Theoretical and numerical study on mass flow rates of smoke exhausted from short vertical shafts in naturally ventilated urban road tunnel fires

The study focuses on the mass flow rate of the buoyancy-driven gases exhausted from the shaft in naturally ventilated urban road tunnel fires. Theoretical analyses and numerical simulations are performed. The model to predict the mass flow rate of the incoming smoke exhausted by the nearest shaft is developed by considering that the smoke is exhausted along the four sides of the shaft separately. Based on the heat balance between the incoming smoke exhausted and the total gas flow exhausted, the model to estimate the total mass flow rate exhausted from the shaft (both smoke and entrained air) is also established. Meanwhile, a series of numerical simulation in a naturally ventilated tunnel considering the heat release rate (HRR), the shaft height, shaft length and width, shaft location was carried out. The simulation results show that the shaft height has a limited contribution to the mass flow rate of the incoming smoke exhausted while a larger shaft cross-sectional area shows a favorable performance in exhausting the smoke. Further, the air entrainment into the shaft increases with both the shaft height and shaft cross-sectional area. Comparisons of the mass flow rates of the incoming smoke and the total mass flow rates exhausted between simple calculations and simulations are made, showing that the simple models perform well. Further, it is found that there exist two regimes for the total mass flow rate corresponding to different smoke modes in the shaft (complete plug-holing, plug-holing and without plug-holing), which is caused by the different driven forces in the shaft. The outcomes of this work could provide some guidance for the design of vertical shaft and smoke control in naturally ventilated tunnel in urban area.