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

Abstract

To cite this version:Alexandre Chiapolino, Pierre Boivin, Richard Saurel. A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows. Computers and Fluids, Elsevier, 2017, 150, pp.31 -45. <10.1016/j.compfluid.2017 AbstractThe present paper aims at building a fast and accurate phase transition solver dedicated to unsteady multiphase flow computations. In a previous contribution (Chiapolino et al. 2017), such a solver was successfully developed to compute thermodynamic equilibrium between a liquid phase and its corresponding vapor phase. The present work extends the solver's range of application by considering a multicomponent gas phase instead of pure vapor, a necessary improvement in most practical applications. The solver proves easy to implement compared to common iterative procedures, and allows systematic CPU savings over 50%, at no cost in terms of accuracy. It is validated against solutions based on an accurate but expensive iterative solver.Its capability to deal with cavitating, evaporating and condensing two-phase flows is highlighted on severe test problems both 1D and 2D.

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

“…A shock tube is indeed considered with liquid water, vapor water and air. In the high pressure chamber, air is initially in major proportion, Y 3 → 1 with thermodynamic conditions p = 30 bars and T = 800 K. In the second chamber, water vapor is in major proportion Y 2 → 1 with p = 1 bar and T = 600 K. The mixture is initially at thermodynamic equilibrium according to the conditions detailed in [13]. The ideal gas reduction of the ENASG EOS is used with parameters for water given in Table 1 while the only coefficients needed for air are: C v,3 = 719 J/kg/K and γ 3 = 1.4.…”

“…When evaporation or condensation phenomena appear, instantaneous phase transition is considered through the stiff thermochemical relaxation solver of Chiapolino et al [12,13]. For the sake of simplicity, the Homogeneous Relaxation Model (HRM) [32] is considered and is reminiscent of the reactive (or multicomponent) Euler equations widely used in chemically reacting flows.…”

“…When the critical temperature is reached, liquid is no longer present and the ENASG EOS is not to be used. Following the strategy of Chiapolino et al [12,13], two expressions of the mixture temperature can be found according to the definitions of the mixture mass and mixture energy,…”

“…The thermodynamic equilibrium is reached through the instantaneous relaxation (ν → ∞) of Gibbs free energies g 1 = g 2 , where the indexes 1 and 2 denote respectively the liquid and vapor phases (see [12,13]). The other constituents of the flow (N = 3 → N) are considered as non-condensable gases.…”

“…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.…”