Aim: The objective of the research was to develop an universal mathematical model which could be displayed in a computer programme as a graphic forecast of the effectiveness of one of the five possible fire extinguishing methods, such as fire gas recirculation, the usage of powder, water mist, vapor-gas mixture or foam. Creation of the model was possible on the basis of the process of development and fighting fires in constructions of considerable length. Obtained by the general results of theoretical and experimental studies. The research was also based on the generalized approach to the use of firefighting equipment in elongated channels.

Methodology: The methods used in the analysis comprised a complex method of research which involved an analysis and synthesis of scientific and technological achievements in the field of ventilation and thermal calculations during a fire in the tunnel; the mathematical modelling of heat and mass transfer in accordance with basic laws of thermodynamics; simulation modelling of the gas flow and temperature distribution in the isolated area of a cable tunnel during recirculation of combustion products. For testing the reliability of the results we also used the statistical techniques.

Results: As the result of the work we obtained the universal mathematical model, the algorithm and the program for calculating thermodynamic parameters of the process of gas burning and fire suppression in the isolated channel volume with the use of one out of five possible firefighting methods or their combination. Mathematical modelling of the temporal concentration of oxygen in the outbreak or beyond the fire was performed with the use of differential equations of unsteady mass transfer, which were solved numerically by the combined scheme and reduced to a set of algebraic equations. The algorithm and the programme for calculating in Excel the temporal concentration of oxygen and the dynamics of the temperature in the source of the fire and in the ambient array were developed.

Conclusions: The authors recapped the results of the mathematical modelling which turned out to be equivalent to numerous experimental data on the development and extinguishing of fires in elongated channels. As a result the universal mathematical model for calculations of intensity and exposure time parameters as well as for determining the amount of fire-extinguishing material was created. The obtained results allow to evaluate the extinguishing agent and to verify visually its advantages or disadvantages. These results can be used in the preparation of emergency response plans and other documents.

Keywords: channel, fire, fire-extinguishing, powder, dispersed water, foam, recycling, water-vapor mixture, mathematical model, inert gases

Type of article: original scientific article