Construction of the stochastic model of thermal radiation from a flammable liquid spill fire

Abstract

The object of this study is the process of liquid combustion in the pool, and the subject of the study is the characteristics of the random process that describes the heat flow by radiation. Such, in particular, are the law of distribution, mathematical expectation, and correlation function. An experimental study of the combustion of used motor oil in a pool measuring 9.5×8.7 m2 was carried out. The mathematical expectation and variance of the cross-sectional area of the flame were determined by video recording followed by the analysis of individual frames. Testing of the hypothesis about the normal law of distribution of the cross-sectional area showed that with a confidence probability of 0.95, the proposed hypothesis does not contradict the experimental data. A selective correlation function and its approximation in the form of σ2exp(–α|τ|) were constructed. Due to the linear relationship between the cross-sectional area and the heat flux by radiation from the fire, the latter will also have a normal distribution law. At the same time, the magnitude of pulsations (the ratio of the rms deviation to the mathematical expectation) for these random processes will be the same. The value of the parameter α of the correlation function will also be the same.

Taking into account the inertial properties of the device for measuring the heat flux density, a comparison of the experimentally measured values of the heat flux density with the calculated ones was carried out. The measurement results fall into the intervals corresponding to the confidence probability of 0.95. At the same time, the maximum deviation between calculated and experimental data is 14 %. From a practical point of view, the built stochastic model opens up possibilities for taking into account random flame pulsations when determining safe zones for the location of personnel and equipment. The model can be used to specify the thermal effect of fire on steel and concrete structures