Major fire spread in a tunnel with water mist: A theoretical model

•A model of the effect of water mist on major fire spread in a tunnel is described.•A case similar to a HGV in the Channel Tunnel has been investigated.•The critical heat release rate for fire spread has been found to be 33–55MW. A model of the effect of water mist on major fire spread in a tunnel is described. It employs the concepts of non-linear dynamical systems theory and identifies the onset of instability with major fire spread in a tunnel. The purpose is to identify the thermo-physical and geometrical conditions which lead to instability and sudden fire spread. It uses as a starting point one of the non-linear models for major fire spread which have been developed by the author over many years and assumes that a water mist system operates. The case considered assumes the existence of a longitudinal forced ventilation and predicts the critical heat release rate needed for a fire to spread from an initial fire to an item with a given assumed shape; in the presence of water mist. There is assumed to be no flame impingement on the target object. The target object may be taken to approximate a vehicle. The illustrative case approximating fire spread from an initial fire to a heavy goods vehicle (HGV) is presented; it is not restricted to this case, however. The model is being identified with the name FIRE-SPRINT C1, which is an acronym of Fire Spread in Tunnels, Model C, Version 1. It has been developed from an earlier model, FIRE-SPRINT A3 and considers a case where, in the absence of a fire fighting system, there is the potential for a major fire.