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Simulation of water-vapor two-phase flows with non-condensable gas.

Lucie Quibel 1, 2, 3
3 TONUS - TOkamaks and NUmerical Simulations
IRMA - Institut de Recherche Mathématique Avancée, Inria Nancy - Grand Est
Abstract : This PhD work deals with the modeling and simulation of multiphase flows that could appear during accidental scenarios which may hypothetically affect a pressurized water reactor. These flows are mainly made up of water, whose gaseous phase is composed of a miscible mixture of non-condensable gases and steam, and which may include in the case of a steam explosion an immiscible third phase formed by molten corium. The considered models aimed to simulate very abrupt phase transitions, during which liquid water and steam are likely to persist in an observable manner outside the conditions of thermodynamic equilibrium. Different aspects of the modeling process are addressed in this work. First, thermodynamic closures are studied by defining realistic and admissible phasic equations of state. A homogeneous two-phase model without non-condensable gases was first equipped with a look-up table based on the IAPWS-IF97 formulation. Since the look-up table was built to fulfill the Gibbs relation, the verification of the model via mesh convergence studies could be achieved. This work also pointed out that the look-up table required a very robust numerical convection scheme, such as the relaxation scheme proposed by C. Chalons and J.-F. Coulombel. A bibliographical review of classical equations of state has therefore been carried out and has shown that semi-analytical equations of state such as the Noble-Able Stiffened Gas appear to be a good compromise in terms of accuracy and efficiency. First results on validation cases have been obtained using a homogeneous model taking into account non-condensable gases, by choosing for liquid water an extension of the NASG EOS, with temperature-dependent heat capacity Cp. Taking into account out-of-equilibrium effects, by correctly defining a time scale describing the return towards thermodynamic equilibrium, seems to be determining to get realistic results. Another part of this work concerns the proposal of a new multifluid three-phase-flow model, designed to model phenomena such as steam explosion. The model has been built step by step in order to guarantee the existence of an entropy inequality. The non-conservative terms have been carefully defined, in order to ensure the uniqueness of the jump conditions. The final model is hyperbolic outside the resonance conditions. Finally, some classical boundary conditions for the monophasic Euler system have been verified. An out-going rarefaction wave leaving the computational domain before the end of the simulation does not raise any issue with the classical conditions used in industrial codes; on the other hand, an out-going shock wave can lead to a numerical inconsistency, depending on the numerical scheme used and the boundary conditions adopted.
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Contributor : Lucie Quibel <>
Submitted on : Thursday, October 1, 2020 - 4:23:48 PM
Last modification on : Wednesday, February 17, 2021 - 3:28:54 AM


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  • HAL Id : tel-02941486, version 3



Lucie Quibel. Simulation of water-vapor two-phase flows with non-condensable gas.. Mathematics [math]. Université de Strasbourg, 2020. English. ⟨tel-02941486v3⟩



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