理想气体一维不定常流自模拟运动的基本微分方程

将一维不定常流自模拟函数推广到一般形式，结合量纲理论和流体力学基本运动方程，导出总能量为常数情况下的理想气体一维不定常流自模拟运动基本微分方程组.该理论模型表明，由流体速率u和自模拟面速率r·〖DD)]组成一个无量纲特性参数L，用L作自变量时理想气体一维不定常流自模拟运动的规律具有常微分方程的最简数学形式.该模型克服了点爆炸Taylor自模拟温度函数原点附近趋于无穷大的问题，具有重要意义. 关键词： 理想气体 自模拟运动 Taylor模型

Basic differential equation of self-similar motion of one-dimensional nonsteady flow of ideal gas

Self-similar function of one-dimensional nonsteady flow is extended to a general form. With total energy kept constant, basic differential equation of self-similar motion of one-dimensional nonsteady flow of ideal gas is derived using dimension theory in combination with the basic motion equations of hydromechanics. When a non-dimensional natural parameter L, which is the ratio of velocity of fluid (u) and self-similar surface (r·), serves as the independent variable, the theoretical model reveals that self-similar law of non-dimensional nonsteady flow of ideal gas has the simplest mathematical form. The model overcomes the difficulty of divergence at the origin of self-similar function of Taylor and thus has significant importance.