Mathematical modeling of forest fire extinguishing using water capsules with a thermoactive shell

The paper proposes a new mathematical model of the process of extinguishing a forest fire with dispersed water delivered to the fire source with water capsules with a thermoactive shell. When moving in a medium with a temperature above the critical, the capsule shell accumulates the integral value of the damage with the intensity proportional to the distance traveled and the critical temperature exceed. When the integral parameter of the thermal stability of the shell is reached, the capsule ruptures and water is released in dispersed form. During the sequential discharge of several capsules, each of them is affected by the temperature of the medium formed after exposure to the previous capsules. After calculating the distribution of dispersed water from the capsules, the calculation of the dynamics of a forest fire based on a physical and mathematical model is resumed. The analysis of key parameters and effects that determine the effectiveness of extinguishing is carried out. The extinguishing dynamics is shown for a different number of capsules per unit length of the fire front, an integral parameter of thermal stability, and the amount of water in the capsule. The results of numerical modeling showed that in the case of a small value of the capsule integral parameter of thermal stability, the capsule ruptures in the upper part of the vegetation layer, and therefore a great number of water capsules must be sequentially dumped to extinguish. Too high value of the thermal stability coefficient leads to rupture of capsules on the ground and to continuation of the combustion process in the upper part of the vegetation layer. The greatest efficiency of forest fire extinguishing occurs when the thermoactive shell of capsules ruptures in the middle of the combustion front. Sequential discharge of capsules allows one to distribute water vertically, more fully covering the zone of vulnerability of the fire. It is shown that the use of capsules with a thermoactive shell allows one to deliver water in the zone of vulnerability of the fire, thereby providing more effective firefighting.