双圆诱导不可压缩势流的几个精确解

Lagally(1929)给出了两个静止圆在均匀来流中的扰动速度势精确解。本文通过使用 Apollonius 保角变换,将两圆外部区域变为圆环内部区域,并在变换平面上用 Fo-urier 级数方法求解 Laplace 方程,从而得出双圆扰动势流的另外三个精确解。它们分别对应于静止流体中两圆膨胀(收缩)、沿连心线相向(相背)运动和垂直连心线反向运动(错动)所诱导的速势场。

THREE EXACT SOLUTIONS OF INCOMPRESSIBLE POTENTIAL FLOW INDUCED BY TWO CIRCLES

Lagally (1929) has given the exact solution for the two dimensional incompressible potential flow indued by two fixed circles in a uniform stream. In this paper, three exact solutions are obtained for two dimensional incompressible potential flow induced by two circles moving or expanding in a still fluid in three cases: (i) expansion (or contraction) of themselves, (ii) approach to (or departure from) each other, (iii) their movements perpendicular to the connected-centre-line in opposite directions.