Stochastic model of heating the shell of a tank under the thermal effect of a fire

Yuriy Abramov

National University of Civil Defence of Ukraine

https://orcid.org/0000-0001-7901-3768

Oleksii Basmanov

National University of Civil Defence of Ukraine

https://orcid.org/0000-0002-6434-6575

Volodymyr Oliinik

National University of Civil Defence of Ukraine

https://orcid.org/0000-0002-5193-1775

Vitalii Kolokolov

National University of Civil Defence of Ukraine

https://orcid.org/0000-0002-1155-5170

DOI: https://doi.org/10.52363/2524-0226-2022-35-1

Keywords: stochastic model, tank fire, fire heat impact, radiant heat transfer, convective heat transfer

Аnnotation

The forecasting of the consequences of emergencies caused by the fire in the vertical steel tank with oil product is considered. It takes into account the random nature of the heat flow from the fire. The model of heating of the tank shell includes radiant heat transfer from fire, to environment, to inter-nal space of the tank; convective heat transfer to ambient air and steam-air mixture in the gas space of the tank. The initial data for the model are probability distribution and its parameters for the stochastic process that describes the fire. The result is the probability distribution and its parameters for stochastic process that describes the temperature of the tank shell. It is assumed stationarity and normality of a sto-chastic process that describes pulsations of the mutual irradiation coefficient. For this case a system of nonlinear first order differential equations is built. It based on the heat balance equation for an arbitrary point on the tank shell and describes the dynamics of changes of mathematical expectation and variance of temperature. The system of equations can be solved using the finite difference method. The obtained results allow specifying the deterministic model by constructing confidence intervals for the tank shell temperature. It is shown when the temperature of the tank shell reaches a critical value rapidly then deterministic and stochastic models will give almost the same result. Conversely, when temperature ap-proaches to the critical value slowly then forecasting time of reaching the critical value will differ sig-nificantly for these types of models. For example, the time to reach a temperature of 300 ºC by 10000 m3 tank is almost 30 minutes for a deterministic model. But the stochastic one shows that this temperature can be reached in 14 minutes.

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