Procedure for constructing a mathematical model to determine the time of the initial stage of fire evolution

To develop appropriate measures and means of fire protection at facilities, it is relevant to form an idea of the phenomenology of the processes of the occurrence, evolution, and termination of combustion. This paper proposes procedures for building mathematical models of the energy component of those physicochemical processes that occur in wood under the influence of fire, which make it possible to determine the time from the beginning of such an impact to the onset of the phase of flame combustion. The adequacy of mathematical modeling was tested experimentally at a standardized installation for studying flame propagation over the surface of wood. The samples used for the reported theoretical and experimental studies were the specimens of unprotected wood made from 20-mm-thick pine sapwood with a density of 400‒550 kg/m3. The samples of fireproof wood (of the same variety, thickness, and density) were impregnated with a fire retardant based on diammonium phosphate and ammonium sulfate (at consumption of 168.2 g/m2 of dry fire-retardant components). The modeling employed the results from the experimental determining of the ignition temperature of unprotected and fire-proof wood, specifically: 235 °C – for unprotected wood, 410 °C – for fire-proof wood, respectively. The results of mathematical modeling and experimental studies confirm the possibility of significant lengthening of time from the onset of fire exposure to the ignition of fire load from wood when nitrogen-phosphorus impregnating agents are used for fire protection. Procedures of mathematical modeling have been proposed to build models for determining the cooling effect from the use of impregnating fire retardants to protect the wood on the prolongation of the stage of a fire start. Mathematical modeling data could be applied when making impregnating fire retardants