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。     

蠕动流中连续奇点线分布法的分段线性近似

本文考虑了连续奇点线分布法的分段线性近似去处理任意形状长轴对称体的Stokes流动,成功地得到了流场的封闭形式的分析表达式.通过长球和卡西尼卵形体的数值计算表明此法改进了分段等强度近似的收敛性和精度并具有更大的细长比的适用范围.文中还给出实例说明分段线性近似还可用来计算任意形状尖头长轴对称体的Stokes流动.     

蠕动流中圆球阻力系数的入口效应

本文研究了圆球在半无穷长圆管入口处的蠕动流。得到了速度分布,压力分布和流函数的无穷级数形式的分析解.采用配置法将无穷级数截断并确定出级数中各项系数.求出了均匀入口流绕静止圆球以及圆球以瞬时速度在管内静止流体中运动这两种情形下圆球的阻力系数以及圆球表面上的应力分布.结果表明,当圆球在入口处运动时会遭受到较无穷圆管内为大的阻力.本文还对配置法的收敛性进行了数值实验.试验证明,该法具有好的收敛性.     

三维斯托克斯流动在扁球坐标系中的基本解及其应用

通过把Lamb基本解中的调和函数转换为扁球坐标系下的表达式,这项研究成功地得到了一个新的Stokes流动三维基本解.此基本解可用于解决任意多个扁椭球处于任意位置和方向时的流动问题.应用最小二乘法,三维流动问题中常遇到的收敛性差的困难在此得以完全克服.结果表明该方法具有准确度高,收敛性好和计算量小的特点.由于扁球可用于模拟从圆盘到圆球的多种物体形状,此基本解被用于系统地分析了各种几何因素对两个扁球所受力和力矩的影响.为了显示此方法的通用性,该基本解还用于研究了两例三个扁球的问题.     

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.     

三维Stokes绕流问题的无限元逼近(英文)

设计了一种最少自由度的无限元方法来实现三维Stokes绕流问题的求解.通过验证强制性和inf-sup条件,我们证明了相应的离散混合变分问题解的适定性,并在加权Sobolev空间中得到了误差的先验估计.数值实验结果验证了解的收敛性.     

软物质准晶广义流体动力学的一个应用——圆柱绕流的近似解

文中报道了笔者建议的软物质准晶广义流体动力学的一个应用——软物质准晶圆柱绕流的近似解.人们熟知,在普通流体动力学中, 二维圆柱绕流问题遇到很大的困难,Stokes求解它,未能成功,这就是著名Stokes佯谬.为了克服这一困难, Oseen分析了原因不在边界条件的提法,也不在Stokes的求解,问题出在Navier-Stokes方程, 他对方程进行了修改, 得到了二维绕流问题的有物理意义的近似分析解.本文借助于Oseen的方法讨论12次对称软物质准晶广义流体动力学二维绕流问题.由于问题比普通流体动力学复杂得多,严格的求解,在目前的条件下是根本不可能的.笔者提出一种近似方法——交替程序去构造其零级近似解,并且把该结果用于软物质准晶的位错问题.     

Stokes流和理想流体轴对称问题的解析函数法

本文利用流函数解的完备性和共轭势函数的概念,导出了轴对称Stokes流和理想流体完备的速度和压力的解析函数表达式解.作为它的应用,我们求出关于球的缓慢绕流问题的解.     

任意形状长轴对称体沿长轴方向垂直地向一无界平板运动时所产生的Stokes流

在任意形状长轴对称体内连续地分布Sampson平扳反演流子,采用分段等强度,分段线性和分段抛物三种近似,成功地得到了流场的封闭形式的分折表达式。计算了物体和平板有不同间距,长短轴比取一系列不同值时,长球和卡西尼长卵形体的阻力系数。计算结果表明,方法具有良好的收敛性。在长球情况下和已有的数据进行了对比。符合程度是十分令人满意的。     

基于外场实验的风力机叶片三维效应研究

针对一台33 kW水平轴风电机组开展了外场实验,得到其叶片7个断面翼型的压力分布曲线;基于求解时均N-S方程对风轮进行三维数值模拟,以及将叶片各断面作为二维翼型进行数值计算,分别得到各断面翼型的压力分布曲线及升阻力系数．通过将外场实验、三维和二维数值计算所得压力分布曲线及升阻力系数进行对比分析,研究了三维效应对风力机气动性能的影响．研究表明,从叶尖到叶根各断面翼型的压差先增大后逐渐减小,叶片表面压力分布曲线比较明显地反映了从叶尖到叶根流动分离的变化;叶片表面压力分布的三维数值计算结果较二维计算结果更加接近于外场实验值;风力机叶片表面的三维流动对叶片的气动性能影响较大,在叶尖和叶根部分尤为突出.     

