具有化学反应的有限长圆柱热传导问题的求解

HEAT CONDUCTION PROBLEMS OF A FINITE CYLINDER WITH CHEMICAL REACTIONS INVOL VED—SOLUTION WITH NUMERICAL METHODS

编制了一个有限差分计算程序——4 TEO,用于求解具有内部化学反应项,且热物理参数随温度而交的有限长圆柱热传导问题。对基本的热传导方程用P-R交替方向法建立差分格式,所得非线性方程组,用牛顿迭代法求解,并考虑并行反应、链式反应、独立型反应、自催化反应等化学反应类型和反应产物对热传导的影响。通过对几个典型算例进行试算,程序的精度和可靠性令人满意。该程序可给出某一时刻所计算系统的温度,反应物消耗的空间分布图,以及感兴趣的时间范围内的系统完整的温度和反应物消耗的时空分布。可用于计算和预测含能系统是否发生热爆炸和热爆炸发生的位置等问题,对设计新型耐热型含能系统有一定参考价值。

A finite differential code has been compiled for computing two dimensional heat conduction problems of a finite cylinder whose thermophysical properties vary with its temperature and in which there are chemical reactions involved. The differential form for general heat conduction equation has been established with the P-R Alternative Direction Method, from which the non-linear equation group was solved with the Newton Iteration Method. The effect of competitive chain, independent, self-catalytic chemical reactions, as well as reaction products on thermal conduction has been considered. The code demonstrated a satisfactory precision and reliability when tested with two examples. The results computed by this code for problems not satisfied with analytical approximation correspond with the results from the theoritical analysis. It can give space-temperature, reaction consumptiontemperature profile of the system at any time. It can be used to foresee whether or not an energetic system with a finite cylinderical shape would lead to thermal explosion and to calculate the time and position of the explosion.