Velocity and energy relaxation in two-phase flows

TL;DR

This paper analytically investigates velocity and energy relaxation in two-phase flows, simplifying the complex six-equation model by adding relaxation terms, and discusses invariant regions, incompressible limits, and numerical results.

Contribution

It introduces a simplified two-phase flow model with relaxation terms, making simulations more computationally feasible while maintaining key physical properties.

Findings

Simplified model converges to common velocities and energies as relaxation time approaches zero.

Invariant regions are preserved in the simplified model.

Numerical results demonstrate the model's effectiveness in simulating violent aerated flows.

Abstract

In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This model assumes each phase to possess its own velocity and energy variables. Despite recent advances, the six equations model remains computationally expensive for many practical applications. Moreover, its advection operator may be non-hyperbolic which poses additional theoretical difficulties to construct robust numerical schemes |Ghidaglia et al, 2001]. In order to simplify this system, we complete momentum and energy conservation equations by relaxation terms. When relaxation characteristic time tends to zero, velocities and energies are constrained to tend to common values for both phases. As a result, we obtain a simple two-phase model which was recently proposed for simulation of violent aerated flows [Dias et al, 2010]. The preservation of invariant regions and incompressible limit of the simplified model are also discussed. Finally, several numerical results are presented.