A hyperbolic model of boiling liquid
DOI:
https://doi.org/10.7242/1999-6691/2019.12.2.16Keywords:
boiling liquid, hyperbolic model, nodal method of characteristicsAbstract
A model of a boiling liquid is presented, built on the basis of the single-speed two-temperature generalized equilibrium model of a mixture previously proposed by the author, which takes into account the forces of interfractional interaction. The liquid fraction is assumed to be incompressble. A characteristic analysis of the model equations is carried out and their hyperbolicity is shown. Relations for characteristic directions and differential relations holding along them are derived. An analytical formula for calculating the speed of sound in a boiling liquid is obtained. It is noted that the speed of sound in a liquid, when phase transitions are taken into account, turns out to be slightly less than Wood's formula gives. Calculation formulas are given 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 taking into account interfractional heat exchange. In the calculations, it has been assumed that the phase transition in the boiling process occurs under the conditions of a superheated state, when the temperature of the liquid exceeds the saturation temperature. It is shown that taking into account the phase transformation leads to a significant increase in the vapor concentration in the unloading wave, as well as to a slight increase in both the velocity of the mixture and the pressure. The concentration of the vapor fraction behind the front of the shock jump decreases.
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