无限长圆管中任意轴对称体绕中心轴旋转的小Re数问题

本文以Sampson旋转子在圆管中反演得到的无穷级数作为基本奇点,对分布函数采用离散奇点线分布法和分段二次抛物分布法,解决了任意轴对称体在无限长圆管中绕中心轴旋转的Stokes流动问題。通过对长球的数值计算,比较了两种方法,结果表明分段二次抛物分布法各方面都优于离散法。此外,本文还研究球串在无穷长圆管中绕中心轴旋转的小Re数问题,第一次给出了每个球所受的阻力矩系数。

A LOW-REYNOLDS-NUMBER PROBLEM OF AN ARBITRARY AXISYMMETRIC BODY ROTATED IN AN LNFINITE LONG TUBE

In this paper, an axisymmetric Stokes flow induced by the rotation of an arbitrary axisymmric boby in an infinite long tube is studied. An infinite series of Sampson rotlets is taken as the fundamental singularities. For the strength of the continuous distribntion ofsing-ularities along the axis of symmetry both a discrete distribution and a piecewise parabolic distrobution are used. The above analgtical treatment greatly reduce the amount of numerical computation of the stokes flow, while giving very accurate numerical results. Analysis of the numerical results indicates that the parabolic distribution method has advantage over the discrete one in every aspect. Besides, the creeping motion of finite clusters of rotating spheres in the tube is also treated eggiciently and the torque coefficients of each sphere are given.