蠕动流中圆球阻力系数的入口效应

The Inlet Effect on the Drag Factor of a Sphere in a Tube

1.
Department of Mechanics, Peking University, Beijing;
2.
Department of Civil Engineering and Engineering Mechanics, Bioengineering Institute, Columbia University, New York, U. S. A

摘要: 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.

Abstract: The creeping motion oround a sphere situated axisymmetricnlly near the entrance of a semi-infinite circular cylindrical tube is analyzed using infinite series solutions for the velocity components, pressure and the stream function. Truncating the infinite series, the corresponding coefficients in the series are determined by a collocation technique. The drag factor and the stress distribution on the surface of the sphere are calculated for the sphere in motion in quiescent fluid and for the flow with uniform velocity at the entrance past a rigidly held sphere. The results indicate that a sphere near the entrance which has a uniform entrance velocity profile will suffer larger drag than that in an infinite tube. The convergence of the collocation technique is tested by numerical calculation. It is shown that the technique has good convergence properties.

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