Estimating the Influence of the Wind Exposure on the Motion of an Extinguishing Substance

Abstract

One of the tasks to be solved when deploying fire extinguishing systems is to determine the range of the fire extinguishing agent supply to the combustion center. This problem is solved using data on the trajectory of the fire-extinguishing agent in the combustion center. The presence of wind impact on the process of supplying a fire extinguishing agent will lead to a change in its trajectory. To take into account wind impact, it becomes necessary to assess the result of such impact. Using the basic equation of dynamics for specific forces, a system of differential equations is obtained that describes the delivery of a fire extinguishing agent to the combustion center. The system of differential equations takes into account the presence of wind impact on the movement of the extinguishing agent. The presence of wind action is taken into account by the initial conditions. To solve such a system, the integral Laplace transform was used in combination with the method of undefined coefficients. The solution is presented in parametric form, the parameter of which is time. For a particular case, an expression is obtained that describes the trajectory of the supply of the extinguishing agent into the combustion center. Nomograms are constructed, with the help of which the operative determination of the estimate of the maximum range of the fire-extinguishing agent supply is provided. Estimates are obtained for the time of delivery of a fire-extinguishing agent to the combustion center, and it is shown that for the characteristic parameters of its delivery, this value does not exceed 0.5 s. The influence of wind action on the range of supply of a fire extinguishing agent is presented in the form of an additive component, which includes the value of the wind speed and the square of the time of its delivery. To assess the effect of wind impact on the movement of the fire extinguishing agent, an analytical expression for the relative error was obtained and it was shown that the most severe conditions for supplying the fire extinguishing agent to the combustion center, the value of this error does not exceed 5.5%. Taking into account the wind effect when assessing the range of supply of a fire-extinguishing agent makes it possible to increase the efficiency of fire-extinguishing systems due to its more accurate delivery to the combustion center

Models of Extinguishing Agent Movement in Air Space

“…Для такого опису використовується традиційний підхід -математичні моделі, представлені у вигляді диференційних рівнянь. Математичні моделі руху вогнегасної речовини в повітряному просторі описуються системою диференційних рівнянь [3], які можуть бути лінійними [4] або нелінійними [5]. Слід відмітити, що дослідження, які пов'язані із використанням математичних моделей стосовно до опису руху вогнегасної речовини як в полум'ї, так і в повітряному просторі носять в переважній більшості випадків локальний характер.…”

“…8% при відсутності вітру, на 32,9% при зустрічному напрямку вітру та на 19,0% при його попутному напрямкускладає відповідно ± 13,1% та ± 24,9%.В[4] показано, що при 0   час досягнення максимальної дальності подачі вогнегасної речовини може оцінюватись за допомогою виразу: , V та  . Із аналізу табл.…”