A model of random pulsations of radiant heat flow from a flammable liquid fire

Abstract

The object of the study is the process of liquid combustion in a tank or in a spill. Unlike the standard approach that assumes the shape of the flame is constant, random pulsations of the flame due to the turbulent mode of liquid combustion are considered. The pulsations lead to the random nature of the mutual radiation coefficient and the temperature of the radiating surface of the flame. This leads to a random value of the radiant heat flux density from the fire. Using the central limit theorem allows justifying the assumption about the normal law of the distribution of the radiant heat flux density, the mutual radiation coefficient and the temperature of the radiating surface of the flame. The assumption of a normal distribution law allows calculating the mathematical expectation of the heat flux density. It is shown that the average value of the heat flux density increases with an increase in the dispersion of the temperature of the radiating surface and the coefficient of mutual radiation, as well as with an increase in the correlation coefficient between them. It means that neglecting random flame pulsations can lead to underestimates of the average heat flux density from a fire. The dispersion of the radiant heat flux density was found and it was shown that it increases with the growth of the dispersion of the flame temperature and the mutual radiation coefficient. The standard deviation of the heat flux density can be more than 40 % of its average value if the standard deviations of the flame temperature and the mutual radiation coefficient are up to 10 % of their average values. The obtained results can be used to clarify the thermal effect of a liquid fire on neighboring objects.