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Article

Mathematical Modeling and Associated Numerical Simulation of Fusion/Solidification Front Evolution in the Context of Severe Accident of Nuclear Power Engineering

1
Institut de Mathématiques de Bordeaux, University of Bordeaux, CNRS, UMR 5251, 33400 Talence, France
2
CEA-DES-IRESNE-DTN, CEA Cadarache, 13108 Saint Paul-lez-Durance, France
3
CEA-DES, Université Paris—Saclay, 91191 Gif-sur-Yvette, France
*
Author to whom correspondence should be addressed.
Academic Editor: Arturo Hidalgo
Mathematics 2022, 10(1), 116; https://doi.org/10.3390/math10010116
Received: 28 November 2021 / Revised: 22 December 2021 / Accepted: 24 December 2021 / Published: 31 December 2021
(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)
Considering transient processes where liquid/solid phase change occurs, this paper focuses on the associated modeling and numerical treatment in the frame of “Computational Fluid Dynamics” simulations. While being of importance in many industrial applications involving solidification and melting of mixed materials, including power and manufacturing engineering, the first application of this work pertains to the analysis of severe accidents in a nuclear reactor. Indeed, in this context, the molten core materials (a.k.a. corium) can form a high-temperature multiphase liquid pool at the boundary of which fusion and solidification phenomena are of prime importance. In this context, even if materials at play are treated as pure components, it is mandatory to distinguish two different phase change temperatures with a solid fusion temperature and a liquid solidification temperature. Accordingly, in the frame of a sharp interface representation, the paper introduces non-classical heterogeneous conditions at the liquid/solid boundary in such a way that both moving interface (through Stefan conditions associated with fusion or solidification) and static interface (imposing heat flux continuity) are supported at the same time on different spatial locations along this boundary. Within a monolithic resolution of Navier–Stokes and heat conduction equations, this interface is explicitly tracked with combined Front-Tracking and VOF methods. In order to ensure zero velocity in the solid phase, an Immersed Boundary Method and a direct forcing penalization are also introduced. The main relevant features of this combination of numerical methods are discussed along with their implementation in the TrioCFD code taking advantage of the pre-existing code capabilities. Numerical simulations including both verification tests and a case of interest for our industrial application are reported and demonstrate the applicability of the proposed triptych model+methods+code to treat such problems. The numerical tools and the simulation code developed in this work could be used not only in the several accident context but also to simulate melting, solidification and fusion processes occurring in aerodynamics, hypersonic reentry vehicles and laser applications to cite but a few. View Full-Text
Keywords: simulation of front; fusion; solidification; corium crust; 2D heat conduction; phase changes; Navier–Stokes; modeling simulation of front; fusion; solidification; corium crust; 2D heat conduction; phase changes; Navier–Stokes; modeling
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MDPI and ACS Style

Drouillet, A.; Bois, G.; Le Tellier, R.; Loubère, R.; Peybernes, M. Mathematical Modeling and Associated Numerical Simulation of Fusion/Solidification Front Evolution in the Context of Severe Accident of Nuclear Power Engineering. Mathematics 2022, 10, 116. https://doi.org/10.3390/math10010116

AMA Style

Drouillet A, Bois G, Le Tellier R, Loubère R, Peybernes M. Mathematical Modeling and Associated Numerical Simulation of Fusion/Solidification Front Evolution in the Context of Severe Accident of Nuclear Power Engineering. Mathematics. 2022; 10(1):116. https://doi.org/10.3390/math10010116

Chicago/Turabian Style

Drouillet, Adrien, Guillaume Bois, Romain Le Tellier, Raphaël Loubère, and Mathieu Peybernes. 2022. "Mathematical Modeling and Associated Numerical Simulation of Fusion/Solidification Front Evolution in the Context of Severe Accident of Nuclear Power Engineering" Mathematics 10, no. 1: 116. https://doi.org/10.3390/math10010116

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