基于尖点突变模型的微波加热固体介质的热失控分析

Analysis of thermal runaway in microwave heating of solid medium based on cusp catastrophic model

为实现定量研究微波加热发生的热失控现象,提出一种基于突变理论尖点模型的微波加热过程的热失控分析方法。首先,通过微波加热的能量势函数推导出热失控发生的理论判据。在微波加热热失控尖点模型构建过程中,引入微波加热能量作为势函数,从而用尖点突变模型对热失控现象进行描述,进一步得到判断热失控的充要判据及临界温度表达式。其次,在采用有限元方法对微波加热陶瓷介质进行定量模拟过程中,将解析表达的热失控判据进行有限元数值计算及临界温度表达融合判断,从而实现微波加热过程热失控定量分析。最后对微波加热固体陶瓷的热失控过程进行数值模拟。研究结果表明:本研究构造的尖点突变模型能定量描述热失控现象;通过与有限元方法数值模拟微波加热陶瓷固体介质过程进行比较验证,可知提出的热失控尖点突变模型具有可行性和有效性。

To quantitatively study the thermal runaway phenomenon of microwave heating,an analysis method of thermal runaway of microwave heating based on the cusp model of catastrophe theory was proposed.Firstly,during the construction of the cusp model of thermal runaway in microwave heating,the theoretical criterion of the thermal runaway was derived from the energy potential function of microwave heating by introducing the energy of microwave heating as potential function,then the phenomenon of thermal runaway was described by the model of the cusp catastrophe.Further the necessary and sufficient criteria for judging the thermal runaway and the expression of critical temperature were obtained.Secondly,during the simulation of microwave heating ceramic was quantitatively adopted by the finite element method,the thermal runaway of the process of heated by microwave energy was quantitatively analyzed by means of fusion judgment both the finite element numerical calculation of the expressed analytical criterion of thermal runaway and the expressed function of the critical temperature.Finally,the thermal runaway of microwave heating solid ceramics was simulated by numerical computation.The results show that the modeling of the cusp catastrophe can quantitatively describe the phenomenon of the thermal runaway of microwave heating solid ceramics,moreover compared with the numerical simulation of the process of microwave heating solid ceramics by finite element method,the proposed cuspcatastrophe model of the thermal runaway is feasible and effective.