Mathematical model of foam expansion rate generated in sprinklers

Foam solution discharge is always accompanied by changes in the operating pressure due to different pressure losses along the pipeline in automatic foam extinguishing systems. Changes in the operating pressure affect the process of a liquid jet fragmentation into droplets and the formation of foam films. Therefore, to increase the accuracy of calculations when designing automatic foam extinguishing systems, it is worthwhile to evaluate the main characteristics of the foam in terms of fire extinguishing efficiency, in particular, its expansion. For this purpose, the generalization of the experimental data using the theory of similarity and taking into consideration the hydrodynamic features of the deflector type sprinkler operation and the properties of foam solution was carried out to develop a novel simplified mathematical model. This model allows to predict the foam expansion depending on the geometric parameters of the sprinkler elements and the empirical coefficient, which takes into account the peculiarities of the chemical composition of the foam concentrate. This new model predictions of foam expansion show good agreement with the experimentally measured foam expansion. The average error in foam expansion was less than 9 %.