分布法

本文以Sampson球形无穷级数作为基本奇点,采用分段等强度和分段二次抛物分布两种体内连续分布法解任意形状扁轴对称体的Stokes流动.通过扁球的无界绕流问题,对这两种方法的收敛性,精度和适用范围做了检验和比较.结果表明,在一定的范围内,无论是阻力系数或压力分布,它们的计算结果都和精确解符合得很好,而且,随着分布函数逼近程度的提高,其收敛性得到改善,适用范围也随之扩大.作为一般算例,分别用这两种方法解决了卡西尼扁卵形体的绕流问题,得到了一致的结果.最后,用分段二次连续分布法计算了具有一定生理意义的红细胞体的Stokes流动,首次得到了它的阻力系数和表面压力分布.     

半无穷平面到半无穷长圆管的低雷诺数流动

本文利用匹配法和配置法求出了粘性流体从半无穷平面到半无穷长圆管的Stokes流动的无穷级数形式的解.结果表明,经过圆柱半径的一半路程之后,速度剖面和Poiseuille剖面只差1%.初始段长度比Dagan的有限长圆管情形显著缩短,在孔口外的半无穷空间内,孔口右边的边界只对孔口附近一倍管径的区域有强烈影响.在此以外的区域内几乎没有影响.此外,本文还对压力和流量的关系进行了研究.     

解任意形状非细长长轴对称体Stokes流动的一种新方法

本文提出离散奇点线分布法和连续奇点线分布法解决任意形状非细长长轴对称体的Stokes流动。取Sampson球形无穷级数为基本奇点。通过长球无界绕流问题检验了上述两种方法的收敛性及精度。与精确解比较表明,在一定的细长比下无论在阻力系数或压力分布上,这两种方法都具有良好的收敛性及高精度的计算结果,而且连续奇点线分布法和离散奇点线分布法相比较具有更好的收敛性能。最后,作为计算任意形状非细长长轴对称体的一个例子,利用这两种方法计算了卡西尼卵形体的阻力系数及压力分布值,得到了收敛的一致结果。     

正项级数比值判敛法的推广形式

对正项级数收敛性的讨论,是无穷级数研究中的一个基本问题。本文试将D'Alembert法(比值法)加以推广,并称作“广义比值法”。此法较为“细致”,便于应用。引理.设u_n>0,有     

常微分方程的级数解法探源

级数法是求解常微分方程最有效的方法之一.牛顿是第一位真正开始求解微分方程的数学家,级数法是其采用的第一种求解方法.在研读牛顿的微积分论文《流数法与无穷级数》基础上,探讨级数法形成的根源,揭示其思想方法对今日微分方程课程教与学的启迪作用以及对创立和发展微分方程学科的重要理论意义.     

关于用比较判别法判断无穷级数的敛散性问题

<正> 无穷级数是数学分析的一个重要组成部分,内容十分丰富。研究的问题大致有如下几个方面:敛散性问题;求和、误差估计问题;收敛速度的估计等。无穷级数在应用上也是十分广泛的。如何判断无穷级数的敛散性是很重要的问题,教材中介绍了许多方法可供使用。但是,学生往往对用比较判别法判断无穷级数的敛散性感到困难,本文仅就这方面问题做些讨论。我们先将比较判别法叙述如下:     

复模糊值函数级数的收敛性

在新的模糊数序关系意义下,介绍了复模糊数的概念及运算性质,复模糊数列收敛的定义及复模糊级数收敛性的判别法.并以此为基础,定义了复模糊值函数级数的收敛性及一致收敛性,讨论了复模糊值函数级数的收敛判别法及其基本性质,以及一致收敛的判别法.     

关于级数敛散性的导数判别法

<正> 关于无穷级数绝对收敛性的讨论,是一个有意义的问题,毛毓球译《级数绝对收敛的导数判别法》一文给出了一种建立在导数基础上的判别法则,叙述如下: 定理1(导数判别法)设为实     

多个球形液滴的蠕动流

本文利用Sampson奇点及配置法求解多个球形液滴在蠕动流中的阻力系数.计算了由不同数目液滴组成的液滴串在不同液滴间距下的阻力系数并揭示了粘度比对遮蔽效应和端缘效应的影响.文章还对方法的收敛性进行了研究.     

Slip at the surface of a sphere translating perpendicular to a plane wall in micropolar fluid

The Stokes axisymmetrical flow caused by a sphere translating in a micropolar fluid perpendicular to a plane wall at an arbitrary position from the wall is presented using a combined analytical-numerical method. A linear slip, Basset type, boundary condition on the surface of the sphere has been used. To solve the Stokes equations for the fluid velocity field and the microrotation vector, a general solution is constructed from fundamental solutions in both cylindrical, and spherical coordinate systems. Boundary conditions are satisfied first at the plane wall by the Fourier transforms and then on the sphere surface by the collocation method. The drag acting on the sphere is evaluated with good convergence. Numerical results for the hydrodynamic drag force and wall effect with respect to the micropolarity, slip parameters and the separation distance parameter between the sphere and the wall are presented both in tabular and graphical forms. Comparisons are made between the classical fluid and micropolar fluid.      

