A hyperbolic phase-transition model coupled to tabulated EoS for two-phase flows in fast depressurizations

Liquid–vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations, where the mass transfer is modeled by a kinetic relation, have been investigated analytically in [M. Hantke, W. Dreyer and G. Warnecke, Exact solutions to the Riemann problem for compressible isothermal Euler equations for two-phase flows with and without phase transition, Quart. Appl. Math. 71(3) (2013) 509–540]. This work was restricted to liquid water and its vapor modeled by linear equations of state. The focus of this work lies on the generalization of the primary results to arbitrary substances, arbitrary equations of state and thus a more general kinetic relation. We prove existence and uniqueness results for Riemann problems. In particular, nucleation and cavitation are discussed.

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

Computers & Fluids ◽

10.1016/j.compfluid.2017.03.022 ◽

2017 ◽

Vol 150 ◽

pp. 31-45 ◽

Cited By ~ 17

Author(s):

Alexandre Chiapolino ◽

Pierre Boivin ◽

Richard Saurel

Keyword(s):

Phase Transition ◽

Two Phase Flows ◽

Two Phase ◽

Fast Phase

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WELL-POSEDNESS OF A PHASE TRANSITION MODEL WITH THE POSSIBILITY OF VOIDS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202506001261 ◽

2006 ◽

Vol 16 (04) ◽

pp. 559-586 ◽

Cited By ~ 11

Author(s):

MICHEL FRÉMOND ◽

ELISABETTA ROCCA

Keyword(s):

Phase Transition ◽

Balance Equation ◽

Strain Tensor ◽

Absolute Temperature ◽

Phase System ◽

Transition Model ◽

Well Posedness ◽

State Variables ◽

Two Phase ◽

Two Phases

The paper deals with a phase transition model applied to a two-phase system. There is a wide literature on the study of phase transition processes in case that no voids nor overlapping can occur between the two phases. The main novelty of our approach is the possibility of having voids during the phase change. This aspect is described in the model by the mass balance equation whose effects are included by means of the pressure of the system in the dynamical relations. The state variables are the absolute temperature (whose evolution is ruled by the entropy balance equation), the strain tensor (satisfying a quasi-static macroscopic equation of motion), and the volume fractions of the two phases (whose evolutions are described by a vectorial equation coming from the principle of virtual power and related to the microscopic motions). Well-posedness of the initial-boundary value problem associated to the PDEs system resulting from this model is proved.

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