Fire eruption through intensity and spread rate interaction mediated by flow attachment

Abstract

Conditions under which a fire has a stable steady spread rate or under which it is able to spread eruptively up a slope or in confined topography are of considerable interest from a practical and safety point of view. The physical interactions that give rise to either form of behaviour are investigated by way of a mathematical model, in which different expressions for the rate of feedback from intensity into spread-rate are found to identify a threshold between eruptive and stable spread of a line fire. In turn, changes in the fireline intensity in any unsteady evolution are mainly determined by the history of the spread-rate over a burnout time (in effect, by changes in flame depth). Under stable conditions, any initial spread-rate evolves towards the steady spread rate on a time-scale of the order of the burnout time. But above the threshold, eruptive fire-growth sets in; the spread-rate and intensity both grow indefinitely.

It is argued that a change in the nature of the flow field around a line fire engenders the change from one form of behaviour to another. If the air flow separates at the flame, so that air is drawn away from the ground and vegetation surface, then the model provides strong reasons to expect that the steady spread rate is stable. On the other hand, laboratory experiments and a controlled field burn confirm that eruptive behaviour is more likely to be associated with flow attachment.

As a result, if the air immediately ahead of a fire that is spreading uphill, flows up the slope away from the fire then conditions arise for a potentially very dangerous acceleration in the spread-rate of the fire, along with a corresponding growth in its intensity. As is shown by the experiments, this form of air-flow can be generated by the fire itself without any change in external conditions such as ambient wind.

Keywords:

• bushfire
• wildfire
• forest fire eruption
• fire blowup
• Byram number

Acknowledgments

The authors are grateful to Prof. Domingos Xavier-Viegas for many valuable discussions about the nature of eruptive fires, for making his laboratory available for experimental work, for invitations to observe field experiments and (most particularly) for his encouragement, warm hospitality and friendship. They are also deeply grateful to Rui Figueiredo, Nuno Luis, Miguel Almeida, Luis-Paulo Pita, Pedro Palheiro, Carlos Rossa, Luis-Mario Ribeiro and all other members of the group at the Centro de Estudos Sobre Incêndios Florestais in Coimbra for their help, advice, discussions and for generously assisting in the laboratory experiments. The encouragement and valuable advice of Rodney Weber, Jason Sharples and Albert Simeoni are also very much appreciated as is the financial support of the EPSRC.

Notes

¹Interestingly, in his original article Byram [8] presented an alternative formula of the form I = [qdot]d that does hold for unsteady fire spread, where [qdot] represents a ‘combustion rate’ measured in kW m⁻² and d is the flame depth in metres. This formula is closer in character to Equations (9) in which [qdot] = Qϖ.

²For axisymmetric fires, turbulent buoyant flame lengths are found to scale with I ^2/5 [16].

³Byram's formula, I=QmR, is often used in this way as if it were the definition of fireline intensity even though, as has been seen, it correctly represents the rate of energy release per unit length of fireline (which is the true definition of fireline intensity) only for a straight fireline with a constant rate of spread.