Study on the critical velocity in a sloping tunnel fire under longitudinal ventilation

•The sectional coefficient ζ was introduced to describe the tunnel cross section.•The dimensionless backlayering length and critical velocity were proposed.•Two hundred fifty simulations based on nine typical tunnels were carried by FDS.•Forty-five small-scale model experiments were carried out in a 1/10 scale model tunnel.•The slopes of the tunnels in simulations and tests were from −3% to 3%.

The critical velocity and the backlayering length of smoke in tunnel fires are the two most important parameters in longitudinal ventilation design. This paper deduced the dimensionless expression of backlayering length and critical velocity of smoke in tunnel fires using the dimensional analysis method. The sectional coefficient ζ (ζ = A/H2) was introduced to describe the geometrical characteristic of the tunnel section, and the characteristic hydraulic diameter of the tunnel H¯ replaced the tunnel height H. Then, CFD simulations were conducted in nine tunnels with different cross sectional shapes using the proprietary software Fire Dynamic Simulator (FDS), version 5.5. With the FDS simulations, prediction models for backlayering length and critical velocity modified by the sectional coefficient ζ and the tunnel slope were proposed. Meanwhile, complementary experiments were carried out in a 1/10 scale tunnel in order to provide a verification. The experimental results show a good agreement with the numerical simulations. Moreover, the prediction models for critical velocity on different slopes were compared with the prediction models proposed by others.