On a Model of the Dynamics of Liquid/Vapor Phase Transitions

A model for the liquid/vapor phase transitions in a shock tube is studied. Mathematical analysis for the one-dimensional isothermal case is carried out. A sufficient condition for the existence of traveling waves is given. These traveling waves represent liquefaction and evaporation shocks. The nonexistence of some of these traveling waves when the shock speed is smaller than some number is proved. Major one-dimensional wave patterns observed in actual experiments with retrograde fluids are also observed in solutions of Riemann problems. A rough estimate of the difference of the calculated pressure in the solution of the Riemann problem and that in experimental data due to the modeling is given.

[1]  R. Menikoff,et al.  The Riemann problem for fluid flow of real materials , 1989 .

[2]  Asymptotic Stability of Rarefaction Waves for 2 * 2 Viscous Hyperbolic Conservation Laws , 1988 .

[3]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[4]  Vitaly Volpert,et al.  Traveling Wave Solutions of Parabolic Systems , 1994 .

[5]  Michael Shearer,et al.  Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type , 1986 .

[6]  C. F. Lee,et al.  Condensation by homogeneous nucleation of H2O, C6H6, CCl4 and CCl3F in a shock tube , 1983 .

[7]  I. I. Glass,et al.  Flows with nucleation and condensation , 1979 .

[8]  L. Hsiao.  Uniqueness of admissible solutions of the Riemann problem for a system of conservation laws of mixed type , 1990 .

[9]  D. Barschdorff.  Carrier gas effects on homogeneous nucleation of water vapor in a shock tube , 1975 .

[10]  Gerd E. A. Meier,et al.  Wave splitting in a fluid of large heat capacity , 1987, Journal of Fluid Mechanics.

[11]  I. I. Glass,et al.  Condensation of water vapor in rarefaction waves. I - Homogeneous nucleation , 1976 .

[12]  Haitao Fan.  Traveling Waves, Riemann Problems and Computations of a Model of the Dynamics of Liquid/Vapor Phase Transitions , 1998 .

[13]  P. Wegener,et al.  Condensation of Water Vapor in the Shock Tube Below 150°K , 1951 .

[14]  P. A. Thompson,et al.  An experimental study of reflected liquefaction shock waves with near-critical downstream states in a test fluid of large molar heat capacity , 1994, Journal of Fluid Mechanics.

[15]  Zhouping Xin,et al.  Nonlinear stability of viscous shock waves , 1993 .

[16]  D. Oxtoby.  Homogeneous nucleation: theory and experiment , 1992 .

[17]  G. Wallis.  One Dimensional Two-Phase Flow , 1969 .

[18]  R. L. Rabie,et al.  The polymorphic detonation , 1979 .

[19]  P. A. Thompson,et al.  Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube , 1986, Journal of Fluid Mechanics.

[20]  M. Slemrod.  Admissibility criteria for propagating phase boundaries in a van der Waals fluid , 1983 .

[21]  P. Wegener,et al.  Gasdynamics and homogeneous nucleation , 1977 .