Velocity and energy relaxation in two-phase 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.

Keywords

Bibliographic record

BibTeX Citation

@article{Meyapin2010velocityenergy,
  author = {Meyapin, Y. and Dutykh, D. and Gisclon, M.},
  title = {Velocity and energy relaxation in two-phase flows},
  journal = {Studies in Applied Mathematics},
  year = {2010},
  volume = {125},
  number = {2},
  pages = {179--212},
  doi = {10.1111/j.1467-9590.2010.00484.x},
  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.},
  keywords = {compressible flow, Numerical simulation, Velocity relaxation, Momentum conservation, single velocity model, velocity relaxation, invariant region, Simplified two-phase model, Energy conservation, two-phase flow, Six-equation model, Two-phase flows, Energy relaxation, low Mach limit, energy relaxation, Chapman-Enskog expansion}
}