Models of Extinguishing Agent Movement in Air Space

Abstract

A system of linear differentiated equations, which takes into account the resistance of the air medium and the presence of wind, is used to formalise the movement of an extinguishing agent. Furthermore, using the integral Laplace transform allows the construction of a structural and dynamic scheme that reflects the process of supplying an extinguishing agent to the fire. Such a structural and dynamic scheme opens up opportunities for building a simulation model of the extinguishing agent movement using the Simulink mathematical visual modelling package. This simulation model provides for the determination of the current coordinates of the extinguishing agent and the speed of its movement to the fire. The parameters of this simulation model are the initial velocity of the extinguishing agent, the height from which it is supplied, the resistance of the air environment, the angle of supply of the extinguishing agent, and the presence of wind. We used the Simulink package to simulate the process of the extinguishing agent supply to the fire. Data sets were obtained for the time of the extinguishing agent supply to the maximum range, for the maximum supply range, and for the value of the extinguishing agent velocity at the maximum range. We have noted that for small angles of the extinguishing agent, there is a slight increase in the time of its supply to the maximum range by no more than 3.0% with a threefold increase in the resistance of the air medium and regardless of the variation in the value of the initial speed of the extinguishing agent supply. The analytical dependence of the time of supplying an extinguishing agent to the maximum range on the rate of its supply is obtained. In particular, the time of the extinguishing agent supply to the maximum range at small angles lies within (0.66÷0.88) s, which is quite significant for low-inertial fire extinguishing systems, the inertial properties of which are characterised by time parameters. This circumstance necessitates considering the time of supplying an extinguishing agent to the fire when solving problems of analysis and synthesis of fire extinguishing systems. This factor can be accounted for through the transfer function of the lagging link. The time parameter of such a transfer function is equivalent to the time of supplying the extinguishing agent to the fire. Keywords: extinguishing agent, delivery range, travel speed.