A simplified calculation method on the smoke back-layering length and inlet air velocity in a tilted tunnel fire without shaft

In a tilted tunnel fire, the inlet air velocity caused by the stack effect at the entrance of the tunnel would be beneficial to smoke control whether the longitudinal ventilation system is used or not. This paper conducted the simulation to investigate the smoke spread behaviours caused by fires in tilted tunnels with natural ventilation. The expression of the smoke back-layering length and the inlet air velocity induced by fires were deduced in the tilted tunnel fire scenarios by the method of dimensional analysis. The effect of various tunnel slopes (5–15%) on the smoke behaviours characteristics and the inlet air velocity were specifically considered. The proposed correlation reveals that the dimensionless back-layering length is independent of the heat release rate (HRR) and its relationship with the tunnel slope is proportional to −1.96 power. The established equation reveals that the dimensionless inlet air velocity is proportional to 0.31 power of the dimensionless HRR and it increases exponentially with the tunnel slope. This research on this topic may contribute to optimize the application of natural ventilation systems or mechanical ventilation in tilted tunnels.