Variation principle in calculating the flow of a two-phase mixture in the pipes of the cooling systems in high-rise buildings

Andrey Aksenov,Anna Malysheva,D Safarik,V Murgul,Y Tabunschikov

doi:10.1051/e3sconf/20183302063

Andrey Aksenov, Anna Malysheva + Show 3 more

Open Access

https://doi.org/10.1051/e3sconf/20183302063

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Abstract

The analytical solution of one of the urgent problems of modern hydromechanics and heat engineering about the distribution of gas and liquid phases along the channel cross-section, the thickness of the annular layer and their connection with the mass content of the gas phase in the gas-liquid flow is given in the paper.The analytical method is based on the fundamental laws of theoretical mechanics and thermophysics on the minimum of energy dissipation and the minimum rate of increase in the system entropy, which determine the stability of stationary states and processes. Obtained dependencies disclose the physical laws of the motion of two-phase media and can be used in hydraulic calculations during the design and operation of refrigeration and air conditioning systems.

Highlights

Questions related to the distribution of a two-phase medium in a stream, i.e. with the true volumetric gas content in the gas-liquid flow, and with the slip coefficient are key in the hydrodynamics of two-phase flows, for example, in the study of steam flow in air conditioning systems of industrial civil tall buildings
It is made an attempt to solve the problem of the volume gas content and the phase slip coefficient applied to two-phase annual flows on the basis of the principle of minimum energy dissipation in a stabilized flow associated with irreversible losses by internal friction during the motion of real media
Since the velocity at the boundary between the gas and liquid phases for the values xx > 0,1 is much less than the absolute velocity of the gas phase, with sufficient accuracy for practical calculations it can be assumed that ww0gg = kk1wwgg, (55)

Summary

Introduction

(ρρρρglgl ), where wg - gas phase velocity; wl - liquid phase velocity; ρl – liquid density; ρg – gas density. The first of these formulas is derived from the minimum of the total amount of motion of the liquid and gas phases in a two-phase flow. It is made an attempt to solve the problem of the volume gas content and the phase slip coefficient applied to two-phase annual flows on the basis of the principle of minimum energy dissipation in a stabilized flow associated with irreversible losses by internal friction during the motion of real media

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