The bifurcational behaviour is investigated of a simple mathematical model of the self-heating of combustible vapour from the evaporation of combustible fluid within (fibrous) lagging material. The lagging is considered to be completely soaked in the combustible fluid so that the fibres are completely covered; hence the evaporation term in this model is not dependent on the amount of liquid present and the main ignition event (due to oxidation of vapour) is countered by the endothermic evaporation and Newtonian cooling. This leads to a simpler equation set in the temperature and amount of vapour only (the liquid equation is decoupled). It is found that depending on the dimensions of the material (proportional to the volume to surface area ratio in this well-stirred approach), there are not only saddle-node bifurcations but important Hopf bifurcations leading to stable limit cycles in the temperature-fuel vapour concentration phase plane.
|Number of pages||21|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 1997|