# Fast Calculation of Transient Thermal Stress in Surge Lines with Thermal Stratification Region
###### Abstract  
Nuclear power plants applying for license renewal are required to undertake a fatigue assessment of various components, which demands the fast calculation of transient thermal stress of the fatigue-sensitive components such as surge lines. In this study, the strategy of Green's function database construction for the thermal stratification region was investigated, and the thermal stress calculation was shown to be more accurate by dividing the flow cases and thermal zones. Furthermore, a method to determine the fluid temperature for the thermal zones of the thermal stratification region was studied. In addition to the temperature of the hot leg fluid and the outlet fluid from the pressurized, seven thermocouples installed on the outside wall in the thermal stratification region were used to determine the fluid temperature of thermal zones with stratification, and the calculation result of the fluid temperature was verified with the temperature Green's functions. surge line; thermal stratification; thermal stress; Green's function +
Footnote †: journal: Applied Sciences  
16 March 2021  
13 March 2021  
Subject: 3 April 2021  
**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. pressurizer. The thermal stratification phenomenon is obvious in surges line. When two fluids with different densities flow in the pipeline, a stratified flow phenomenon may occur. If the density difference is caused by the fluid temperature, thermal stratification may occur, which can cause huge bending stress. The causes of thermal fatigue in the surge line are thermal stratification and thermal shock oscillation. The temperature of the fluid from the pressurized is high, and the temperature of the fluid from the hot leg is low. Because of the difference in density of the cold and hot fluid, stratification occurs in the surge line when the surge flow is relatively low [7]. In May 1988, researchers discovered that the pressurized surge line of the power plant had shifted and deformed beyond design at the Troy Power Station of the Portland Power Company in the United States. After investigation and research, it was proved that this was caused by thermal stratification in the surge line. Then, the Nuclear Regulatory Commission issued Bulletin No.88-11, which decreed that all pressurized water reactor (PWR) nuclear plants owners should verify the integrity of the surge line of the pressurizer [8]. More than 12 cracks have been identified since 1979, as a result of thermal stratification, and cracks due to thermal stratification were found in French nuclear power plants as well. Hungary installed a large-scale program at its only nuclear power plant, the Paks Nuclear Power Plant. [PERSON] and [PERSON] conducted a finite element simulation analysis on the surge line, and the result showed that the phenomenon of thermal stratification existed symmetrically in the surge line [9], and the maximum temperature difference of the measuring points can reach 130-140 \({}^{\circ}\)C.  
In order to avoid the occurrence of thermal stratification, French experts optimized the surge line's structure. In CATTENOM Nuclear Power Plant Unit 1, the inclination angle of the surge line and the hot section joint of the hot leg was designed to be 45\({}^{\circ}\) to reduce the stratification of cold and hot fluids in the radial direction, caused by the density difference between hot and cold fluids [9]. For nuclear power plants that have already been built, fatigue monitoring of the surge line is required. As a key part of fatigue monitoring project, fast calculation of thermal stress has been studied for many years and there are many methods for doing this. For example, the BOSSES system in India uses the online finite element method, but this method requires a lot of computing resources [10]. At present, [PERSON]'s function method is the most widely used and generally recognized method.