PSI - Issue 60

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

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1. Introduction Limited Core Damage Accidents (LCDAs) in Pressurized Heavy Water Reactors (PHWRs) are typically considered within the design basis, as preventive and mitigation measures are incorporated. LCDAs can involve a single-pressure tube event where system pressure and power remain high for an extended period. This event may get started by a reduction or blockage of flow. As flow decreases, voiding occurs in the pressure tube, hampering the heat transfer from the fuel bundles (Mukhopadhyay et al. 2002). Consequently, the pressure tube (PT), exposed to radiation from the fuel bundles, heats up and undergoes radial deformation under high pressure and temperature. The increase in PT diameter reduces the resistance in the heat transfer gap between the PT and the calandria tube (CT). In extreme cases, the PT may come into direct contact with the CT, enabling the direct transfer of core heat to the moderator. Thus, in this scenario the moderator inventory would serve as heat sink and would prevent fuel damage. Estimation of PT temperature when such scenario occurs and the time taken for this scenario to arrive is needed to make the safety related decisions. The modelling of this scenario involves determination of the heat transfer from the PT and its subsequent temperature profile. This temperature profile is responsible for the ballooning of the PT due the creep phenomenon. The temperature of the PT can reach a temperature of the order of 800 o C, which again depends upon the scenario of heat removal. The creep is modelled using the established creep correlation for the PT material. The time interval for PT-CT contact along with the temperature of the PT at this instant is the parameter of interest. Scaled experiments have been reported by Nandan et.al. 2012 to understand the phenomenon and validate the estimation models. The PT is heated and is maintained under internal pressure in their experiments. The time required for PT-CT contact and the temperature profile of the PT during the progression of the event is also reported. Similar experiments on asymmetrical heating of PT have been reported by Yadav et al. 2013 to find out the contact time and structural integrity sufficiency of PT under different pressure values and different heating rates. Shewfelt et.al. 1984 have provided the material parameters for the creep law of Zr2.5Nb pressure tube material. Majumdar et.al. 2004 have used this model to predict the creep deformation in the conte xt of the Indian PHWR’s and the study of the simultaneous ballooning and sagging behavior of a PT. A methodology presented by Singh et al. 2011 gives a model on coolant channel disassembly. This model provides criteria to decide when under severe accident condition coolant channels will rupture due to deterioration in material properties at high temperatures and increase in load due to creep sag of channels above it and hence get disassembled. The uncertainty modeling of this phenomenon addressing the variables involved has not been attempted. In this paper, the PT ballooning modeling is first established using suitable heat transfer and creep theory. The model is validated using the experimental data reported in the literature. Subsequently, the uncertainties associated with the variables of the model are quantified and the results are now evaluated by applying the probabilistic framework. A Monte Carlo simulation based estimation gives reasonably accurate results, however, due to the detailed finite element modeling involved to predict the creep behavior of PT, it becomes computationally very expensive. In this paper, the uncertainty propagation is achieved by employing the Wilk’s method and the 95/95 results are reported. Subsequently the application of Monte Carlo simulation method for uncertainty propagations is also demonstrated. 2. Methodology for Modelling PT ballooning In this paper the ballooning experimental study reported by Nandan et.al. 2012 has been modeled. They had done experiments by taking miniature model of Indian 220 MWe, PHWR for calculating the radial expansion and to find out the time for PT-CT contact at different axial and circumferential positions. In the experiment, a single channel, consisting of PT and CT, is submerged in a large pool of normal water, though the sink shall be heavy water in actual reactor