当绝热指数很大时气体的一种非定常平面平行运动的渐近解

文献1]在气体的速度分量只与极角θ及时间t有关,而与极距r无关的条件下求解理想气体的非定常平面平行具势运动方程组(1.2)～(1.3).文献1]指出,在一般的情况下,不能得到解的显式表示式,只是对于二种特殊情况得到了显式解.本文研究了文献1]的同样问题.第一部分,对音速作了一些补充限制,从而得到了方程组的显式解.第二部分,假设气体的绝热指数γ>>1,求得了方程组的一级近似解.

The Asymptotic Solution of the Unsteady Planar Parallel Gas Flow for the Case that the Adiabatic Index Number Y is Big

In ref. 1], under the condition that the components of velocity are only the functions of time and polar angle, Dvornikov solved eqs. (1.1)~(1.3) of the ideal gas unsteady planar parallel potential flow. It was pointed out in ref. 1] that in general case, the evident solutions could not be obtained. Only for two especial cases, the evident solutions were obtained. In this paper, the author studies the same problem as that in ref. 1]. In the first section we obtain the evident solution of equations (1.1)~(1.3) under the condition that the sonic velocity is restricted by some complemental conditions. In the second section, we obtain the first-order approximate solutions of the fundamental equation for the case that r>>1