A simplified mathematical model for estimating gas temperature and velocity under natural smoke exhaust in sloping city tunnel fires

In the previous study, the prediction of gas temperature and velocity in the naturally-ventilated inclined tunnels under traffic blockage has been well concerned (Y. Zhou et al., Sustain. Cities Soc. 45, 2019, 258-270). In this paper, we continue to pay attention to the estimation of internal gas temperature and velocity under natural smoke extraction in both single-slope and gable-slope tunnel fires, a more hazardous scenario. A series of simplified mathematical models based on the equations of continuity, energy and pressure balance was proposed to estimate the gas temperature and velocity in sloping tunnel fires, in which the influences of fire source location, tunnel slope and tunnel geometry were taken into account. In addition, corresponding numerical simulations based on full-size tilted urban tunnel fires were performed using Computational Fluid Dynamics (CFD) method. The results show that the variation trends between CFD and analytical results are basically the same, and the iterative values of gas temperature and velocity coincide well with the simulations. A fast and convenient method for the estimation of gas temperature and velocity in sloping tunnel fires has been proposed, and the results of this work can provide a reference for the optimal design and management of natural smoke extraction systems, and help to ensure the fire safety of single-slope and gable-slope city tunnels.