Propagation of a reaction front in a narrow sample of energetic material with heat losses: Chaotic regimes, extinction and intermittency

摘要

The influence of heat-losses on the flame dynamics in narrow samples of energetic material is investigated numerically. The model is reduced to a one-dimensional form with the flame-sheet approximation applied for the reaction rate. Both the steady-state solutions and its linear stability analysis are treated analytically. A typical C-shaped response curve is found for the dependence of the flame-propagation velocity on the heat-loss parameter, with solutions along the lower branch of slower flames being always unstable. It is found that a part of the upper branch of the C-shaped response curve is also unstable and the Poincare-Andronov-Hopf bifurcation takes place at a certain value of heat-loss intensity even if the steady state solution is stable under the corresponding adiabatic conditions.