Université Paris-Sud

  Fluides, Automatique
  et Systèmes Thermiques

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   Accueil > Annuaire > C. Ruyer-Quil > resume-Demay-161215

Charles Demay (EDF)

This work is dedicated to the modelling of air/water flows in pipes. As a 1rst step, a new 1D model is proposed to deal with the stratified regime. The starting point is the 2D Isentropic Euler set of equations for phase k where the classical hydrostatic assumption is made for water (k = 1) while the gravitational ects are neglected for air (k = 2). The main difference with the models issued from the classical literature is that water as well as air are assumed compressible. In that framework, an averaging process across the layer depth results in a five-equation system where the hydrostatic constraint has been introduced in an original manner. Closure laws for interfacial terms and source terms are provided following an entropy inequality and the overall model is hyperbolic with non conservative terms. Therefore, the definition and uniqueness of jump conditions is studied carefully and acquired. Regarding the Riemann problem associated with the homogeneous problem, the nature of characteristic fields and the corresponding Riemann invariants are exhibited. Positivity is also obtained for heights and densities.