ANALYSIS OF THE BIFURCATIONAL BEHAVIOR OF A SIMPLE-MODEL OF VAPOR IGNITION IN POROUS MATERIAL

The bifurcational behaviour is investigated of a simple mathematical m odel of the self-heating of combustible vapour from the evaporation of combustible fluid within (fibrous) lagging material. The lagging is c onsidered to be completely soaked in the combustible fluid so that the fibres are completely covered; hence the evaporation term in this mod el is not dependent on the amount of liquid present and the main ignit ion event (due to oxidation of vapour) is countered by the endothermic evaporation and Newtonian cooling. This leads to a simpler equation s et in the temperature and amount of vapour only (the liquid equation i s decoupled). It is found that depending on the dimensions of the mate rial (proportional to the volume to surface area ratio in this well-st irred approach), there are not only saddle-node bifurcations but impor tant Hopf bifurcations leading to stable limit cycles in the temperatu re-fuel vapour concentration phase plane.