Simultaneous estimation of fluid temperature and convective heat transfer coefficient by sequential function specification method

Abstract

In pressurized water reactor (PWR) with multiple loops, abnormal working conditions occur when coolant pumps do not work in some loops. In these closed-loop pipelines, thermal stratification is formed under the effect of natural convection cooling and this poses a threat to the safe operation of the reactor. In this paper, the sequential function specification method (SFSM) is implemented to simultaneously predict the spatially and temporally varying internal fluid temperature and convective heat transfer coefficient of two-dimensional pipe under thermal stratification. In the direct problem, the finite volume method (FVM) is adopted to solve the governing equations subjected to initial and boundary conditions. In the inverse problem, the least-square method is employed to obtain the heat flux of the inner wall, and then Newton's law of cooling and the natural-convection correlation are adopted to obtain the fluid temperature and convective heat transfer coefficient. Numerical experiments of natural convection cooling are carried out under different outer wall boundary conditions to demonstrate the effectiveness of the proposed inversion method. The results of temperature estimation are consistent with the results of natural cooling numerical experiment and the relative error is below 4%, whereas the convective heat transfer coefficient is slightly worse due to the difference in the extraction positions. The effects of the number of involved future time steps and the measurement noise on the accuracy of the inverse analysis are also investigated in detail. Our results show that the fluid temperature and convective heat transfer coefficient of natural cooling may be effectively estimated using the proposed inverse method.