From dense to dilute two-phase flows

Ashwin Chinnayya (1) , Richard Saurel (2) , Quentin Carmouze (2)

1 PPrime [Poitiers] - Institut Pprime [UPR 3346]
2 RS2N - Recherche Scientifique et Simulation Numérique [Roquevaire]

Many two-phase flow situations, from engineering science to astrophysics, deal with transition from dense (high concentration of the condensed phase) to dilute concentration (low concentration of the same phase), covering the entire range of volume fractions. Some models are now well accepted at the two bounds, but none is able to cover accurately the entire range, in particular regarding waves propagation. In the present work an alternative to the Baer and Nunziato (1986) (BN for short) model is built. The corresponding model is hyperbolic and thermodynamically consistent. Contrarily to the BN model that involves 6 wave speeds, the new formulation involves 4 waves only, in agreement with the Marble (1963) model based on pressureless Euler equations for the dispersed phase, this model being well accepted for low particle volume concentrations. In the new model, the presence of pressure in the momentum equation of the particles and consideration of volume fractions in the two phases render the model valid for large particle concentrations. A symmetric version of the new model is derived as well for liquids containing gas bubbles. This model version involves 4 wave speeds as well, but with different wave's speeds. Last, the two sub models with 4 waves are combined in a unique formulation, valid for all volume fractions. It involves the same 6 wave's speeds as the BN model, but at a given point of space 4 waves only emerge, depending on the local volume fractions. Basically, when the gas phase is in dominant concentration, it carries sound waves and reversely for the liquid phase. The new model is tested numerically on various test problems ranging from separated phases in a shock tube to shock – particle cloud interaction. Its predictions are compared to BN and Marble models.

Mots clés: hyperbolic; two-phase; compressible; shocks

Domaines: Mécanique des fluides [physics.class-ph]; Milieux fluides et réactifs; Equations aux dérivées partielles [math.AP]; Thermique [physics.class-ph]

Ashwin Chinnayya, Richard Saurel, Quentin Carmouze. From dense to dilute two-phase flows. 2016. ⟨hal-01347785⟩