Abstract: Critical velocity is an important indicator of the smoke control design for longitudinal ventilation tunnel fires. Currently, two calculation methods, i.e., the critical Froude model (recommended by the World Road Association, PIARC) and the piecewise function model (recommended by National Fire Protection Association, NFPA) are widely adopted in practice. Nevertheless, the calculation result of the two models shows a significant difference, causing confusion and disagreement regarding tunnel fire safety design. This work analyzes the differences between the PIARC equation and the NFPA equation under various heat release rates, tunnel widths, and tunnel heights, respectively and the reasons are discussed in detail. Then, the smoke control performances and feasibilities of these two models are compared with a set of numerical simulations, full-scale and reduced-scale test data. Results show that the PIARC equation fails to describe the correlation between critical velocity and heat release rate due to the fixed Frc value and unrealistic uniform mixing assumption. The PIARC equation will underestimate the critical velocity and the error increases with the tunnel aspect ratio. The NFPA formula comprehensively considers the impact of the relationship between the fire plume and the tunnel structure on critical velocity. Therefore, the prediction shows a better smoke control performance and agrees well with physical test data. Moreover, realistic factors, e.g., blockage, altitude, fire source rising, and lateral locations will also affect the value of critical velocity and should be considered in future work.

Key words: tunnel fire, longitudinal ventilation, critical velocity, full-scale test, numerical simulation, feasibility