【摘要】 本文首先采用解析反演技巧,求得了当一无穷平壁垂直于圆球的旋转轴时Stokes流的基本奇解,然后按照吴望一提出的方法把奇点沿旋转轴分布,分析了无穷平壁的存在对于长轴垂直该壁的任意形状长轴对称体旋转时Stokes流场的影响。文中以长球为例,对长细比1<a/b≤100和长球中心至板距离d≥1.001a的范围进行了广泛的计算(a是长球的半长轴长度)。本法收敛性能良好,所算出的长球上阻力矩在两种极限情形下(即 a/b→1或d→∞时)与已有精确解一致,达到很高的精度。更多还原

【Abstract】 In this paper the basic singular solution of the Stokes flow for the rotation of a sphere in the presence of an infinite plane wall perpendicular to the axis of rotation is first derived, using the technique of analytical inversion. This solution is then used to analyse the effect of the presence of the plane on the Stokes flow around a rotating axisymmetric body of arbitrary shape by distributing the singularities along the axis of rotation, as proposed by Wu Wangyi, Numerical results are presented for prolate spheroids with the ratio of the-major-to-minor-axes 1<a/b≤100 and with the distance of the spheroid center from the plane d≥1.00la (a is the semi-major axis). The computed torque exrted on the spheroid agree excellently with the exact solutions for the two limiting cases, i. e. a/b=l or d→∞. It is found that the convergence is good and the attained accuracy is high.更多还原