反应气体流动对热爆炸条件的影响
The influence of the flow of the reacting gas on the conditions for a Thermal Explosion
AI总结：
本研究修改经典热爆炸问题，考虑反应气体在长圆柱管道中流动，通过数学分析和数值实验确定临界半径与临界距离，将解的存在性丧失解释为热爆炸，并揭示标度律。
摘要：
经典的热爆炸问题被修改，使得化学活性气体不是静止的，而是在长圆柱管道中流动。在某一截面之前，管道的导热壁保持在低温，因此反应速率很小且没有热量释放；在该截面处，环境温度升高，放热反应开始。问题是会建立缓慢反应状态还是发生热爆炸。给出了问题的数学表述。结果表明，当管道半径大于临界值时，新问题的解仅沿轴线存在到一定距离。临界半径由具有均匀轴向温度的问题中的条件决定。解的存在性丧失被解释为热爆炸；临界距离是安全反应器的长度。考虑了层流和充分发展的湍流两种流动状态。在计算实验中，解的存在性丧失表现为数值过程的发散；数值计算揭示了临界距离的具有简单幂次的渐近标度律。
英文摘要：
The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor's length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.
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