求解对流换热反问题的低阶模型

Reduced Order Model Based Algorithm for Inverse Convection Heat Transfer Problem

在低阶模型的基础上开发了一种求解对流换热反问题的算法,并采用最佳正交分解方法分别建立了直接问题、敏感度问题和伴随问题的低阶模型,反问题求解采用了共轭梯度法.算例为一圆管内流动充分发展、换热初始段时,反求圆管壁面外未知热流密度的反问题.分别研究了测量位置、测量误差对算法性能的影响,结果表明通过将测量位置移向未知热流可以显著地提高解的精度和算法的稳定性,同时共轭梯度法可以显著地减小测量误差对结果的影响.所开发的算法可以在非常短的时间内得到较准确的解,基于CFD模型的反问题算法迭代一步需要6.5 s,而文中算法迭代一步仅需要0.078 s,与基于CFD模型的反问题算法相比,速度提高了80倍.

In this study, a reduced order model based algorithm was developed for inverse convection heat transfer. The reduced order models were established for the direct problem, the sensitivity problem and the adjoint problem respectively with the proper orthogonal technique（POD）. The performance of the present algorithm was examined by an inverse forced convection problem to determine the unknown space-dependent heat flux at the outer boundary of a circular pipe. The inverse problem was resolved in a function optimization way by the conjugate gradient method. The results show that the present POD based inverse algorithm can significantly reduce the influence of measurement error on the computational results and obtain accurate solution in very short time. The computational speed of the present inverse algorithm is 80 times higher than that of the CFD based inverse algorithm.