CIFRE-Study of bifurcations in the 2-fluid system of equations of a thermohydraulic calculation code F/H

This thesis proposal aims to address the problem of foliage clogging in the spacer plates of steam generators (GV). Clogging of the secondary fluid passage surface of boiler type SGs can cause the appearance of unstable behavior presenting potentially divergent oscillations characteristic of Hopf bifurcations.

The objective of the thesis is therefore to better understand the apparition of those instabilities, through the crossing of bifurcation and transition phenomena between stable solution under perturbation, by taking advantage of numerical method used in the literature to analyze stationary regime of ODE.

Main tasks:

• The first year will begin with a bibliographic study of contact modeling techniques and thermohydraulic system. The application framework will initially be oriented towards the reconstruction of the toy model from the literature known for featuring density wave oscillation. Existing numerical method in the literature (HBM, stability and bifurcation analysis, continuation method) are then going to be implemented and verified on the toy model. The development of continuation method for bifurcation will carry on until the continuation of the limit between the sub-critical and super-critical nature of the Hopf bifurcation who plays an important role in the apparition of transition phenomena.
• The second year will consist in further bibliographic study of numerical method allowing to quantify uncertainty of stationary regime and bifurcation under perturbation. Numerical methods will be developed for quantifying the influence of uncertainty on the stationary regimes and then on the apparition of the bifurcations.
• Finally, the third year will be devoted, depending on the progress and obstacles encountered, to the implementation of new approaches to quantify the probability of transition between the stable equilibrium and stable limit cycle presents in case of sub-critical Hopf bifurcation.

Holder of a master’s degree in mathematics, you are specialized in functional analysis, PDEs, numerical analysis, and mathematical physics.

You are interested in fluid mechanics and in the numerical resolution of related equations.

You are dynamic, autonomous and enjoy working in a team.

With a good relationship, you are rigorous, attentive and proactive.

Specialization: TAH - Safety, process and systems design - Reactor operation & functional design

Min. level of education required Master

Place: Auvergne-Rhône-Alpes, Rhône (69), Lyon

Employment level: Cadre

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