A two-dimensional inverse heat conduction estimate of the inner wall temperature fluctuations in a horizontal T-junction pipe with turbulent penetration

摘要

Turbulent penetration can occur when hot and cold fluids mix in a horizontal T-junction pipe at nuclear plants.Temperature fluctuations with large amplitude and high frequency caused by the unstable turbulent penetration can lead to time-varying wall thermal stress and even induce thermal fatigue on the inner wall.Numerous cases,however, exist where the inner wall temperatures are not available and only an outside wall temperature measurement is feasible.Therefore, it is one of the hot spots in nuclear science and engineering research to study how to accurately estimate temperature fluctuations on the inner wall from measurements of outside wall temperatures without damaging the whole structure of the pipe system.In this paper, both one-dimensional and two-dimensional numerical models were developed based on the strategy of inverse heat conduction problem (IHCP) to estimate the temperature distributions and fluctuations on the inner wall from the temperature measurements on the outer wall.The developed models can be used to calculate the inner wall temperature fluctuations without any a priori information about the fluid and wall inside the pipe, without simulating the complicated mixture of the fluids.Both one-dimensional and two-dimensional direct heat conduction problem (DHCP) models were structured based on the finite element method (FEM).The inverse problem model was developed based on the complex variable differential method (CVDM).During the analysis of two-dimensional IHCP, an effective and accurate DHCP numerical model was structured with the quadrilateral isoparametric element based on the FEM and the inverse problem was solved with the temperature measurements on the outer wall.Both one-dimensional IHCP and two-dimensional IHCP were solved with temperatures on the outer wall obtained from the DHCP results to estimate the temperatures on the inner wall.Furthermore, we compared the temperatures on the inner wall estimated by one-dimensioual IHCP with those estimated by two-dimensional IHCP in four cases: (1) when the maximum disturbance of temperature of fluid inside pipe was 3 °C;(2) when the maximum disturbance of temperature of fluid inside pipe was 30 °C;(3) when the maximum disturbance of temperature of fluid inside pipe was 160 °C;(4) when the temperature of fluid inside pipe was random from 50 °C to 210 °C.