Revisiting Alpert’s Correlations: Numerical Exploration of Early-Stage Building Fire and Detection

Alpert’s correlations of fire ceiling jets have been widely used in the design of heat detectors and sprinklers since the 1970s. However, these correlations are primarily derived from large fire tests of 3.8–98 MW, high ceilings, and ideal liquid spraying flames. Thus, the feasibility of Alpert’s correlations for the smoke ceiling jet in early-stage fire detection with smaller fire sizes is still unclear. This study constructs a numerical model that is first validated by Alpert’s original ceiling temperature and velocity data of large fire powers. Then, the numerical model further explores the feasibility of Alpert’s correlations in predicting the gas temperature and velocity in steady-burning fires with 50–500 kW. Modelling confirms the accuracy of Alpert’s temperature correlations for the ceiling jet region, but suggests a large uncertainty of assuming a constant turning-region temperature for early-stage fires. Moreover, the modelled velocity pattern of smoke ceiling jet in the plume region is non-uniform, and its value in the ceiling jet region is significantly higher than Alpert’s fitting correlation. Finally, the response time of the heat detector and sprinkler in the ceiling jet region predicted by the numerical model is shorter than Alpert’s correlations, which suggests the conventional design based on Alpert’s correlations is sufficiently conservative.