Efficient Inverse Analysis for Solving a Coupled Conduction,Convection and Radiation Problem Involving Non⁃gray Participating Media

求解非灰介质参与的导热⁃对流⁃辐射耦合传热问题的快速逆分析

The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.

吸收、发射和非灰体参与的加热炉介质中的非灰辐射特性的存在,使得求解辐射传热问题变得复杂,并进一步增加了导热⁃对流⁃辐射耦合传热问题的求解难度,导致效率低下,且无法满足实时控制需求。为了克服这些困难,本文提出通过求解反问题预测非灰介质的等效灰体辐射特性。然而,采用最小二乘法所需的迭代次数很多,导致反演效率很低,因此亟需一种高效快速的方法。本文采用列文伯格⁃马夸尔特(Levenberg⁃Marquardt)算法求解耦合传热反问题,预测了等效灰体辐射特性,旨在解决采用最小二乘法时的反演效率低的问题。为提升列文伯格⁃马夸尔特算法的性能,本文对阻尼因子的确定方法进行了改进,并且对该算法的准确性、收敛稳定性、效率和鲁棒性进行了详细研究。最后,对两种方法获得的结果进行了比较。