A quadrangular pyramid thermal radiation model based on flame geometry of two-dimensional diffusive spill fires under longitudinal airflow

Abstract

An investigation of spill fire thermal radiation under longitudinal airflow enhances understanding of thermal management in energy safety. This study examined heat transfer mechanisms between flame and substrate, flame substrate diffusion shape, burning rate, and flame height in two-dimensional diffusion spill fires under longitudinal airflow, proposing a quadrangular pyramid flame radiation model. The results show that increased airflow velocity divides heat transfer process into conduction through the flame-fuel layer-substrate and radiation heating through flame to substrate, while fuel temperature gradually rises to boiling temperature along the diffusion direction due to heat absorption. Horizontal inertial forces reshape substrate flame shape into an asymmetric rhombus, decreasing windward-side flame length while increasing leeward-side length. The burning rate exhibits a non-linear trend, initially increasing then decreasing with airflow velocity increasing due to counteracting effects between enhanced combustion and convective heat dissipation. Flame height evolution progresses with longitudinal airflow increase through three distinct stages: slow decrease, rapid decline, and stabilization, captured by the dimensionless model based on buoyancy plume versus horizontal inertial force dynamics. Based on the remodeling effect of airflow on the flame diffusion shape, a quadrangular pyramid flame thermal radiation model was proposed. Compared with the triangular prism and rectangular prism models, the new model significantly improves the prediction accuracy of radiant heat flux of spill fire, with the overall error controlled within 20 %. This provides a reliable theoretical model for the management of thermal hazards in the application field of energy storage, utilization and transportation.