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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 ablative sweat cooling system is a distributed parameter control system over a variable domain, which in this paper transforms it into a fixed solution problem over a fixed domain. The Crank-Nicholson implicit difference scheme with second-order accuracy and unconditionally stability is used to simulate the dynamic performance. The variation law of temperature rise distribution, ablation volume and ablation speed over time are given, and the start time of ablation, The end time and the maximum ablation speed of the three and the relationship between the amount of sweating. This numerical simulation method succeeds in overcoming the difficulty of numerical computation caused by variable domains. This paper also through the theoretical analysis, gives the surface of the hot layer ablation of the critical amount of sweat, the surface ablation of the termination time and the maximum ablation rate.