A one-dimensional full-range two-phase model to efficiently compute bifurcation diagrams in sub-cooled boiling flows in vertical heated tube
Résumé
This paper presents a powerful numerical model to compute bifurcation diagrams in liquid-vapor two-phase fluid flows in vertical heated tube. This full range two-phase model is designed to deal with both single phase (purely liquid or purely vapor) and mixed liquid-vapor configurations that span all flow regimes (laminar and turbulent) in forced, mixed and natural convections. The originality of the proposed methodology is to faithfully integrate the implicit highly nonlinear system of governing equations along branches of steady-state solutions. This is performed by means of a continuation algorithm based on the Asymptotic Numerical Method supplemented with Automatic Differentiation. Then, linear stability analyses are performed at various points of interest, enabling to figure out stability limits within the parameter space in natural circulation configurations. Markedly, Hopf bifurcations that indicate limit-cycle occurrences are identified at low and medium void fractions, respectively, showing the added-value of the approach to track density-wave mechanisms and potential failure of standard application of Ledinegg stability criteria on such cases.
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