Simulation and preliminary validation of a three-phase flow model with energy

Abstract

This paper is devoted to the simulation of the three-phase flow model [20], in order to account for immiscible components. The whole model is first recalled, and the main properties of the closed set are given, with particular focus on the Riemann problem associated with the convective subset that contains non-conservative terms, and also on the relaxation process. The model is hyperbolic, far from resonance occurrence, and a physically relevant entropy inequality holds for smooth solutions of the whole system. Owing to the uniqueness of jump conditions, specific solutions of the one-dimensional Riemann problem can be built, and these are useful (and mandatory) for the verification procedure. The fractional step method proposed herein complies with the continuous entropy inequality, and implicit schemes that are considered to account for relaxation terms take their roots on the true relaxation process. Once verification tests have been achieved, focus is given on the simulation of the experimental setup [8,9], in order to simulate a cloud of droplets that is hit by an incoming gas shock-wave. Finally, the study of a three-phase flow setup involving thermal effects is presented, it is based on the KROTOS experiment [25] which focuses on vapour explosion simulation.

Relaxation Process in an Immiscible Three-Phase Flow Model

“…The overall scheme is quite similar to the one detailed in [1]. It is a Finite Volume scheme for unstructured meshes.…”

“…Some recent computations of immiscible three-phase flow models have highlighted some weaknesses of existing numerical schemes, for instance when representing vapor explosion [1], and thus have urged the building of robust implicit schemes. This has also motivated to investigate the behavior of solutions of rather complex sets of PDEs, such as those arising in [7], which are used in [1]. Moreover, it is widely admitted by the scientific community that the hyperbolic models at stake here contain inner relaxation processes that guarantee the return-to-equilibrium.…”

BGK source terms for out-of-equilibrium two-phase flow models

“…Nevertheless, source terms of the form ( 17)-( 19) have a known drawback when turning to numerical simulation. Building efficient and robust schemes for these source terms can be tricky, see for instance [12,18,17,29,28,3,4,24]. When considering two-fluid models, BGK-like source terms have been recently proposed in order to avoid such difficulties [22,24].…”

Simulations of liquid-vapor water flows with non-condensable gases on the basis of a two-fluid model

“…The latter is built by reducing the Baer-Nunziato model [28] to a five-equation model. Some applications require to compute a relative velocity between the liquid phase and the gas phase, for instance when dealing with the fragmentation of droplets for steam-explosion as in [41,42]. For homogeneous models, the relative velocity is not computed and it could only be reconstructed using correlations.…”

“…Despite many accurate schemes are available in the literature for two-fluid two-phase flows [43,44,45,46], there exists less possibilities when turning to a higher number of components [47]. Moreover, it has been shown in [41,42] that the numerical simulation of the relaxation source terms of multifluid models requires complex numerical schemes whereas some robust schemes are available for twofluid models [48,49,50,51,52]. Considering these points, we choose as a modeling basis a two-fluid model with pressure relaxation as proposed in [28].…”