有烧蚀的发汗冷却控制系统动态性能的分析和数值模拟

The Analysis and Numerical Simulation of Dynamical Functions of the Transpiration Cooling Control System with Surface Ablation

一维有烧蚀的发汗冷却系统是一个可变域上的分布参数控制系统,本文将其转化为固定域上的定解问题。采用二阶精度无条件稳定的Crank—Nicholson隐式差分格式进行动态性能的数值模拟,给出热层温升分布、烧蚀量和烧蚀速度三者随时间的变化规律,以及烧蚀开始时间、结束时间和最大烧蚀速度三者与发汗量的关系等。这一数值模拟方法成功地克服了可变域给数值计算带来的困难。本文还通过理论分析,给出热层表面是否出现烧蚀的临界发汗量、表面烧蚀的终止时间和最大烧蚀速度。

The one-dimensional transpiration cooling system with surface ablation is a control system of variable-domain distributed parameter. In this paper, the numerical simulation of the dynamic functions has been carried out by transforming this problem to a fixed-domain initial-boundary value problem. And the following results are given:(l) How do the distribution of temperature in the thermal shield, the ablation amount and velocity vary with the time; (2) How are the maximum ablating velocity, the time of the ablation beginning and ending related to the transpiration quantity. This method succeeds in overcoming the difficulty brought by variable domain. On the other hand, the critical transpiration quantity of the surface to ablate or not to ,the maximum ablating velocity and the time of the ablation ending are obtained theoretically.