Numerical simulation of the critical ventilation velocity in navigation tunnel fires

The continuous advancement of inland waterway infrastructure has led to the emergence and growing prominence of a distinct type of navigation structure—ship navigation tunnels. These specialized passages, designed to enable vessel transit beneath natural or artificial barriers, present unique challenges for fire safety management. A central issue lies in accurately predicting the critical ventilation velocity required to prevent smoke back-layering during a fire. Focusing on this key parameter, the present study examines its determination in ship tunnel environments using advanced numerical simulation techniques. The methodology involved constructing three detailed simulation models representing tunnels for 1,000-ton, 8,000-ton, and 10,000-ton vessels. In each model, a fire source was located at the tunnel center. A comprehensive series of numerical experiments was then conducted for each configuration, with the heat release rate (HRR) systematically varied from 20 MW to 90 MW. The initial longitudinal ventilation velocity in each simulation was set according to established empirical formulas. The smoke dispersion patterns were meticulously analyzed based on the resultant data. Subsequently, an iterative procedure was employed: the longitudinal ventilation velocity was adjusted in increments of 0.1 m/s until smoke back-layering was effectively suppressed (i.e., no upstream smoke reflux was observed). The velocity meeting this condition was identified as the critical velocity for the corresponding scenario. A comparative analysis between the critical velocities obtained from simulations and those calculated using existing empirical formulas reveals notable discrepancies and uncertainties. The values predicted by the Li formula are generally overestimated across all cases. For tunnels accommodating 1,000-tonne and 8,000-tonne vessels, the Xu and Wu formulas consistently yield lower predictions than the simulation results. Conversely, for the 10,000-tonne tunnel, the values from the Xu and Wu formulas predominantly exceed the numerical results. Moreover, the divergence between the empirical predictions and simulation outcomes increases progressively with the heat release rate of the fire source. In terms of applicability, the Li formula demonstrates relatively satisfactory performance for the 1,000-tonne and 8,000-tonne tunnels, whereas the Wu formula exhibits superior suitability for the 10,000-tonne tunnel design. These identified deviations underscore a significant finding: existing empirical models and standard provisions—originally developed for conventional road or rail tunnels—are not directly applicable to ship navigation tunnels. The geometric proportions, ventilation dynamics, internal surface characteristics, and ambient boundary conditions inherent in large, navigable waterway tunnels differ substantially from those of their land-based counterparts. Consequently, traditional approaches often yield inaccurate estimates of the airflow required for effective smoke control in these unique environments, thereby limiting their practical reliability in design and safety engineering. Building on these findings, the study further examines the fundamental parameters governing critical velocity in ship tunnels. Through rigorous statistical analysis and regression modeling, it is demonstrated that the critical velocity exhibits a strong correlation with three primary variables: (1) the heat release rate (HRR) of the fire source, (2) the net cross-sectional perimeter (L) of the tunnel, and (3) the net clearance height (H), or headroom, available within the tunnel. These parameters exert a dominant influence on the minimum ventilation threshold required to prevent back-layering and maintain tenable conditions. To more effectively integrate the defining geometric attributes of ship tunnels into a predictive framework, this study introduces a novel dimensionless parameter—the tunnel cross-sectional coefficient, ω. This coefficient is defined as the ratio of the net cross-sectional perimeter (L) to four times the net clearance height (4H), i.e., ω = L/(4H). The introduction of ω offers a unified metric that encapsulates the combined influence of tunnel shape and scale. Drawing on the dataset generated from the simulations and the insights derived from the correlation analysis, a new empirical formula for predicting the critical velocity in ship navigation tunnels is developed. This proposed model incorporates the principal influencing factors, including the fire’s HRR, the tunnel cross-sectional coefficient ω, and the geometric parameters L and H. Comparative validation indicates that the new formula achieves markedly higher predictive accuracy than the existing models evaluated in this study. In summary, this research highlights the limitations of conventional fire safety engineering models when applied to the emerging typology of ship navigation tunnels. It systematically identifies the governing factors affecting critical velocity in such structures and introduces a tailored predictive approach centered on a new geometric coefficient. The findings and the proposed model provide a refined analytical tool for improving the design and safety assessment of future waterway transport infrastructure.