轴对称流中音速线附近的特征线方程

 从Ｏｓｗａｔｉｔｓｃｈ的无粘、跨音速、轴对称无旋流的基本方程出发,在细长体条件下,通过新变量将物理面上的运动方程变成形式简单的速度面方程。利用音速线附近条件对速度面方程进行积分,可得解析解；由此可按Ｃｏｕｒａｎｔ理论推导出音速线附近的特征线方程,结果表明,特征线有两族,均为２／３次幂曲线,其数学形式与平面流相同。

CHARACTERISTIC EQUATION NEAR THE SONIC LINE OF AXISYMMETRIC FLOW

Under the assumption of slender body,starting from Oswatitschs non-viscous transonic axisymmetric irrotational basic equation,the motion equation of physical plane is transferred to hodograph equation in simpler form by new variables.Then,the latter is integrated by the conditions in the vicinity of the sonic line and the analytic solution can be acquired. And then,a characteristic equation in the vicinity of the sonic line is derived by Courant’s theo- ry,which is an analytic expression. It indicates that there are two families of characteristics and they are all curves of 2/ 3 power.