Calculation of quasi-dimensional flows of boiling liquid
DOI:
https://doi.org/10.7242/1999-6691/2019.12.3.28Keywords:
boiling liquid, quasi-dimensional flows, hyperbolic model, nodal method of characteristicsAbstract
The flow of superheated liquid from a variable-section pipe is studied within the framework of the single-speed two-temperature hyperbolic model of boiling liquid previously proposed by the author. The model is based on the conservation laws for each of mixture fractions and takes into account forces of interfractional interaction. The flow is calculated using a quasi-one-dimensional approximation; liquid fraction is considered to be incompressible. In the calculations, it was assumed that the phase transition occurs under the conditions of a superheated state, when the temperature of the liquid exceeds the saturation temperature, and the intensity of the water - vapor phase transformation is proportional to the superheating of the liquid. A characteristic analysis of the equations of a quasi-one-dimensional fluid flow with phase transformations is carried out and their hyperbolicity is demonstrated. Relations for characteristic directions and differential relations along these characteristics are written. An analytical formula is obtained for calculating the speed of sound in a boiling liquid. 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. The calculation formulas of the iterative algorithm for the node method of characteristics, including the relations at the boundary points, are given. It is shown that taking into account the phase transformation leads to an increase in the concentration of steam, an increase in pressure in the region covered by the rarefaction wave, and the velocity of the mixture at the output section of the pipe increases significantly. In the narrowing sections of the pipe, a decrease in the volume fraction of steam is observed.
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