Singular perturbations of variational problems arising from a two-phase transition model

1990 ◽  
Vol 21 (1) ◽  
pp. 289-314 ◽  
Author(s):  
Guy Bouchitte
Keyword(s):  
Phase Transition ◽  
Singular Perturbations ◽  
Variational Problems ◽  
Transition Model ◽  
Two Phase

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

2006 ◽  
Vol 16 (04) ◽  
pp. 559-586 ◽  
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.

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

2021 ◽  
Vol 371 ◽  
pp. 110954
Author(s):  
M. De Lorenzo ◽  
Ph. Lafon ◽  
M. Pelanti ◽  
A. Pantano ◽  
M. Di Matteo ◽  
...  
Keyword(s):  
Phase Transition ◽  
Transition Model ◽  
Two Phase Flows ◽  
Two Phase

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

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