Modelling phase transition in metastable liquids: application to cavitating and flashing flows

Abstract

A hyperbolic two-phase flow model involving five partial differential equations is constructed for liquid–gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves in the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast at specific locations only, typically at evaporation fronts. Thus, metastable states are involved for locations far from these fronts. Computational results are compared to the experimental ones. Computed and measured front speeds are of the same order of magnitude and the same tendency of increasing front speed with initial temperature is reported. Moreover, the limit case of evaporation fronts propagating in highly metastable liquids with the Chapman–Jouguet speed is recovered as an expansion wave of the present model in the limit of stiff thermal and chemical relaxation.

Numerical simulation of unsteady cavitation in liquid hydrogen flows

“…These cases are similar to those proposed in (Saurel et al 2008) with hot water. It consists in a one meter long tube filled with a liquid and a weak volume fraction of vapour α =0.01 is added.…”

“…In order to investigate thermal effects in LH 2 cryogenic cavitating flows, one-dimensional cavitation tube problems are proposed. Such rarefaction tube problems involving cavitation are one of the most used case to study the behaviour of phase transition models and to test and develop numerical schemes (Saurel & Metayer 2001, Barberon & Helluy 2005, Saurel et al 2008, Zein et al 2010, Causon & Mingham 2013, Spina et al 2014, Pelanti & Shyue 2014. This paper is organized as follows.…”

On the effect of temperature and velocity relaxation in two-phase flow models

“…This model was also considered by Saurel et al [35], who included the effect of phase transitions. Zein et al [46] considered the Baer-Nunziato model under velocity equilibrium, including heat and mass transfer terms.…”

An exponential time-differencing method for monotonic relaxation systems

“…Such systems model many relevant physical problems, such as two-phase flows which are locally not in thermodynamic equilibrium [7,8,32,37]. The limiting process → 0 in systems in the form (55) was extensively analysed by Liu [24] and Chen et al [4], with a particular focus on the relationship between stability and wave propagation.…”