The nonlinear dynamics of flashover in compartment fires

The development of a fire within a compartment represents an event of both theoretical and practical interest, displaying a variety of nonlinear behaviour. Of particular importance is the flashover transition, whereby a small fire undergoes a rapid intensification to engulf the whole compartment. In this thesis we examine the influence of the controlling parameters, on the qualitative nonlinear behaviour of three different simplified compartment fire models, by applying some of the techniques of nonlinear dynamics. The variation in response of a nonlinear model, indicated by some representative quantity (e.g. temperature) as a particular distinguished parameter varies, can be traced out to produce a bifurcation diagram. The effect of the remaining auxiliary control parameters can then be mapped out by locating the boundaries or varieties which separate the different qualitative types of bifurcation diagram exhibited by the model. Such varieties are defined in terms of the singularities of the function(s) defining the model, and its derivatives. We show that these definitions can be extended to include the transition points between fuel and ventilation controlled burning exhibited by compartment fire models. Path following techniques are also presented as a means of obtaining bifurcation diagrams and varieties numerically. These techniques are applied to construct parameter maps and classify the possible bifurcation diagram types for three different simplified compartment fire models, incorporating the effect of; radiation feedback from the compartment, vitiation of the compartments oxygen atmosphere and varying combustion efficiency. Based upon this analysis, an index is derived as a means of evaluating the tlashover potential of a given compartment. Finally a comparison of experimental data obtained for two thermoplastic fuels is made, confirming the occurrence of the qualitative nonlinear features predicted theoretically, and in particular the critical nature of the flashover transition