Mathematical model for predicting fire-extinguishing foam expansion rate in deflector type sprinklers

Abstract

Purpose. Based on the results of experimental studies, develop a mathematical model for predicting the foam multiplicity, taking into account the main parameters of the foam formation process in deflector type sprinklers for automatic fire extinguishing systems.

Methods. The general methodology of the work included the theoretical (analysis, synthesis, comparison) and experimental research methods. The foam expansion rate was determined experimentally using the developed method. Statistical analysis of experimental data and formulation of the mathematical model included regression and correlation analyses, as well as analysis of residuals, including the normality of their distribution using the Pearson criterion.

Findings. Based on experimental data, the mathematical model has been developed for predicting fire-extinguishing foam expansion rate based on sprinkler geometry, hydrodynamic conditions, and the physical and mechanical properties of the foaming solution. The model's structure includes dimensionless complexes reflecting the influence of the effective surface area coefficient of the deflector K_s, the relative length of the frame arms L_f / D, the relative diameter of the deflector D / D_max, and the capillarity number Ca, providing a comprehensive account of the sprinkler geometry and foaming process parameters. The average deviation of the calculated foam expansion rate values from the experimental data does not exceed 11 %, and the maximum deviation is 27 %. An analysis of the residuals revealed no systematic relationship between the residuals and the predicted values and confirmed the normality of the residual distribution. Furthermore, the relationships identified during the experiment indicate the complex influence of the sprinkler's geometric parameters on foam expansion rate, particularly relative length of the frame arms L_f / D. The most significant increase in foam expansion rate is achieved by increasing the capillarity number and the working surface coefficient of the deflector, while the influence of the relative diameter of the deflector is less pronounced.

Application field of research. Design and operation of deflector sprinklers for automatic fire extinguishing systems. The proposed model allows for the selection of the required foam generation configuration, taking into account the foam concentrate used, the foam solution delivery conditions, and the sprinkler's key geometric parameters to produce foam with a specified expansion rate.