Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with non-solenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and breakup dynamics of droplets including pinching due to gravity.

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Multiscale Time-Splitting Strategy for Multiscale Multiphysics Processes of Two-Phase Flow in Fractured Media

Journal of Applied Mathematics ◽

10.1155/2011/861905 ◽

2011 ◽

Vol 2011 ◽

pp. 1-24 ◽

Cited By ~ 7

Author(s):

Jisheng Kou ◽

Shuyu Sun ◽

Bo Yu

Keyword(s):

Porous Media ◽

Two Phase Flow ◽

Phase Flow ◽

Step Size ◽

Time Step ◽

Two Phase ◽

Time Step Size ◽

Multi Scale ◽

Rapid Changes ◽

Time Splitting

The temporal discretization scheme is one important ingredient of efficient simulator for two-phase flow in the fractured porous media. The application of single-scale temporal scheme is restricted by the rapid changes of the pressure and saturation in the fractured system with capillarity. In this paper, we propose a multi-scale time splitting strategy to simulate multi-scale multi-physics processes of two-phase flow in fractured porous media. We use the multi-scale time schemes for both the pressure and saturation equations; that is, a large time-step size is employed for the matrix domain, along with a small time-step size being applied in the fractures. The total time interval is partitioned into four temporal levels: the first level is used for the pressure in the entire domain, the second level matching rapid changes of the pressure in the fractures, the third level treating the response gap between the pressure and the saturation, and the fourth level applied for the saturation in the fractures. This method can reduce the computational cost arisen from the implicit solution of the pressure equation. Numerical examples are provided to demonstrate the efficiency of the proposed method.

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Numerical Prediction of Two-Phase Flow in Tube Bundles with a CFD Porous Media Approach Based on Mixture Model and a Void Fraction Correlation

E3S Web of Conferences ◽

10.1051/e3sconf/202132101002 ◽

2021 ◽

Vol 321 ◽

pp. 01002

Author(s):

Claire Dubot ◽

Vincent Melot ◽

Claudine Béghein ◽

Cyrille Allery ◽

Clément Bonneau

Keyword(s):

Porous Media ◽

Mixture Model ◽

Void Fraction ◽

Two Phase Flow ◽

Numerical Prediction ◽

Phase Flow ◽

Two Phase ◽

Mixture Density ◽

Tube Bundles ◽

Phase Mixture

Being able to predict the void fraction is essential for a numerical prediction of the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture density and affects two-phase mixture velocity which enable to evaluate the pressure drop of heat exchanger, the mass transfer and heat transfer coefficients. In this study, the flow is modelled by coupling Ansys Fluent with an in-house code library where a CFD porous media approach is implemented. In this code, the two-phase flow has been modelled so far using the Eulerian model. However, this two-phase model requires interaction laws between phases which are not known and/or reliable for a flow within a tube bundle. The aim of this paper is to use the mixture model, for which it is easier to implement suitable correlations for tube bundles. By expressing the relative velocity, as a function of slip, the void fraction model of Feenstra et al. developed for upward cross-flow through horizontal tube bundles is introduced. With this method, physical phenomena that occur in tube bundles are taken into consideration in the mixture model. The developed approach is validated based on the experimental results obtained by Dowlati et al.

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