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Concept# Steady state

Summary

In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so:
: \frac{\partial p}{\partial t} = 0 \quad \text{for all present and future } t.
In discrete time, it means that the first difference of each property is zero and remains so:
:p_t-p_{t-1}=0 \quad \text{for all present and future } t.
The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering. If a system is in a steady state, then the recently observed behavior of the system will continue into the future. In stochastic systems, the probabilities that various states will be repeated will remain constant. See for example Linear difference equation#Conversion to homog

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2010The calculations performed for the design and operation of a Nuclear Power Plant (NPP) are a key factor for their safety analyses. The standard for the computational analysis of NPPs is the so called conventional approach, which relies on coarse mesh diffusion for the neutronic solver and 1D channels for the T/H solver. The recent evolution of computing clusters allows the use of a novel approach, with codes performing first-principle based multi-physics simulations with high-resolution of the calculated parameters. Due to their computational cost, these methods can only be used as an audit tool of the conventional approach. In recent years, the nuclear industry has moved towards the establishment of Best Estimate Plus Uncertainty safety limits. The novel approach is a step forward to that direction. At the same time, VVER technology is expanding, with new reactors being built worldwide. However, there is currently no high-resolution tool available for VVER steady state and cycle analysis. There is a clear need for more refined simulation tools capable of handling hexagonal geometries.The goal of this PhD is the development of a novel computational scheme based on the 3D sub-pin neutron transport code nTRACER-FAST (nTF), coupled to the sub-channel code COBRA-TF (CTF) for VVER full core steady state and cycle analysis. The coupling of a neutronic code with sub-pin resolution to a sub-channel T/H solver, as well as the use of CTF for full core VVER sub-channel analysis are one of the main novelties of this work, to the extent of the writer's knowledge. In this thesis, nTF is verified & validated for VVER 3D core standalone neutronic calculations against data published in international benchmarks. The internal sub-pin coupling of nTF to CTF for hexagonal geometries is fully developed on the course of this study. A double domain decomposition scheme that allows both codes to be executed in parallel is designed. The multi-physics core solver is verified for steady state simulations. nTF/CTF is also compared with nTF using a simplified 1D T/H solver, proving that to achieve accurate predictions, computational tools of different fidelity should not be mixed. Finally, nTF/CTF is developed for 3D full core cycle analysis. The coupled code system is validated with experimental data, achieving the target accuracy set for industrial use. The capability of the solver for sub-pin predictions throughout the depletion cycle is demonstrated.A conventional computational route for VVER analysis, built with CASMO5-VVER as a lattice code for the nodal neutronic solver PARCS, is also established. The use of PARCS with CASMO5-VVER is another novelty of the present work. CASMO5-VVER/PARCS is verified and validated for VVER standalone neutronic and multi-physics steady state simulations and cycle analysis. The modeling options that optimize the use of the code system and the generation of CASMO5-VVER cross-sections for PARCS are described. The comparison of the novel and conventional computational routes demonstrates the accuracy enhancement enabled by the high-resolution core solver, during steady state and depletion calculations. The work performed during this thesis also showed that the nTF/CTF computational requirements are manageable for VVER cycle analysis, when a state-of-the-art computing cluster is used. This illustrates that such high fidelity, high-resolution computational scheme can be used as an audit tool for the conventional route.

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2010