Unsteady outflow of a warm dense Van der Vaals medium from a plane layer, a cylinder, and a sphere

Abstract

The unsteady outflow of a warm dense boiling compressiblemedium, initially at rest, from a plane layer, a cylinder, and a sphere into a vacuumis investigated in the approximation of an inviscid and non-heat-conducting two-parameter “gas-liquid”, whose thermodynamic properties are determined by the Van der Vaals equation of state. The expansion, the boiling, and the two-phase medium generation are assumed to be thermodynamically equilibrium, while the transition is instantaneous. The speed of sound suffers a discontinuity across the phase transition line of the second kind (binodal), whereas the pressure, the temperature, the density, the entropy, and the enthalpy remain continuous. The main issue in the thermodynamic calculations, which are the same for all the problems, is the construction of the binodal and, at the same time, an isentrope in an equilibrium two-phase mixture, reduced to the numerical integration of two ordinary differential equations. The one-dimensional problems of unsteady outflow are solved by means of the method of characteristics using the isentropes obtained in the thermodynamic calculations. As distinct from the plane problem, in the cylindrically and spherically symmetric problems there are no regions of homogeneous boiling liquid, which would be finite in space and time.