Three‐dimensional Stokes flow caused by a translating–rotating sphere bisected by a free surface bounding a semi‐infinite micropolar fluid

Explicit velocity and microrotation components and systematic calculation of hydrodynamic quasistatic drag and couple in terms of nondimensional coefficients are presented for the flow problem of an incompressible asymmetrical steady semi‐infinite micropolar fluid arising from the motion of a sphere bisected by a free surface bounding a semi‐infinite micropolar fluid. Two asymmetrical cases are considered for the motion of the sphere: parallel translation to the free surface and rotation about a diameter which is lying in the free surface. The speed of the translational motion and the angular speed for the rotational motion of the sphere are assumed to be small so that the nonlinear terms in the equations of motion can be neglected under the usual Stokesian approximation. A linear slip, Basset‐type, boundary condition has been used. The variation of the resistance coefficients is studied numerically and plotted versus the micropolarity parameter and slip parameter. The two limiting cases of no‐slip and perfect slip are then recovered. Copyright © 2008 John Wiley & Sons, Ltd.     

Slow motion of a sphere moving normal to two infinite parallel plane walls in a micropolar fluid

In the present work, we consider the slow steady motion of a rigid sphere moving normal to two parallel plane walls in a micropolar fluid. Non-dimensional variables are introduced. A combined analytical-numerical technique based on the superposition principle and a numerical method, namely the collocation method, is used. The drag force and the wall correction factor are evaluated. Numerical results are obtained and represented graphically.     

Creeping flow of a sphere nearby a cylinder

We present a three-dimensional solution of a sphere nearby an infinite cylinder at low Reynolds number. We utilize the Lamb’s general solution based on spherical harmonics and develop a framework based on cylindrical harmonics to solve the flow field around the sphere and outside the cylinder, respectively. The solution is solved semi-analytically by considering geometrical parameters, including sphere radius, sphere velocity, separation distance and cylinder radius. The drag force coefficients of the sphere which are dependent on the distance between the cylinder surface and the sphere, as well as the velocity contours in the vicinity of the sphere, are analyzed. We also provide an analytical formula to calculate the drag force. The analytical formula has good quantitative agreement with the semi-analytical solution when the radius of the cylinder is smaller than the sphere. Such analysis can give insights into the details of the complex interaction between the sphere and cylinder.     

Finite element calculations of flow past a spherical bubble rising on the axis of a cylindrical tube

The velocity and pressure fields of a Newtonian fluid with homogeneous and constant physical properties flowing around a sphere on the axis of a cylindrical tube with no slip, free slip and partial slip at the sphere surface and no slip at the cylinder wall have been calculated by solving the Navier-Stokes equations and the continuity equation using the finite element technique with the penalty function method. Terminal rise velocities of spherical air bubbles in water have been calculated as function of the bubble radius and some conclusions have been drawn about the nature of the interface. Finally, the influence of the presence of a cylindrical wall on the drag force has been determined and a new empirical equation is derived for the wall correction factor for a sphere rising with free slip at its surface at low Reynolds number.     

Electromagnetic interaction of moving conductors with magnets: kinematic solutions for infinitely long square and cylindrical geometries

The electromagnetic drag force on a point dipole near a moving conductor caused by the induced electric currents is investigated by numerical and analytical computations. Our focus is on prototypical configurations for Lorentz force velocimetry, i.e. velocity measurement from the electromagnetic drag force on the dipole. We examine the particular cases of conducting infinite bars of square or round cross-section, which are moving with constant velocity in the field of arbitrary oriented magnetic dipole. In addition, we study the laminar liquid-metal flow in a square duct. The motion of the conductor is prescribed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A solution for the problem of stokes flow past a porous sphere

The problem of a general non-axisymmetric Stokes flow of a viscous fluid past a porous sphere is considered. The expressions for the velocity and pressure, both inside and outside the sphere are given, when the flow outside satisfies the Stokes equations and the flow inside the sphere is governed by Darcy's law. The expressions for drag and torque are given. It is found that the drag is greater or smaller than the drag in the rigid case, depending on whether the undisturbed velocity is a pure biharmonic or a harmonic respectively. The torque is same as in the rigid case.     

On slow motion of a sphere in a viscous liquid

Stokes’ and Seth’s solutions for the slow motion of a sphere in a viscous, incompressible liquid have been discussed from the viewpoint of the structure of the velocity field and its relation to the drag of the sphere. The problem is analysed from a different angle in this paper. It is believed that it throws more light on thephysics of the problem.