基于求解双侧对流条件Stefan问题的高炉炉缸凝壳生成过程数学模型

A mathematical model for skull buildup process in blast furnace hearth based on solving a Stefan problem with bilateral convective boundary conditions

高炉炉缸凝壳的生成可视为双侧均为对流条件的Stefan问题.基于求解这类Stefan问题,结合理论分析和数值计算方法,建立了能够准确描述高炉炉缸内衬热面凝壳生成过程的数值传热模型,并推导了相应的准稳态模型.借助相应条件下的实验测量值对上述两种模型进行了校验.结果表明,相比于准稳态模型,数值传热模型针对双侧对流条件Stefan问题的计算精度更高.最后,为展示数值传热模型的应用性,以典型陶瓷杯结构炉缸为例,研究了陶瓷杯壁厚度对炉缸热面凝壳生成过程的影响.

Skull buildup process in the blast furnace hearth can be regarded as a Stefan problem with bilateral convection boundary conditions.Based on solving this type of Stefan problem,a numerical heat transfer(NHT)model accurately describing the skull buildup process was developed by integrating theoretical analyses with numerical calculation methods.Also,a corresponding quasi-steady state model was derived.The two mathematical models were verified by using the experimental data under specified conditions.The results indicated that,with respect to the Stefan problem with bilateral convective boundary conditions,the accuracy of the NHT model is higher than that of the quasi-steady state model.Finally,in order to demonstrate the practical applicability of the NHT model,influence of the ceramic cup sidewall thickness on skull buildup process in a ceramic cup synthetic hearth was investigated.