Stokes flow with slip and Kuwabara boundary conditions

The forces experienced by randomly and homogeneously distributed parallel circular cylinder or spheres in uniform viscous flow are investigated with slip boundary condition under Stokes approximation using particle-in-cell model technique and the result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but little in shape from a sphere is also investigated. The explicit expression for the stream function is obtained to the first order in the small parameter characterizing the deformation. As a particular case of this we considered an oblate spheroid and evaluate the drag on it.     

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.      

A new approach to the classical Stokes flow problem: Part I Methodology and first-order analytical results

The problem of determining the axisymmetric Stokes flow past an arbitrary body, the boundary shape of which can be represented by an analytic function, is examined by developing an exact method. An appropriate nonorthogonal coordinate system is introduced, and it is shown that the Hilbert space to which the stream function belongs is spanned by the set of Gegenbauer polynomials based on the physical argument that the drag on a body should be finite. The partial differential equation of the original problem is then reduced to two simultaneous vector differential equations. By the truncation of this infinite-dimensional system to the one-dimensional subspace, an explicit analytic solution to the Stokes equation valid for all bodies in question is obtained as a first approximation.     

Creeping flow about a slightly deformed sphere

The problem of slow streaming flow of a viscous incompressible fluid past a spheroid which departs but little in shape from a sphere with mixed slip-stick boundary conditions, is investigated. The explicit expression for the stream function is obtained to the first order in the small parameter characterising the deformation. The case of an oblate spheroid is considered as a particular example and the force on this non-spherical body is evaluated. It is found that the parameter ₁, which arises in connection with the boundary condition, has significant effect upon the hydrodynamic force. In fact, it is shown that, the force is a quadratic function of this parameter up to the first order of deformation. Also, it is observed that the drag in the present case is less than that of the Stokes resistance for a slightly oblate spheroid. Some other special cases are also deduced from the present result. A brief discussion of the results to other body shapes is presented.     

Stokes flow inside a porous spherical shell: Stress jump boundary condition

An arbitrary Stokes flow of a viscous, incompressible fluid inside a sphere with internal singularities, enclosed by a porous spherical shell, using Brinkmans equation for the flow in the porous region is discussed. At the interface of the clear fluid and porous region stress jump boundary condition for tangential stresses is used. The drag and torque are found by deriving the corresponding Faxens laws. It is found that drag and torque not only change with the varying permeability, but also change for different values of stress jump coefficient. Critical permeability is found for which drag and torque change their behavior. As a limiting case the corresponding Faxens laws for the rigid spherical shell with internal singularities has been obtained.Received: December 17, 2002; revised: February 3, 2004     

平面边界前Stokes流动基本的奇异性

利用双调和函数A和调和函数B，给出了三维Stokes流动速度场和压力场的描述．由此建立了计算区域边界为固定无滑移平面边界Stokes流动基本奇异性的一般定理．刚性平面前轴对称Stokes流动的Collins定理成为本定理的特例．给出的几个例证说明了方法的有效性．     

On the effective viscosity of a dilute emulsion of gas bubbles

The problem of the motion of a rigid spherical body in a homogeneous emulsion of gas bubbles is considered in the Stokes approximation, using the self-consistent field method. An expression is obtained for the correction factor in the Stokes formula for the drag of the body in the first approximation with respect to the volume concentration of the dispersed phase. An analytical relation between the correction factor and the ratio of the sizes of the bubbles and the body is found. It is shown that, in the limit when this ratio tends to zero, the correction factor obtained is identical to Taylor's result for the effective viscosity of an emulsion of gas bubbles. In the case of non-point bubbles, the coefficient on the volume concentration in the expression for the effective viscosity of the emulsion can be considerably different from Taylor's result. A similar conclusion was also obtained in the case of the problem of the motion of a spherical bubble of arbitrary size in an emulsion of gas bubbles.     

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.