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Published on 01 February 2020

# MATHEMATICAL SIMULATION OF WATER DROP MOTION IN VERTICAL SHAFT VENTILATION

## A.N. Fomin, S.N. Kuznetsov

The aim of the work is to create a mathematical model of the movement of droplets (particles) in the turbulent air flow in the vertical pipe of the ventilation shaft of the mine (mine). The use of ore (mine) ventilation pipes of different cross-sections allows more efficient and energy-intensive to organize ventilation in the faces. However, the use in the mountain (mine) workings of abundant water irrigation to combat dust and ensure acceptable temperature conditions of people's stay leads to increased humidity (90% – 100%) in the atmosphere of deep mines, which in turn at temperature differences between the bottom-hole horizon and the earth's surface leads to abundant droplet formation and deposition of water masses on the inner surface of the ventilation pipe of the issuing shaft of the mine. Water, flowing down the walls of the pipe, enters the counterflow with the upward flow of exhaust gases, which leads to failures in the ventilation system and emergency situations in the mine ventilation system. In order to understand the process of deposition of droplet liquid in the vertical pipe of the ventilation shaft of the mine (mine), this article presents a corresponding mathematical model of the movement of droplets (particles). The influence of forces acting on the droplets in the upward ventilation flow is considered. Based on Newton's second law, a system of differential equations of the first order is derived and as a result of its solution the trajectories of droplets (particles) in a vertical pipe are obtained by numerical method. The motion graphs of particles (droplets) distributed over the entire section of the pipe, distributed in the boundary layers of the air flow and turbulent zone are presented. The process of subsidence of droplets on the inner wall of the vertical ventilation channel of the outstanding shaft of the mine (mine) is justified and the dependence of the place of subsidence of droplets on their radial location in the plane of the cross-section of the pipe is established.

 City Vladikavkaz Country Russia UDC 622.23 Issue 2019, № 4 (Т. 11) Key words mine ventilation, ventilation shaft, ventilation flow, droplets in the pipe, droplet trajectory, droplet subsidence, mathematical model.
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Tags: математическая модель., вентиляция шахт, вентиляционный ствол, вентиляционный поток, капли в трубе, траектория капель, оседание капель

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ISSN 1998-4502 (Print)                                                            ISSN 2499-975Х (Online)