Combustion waves in narrow samples of solid energetic material: Chaotic versus spinning dynamics

In this work, we study the conditions determining the appearance of chaotic or spinning dynamic regimes for flames propagating in narrow cylindrical samples of energetic materials. Two models for heat losses from the sample surface are explored. The first model allows for a linear dependence of heat-loss intensity on the surface temperature. Another model assumes radiative heat losses modeled by the fourth degree of temperature. The global stability analysis of steady-state solutions is carried out for both models. It is shown that the main factor determining the wave dynamics is the sample thickness. In sufficiently thin samples, the axisymmetric instability mode prevails and the flame dynamics depends on the intensity of heat-losses. With an increase in their intensity, the auto-oscillatory dynamics first transforms into chaotic through the period doubling Feigenbaum’s cascade and, with a further increase in heat-losses, the dynamical extinction occurs. However if the sample is sufficiently thick, the most unstable mode is the mode with a nonzero azimuthal wave number. In this case, the spinning propagation regime is finally realized with a multi-headed flame structure formed. It is found that, qualitatively, this scenario is independent of the specifics of the heat-loss model.