Simple prediction equation for ceiling jet flow arrival time in space without vertical wall soffit

Currently, in two-zone models, smoke flow is calculated based on the assumption that the fire plume, which develops directly above the fire source, depends solely on the amount of entrained surrounding air. However, in large flat spaces, which have been growing larger in recent years, the horizontal travel distance of ceiling jet flow is long, and it is possible that the amount of smoke due to entrainment of air during the horizontal spread process is underestimated. In this study, we performed experiments that reproduced an unconfined ceiling without a vertical wall soffit and determined the amount of entrainment in the ceiling jet flow by analyzing the gas concentration of ceiling jet flow at various flow distances. Next, we formulated the ceiling jet flow rate by expressing this in terms of dimensionless flow rate and dimensionless flow distance. Furthermore, we derived a simple prediction equation for ceiling jet flow arrival time based on the model equation. Finally, we validated the proposed equation and range of applicability through comparison with the results of several experiments.