Theoretical studies on buoyancy-driven ceiling jets of tunnel fires with natural ventilation

The paper presents a theoretical study on the ceiling jets induced by small fires in tunnels. The ceiling jet thickness, temperature rise and velocity are analyzed theoretically with Non-Boussinesq approximation. The study focuses on the radial and one-dimensional ceiling jets. Numerical solutions in the radial region and one-dimensional shooting region are obtained and new analytical solutions in the critical flow region are achieved. Analytical solutions indicate that the ceiling jet thickness increases with distance away from the fire source, which largely differs from the existing models implying that the ceiling jet thickness in the one-dimensional critical flow remains constant. Additionally, impacts of the air entrainment, friction and heat transfer on the ceiling jet are analyzed. It is found that in the radial and one-dimensional shooting flow regions, the air entrainment has a much more significant effect than the friction and heat transfer. However, in the one-dimensional critical flow region, the impact of air entrainment seems to be negligible and the flow is dominated by the friction and heat transfer. Further, validation of the present theory is made by comparing with previous theories, semi-empirical models, and experiments. The results show that the present theory provides a good prediction of the ceiling jet properties with natural ventilation for a small fire.