Flashover condition analysis on passenger carriage fire by using swallowtail catastrophe theory

Flashover in compartment fire itself is a catastrophe process. Its catastrophe behavior can be analyzed, and its topological function equation can also be set up by catastrophe theory. On the basis of analyzing swallowtail catastrophe characteristic, a flashover model of hot smoke layer, which is established based on energy conservation, is transformed in the dimensionless form firstly, and then diffeomorphism is applied to simplify it. By these transform, a catastrophe potential function is gained. The format of the catastrophe potential function makes it clear that this type of flashover belongs to swallowtail catastrophe. Subsequently, taking passenger carriage fire as an idiographic object, the connection between system control variable and burning condition is discussed. The results show that the space of catastrophe bifurcation in muster divide the fire into two section, namely flashover section and non-flashover section. If in flashover section, an unstable point can be obtained by using qualitative curve or differential coefficient curve of potential function. Furthermore, the temperature of hot smoke layer is calculated by the value of the critical point when flashover occurs. The calculation case of passenger carriage fire shows that the temperature of hot smoke layer is 625.3 degrees C when flashover occurs in the carriage, which is agreement with real instance.