One of the main protective measures to be adopted in case of fires in road/rail tunnels is represented by suitable longitudinal ventilation systems being able to avoid fire and smoke exposure of humans, and to create a safe route upstream for evacuation. The key design parameter is the so-called critical ventilation velocity, i.e. the minimum speed of the longitudinal ventilation avoiding the spread of the smoke produced by fire in the upstream direction, known as ‘backlayering’. In several studies, the critical velocity was correlated to the fire heat release rate on the basis of semi-empirical models, already adopted in describing nonconfined fires. However, experimental runs both on a laboratory scale and on a real scale, evidenced that such correlations are valid only in connection with fires of limited extent, while at high rates of heat release and when the flame height reaches the tunnel ceiling, the critical velocity can tend asymptotically to a maximum value vca. In this study, reference was made to the worst scenario of hydrocarbon pool fire extended to the whole tunnel section. The main hypotheses the model is based upon are uniform distribution of chemico-physical properties of fire and smoke along the considered transverse section of the tunnel. The evaluation of the critical velocity is performed by solving mass, momentum and energy balances obtained considering possible dynamic interactions among the different fluxes (backlayering, air, flame/smoke column). In particular, the inertial action exerted by fresh air on backlayering was determined on the basis of the experimental results. The asymptotic value of the critical velocity resulting by mathematical modelling is in good agreement with those proposed by other authors, for example by means of complex CFD (computational fluid dynamics) studies. Moreover, the developed model is easily adaptable to the evaluation of vca, when dealing with geometrical conditions different from the ones studied here e.g., tunnel of different geometry, fire not extended to the whole section of the tunnel, obstacle presence in the tunnel, sloping tunnels.
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