Discussions on critical velocity and critical Froude number for smoke control in tunnels with longitudinal ventilation

Determination of critical velocity is a key issue for smoke control in any tunnel with longitudinal ventilation. The critical Froude model using single Froude number of 4.5 has for decades been widely used in engineering applications. This value was originally used by Danziger and Kennedy and they argued that the critical Froude number obtained by Lee et al. was in a range of 4.5 and 6.7 and therefore a conservative value of 4.5 was obtained. This paper explores the validity of using single critical Froude number of 4.5 by investigating the original sources and comparing it to recent research results. It was found that the value of 4.5 obtained in the original source corresponds to a large tunnel fire and it correlates well with data from other literature within a narrow range of large fire sizes. Using this value produces a significantly lower critical velocity for a wide range of fire sizes and therefore it is not conservative. The Froude number of 6.7 obtained by Lee et al. corresponds to another Froude number with a different definition and it is therefore not comparable with the value of 4.5. It is found that the use of a single value of 4.5 for the critical Froude number is not reasonable in calculation of the critical velocity for smoke control in tunnels with longitudinal ventilation.