PSI - Issue 60

A. Kumar et al. / Procedia Structural Integrity 60 (2024) 541–552

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Akshay Kumar/ Structural Integrity Procedia 00 (2023) 000 – 000

Thermal Analysis Temperature of the pressure tube changes continuously with time because of the heat generation. Thus, transient thermal analysis is performed to find out the temperature distribution with circumferential direction with time. This temperature profile acts as input data for structural analysis. A 3D model of pressure tube is created in a multipurpose finite element package. The material properties required for thermal analysis conductivity, density, and specific heat are required for thermal analysis. The variation of conductivity and specific heat is shown in Fig. 5. The 20-noded solid 3D brick type element has been used in this work to model the geometry. A quarter-symmetry model of the pressure tube has been employed (Fig. 1b). The length of PT has three parts, the middle part is enclosed by CT and outer parts are open to atmosphere. A very fine mesh is generated at the interface of pressure tube which is open to atmosphere because the heat transfer coefficient for CT and atmospheric air is different. So the effect on the temperature distribution can be seen clearly. This will ensure one-to-one correspondence between the nodes of the model used for thermal and stress analysis for transfer of nodal temperatures.

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Conductivity (W/m.k) Specific Heat(J/Kg.K)

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Specific Heat(J/Kg.K)

Conductivity (W/m.k)

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Temperature (K)

Fig. 5 : Material Properties of Pressure Tube for Thermal Analysis

The only input to this problem is heat generation i.e. 21kW to a pressure tube of 1.5 m as given in the paper by Nandan et al 2012. The rectifiers are used to input the heat generation in the experiment model but the rectifiers are placed at closer position not at very end of the pressure tube, so the equivalent length for the heating is taken as 1.2 m. Heat generation rate is given as 15.63 MW/m 3 . Material used for Pressure tube is Zr2.5Nb in Indian PHWR. The density of the alloy is taken as 6440 kg/m 3 at all temperatures. Heat transfer coefficient which is calculated earlier is input data for the thermal analysis. Three type of heat transfer coefficient are calculated i.e. one is between PT and CT, Second is between PT and atmosphere, third one is between PT and argon gas. The temperature of the tube along the surface at different time steps is evaluated using this model. This transient temperature profile is used to perform the creep based structural analysis to ascertain the time for PT-CT contact due to ballooning. 2.3.2 Structural Analysis The thermal analysis is followed by creep analysis. The temperature distribution which is an outcome of the thermal analysis is input for the creep analysis. Finite element software used in this analysis is same as in thermal analysis. A 3D model of pressure tube is created for analysis and the same is shown in Fig. 1(b). In both thermal and structural analysis, a quarter of the pressure tube was modelled due to symmetric boundary and loading conditions of the PT. The material properties like Young’s modulus, P oison ’ s ratio and Norton ’s creep constants are required for structural analysis. Poisson ’ s ratio of the material of PT is taken as 0.35 at all temperatures. The variation of Young’s modulus with temperature is linear with a slope of -57.14 MPa and its value is 95 GPa at 300 K. Norton ’s creep strain rate equation is used to find the deformation behaviour of pressure tube. The stress exponent value is taken are 1.8. Other parameters are Stefan Boltzmann constant=5.67x10 -8 W m -2 K -4 and Q/R=29000 K. The element type chosen for meshing is 20