PSI - Issue 60

A. Kumar et al. / Procedia Structural Integrity 60 (2024) 541–552 Akshay Kumar/ StructuralIntegrity Procedia 00 (2023) 000 – 000

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The heat gets removed from the PT in three ways:  From PT to Moderator

The heat is being produced in PT. The moderator is at a temperature of 52 o C. The electrical resistance analogy for the heat transfer is given in Fig. 2. This analogy is used to calculate the overall heat transfer through this route.  From PT assembly to Atmospheric air There is heat loss from the ends of the PT to the surrounding air.  From PT to argon gas. The PT is filled with argon gas. This gas initially is at room temperature. The same heat from the PT goes to this enclosed space. Heat transfer coefficient needs to be determined to simulate this experiment in FE. The heat transfer coefficient is different for all three cases. The heat transfer coefficient obtained from the scenarios described were used to estimate the temperature profile of the pressure tube. The heat input to the PT is more than what is dissipated due to different modes. This results in increase of temperature of the PT. The increased temperature results in initiation of diametrical creep in the PT. This diametrical creep under internal pressure leads to the ballooning of the PT. The transient temperature of the PT is estimated using thermal finite element model. Results of this model is coupled to a structural finite element model which estimates the diametrical creep growth as a function of time. Heat Transfer between PT and moderator Resistance due to radiation, R1 Heat transfer due to radiation between PT and CT is given by Eq. 1. = 1 ( ℎ 4 − 4 ) (1) is heat transfer due to radiation between CT and PT, is emissivity of PT, is Stefan Boltzmann Constant, ℎ is temperature of PT, is temperature of CT, 1 is surface area of PT enclosed by CT. R1 is resistance due to radiation, R2 is resistance due to air conductivity, R3 is resistance due to CT conductivity, R4 is resistance due to convection between CT and moderator. The thermal resistance of the pressure tube is explicitly modelled in the finite element model and hence, it is not required to be included here.

Fig. 2: Electrical resistance analogy for heat transfer from PT to moderator

T he heat flow and resistance relations as used in this analysis are given below. = ( ℎ − ) 1 1 ( ℎ + )( ℎ 2 + 2 ) ⁄ Thus, the resistance 1 due to radiation heat transfer is given by Eq. 3. 1 = 1 1 ( ℎ + )( ℎ 2 + 2 ) Resistance due to conduction R2

(2)

(3)