Fast non-intrusive estimation of liquid-phase interface and boundary heat flux in participating media by the Kalman filtering methods

Abstract

The non-intrusive inverse heat transfer technique based on the Kalman filtering (KF) method is proposed for on-line retrieving the time-dependent boundary heat flux, internal temperature distribution, and liquid-phase interface of the participating medium simultaneously. To obtain the measured temperature signals, the nonlinear conduction-radiation heat transfer with phase change in the participating medium is solved by the enthalpy method combined with discrete ordinate method. Three different types of retrieval algorithms have been employed: the original Kalman filter (KF), the extended KF (EKF), and the unscented KF (UKF). The ideal participating media, which is assumed to be anisotropic scattering, and opaque and diffuse gray boundary, is employed to verify the reliability and validity of the proposed algorithm. Comparing with the EKF and UKF, the original KF cannot be applied to solve the nonlinear problems. Comparing with the UKF, the EKF can only be employed to solve the weak nonlinear problem. For the inverse coupled conduction-radiation problem with phase change, the UKF is proved to be more robust to estimate the time-dependent heat flux, internal temperature distribution, and liquid-phase interface simultaneously in real time.