A Hyperbolic Model of Boiling Liquid

Abstract

A model of a boiling liquid is presented that is based on the single-speed two-temperature generalized equilibrium model of a mixture with account for the forces of interaction between the fractions previously proposed by the author. The liquid fraction is assumed to be incompressible. The characteristic analysis of the model equations is carried out and their hyperbolicity is revealed. The relations for the characteristic directions and the differential relations along them are derived. The analytical formula for calculating the speed of sound in a boiling liquid is obtained. It is noted that when the phase transitions are taken into account the speed of sound in a liquid turns to be slightly lower than the speed calculated by the Wood formula. The calculation formulas are provided for the iterative nodal method of characteristics, which is used to calculate the flow during the decay of an arbitrary discontinuity in a boiling liquid without account for the interfractional heat exchange. In the calculations it is assumed that the phase transition in the boiling process occurs under the superheated state conditions when the temperature of the liquid exceeds the saturation temperature. It is demonstrated that accounting for the phase transformation leads to a significant increase in the vapor concentration in the unloading wave and to a slight increase in both the velocity of the mixture and its pressure. The concentration of the vapor fraction behind the front of the shock jump decreases.