Dynamic relaxation processes in compressible multiphase flows. Application to evaporation phenomena

Abstract

Phase changes and heat exchanges are examples of physical processes appearing in many industrial applications involving multiphase compressible flows. Their knowledge is of fundamental importance to reproduce correctly the resulting effects in simulation tools. A fine description of the flow topology is thus required to obtain the interfacial area between phases. This one is responsible for the dynamics and the kinetics of heat and mass transfer when evaporation or condensation occurs. Unfortunately this exchange area cannot be obtained easily and accurately especially when complex mixtures (drops, bubbles, pockets of very different sizes) appear inside the transient medium. The natural way to solve this specific trouble consists in using a thin grid to capture interfaces at all spatial scales. But this possibility needs huge computing resources and can be hardly used when considering physical systems of large dimensions. A realistic method is to consider instantaneous exchanges between phases by the way of additional source terms in a full non-equilibrium multiphase flow model [2,15,17]. In this one each phase obeys its own equation of state and has its own set of equations and variables (pressure, temperature, velocity, energy, entropy,...). When enabling the relaxation source terms the multiphase mixture instantaneously tends towards a mechanical or thermodynamic equilibrium state at each point of the flow. This strategy allows to mark the boundaries of the real flow behavior and to magnify the dominant physical effects (heat exchanges, evaporation, drag,...) inside the medium. A description of the various relaxation processes is given in the paper.

A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows

“…(2013) [9]. Unlike this last algorithm, the notion of vapor molar fraction and partial pressures in the gas phase must be taken into account, bringing additional difficulties.…”

“…However this strategy would require tremendous computing resources and can hardly be envisaged when considering large-sized problems. Nevertheless a realistic method in specific limit situations is to consider instantaneous thermodynamical relaxation between phases by the use of additional source terms [9]. In the present work, ν is considered very large, so that relaxation to thermodynamic equilibrium is immediate.…”

“…The idea of our method is to gradually reach the exact solution (typically in 1 to 3 time steps of the flow solver), by providing a fair approximation for Y * 1 , while iterative approaches, such as the one promoted in Le Métayer et al (2013) [9], directly computes the exact solution. In that direction, we will follow a similar strategy than in our previous work [1], extended to the fact that the relation between pressure and saturation pressure is modified compared to (3.3), and now depends on the result (since the partial pressure is a function of Y 2 ).…”

“…When dealing with more sophisticated formulations, as for example the 7-equation model, extra ingredients have to be presented, such as velocity, pressure and temperature relaxation solvers, as done for example in [9,10]. Here, there is a single step Here Y l,g , α l,g , ρ l,g denote respectively the mass fraction, the volume fraction and the material density of the liquid (l subscript) and gas (g subscript) phases.…”

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

“…When phase transition is addressed, it occurs through mass transfer terms that can be considered finite rate (Saurel et al [8], Furfaro and Saurel [10]) or assumed stiff when the physical knowledge of the phase change kinetics is not enough documented (Le Métayer et al [11], Chiapolino et al [12,13]) or unnecessary. -The second limitation is related to the lack of convexity of cubic EOSs, having dramatic consequences on sound propagation during phase transition.…”